Answer:
Step-by-step explanation:
Let the other diagonal be d.
From the Pythagorean theorem,
d2 = 82 + 1442
d2 = 64 + 20736
d2 = 20800
d = √20800
d = 144 cm
can anyone explain how to solve this?
Answer:
E
Step-by-step explanation:
Let x be the initial value
after 1 year value = 1.1 x
after 2 yrs v = 1.1 * 1.1 x
after 3 yrs v = 1.1 * 1.1 * 1.1 x
after 4 yrs v = 1.1 * 1.1 * 1.1 * 1.1 x
or simply : value = ( 1.1)^n x where n = number of years
for n= 4 years value = (1.1)^4 x = 1.4641 x
this represents a .4641 increase or 46.41 % increase Answer E
Choose the correct option.
Which option is most similar in relation to the following word pair?
Water: Ocean
OPTIONS
House: Bricks
Book : Library
Biscuit : Tea
Cloth: Body
Answer:
Book: Library is most similar in relation to the following word pair Water: Ocean. Both pairs are closely related and are often found together.
John needs to decide about whether to spend $10,000 on a two year degree that will qualify him for a $35,000 a year job or go to work now and make $20,000 a year. How long will it take Anthony to recover his investment if he goes to school? Assume he will not work at all while in college. Round to 1 decimal place.
John needs to decide about whether to spend $10,000 on a two year degree that will qualify him for a $35,000 a year job or go to work now and make $20,000 a year. How long will it take Anthony to recover his investment if he goes to school? Assume he will not work at all while in college. Round to 1 decimal place.
Answer:
Step-by-step explanation:
To calculate how long it will take John to recover his investment, we need to divide the cost of the degree by the difference in income between the two options.
$10,000 / ($35,000 - $20,000) = $10,000 / $15,000 = 0.67 years or 0.67*12 = 8 months.
So, it will take John 8 months to recover his investment if he goes to school.
Please note that this is a simplified calculation as it does not take into account the cost of living, taxes, and other expenses.
(2%)Find the solution set ofx^2+4x-21≤0.
Answer:
The solution set of x^2 + 4x - 21 ≤ 0 is (-7, -3)
Step-by-step explanation:
To solve this inequality, we first set x^2 + 4x - 21 = 0 and factor it to get (x + 7)(x - 3) = 0. This gives us x = -7 and x = 3 as the solutions.
To find the solution set of x^2 + 4x - 21 ≤ 0, we need to determine the values of x that make the expression on the left-hand side non-positive. Since x^2 + 4x - 21 is a quadratic function, it is non-positive when x is less than -3 or x is greater than -7.
Therefore, the solution set of x^2 + 4x - 21 ≤ 0 is the set of all x such that x ∈ (-7, -3).
Jeremy analyses one of his parachute jumps.
He draws a graph showing his velocity up to the opening of his parachute.
The acccceleration will be 1m/s² and the average speed is 47m/s.
How to calculate the acceleration?For the acceleration problems, you must draw a tangent on curved velocity-time graphs. Since it requested acceleration at t = 10 seconds, we must create a straight line that only touches the graph once, at 10 seconds.
Now, when drawing tangents, you must be as precise as you can because they can only contact the line once.
Next, determine the gradient using the tangent. You can accomplish this by creating a triangle out of two additional lines drawn from the tangent, then dividing the rise by the run, or Y/X. The triangle that comes before the Y and the X simply denotes the Greek letter delta, which symbolizes change. Change in Y so prevails over Change in X. So 10/10 = 1. So 1m/s^2.
If we estimate the speed at 5 seconds intervals, then we have
Average speed = (36 + 46 + 49 + 50 + 50 +50 + 50) ÷ 7
Average speed = 331/7 = 47.29 m/s
Average speed = 47 m/s
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A recipe calls for the following spices: 1/8 teaspoon of turmeric, 1/4 teaspoon of ginger, and 1/2 teaspoon of cumin. What is the total quantity of these three spices?
The total quantity of the three spices is 7/8
How to calculate the total quantity of the three spices ?A recipe has three spices
1/8 teaspoon of turmeric
1/4 teaspoon of ginger
1/2 teaspoon of cumin
The total quantity of the three spices can be calculated as follows
1/8 + 1/4 + 1/2
= 7/8
Hence the total quantity of the three spices is 7/8
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NO LINKS!!
Make and test a conjecture about the given quantity. Test at least three sets of numbers. (NOT MULTIPLE CHOICE)
a. product of any two odd integers
b. the sum of two negative integers
Answer:
a) The product of any two odd integers is an odd integer.
b) The sum of two negative integers is always smaller than the smallest negative integer.
Step-by-step explanation:
Part aGiven:
The product of any two odd integers.Carry out a few examples to find a pattern:
1 × 3 = 33 × 5 = 155 × 7 = 35Pattern:
The solution is always odd.Write the conjecture based on the found pattern.
Conjecture:
The product of any two odd integers is an odd integer.Test the conjecture for accuracy using at least three sets of numbers.
Test:
277 × 109 = 3019315 × 23 = 3459 × 61 = 549-------------------------------------------------------------------------------------
Part bGiven:
The sum of two negative integers.Carry out a few examples to find a pattern:
-1 + -2 = -3-10 + -3 = -13-20 + -1 = -21Pattern:
The solution is always smaller than the smallest number.Write the conjecture based on the found pattern.
Conjecture:
The sum of two negative integers is always smaller than the smallest negative integer.Test the conjecture for accuracy using at least three sets of numbers.
Test:
-5 + -5 = -10-40 + -52 = -92-13 + -14 = -27The rule of a function changes from
f(x) = x² − 4 to g(x) = -x² + 4 when it is dilated.
Which statement best describes how this dilation affects the graph of f(x)?
A. The graph is reflected across the x-axis.
B. The graph is reflected across the y-axis.
C. The graph moves up 8 units.
D. The graph moves down 8 units.
The rule for the graph changes form of the function is A)The graph is reflected across the x-axis.
What is function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). Function is a relation that connects members of one set in a certain way to those of another set. Formally speaking, a function from to is an object such that each is specifically linked to an object. Therefore, a function is a many-to-one (or occasionally, one-to-one) relation.
Here Through moving up c units, the graphs of g can be determined from the graph of f. If we subtract c from f(x), the graph shifts downward. Let h(x) = f(x)-c Shifting downward c units yields this graph of h from the graph of f.
We know that if the function reflected over x-axis then
g(x) = -f(x)
Here the given function f(x) = [tex]x^2-4[/tex] then reflection over x-axis then
=> g(x) = -f(x)
=> g(x) =-( [tex]x^2-4[/tex])
=> g(x) = [tex]-x^2+4[/tex]
Hence the correct option is A)The graph is reflected across the x-axis.
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3) You inherit $2,500 and decide to invest it in an account that earns 1.5% interest
compounded monthly.
a) Write an equation to model this scenario.
b) How much money is in the account 15 years after you first invested?
Therefore , the solution of the given problem of interest comes out to be
A = $3,130.37 is the amount after 15 years.
What exactly is meant by interest?Simple interest is calculated by dividing the principal by the borrowing cost, the remaining time, and other elements. The simple return formula in marketing is principal + interest plus hours. Utilizing this method is the simplest way to calculate interest. As a percentage of the principle sum is the most frequent way to calculate income. For instance, he will only pay his portion of the 100% cost if he borrows $100 from a friend and agrees to pay the loan back with 5% interest.. You have to pay interest on money you borrow, and you have to charge interest on money you lend.
Here,
Given :
a ) the equation that can be formed is
2500x - 1.5y = 30
b)
Using compound formula :
=> Then solve the equation for A
A = P(1 + r/n)nt
A = 2,500.00(1 + 0.015/12)(12)(15)
A = 2,500.00(1 + 0.00125)(180)
A = $3,130.37
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Serena added 10 grams of sugar to 20 grams of water.
She made
grams of
%
sugar syrup.
Serena added 10 grams of sugar to 20 grams of water to make a sugar syrup.
The total amount of sugar syrup made is the sum of the weight of sugar and the weight of water, so:
10 grams (sugar) + 20 grams (water) = 30 grams (sugar syrup)
To find the percentage of sugar in the syrup, we can divide the weight of the sugar by the total weight of the syrup and multiply by 100.
% sugar = (weight of sugar / total weight of syrup) * 100
% sugar = (10 / 30) * 100 = 33.333 %
So the sugar syrup made by Serena contains 33.333% sugar by weight.
It's important to note that the sugar syrup doesn't have only sugar, it also have water, the sugar is just the main ingredient and the percentage of sugar is just the proportion of sugar within the syrup.
3.5% as a fraction or mixed number
Answer:
[tex]3.5\% = \frac{3.5}{100} = \frac{35}{10} (fraction) = 3 \frac{5}{10} (mixed)[/tex]
ES = ___ units
Round your answer to the nearest tenth.
ES = 10.63 units
How to find the length of the line ?The length of the line segment connecting any two points represents the distance between them. There is just one line that connects the two places. Therefore, by measuring the length of the line segment that connects the two sites, the distance between them may be determined.
When given a straight line on a graph, you can find the length of this line by using the Distance Between Two Points Formula. This formula uses the vertices of the beginning and ending points of a straight line to find the length of the line, which is the distance between the two points.
The Distance Between Two Points Formula is:
= √(( x₂ – x₁ )² + ( y₂ – y₁) ²)
The vertices of the line ES are E ( -3, -4 ) and S ( 4, 4 ).
The distance is:
= √(( 4 – (-3) )² + ( 4 ( - 4 )) ²)
= 10. 63 units
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←
The perimeter P of a parallelogram is given by the formula P = 2a + 2b, where a is the length of one side of the
parallelogram and b is the length of the adjacent side.
(a) Solve the formula for a.
(b) Find the length of one side of a parallelogram whose perimeter is 100 cm and length of the other side is 30 cm.
We are aware that P = 2(a + b) units is the perimeter of a parallelogram.Consequently, the parallelogram's sides are 50 cm, 25 cm, 50 cm, and 25 cm.
Find the length of parallelogram ?We are aware that P = 2(a + b) units is the perimeter of a parallelogram.Adding up all four sides will reveal a parallelogram's perimeter.An area of a circle of radius r is known as r2 in geometry.
The circumference-to-diameter ratio, which is always the same and is roughly equivalent to 3.14159 in this context, is denoted by the Greek letter.
Let side a and the side next to it in the parallelogram be a and b, respectively.
The parallelogram's perimeter is equal to 2(a+b)=150, where a+b=75.
Since an is 25 cm taller than b, a=b+25.
By changing it in equation 1, b+25+b=75 2b=50 b=25 is obtained.
a+b=75\sa=75=25\sa=50
Consequently, the parallelogram's sides are 50 cm, 25 cm, 50 cm, and 25 cm.
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what is 36 percent of 128
Answer:
Step-by-step explanation:
36 percent can be written as 36/100. So now the question is 36/100 x 28.
Its easier if you simplify 100 and 28 by a common factor, which im going to use 4 for. So instead you get 36/25 x 7.
36x7=252
252/25=10.08
Answer:
46.08
Step-by-step explanation:
Remember that a percent is always a fraction out of 100, in this case 36/100, so it can also be written as a decimal number, in this case 0.36. Now all you need to do is multiply 128*0.36
Pls help Darnell is an election officer. On election day, he travels to the polling place, which is 4.4 miles away from his home. On a map of Harrison County, these two places are 8 inches apart. What is the scale of the map? Write your answer in simplest form using whole numbers.
Answer:
The scale of the map is 1 : 34848---------------------------------
Real distance is 4.4 miles and on the map it is 8 inches.
The scale is:
8 in : 4.4 miles = Divide both sides by 81 in : 0.55 milesor
1 in : 0.55 * 63360 in = Convert 1 mile = 63360 inches1 : 34848Jasmine claims “to find the lowest common multiple of two numbers, you can multiply them together. For example, 5 × 8 = 40 and the LCM of 5 and 8 is 40”
Is Jasmine correct? Justify your answer.
Answer:
No, Jasmine is not correct. The Lowest Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. Multiplying the two numbers together is not always the correct method to find the LCM.
For example, the LCM of 5 and 8 is 40, but the product of 5 × 8 = 40 is not the LCM.
A more accurate way of finding the LCM is by using the prime factorization of the numbers. By finding the prime factorization of the two numbers, you can take the highest exponent of each prime factor and multiply them together. The result of that multiplication is the LCM of the two numbers.
In this case, the prime factorization of 5 is 5 and 8 is 2^3. The LCM of 5 and 8 is 2^3*5 = 40. So Jasmine's claim that 5 x 8 = 40 and the LCM of 5 and 8 is 40 is not correct.
In 2018, the population of Sydney was 5.48 million.
This was 22% of the total population of Australia.
Work out the total population of Australia in 2018
Give your answer correct to 3 significant figures.
The population of Australia in 2018 was 24.909 million.
Given: The population of Sydney in 2018 = 5.48 million
This population of Sydney is equal to 22 % of the total population of Australia.
To find: Total population of Australia
Solution:
According to the Question,
Total population of Australia * 22% = total population of Sydney
Total population of Australia * 22/100 = 5.48 million
= 5.48 million * 100/22
= 24.909 million (approx.)
Hence, the population of Australia in 2018 was 24.909 million.
The total population of Australia in 2018 was 24.90 million.
What is percentage?A percent is a dimensionless number, meaning that it has no units of measurement, since it represents a part of whatever whole is being measured.
Given that, the population of Sydney was 5.48 million, which was 22% of the total population of Australia.
We need to find the total population of Australia.
Let the total population of Australia be y.
Therefore,
y × 22% = 5.48
y = 5.48 × 100/22
y = 24.90
Hence, the total population of Australia in 2018 was 24.90 million.
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HELP I NEED HELP I NEED HELP I NEED HELP
Answer:
A is an Irregular Polygon
B is Neither a Polygon
C is an Irregular Polygon
D is a Regular Polygon
E is a Regular Polygon
I need help ASAP!! thanks if you help <3
The integers that -3.425 lie between are -3 and -4.
The rational numbers that -3.425 lie between to the nearest tenth are -3.4 and -3.5.
The rational numbers that -3.425 lie between to the nearest hundredth are -3.42 and -3.43.
What are the integers and rational numbers ?Integers are numbers without decimals and fractions. They are whole numbers. Integers can either be positive, negative or zero. Examples of integers are -5 and 10.
A rational number is a number that can be expressed as a fraction of two integers. Examples of rational numbers are 1/4, -2/3
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4. Renuka's teacher asks her to factorise completely 8x²-12x. Renuka wrote 2x (4x-6) as her answer Explain why she does not score full marks and give the correct answer.
The answer should be 4x(2x-3) so Renuka does not score full marks.
What is Number system?A number system is defined as a system of writing to express numbers.
The given expression is 8x²-12x.
To factorise this we have to find the highest common factors from both the terms.
Factors of 8 are 1, 2, 4, 8
Factors of 12 are 1, 2, 3, 4, 6,12
The highest common factor is 4.
So we have to take common 4 but Renuka has taken out 2.
So she does not got full marks.
The answer should be 4x(2x-3)
Hence, the answer should be 4x(2x-3) so Renuka does not score full marks.
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Identify the domain of f.
For which values a does lim x -> a f(x) not exist? Find all values a where lim x -> a f(x) exists, f is defined at a, but lim x -> a f(x) does not equal f(a).
The graph shows that the domain and range of the line segment were [-5, 1] & [-4, 7, correspondingly.
Describe domain.A function's domain is the set of values that it can accept. These figures represent a function like f's x-values (x). The domain of a function is the set of possible values on which it can operate. This set is the value which the return type after the x value has been entered. Y = f is a function where x is an independent variable and y is a dependent variable (x). If a value of x can be successfully utilized to produce a single value of y using a value of f, then that value is said to be within the domain of that function.
Here,
The domain denotes all conceivable possibilities for x, whereas the range denotes all possible values of y.
The graph shows that the domain and range of the line segment is [-5, 1] & [-4, 7, respectively.
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Round 843,857 nearest hundred thousands
Answer: 844000
Step-by-step explanation:
843857 = 844000 because you round up
I NEED HELP ASAP I only got 20 minutes to answer this question
If Bob has 2 apples and Jake takes 2 from Bob how many apples does Jake have?
Answer:
Step-by-step explanation:
jake has 2 apples
if bob gotta two apples and Jake took it away then how many apples does bob have
Step-by-step explanation:
Graph the piecewise function
The graph of the given piecewise function is as attached below.
Piecewise function is a function consisted of pieces of different functions over different intervals.
From the case we have:
f(x) = 3x - 5 if x ≤ -1
f(x) = -2x + 3 if -1 < x < 4
f(x) = 2 if x ≥4
To construct the piecewise function, we can try to find the base points of each functions.
f(x) = 3x - 5; if x ≤ -1
We will take x = -1 to approximate the line position
f(-1) = 3(-1) - 5
f(-1) = -3 - 5 = -8
f(x) = -2x + 3; if -1 < x < 4
(x = -1)
f(-1) = -2 (-1) + 3
f(-1) = 2 + 3 = 5
(x = 4)
f(4) = -2 (4) + 3
f(4) = -8 + 3 = -5
f(x) = 2; if x ≥ 4
(x = 4)
f(4) = 2
We can put each points on the graph and try to construct the piecewise function.
Please refer to the attached graph below for the piecewise function graph
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PLS HELP
perform the indicated operation and simplify the answers (image attached )
Son solving the provided question we can say that - the fraction is (2 + 1/x ) / ( 7-1/x ) = 5/13
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
here, the fraction is
(2 + 1/x ) / ( 7-1/x )
2x+1/7x-1
x = 2
5/13
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HELP PLS
Factor the trinomal or stage that the trinomal is prime
The correct answer is x² - 7x - 18 = (x - 9)(x + 2)
If 40 shirts at the dry cleaners are hanging with 5 shirts in each row, how many rows are there?
Answer:
8
Step-by-step explanation:
8 x 5 = 40
On A riverboat traveled 10 miles upstream against the
current in 5 hours. The return trip took only half
da
the amount of time while the boat traveled with the current.
a. Write an equation for the trip upstream.
b. Write an equation for the return trip.
c. Use combination/elimination to find the speed of the boat and the speed of the current.
Answer:
a. Let x be the speed of the boat in miles per hour and y be the speed of the current in miles per hour. Since the boat traveled upstream, the speed of the current is added to the speed of the boat. Therefore, the equation for the trip upstream is:
distance = (x + y) * time
10 = (x + y) * 5
b. For the return trip, the speed of the current is subtracted from the speed of the boat. Therefore, the equation for the return trip is:
distance = (x - y) * (time/2)
10 = (x - y) * (5/2)
c. To find the speed of the boat and the speed of the current, we can use the method of elimination. From the first equation, we have:
10 = 5x + 5y
From the second equation, we have:
10 = 2.5x - 2.5y
Now we can use the elimination method by multiplying the first equation by 2 and then subtracting the second equation from it.
20 = 10x + 10y
20 = 5x - 5y
so we have
0 = 5x + 5y - 5x + 5y
0 = 10y
The equation becomes impossible to solve as we can't divide by 0.
As we know that the speed of the boat and the speed of the current are non-zero numbers, we can't find the exact speed of the boat and the current. We can conclude that the information given is not sufficient to find the exact speed of the boat and the current.
Step-by-step explanation:
What is the solution to this system of equations?
112 divide by 0.16 with solutions
The solution for the expression 112 ÷ 0.16 is 700.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
112 ÷ 0.16
This can be written as,
= 112/0.16
= 700
Thus,
The solution is 700
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