The payback period for Project A is 3 years, and the payback period for Project B is also 3 years.
To calculate the payback period for Project A and Project B, we need to determine the time it takes for the cumulative cash flows to equal or exceed the initial investment of $40,000.
For Project A:
Year 1 cash flow: $42,000
Year 2 cash flow: $22,000
Year 3 cash flow: $10,000
To find the payback period, we start by subtracting the cash flows from the initial investment until we reach a cumulative cash flow equal to or greater than $40,000:
Year 1: $40,000 - $42,000 = -$2,000
Year 2: -$2,000 + $22,000 = $20,000
Year 3: $20,000 + $10,000 = $30,000
The cumulative cash flow reaches $30,000 in Year 3. However, it does not exceed the initial investment of $40,000. Therefore, we can estimate the payback period as follows:
Payback period for Project A = 2 years + ($40,000 - $30,000) / $10,000
= 2 years + 1 year
= 3 years
For Project B:
Year 1 cash flow: $40,000
Year 2 cash flow: $21,000
Year 3 cash flow: $15,000
Using the same process as above, we calculate the cumulative cash flows:
Year 1: $40,000 - $40,000 = $0
Year 2: $0 + $21,000 = $21,000
Year 3: $21,000 + $15,000 = $36,000
The cumulative cash flow reaches $36,000 in Year 3, which is greater than the initial investment. Therefore, the payback period for Project B is:
Payback period for Project B = 3 years
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Which loan will result in the least amount of interest paid?
A. $10,000 at 2 percent interest compounded for four years
B. $10,000 at 2 percent simple interest for four years
C. $5,000 at 4 percent interest compounded for four year
D. $5,000 at 2 percent interest compounded for four years
Based on the calculations, option D, which is $5,000 at 2 percent interest compounded for four years, will result in the least amount of interest paid.
To determine which loan will result in the least amount of interest paid, we need to calculate the total interest for each option and compare them. Let's calculate the interest for each loan:
A. $10,000 at 2 percent interest compounded for four years:
To calculate the compound interest, we use the formula A = P(1 + r/n)^(nt), where A is the future value, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
For option A, the future value (A) can be calculated as:
A = 10,000(1 + 0.02/1)^(1*4) ≈ 10,816.65
The interest paid would be the difference between the future value and the principal:
Interest = 10,816.65 - 10,000 = 816.65
B. $10,000 at 2 percent simple interest for four years:
For simple interest, we use the formula I = P * r * t, where I is the interest, P is the principal amount, r is the interest rate, and t is the number of years.
For option B:
Interest = 10,000 * 0.02 * 4 = 800
C. $5,000 at 4 percent interest compounded for four years:
Using the compound interest formula:
A = 5,000(1 + 0.04/1)^(1*4) ≈ 5,897.77
Interest = 5,897.77 - 5,000 = 897.77
D. $5,000 at 2 percent interest compounded for four years:
Using the compound interest formula:
A = 5,000(1 + 0.02/1)^(1*4) ≈ 5,407.10
Interest = 5,407.10 - 5,000 = 407.10
Comparing the total interest paid for each option:
A: $816.65
B: $800
C: $897.77
D: $407.10
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Drag the tiles to the boxes to form correct pairs. A number line with x-axis marked Negative 2 to 2 marked with a difference of 1 and has 5 points: A at 1.75, B at 1.25, C at 0.5, D at 1 and E at 1.625. Match the points on the number line with the rational numbers. A B C D E arrowBoth arrowBoth arrowBoth arrowBoth arrowBoth
The correct pairs of the given rational numbers with the points on the number line are:A - 7/4B - 5/4C - 1/2D - 1E - 13/8
To form the correct pairs of the given rational numbers with the points on the number line, the given points on the number line and their corresponding rational numbers are:A at 1.75, which is the same as 7/4B at 1.25, which is the same as 5/4C at 0.5, which is the same as 1/2D at 1, which is the same as 1E at 1.625, which is the same as 13/8Let's take a look at the number line:|-2---|---|---|---|---2...-1 0 1 2
We can see that point C is exactly at the center of the number line, at 0.5. This is the same as the rational number 1/2.Point D is located at 1 on the number line, which is the same as the rational number 1.Point A is located between 1 and 2 on the number line, closer to 2. The exact location is 1.75, which is the same as the rational number 7/4.Point B is located between 1 and 1.5 on the number line, closer to 1.5. The exact location is 1.25, which is the same as the rational number 5/4.Point E is located between 1.5 and 2 on the number line, closer to 1.5. The exact location is 1.625, which is the same as the rational number 13/8.
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is 4-(-10)=14 a true statement
Answer:
Yes, it is a true statement
Step-by-step explanation:
Since two negatives cancel out the equation would be
4 + 10 and that equals 14.
So the statement is true!
i-Ready
Use the numbers -10.-
Practice: Multiply and Divide Rationals-Quiz - Level G
or 5 to write an expression.
000
52
2 5
Using only TWO of the numbers, write a division expression with a quotient greater than 10.
10
612
23
5
To write a division expression with a quotient greater than 10 using only two of the numbers -10, 5, and 2, we can choose 5 and 2.
The expression can be:
5 / 2
When we divide 5 by 2, the quotient is 2.5. Since 2.5 is greater than 10, this division expression satisfies the given condition of having a quotient greater than 10.
In mathematical terms, the division expression 5 / 2 = 2.5 meets the criterion requested. Dividing 5 by 2 yields a quotient greater than 10, specifically 2.5.
It is important to note that when working with numbers, careful attention must be paid to the problem statement and the conditions provided. In this case, selecting 5 and 2 and dividing them correctly results in a quotient greater than 10.
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which property allows you to write the expression
(3+7^}+(8-6^}+(3+7^)?
The property that allows you to write the expression (3+7^) + (8-6^) + (3+7^) is the Commutative Property of Addition and the Commutative Property of Exponents.
The Commutative Property of Addition states that when two or more numbers are added, the sum remains the same even if the order of the numbers is changed. For example, a + b = b + a. Therefore, in the given expression, we can add the terms in any order we want, without changing the result. So, we can add (3 + 8 + 3) and (7^ + 6^ + 7^) in any order we want.
Applying the Commutative Property of Addition, we can write the expression as (3+8+3) + (7^+6^+7^).
Then, applying the Commutative Property of Exponents, we can write the expression as (3+8+3) + (7^+7^+6^).
Simplifying further, we get (14) + (2 * 7^) + (6^).
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The percent of battery remaining, y, on a tablet's battery after x hours can be represented by the given graph.
coordinate grid with the x axis labeled time in hours and the y axis labeled percent of battery remaining, with a line that passes through the points 0 comma 50 and 5 comma 0
What is the meaning of the y-intercept in the context of the problem?
After 50 hours, the tablet will have 0 percent of battery left.
The tablet will not have any battery remaining after 5 hours.
The tablet starts with 50 percent of battery remaining.
The tablet loses 5 percent of battery every hour.
when the tablet runs for x hours, the battery remaining percentage can be calculated as y = -5x + 50.
The given graph represents the percent of battery remaining, y, on a tablet's battery after x hours. The tablet starts with 50 percent of battery remaining. The tablet loses 5 percent of battery every hour.From the graph, it is observed that the line passes through the point (0,50) and (10,0) as the maximum battery life is for 10 hours. The slope of the line can be calculated as: Slope = Rise/Run Slope = (Change in y)/(Change in x) Slope = (0 - 50)/(10 - 0) Slope = -5The slope of the line represents the rate of change of battery percentage per hour. Thus, the given information can be concluded as: The tablet loses 5% of battery every hour. Therefore, the equation of the line can be written in the form of y = mx + b where m is the slope of the line and b is the y-intercept. Hence, y = -5x + 50This equation represents the battery remaining percentage, y, as a function of time, x in hours.
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Which of the following gives a single solution of the inequality |x+3|-2\le0 and shows a graph that can be used to determine the entire solution set of the inequality? x = 0 x = –1 x = 2 x = 5
The solution of the inequality [tex]|x+3| - 2 \leq 0[/tex] is x = -1.
The correct answer is B.
To find the solution of the inequality [tex]|x+3| - 2 \leq 0[/tex], we need to solve it step by step.
Add 2 to both sides of the inequality:
[tex]|x + 3| \leq 2[/tex]
Break the inequality into two separate cases:
Case 1: [tex]x + 3 \geq 0-- > x\geq -3[/tex]
Case 2: [tex]x + 3 < 0 -- > x < -3[/tex]
Solve each case separately:
Case 1: [tex]x + 3\geq 0 -- > x\geq -3[/tex]
Since the absolute value of a non-negative number is always non-negative, the inequality becomes:
[tex]x + 3 \leq 2[/tex]
Subtract 3 from both sides:
[tex]x \leq -1[/tex]
Case 2: [tex]x + 3 < 0 -- > x < -3[/tex]
Multiply both sides by -1 (to remove the negative sign):
[tex]-x - 3 > 0[/tex]
Add 3 to both sides:
[tex]-x > 3[/tex]
Divide by -1 (and reverse the inequality sign because we're dividing by a negative number):
[tex]x < -3[/tex]
So, the solution to the inequality is [tex]-3 \leq x \leq -1[/tex].
Now, let's analyze the given options to determine which one represents a single solution in the solution set.
x = 0: This does not satisfy the inequality [tex]-3 \leq x \leq -1[/tex], so it is not a solution.
x = -1: This value satisfies the inequality [tex]-3 \leq x \leq -1[/tex], so it is a solution.
x = 2: This does not satisfy the inequality [tex]-3 \leq x \leq -1[/tex], so it is not a solution.
x = 5: This does not satisfy the inequality [tex]-3 \leq x \leq -1[/tex], so it is not a solution.
Therefore, the only option that represents a single solution in the solution set of the inequality is x = -1.
The correct answer is B.
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How do we determine the domain of a function defined by an equation
Answer:
The domain of a function is the set of all values for which the function is defined. When determining the domain of a function, we need to identify any values that would make the function undefined or result in an error. For instance, in the function f(x) = 1/x, the denominator cannot be zero since division by zero is undefined. Thus, the domain of f(x) would be all real numbers except 0, since substituting 0 for x would result in an undefined expression. The following are some guidelines that can help determine the domain of a function:
1. Check for values that would make the function undefined or result in an error. This includes dividing by zero, taking the square root of a negative number, and taking the logarithm of a non-positive number.
2. Identify any restrictions on the variable or inputs. For instance, if the function represents a physical problem, there may be restrictions on the input values based on the conditions of the problem.
3. Check for any implicit assumptions or requirements in the problem. This could include assumptions about the sign of variables or the existence of certain values.
4. Determine the set of all real numbers that satisfy the above conditions as the domain of the function.
I hope this helps you understand how to determine the domain of a function defined by an equation.
which table represents g(x) when f(x) = 3x-4 and g(x)=f(2x)
The table that represents g(x) when f(x) = 3x - 4 and g(x) = f(2x) include the following: D. table D.
How to determine the table that represents the function g(x)?Based on the information provided above, we can logically deduce the following functions;
f(x) = 3x - 4
g(x) = f(2x)
g(x) = f(2x)
g(x) = 3 × (2x) - 4
g(x) = 6x - 4
By evaluating g(x) based on the given x-values in the tables (x = 1, 2, 3), we have the following:
g(1) = 6 × 1 - 4
g(1) = 6 - 4
g(1) = 2
g(2) = 6 × 2 - 4 '
g(2) = 12 - 4
g(2) = 8
g(3) = 6 × 3 - 4
g(3) = 18 - 4
g(3) = 14
Therefore, the correct table is given by:
x g(x)
1 2
2 8
3 14
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
AT
is tangent to circle
�
O at point
�
A. If
m
∠
�
�
�
=
11
3
∘
m∠JAT=113
∘
, find
m
�
�
�
⌢
m
AWJ
⌢
.
The measure of the arc AWJ between the tangent AT and chord AJ is equal to 226°
How to calculate for angle between the intersection of a chord and a tangent.The angle m∠JAT between the intersection of the chord and a tangent is equal to the arc measure of arc AWJ divided by 2
Given the measure of the angle m∠JAT to be equal to 113°, then the measure of arc AWJ is calculated as:
angle JAT = 108°/2
m∠JAT = arc AWJ/2
113° = arc AWJ/2
arc AWJ = 2 × 113°
arc AWJ = 226°
Therefore, the measure of the arc AWJ between the tangent AT and chord AJ is equal to 226°
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←
Sean has taken three exams and earned scores of 89, 71, and 79 out of a possible 100 points. He needs an average of at least 84 to earn a B in the course. What range of scores on the
fourth (and last) 100-point test will guarantee a B in the course?
The range of scores on the fourth (and last) 100-point test is to
(Simplify your answers.)
Sean to guarantee a B in the course, he needs to score at least 97 on the fourth and last 100-point test.
To determine the range of scores on the fourth test that will guarantee a B in the course, we can set up an equation using the average score formula.
The average score across the four exams should be at least 84.
Since Sean has already taken three exams with scores of 89, 71, and 79, respectively, we can set up the equation as follows:
[tex]\frac{(89 + 71 + 79 + x) }{4} \geq 84[/tex]
Here, x represents the score on the fourth test.
We need to solve this inequality to find the range of scores that will guarantee a B.
Let's simplify the equation and solve for x:
[tex]\frac{(239 + x) }{4} \geq 84[/tex]
Multiply both sides of the inequality by 4 to eliminate the fraction:
[tex]239 + x \geq 336[/tex]
Subtract 239 from both sides:
[tex]x \geq 336 - 239[/tex]
[tex]x \geq 97[/tex]
Therefore, for Sean to guarantee a B in the course, he needs to score at least 97 on the fourth and last 100-point test.
Any score equal to or greater than 97 will ensure an average of at least 84 across all four exams.
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A number is expressed by 2 digits, whose sum is 8, with a decimal point between them, and its
double is one less than the number obtained by interchanging the digits. What is the number?
1) 1.7
2) 5.3
3) 2.6
4) 6.2
2.6 satisfies both conditions of having a digit sum of 8 and its double being 1 less than the number obtained by interchanging the digits. Option 3.
To solve this problem, let's consider the given options one by one and see if any of them satisfy the given conditions.
Option 1: 1.7
The sum of the digits is 1 + 7 = 8, which satisfies the first condition. Now let's check the second condition: its double is 1 less than the number obtained by interchanging the digits.
The double of 1.7 is 3.4, which is not 1 less than the number obtained by interchanging the digits. So, option 1 is not the correct answer.
Option 2: 5.3
The sum of the digits is 5 + 3 = 8, which satisfies the first condition. Now let's check the second condition: its double is 1 less than the number obtained by interchanging the digits.
The double of 5.3 is 10.6, which is not 1 less than the number obtained by interchanging the digits (3.5). So, option 2 is not the correct answer.
Option 3: 2.6
The sum of the digits is 2 + 6 = 8, which satisfies the first condition. Now let's check the second condition: its double is 1 less than the number obtained by interchanging the digits.
The double of 2.6 is 5.2, which is indeed 1 less than the number obtained by interchanging the digits (6.2). Therefore, option 3 satisfies both conditions and is the correct answer.
Option 4: 6.2
The sum of the digits is 6 + 2 = 8, which satisfies the first condition. Now let's check the second condition: its double is 1 less than the number obtained by interchanging the digits.
The double of 6.2 is 12.4, which is not 1 less than the number obtained by interchanging the digits (2.6). So, option 4 is not the correct answer.
In conclusion, the correct answer is option 3: 2.6.
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The population of a local species of flies can be found using an infinite geometric series where a1 = 940 and the common ratio is one fifth . Write the sum in sigma notation, and calculate the sum (if possible) that will be the upper limit of this population. (5 points)
The sum of the infinite geometric series representing the population of the local species of flies is given by the sigma notation ∑ (from n = 1 to ∞) 940 * (1/5)^(n-1). The series converges, and the sum, which represents the upper limit of the population, is 1175.
To write the sum in sigma notation, let's break down the given information step by step:
The first term of the infinite geometric series is a1 = 940.
The common ratio (r) is one fifth (1/5), which means each term is obtained by multiplying the previous term by 1/5.
In sigma notation, the sum of an infinite geometric series can be expressed as follows:
∑ (from n = 1 to ∞) a1 * r^(n-1)
In this case, the first term a1 is 940, and the common ratio r is 1/5. Therefore, the sigma notation for the sum of this series is:
∑ (from n = 1 to ∞) 940 * (1/5)^(n-1)
To calculate the upper limit of this population, we need to find the sum of the series. However, to determine if the sum is possible, we can check if the series converges or diverges.
For a geometric series to converge, the absolute value of the common ratio (|r|) must be less than 1. In this case, |1/5| = 1/5, which is less than 1. Therefore, the series converges.
The sum of an infinite convergent geometric series can be calculated using the formula:
S = a1 / (1 - r)
In our case, a1 = 940 and r = 1/5. Substituting these values into the formula, we can calculate the sum:
S = 940 / (1 - 1/5)
S = 940 / (4/5)
S = 940 * (5/4)
S = 1175
So, the upper limit of the population is 1175.
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Question 2: Which statements about functions g(xx² - 4x +3 and f(x) = x² - 4x are true? Select all
that apply.
The functions g(x) = x² - 4x + 3 and f(x) = x² - 4x are:
The functions have the same range.
The functions have the same domain.
The functions have the same x-intercepts.
Let's analyze the given functions g(x) = x² - 4x + 3 and f(x) = x² - 4x and determine which statements about them are true.
Here are the options:
The functions have the same graph.
The functions have the same range.
The functions have the same domain.
The functions have the same vertex.
The functions have the same y-intercept.
The functions have the same x-intercepts.
The functions have the same graph:
This statement is false. While both functions are quadratic functions, their additional terms make them different. g(x) has an additional constant term (+3) compared to f(x).
Their graphs will be different, with g(x) being shifted upward by 3 units compared to f(x).
The functions have the same range:
This statement is true.
Both functions are quadratic functions, and their range will be the same. The range of a quadratic function is either all real numbers (if the parabola opens upward) or the set of real numbers greater than or equal to (or less than or equal to) the vertex of the parabola.
The functions have the same domain:
This statement is true.
The domain of both functions, unless restricted by any other factors, is all real numbers.
Quadratic functions have a domain of (-∞, ∞).
The functions have the same vertex:
This statement is false.
The vertex of a quadratic function is determined by the values of "a," "b," and "c" in the general form of the quadratic function (ax^2 + bx + c).
Since g(x) has an additional constant term, its vertex will be different from the vertex of f(x).
The functions have the same y-intercept:
This statement is false.
The y-intercept of a function is the value of y when x = 0.
For f(x), when x = 0, we have f(0) = (0)² - 4(0) = 0.
For g(x), when x = 0, we have g(0) = (0)² - 4(0) + 3
= 3.
Their y-intercepts are different.
The functions have the same x-intercepts:
This statement is true.
To find the x-intercepts of both functions, we set y (or f(x) and g(x)) equal to zero and solve for x.
The quadratic equation x² - 4x + 3 = 0 can be factored as (x - 1)(x - 3) = 0, giving x = 1 and x = 3 as the x-intercepts.
Both functions have the same x-intercepts.
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Anne has 5 pints of milk and is planning to make 6 cakes to sell in fundraising. Each cake will require 112
cups of milk. Does she have enough milk to make the 6 cakes? If so, how many cups of milk will be left, and if not, how many extra cups of milk would she need?
How is the stem plot used to determine the following?
The correct statement about the distribution in this problem is given as follows:
The distribution is unimodal.
How to obtain the mode of a data-set?The mode of a data-set is the observation that appears the most times in the data-set.
Considering the stem-and-leaf plot, we have that the observations have the following format:
7|6 = 76.
As 6 is the only observation that appears twice, it is the only mode of the distribution, meaning that the distribution is unimodal.
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PLEASE TWO HOURS LEFT!!!!!
George is going to paint baskets. Below is what one of them looks like:
How much paint will he need to paint the outside of one basket in squared cm?
Answer:
George will need 901 squared cm of paint to paint the outside of one basket.
Step-by-step explanation:
We essentially want to find the surface area of the basket excluding the top portion.Thus, we can find the area of the other five faces and the sum of these areas will give us the surface area of the basket in squared cm.
Total area of the front, back, left, and right face:
We see that the front, back, left, and right faces all have the same dimensions, as they are all 9 cm by 17 cm.Thus, we can find the area of one of these faces and later multiply it by 4 to find the total area these faces cover:
Note that the different dimensions indicates that these faces are rectangular and thus, we multiply 9 by 17 to find the area of one face:
A = 9 * 17
A = 153
Now we can multiply this area by 4 to find the total area covered by the back, front, left, and right faces:
4A = 4(153)
4A = 612
Thus, the basket's front, back, left, and right faces have a total area of 612 squared cm.
Area of the bottom face:
We see that the bottom face has the same dimensions as it is 17 cm by 17 cm.
Thus, it's a square and we can find its area by squaring 17:
A = 17^2
A = 289
Total area of the basket:
Now we can find how much paint George will need to paint the outside (i.e., the surface area represented by SA) by adding the total area of the front, back, left, and right faces and the bottom face:
SA = 612 + 289
SA = 901
Thus, George will need 901 squared cm of paint to paint the outside of one basket.
What is the sample space of the spinner
The sample space of a spinner refers to the set of all possible outcomes that can occur when the spinner is spun. In order to determine the sample space, we need to consider the different sections or options on the spinner.
For example, if the spinner has 4 equal sections, each labeled with a different color (red, blue, green, and yellow), then the sample space would consist of these 4 possible outcomes: {red, blue, green, yellow}.
Alternatively, if the spinner has 6 sections with numbers 1 to 6, then the sample space would be {1, 2, 3, 4, 5, 6}.
In general, the sample space of a spinner depends on the number and nature of its sections. It can include colors, numbers, or any other distinct options available on the spinner.
In summary, the sample space of a spinner is the set of all possible outcomes, which can vary depending on the specific design and labeling of the spinner.
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Write a put together/ take away problem that fits naturally with the equations
? + 17 = 42. or 17+ ? = 42
The students need to sell 25 tickets to reach their fundraising goal. This solution ensures that they will have a total of 42 tickets, including the initial 17 they had.
A group of students is organizing a fundraiser and they want to sell a certain number of tickets to reach their goal. The equation "? + 17 = 42" or "17 + ? = 42" can represent the number of tickets they need to sell. In this context, the variable "?" represents the unknown number of tickets.
To solve the problem, we need to find the value of "?" that satisfies the equation. By subtracting 17 from both sides of the equation "? + 17 = 42," we can determine that "?" is equal to 25.
Similarly, by subtracting 17 from both sides of the equation "17 + ? = 42," we also find that "?" equals 25.
We get:? = 42 - 17? = 25So, the solution of ? + 17 = 42 is ? = 25.17 + ? = 42Subtract 17 from both sides to isolate the variable. We get:? = 42 - 17? = 25So, the solution of 17 + ? = 42 is ? = 25.
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Given the circle below with secant
�
�
�
‾
VUT
and tangent
�
�
‾
ST
, find the length of
�
�
‾
ST
. Round to the nearest tenth if necessary.
Answer:
ST ≈ 15.3
Step-by-step explanation:
given a tangent and a secant from an external point to the circle , then
the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant , that is
ST² = TU × TV = 9 × (9 + 17) = 9 × 26 = 234
take the square root of both sides
ST = [tex]\sqrt{234}[/tex] ≈ 15.3 ( to the nearest tenth )
how many solution does 5x - 1 = 10x -4 - 5 x + 3 have?
Por favor ayuda, quien puede hacer esta operación y saber cuál es el valor de la L
The value of L is equal to 50.
What is a sequence?In Mathematics and Geometry, a sequence refers to a series of real and natural numbers in which each term or list of elements are ordered in a particular order and repetitions are allowed.
Based on the pattern provided about the crosses, we can logically deduce that the middle term is a sum of all the outer four terms, and then multiplied by 2 as follows;
2 + 5 + 5 + 4 = 16 × 2 = 32
4 + 3 + 5 + 0 = 12 × 2 = 24
8 + 1 + 2 + 3 = 14 × 2=28
4 + 6 + 8 + 7 = 25 × 2 = 50
Therefore, L = 50.
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Complete Question:
Look at the values of the crosses and find the value of L.
please help.
definitions: 1. definition of right triangle
2. definition of isosceles TrianglesReflexive
3. HL
4. definition of perpendicular
5. CPCTC
6. reflexive
From the two column proof below, we have seen ∠BAC ≅ ∠DAC by CPCTC
How to solve two column proof problems?The two column proof to show that ∠BAC ≅ ∠DAC is as follows:
Statement 1: ΔABD is Isosceles with base BD, AC ⊥ BD
Reason 1: Given
Statement 2: AB ≅ AD
Reason 2: Definition of isosceles Triangles
Statement 3: ∠1 and ∠2 are right angles
Reason 3: Definition of perpendicular
Statement 4: AC ≅ AC
Reason 4: Reflexive Property
Statement 5: ΔABC and ΔADC are right triangles
Reason 5: Definition of right triangle
Statement 6: ΔABC ≅ ΔADC
Reason 6: HL Congruency
Statement 7: ∠BAC ≅ ∠DAC
Reason 7: CPCTC
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1. (a) In a class of 40 leamers, 4 like both Mathematics and Science 21 learners like Science and 8 learners like neither science nor Mathematics 1. find the number of pupils who like al only science 6) only Mathematics 1. Illustrate the information above on a vean diegen
Based on the given information, we can determine the number of pupils who like only Science and only Mathematics.
1. The number of learners who like both Mathematics and Science is 4.
2. The number of learners who like Science is 21, including those who like both Science and Mathematics.
3. The number of learners who like neither Science nor Mathematics is 8.
4. To find the number of pupils who like only Science, we subtract the number of learners who like both from the total number of Science likers: 21 - 4 = 17. Therefore, there are 17 pupils who like only Science.
Similarly, to find the number of pupils who like only Mathematics, we subtract the number of learners who like both from the total number of Mathematics likers. Since the number of learners who like only Mathematics is not given explicitly, we cannot determine it based on the given information.
To illustrate this information on a Venn diagram, we would draw two overlapping circles representing Mathematics and Science. The area where the circles overlap would represent the learners who like both subjects (4).
The remaining portion of the Science circle outside the overlap would represent the learners who like only Science (17). The portion of the Mathematics circle outside the overlap would represent the learners who like only Mathematics (unknown). The learners who like neither subject would be represented outside both circles.
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Bryan invests $6500 in two different accounts. The first account paid 11 %, the second account paid 7 % in interest. At the end of the first year he had earned $519 in interest. How much was in each account?
$ at 11 %
$ at 7 %
Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).
Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.
The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).
According to the problem, the total interest earned after one year is $519. So we can set up the equation:
0.11x + 0.07(6500 - x) = 519
Simplifying the equation:
0.11x + 455 - 0.07x = 519
0.04x + 455 = 519
0.04x = 64
x = 64 / 0.04
x = 1600
Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).
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Which of the following best describes the pattern in the diagram as you move
from the top to the bottom row?
1
2
3
O A. Row 9 will contain 12 circles.
B. Each row increases by 2 circles.
O C. Row 7 will contain 10 circles.
OD. Each row increases by 1 circle.
Answer:
Step-by-step explanation:
Based on the diagram you provided, the correct answer is D. Each row increases by 1 circle. The top row has 6 circles, the second row has 7 circles, the third row has 8 circles, and so on until the bottom row which has 11 circles.
The cuboid below has a height of 34 mm and a width of 6 mm. It has a volume of 3468 mm³. What is the length of the cuboid? Remember to give the correct units, and give any decimal answers to 1 d.p. 34 mm ? 6 mm Not drawn accurately
Step-by-step explanation:
v = l w h
[tex]v = l \times w \times h[/tex]
3468 = l × 6 ×34
3468/204= 204l/204
17 = l
therefore the height is 17mm
The one-to-one functions g and h are defined as follows.
The values of the inverse of the functions are:
g⁻¹(7) = 4
h⁻¹(x) = (x - 13)/8
(h * h⁻¹)(-3) = 22
How to find the inverse of the functions?An inverse function is defined as a function that can be inverted into another function. Simply put, if the function 'f' brings x to y, the inverse of 'f' brings y to x. Where a function is denoted by 'f' or 'F', the inverse is denoted by f^(-1) or F^(-1).
We are given the one to one function as:
g = {(2, 2), (4, 7), (5, 2), (7, -3), (8, 3)}
h(x) = 8x + 13
g⁻¹(7) will be the value of x when y is 7 and as such we have:
g⁻¹(7) = 4
h⁻¹(x) is:
y = 8x + 13
x = (y - 13)/8
h⁻¹(x) = (x - 13)/8
(h * h⁻¹)(-3) = (8(-3) + 13) * (-3 - 13)/8
= 22
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I’m the figure below, h || l and j || k. Find the values of x and z.
Answer:
x = 103z = 32Step-by-step explanation:
You want the values of x and z in the figure where one pair of parallel lines crosses another.
Transversal anglesWhere a transversal crosses parallel lines, corresponding angles are congruent. This gives rise to several other relationships, each with its own name. The net result is that all acute angles are congruent, and all obtuse angles are congruent. The acute and obtuse angles are supplementary. (If the crossing is at right angles, then all angles are congruent.)
ApplicationHere, the angle marked x° is supplementary to the one marked 77°:
x = 180 -77 = 103
The angle marked (3z -19)° is congruent to the one marked 77°:
3z -19 = 77
3z = 96 . . . . . . add 19
z = 32 . . . . . . . divide by 3
The value of x is 103; the value of z is 32.
__
Additional comment
The various pairs of angles at a transversal can be described as "consecutive", "alternate", "interior", "exterior", "same-side". Of course, where lines cross, the angles can also be "vertical" or "opposite" or "adjacent" or a "linear pair."
Depending on the relationship, the angles will be congruent or supplementary. For example, "alternate exterior angles" are congruent; "consecutive interior angles" are supplementary.
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Please explain your answer to the question in the picture with steps, thank you.
Answer:
(a) y = x/8
(b) y = 7/8
Step-by-step explanation:
You want a direct variation equation that relates x and y, given y = 2 when x = 16.
(a) Direct variationThe equation for direct variation is usually written in the form ...
y = kx
where k is the constant of proportionality.
The value of k can be found from ...
k = y/x . . . . divide by x
For the given values, k is ...
k = 2/16 = 1/8
The direct variation equation is ...
y = (1/8)x
(b) Find yThe value of y for x=7 is found by substituting 7 for x in the equation above:
y = (1/8)·7
y = 7/8
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