Find the indicated measure in parallelogram ABCD m

The solution to the system of equations: x + 3y = 7 and 2x + 4y = 8 is (-2, 3)

Isolate x in the first equation:

x + 3y = 7

x = 7 - 3y

Use the substitution method, Substitute the value for x into the second equation:

2x + 4y = 8

2(7 - 3y) + 4y = 8

Solve for y:

14 - 6y + 4y = 8

-2y = -6

y = 3

Substitute y into either original equation:

x + 3y = 7

x + 3(3) = 7

x + 9 = 7

x = -2

Write the solution as an ordered pair:

The solution is (-2, 3).

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Answer:

the formula for this is y=mx+b

b stands for the y, m is the slope of the line,  and x stands for the x axis!

Step-by-step explanation:

i am pretty sure your answer is -1.4

hope this helps I to help you out attached a screenshot

Therefore, the value of the expression -2f(-6) - 7g(-7) is equal to -99.

In mathematics, a function is a rule that assigns a unique output value to each input value. Functions are often represented as equations or graphs that relate the input (also known as the independent variable) to the output (also known as the dependent variable). The input is usually denoted by the variable x, and the output is usually denoted by the variable y. Functions can be used to model relationships between different quantities, such as time and distance, or temperature and pressure. They are a fundamental concept in mathematics and are used in many fields, including physics, engineering, economics, and computer science.

Here,

Using the function notations given in the problem, the statement can be read as follows:

-2 times the value of the function f evaluated at x = -6, minus 7 times the value of the function g evaluated at x = -7, is equal to:

-2f(-6) - 7g(-7) =

Substituting the expressions for f(x) and g(x) given in the problem, we get:

-2*(3*(-6)+1) - 7*(-2*(-7)+5) =

Simplifying this expression, we get:

-2*(-17) - 7*(19) = 34 - 133 = -99

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The required length of the parking lot is 75 meters.

Perimeter is the measure of the figure on its circumference.

Here,
Let's call the length of the parking lot "L". The perimeter of a rectangle is given by the formula:

Perimeter = 2 × (length + width)

We know that the width is 62 m and the perimeter is 274 m, so we can plug these values into the formula and solve for the length:

274 = 2 × (L + 62)

Dividing both sides by 2, we get:

137 = L + 62

Subtracting 62 from both sides, we get:

L = 137 - 62

L = 75

Therefore, the length of the parking lot is 75 meters.

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Answer:

y=2x-10

Step-by-step explanation:

since the lines are parallel, then their gradients are equal, that to say both lines have the gradient of 2. The following step is to work out the value of c using the equation y= mx+c. Then substitute the values of given points and it will be 2=2(6)+c, and c=-10

then you find an equation

Explanation:

The line y = 2x+4 has the slope 2. Compare that equation to y = mx+b

Parallel lines have the same slope.

The answer will be of the form y = 2x+b, where the b value will be something other than 4. Otherwise, we'll end up with the same exact equation.

To find this new b value, we plug in x = 6 and y = 2. These values are from the point (6,2).

Let's solve for b.

y = 2x+b

2 = 2*6+b

2 = 12+b

b = 2-12

b = -10

We go from y = 2x+b to y = 2x-10 as the final answer.

You can use a tool like GeoGebra to confirm the answer is correct.

1. Point - Corner of a Vaccination room

2. Plane  - Face mask

3. Line - The long chain of children for pediatric vaccination

Point:

A point is represented as a "dot" on paper. There will be no length, width, or height existing for a point. It simply identifies a certain position. Zero dimensions apply to it.

Line:

The line is a one-dimensional shape in geometry. A line, thus, has length but neither width nor height. In any direction, a line never stops. Two end points of lines act as the fundamental determinants of a line.

Plane:

The coordinate plane, which is used to plot points in algebra, is an example of a plane. The number lines on the coordinate plane stretch eternally from left to right and from up to down, respectively. The coordinate plane cannot be seen entirely.

Here we have

Corner of a Vaccination room,  Face mask, The long chain of children for pediatric vaccination

Where

The corner of a Vaccination room represents a point.

Face mask represents a plane

The long chain of children for pediatric vaccination represents a line.

Therefore,

1. Point - Corner of a Vaccination room

2. Plane  - Face mask

3. Line - The long chain of children for pediatric vaccination

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Answer:

Step-by-step explanation:

Here is a more detailed explanation:

We are given two linear functions, f(x) and g(x), and their values for x = 1 and x = 4:

x   f(x)   g(x)

1    3      5

4    9      20

To find the value of a + b at the point of intersection (a, b) of the two functions, we need to first find the equations of the two functions. To do this, we need to find the slope and y-intercept of each function.

For f(x), the slope is (9 - 3) / (4 - 1) = 2, and using the point (1, 3) we can find the y-intercept as:

y - 3 = 2(x - 1)

y - 3 = 2x - 2

y = 2x + 1

So the equation of f(x) is y = 2x + 1.

Similarly, for g(x), the slope is (20 - 5) / (4 - 1) = 5, and using the point (1, 5) we can find the y-intercept as:

y - 5 = 5(x - 1)

y - 5 = 5x - 5

y = 5x

So the equation of g(x) is y = 5x.

To find the point of intersection of the two functions, we can set their equations equal to each other and solve for x:

2x + 1 = 5x

3x = 1

x = 1/3

Substituting this value of x back into either equation, we can find the corresponding value of y:

y = 2(1/3) + 1 = 7/3

So the point of intersection is (1/3, 7/3).

Therefore, a + b = 1/3 + 7/3 = 8/3. This is approximately equal to 2.67. The answer closest to this value is -1, so the correct answer is (b) -1.

Answer:

the answer is A. 11 1/4

Step-by-step explanation:

the base times height for the triangle divided by 2 plus the bxh of the rectangle.

3x3/2 + 1 1/2 x 4 1/2

The solution is, the function is  g(x) = (x -5)² + 1

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

we know that,

The vertex form of a quadratic equation is: y = a(x - h)² + k    where

"a" is the vertical stretch

-a is a reflection over the x-axis

h is the horizontal shift (positive = right, negative = left)

k is the vertical shift (positive = up, negative = down)

given that,

f(x) = (x-2)² + 1

now we have,

Given: 3 units left   -->   h = -3

so, we get,          

g(x) = (x - 2- 3)² +1

       =(x-5)² + 1

Hence, The solution is, the function is  g(x) = (x -5)² + 1.

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a. The period of y = 2tan(4x) on the interval [0,pi] is pi/2.

Justification: The period of a tangent function is pi/b where b is the coefficient of x. Therefore, the period of 2tan(4x) is pi/4, and the function completes two periods on the interval [0,pi], giving a total period of pi/2.

b. The location of vertical asymptotes for y = 2tan(4x) on the interval [0,pi] is x = (2n + 1)pi/8 where n is an integer.

Justification: The vertical asymptotes of a tangent function occur where the cosine of the angle in the argument is equal to zero. In this case, the cosine is equal to zero at (2n + 1)pi/8, giving the location of the vertical asymptotes.

c. The domain of y = 2tan(4x) on the interval [0,pi] is [0, pi/4) U (pi/4, pi/2) U (pi/2, 3pi/4) U (3pi/4, pi].

Justification: The tangent function has vertical asymptotes at odd multiples of pi/2, so the function is undefined at these points, and thus excluded from the domain.

d. The range of y = 2tan(4x) on the interval [0,pi] is (-∞, ∞).

Justification: The range of the tangent function is the set of all real numbers.

e. The x-intercepts of y = 2tan(4x) on the interval [0,pi] are x = k(pi/8), where k is an integer.

Justification: The x-intercepts of a tangent function occur where the function is equal to zero, which happens at integer multiples of pi.

f. The y-intercept of y = 2tan(4x) on the interval [0,pi] is (0,0).

Justification: The y-intercept of a function occurs where x=0, so the y-intercept of this function is (0, 0), as 2tan(4*0) = 0.

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The Total Surface area of cardboard in the box is 992 cm².

The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a shape with a curved base and surface is equal to the sum of the two areas.

Given:

length= 20 cm

width = 12 cm

height= 8 cm

So, the TSA of Cuboid

= 2(lw + wh + lh)

=2( 20 x 12 + 12 x 8 + 8 x 20)

=2( 240 + 96 + 160)

= 2(496)

= 992 cm²

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The sum of the fractions is 7/4

From the question, we have the following parameters that can be used in our computation:

5⁄6 + 2⁄3 + 1⁄4 =

Express the denominators of the fraction as 12

So, we have

5⁄6 + 2⁄3 + 1⁄4 = 10/12 + 8/12 + 3/12

Evaluate the sum

This gives

5⁄6 + 2⁄3 + 1⁄4 = = 21/12

Simplify

5⁄6 + 2⁄3 + 1⁄4 = 7/4

Hence, the solution si 7/4

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The completed balance sheet is given below:

A balance sheet is a financial statement that shows the financial position of a company at a specific point in time. It provides information about a company's assets, liabilities, and equity, and helps to illustrate the overall financial health of the company.

The Balance Sheet

Sheffield company

balance sheet (partial)

December 31, 2023

Plant Assets

Land $3,926,000

Building $28,650,000

Less: Accumulated Depreciation (14,396,250)

Net Building $14,253,750

Equipment $49,569,000

Less: Accumulated Depreciation (4,127,795)

Net Equipment $45,441,205

Total Plant Assets $63,620,955

Note that the buildings and equipment are shown at their net book value, which is the original cost less the accumulated depreciation.

The accumulated depreciation represents the portion of the cost that has been expensed over time due to wear and tear, obsolescence, or other factors.

The land is not depreciated, so its original cost is shown.

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The solution of the system x + y ≥ 75 and 2.5x + 10.5y ≤ 800  of the equation is

The system of equation x + y ≥ 75 and 2.5x + 10.5y ≤ 800 will have a solution that is as written in the equation.

This is done by substituting each value

Using (250, 10)

250 + 10 ≥ 75

260 ≥ 75 correct

2.5x + 10.5y ≤ 800

2.5 * 250 + 10.5 * 10 ≤ 800

730 ≤ 800 correct

since the the values are correct for the equations,  (250, 10) is the solution

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There are 160 tree in each row.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.

To calculate the number of students in the seventh grade, you must divide the number of students in the Environmental Club by the percentage they represent. The answer is 8 divided by 0.05, which equals 160. Therefore, there are 160 students in the seventh grade.

The Environmental Club provides students with an opportunity to learn more about the natural environment and how to help protect it. The club members work together to come up with ideas to promote environmental awareness and action in their school and community. They plan activities such as tree-planting, trash clean-ups, and educational presentations. The club also participates in activities like field trips to local parks and nature preserves.

By joining the Environmental Club, students can gain a better understanding of their local environment and how to protect it. This can help them become more aware of their actions and how they can make a difference in the world. They can also develop leadership and communication skills, as well as an understanding of the importance of teamwork. Furthermore, they can make friendships and connections with other students who share the same values and interests.

Overall, the Environmental Club is an important part of the school community and provides great benefits to its members. It allows students to gain knowledge, build skills, and make a positive difference in their communities.

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The true statements about the populations of the town based on the linear equations in the table are;

A linear equation is an equation of the form; y = m·x + c, where the slope of the graph of the equation is m and the y-intercept of the graph is c.

The analysis of the equations in the table are as follows;

Equation for Pinehill is; P = 800 - 20t

The slope of the above equation is; -20 and the y-intercept is 800. The negative sign for the slope indicates that the population is decreasing;

Therefore, the initial population of 800 in Pinehill is decreasing at a rate of 20 per unit time, t

Population for Rye; P = 500 + 15t

The population of Rye is increasing at a rate of 15 per unit time

Population for Smithfield; P = 10t + 950

The population of Smithfield is increasing at a rate of 10 per unit time

Population for Troy; P = -50·t + 600

The -50 indicates that population is decreasing at a rate of 50 per unit time

The true statements are therefore;

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The area that will be frosted on the bottom layer 680

What are the basic mathematical operations?

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

1. Find the smaller cake first with (lw*amount of sides) and then add it to the larger cake using the same formula.

6*6*6+10*10*6

This equals 816

2. Find the amount not frosted. The bottom and the connection. Simply, (lw).

6*6+10*10

This equals 136

3. Subtract 136 from 816.

816-136= 680 sq inches

Hence, The area that will be frosted on the bottom layer 680

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Answer:

Look at the screenshot.

The direct distance between the White House and the Pentagon is approximately 3.067 miles.

Distance is a measure of how far apart two objects or points are from each other. It is a fundamental concept in mathematics, physics, and other scientific disciplines, and plays a crucial role in our everyday lives.

Distance can be measured in various units, such as meters, kilometers, miles, feet, and inches, depending on the context and application. In mathematics, the distance between two points in a plane can be found using the Pythagorean theorem, which states that the distance between two points (x1, y1) and (x2, y2) is given by the formula:

distance = √((x2-x1)² + (y2-y1)²)

In this formula, the square of the difference in the x-coordinates and the y-coordinates of the two points are added and then the square root of the sum is taken to obtain the distance.

Using the distance formula, the direct distance between the two buildings is:

d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

where (x1, y1) = (-8,-6) and (x2, y2) = (-1,10)

d = sqrt[(-1 - (-8))^2 + (10 - (-6))^2]

d = sqrt[7^2 + 16^2]

d = sqrt(49 + 256)

d = sqrt(305)

Since each unit on the grid represents 0.125 miles, we can convert the answer to miles by multiplying by 0.125:

d = sqrt(305) * 0.125

d = 3.067 miles (rounded to 3 decimal places)

Therefore, the direct distance between the White House and the Pentagon is approximately 3.067 miles.

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It is cheaper to drive the old truck, which costs $11.58 to drive 60 miles, compared to the diesel truck, which costs $15.44 to drive the same distance, given the current fuel prices.

An algebraic expression is a mathematical phrase that consists of variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. It is a combination of constants, variables, and operators that represent a value or a relationship between values.

For example, "3x + 5" is an algebraic expression where "3" and "5" are constants, "x" is a variable, and "+" is an operator. The expression can be evaluated by substituting a value for "x" and performing the necessary operations.

Algebraic expressions can also be simplified by combining like terms and using the rules of arithmetic to simplify the expression. For instance, the expression "2x + 3x" can be simplified to "5x" by adding the coefficients of the like terms "x".

Algebraic expressions are used extensively in algebra to represent equations and relationships between variables. They are also used in a wide range of mathematical and scientific applications, including physics, engineering, and finance.

To compare the cost of driving the old truck to the diesel truck, we need to know the fuel efficiency of the old truck. Let's assume that the old truck uses gasoline and has a fuel efficiency of 20 miles per gallon.

To drive 60 miles, the old truck will use 60/20 = 3 gallons of gasoline.

At $3.86 per gallon, the cost of 3 gallons of gasoline is 3 * $3.86 = $11.58.

The diesel truck uses 4 gallons of diesel to drive 60 miles. The cost of diesel is not given in the problem, so we'll assume it's the same as the cost of gasoline, $3.86 per gallon.

At $3.86 per gallon, the cost of 4 gallons of diesel is 4 * $3.86 = $15.44.

Therefore, it is cheaper to drive the old truck, which costs $11.58 to drive 60 miles, compared to the diesel truck, which costs $15.44 to drive the same distance, given the current fuel prices.

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Answer:

Step-by-step explanation:

the optimal point is (40,000, 40,000, 20,000), which gives an annual income of $680,000. The slack for the first, second, and fourth constraints is 0, and the slack for the third constraint is also 0.

Answer:

88 days

Step-by-step explanation:

inversely proportional means for a response y and input x, we have the formula

y = k/x

10 days = k/44 workers

multiply both sides by 44 to find k

44 workers * 10 days = k

k = 440 workers * days

y = k/x

x = 5 workers

440 workers * days / 5 workers = y

88 days = y

The answer here would be D. In choice A, this would be incorrect because he would divide the millage cost before the passenger fee. In choice B, this would be incorrect because he would add the passenger fee, when it is required to subtract it. Choice C would be incorrect, because yet again, you are not supposed to add the passenger fee. This leaves choice D, which is correct.

The domain are the possible input while the range are the possible output of a function.

(a) The domain = [-√2, √2], the range = [0, 2]

(b) The domain = [-1, 1], the range = [0, 1]

(c) The domain = [-1, 1], the range = [0, -1]

(d) The domain = [0, 2], the range = [0, 1]

(e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]

Reasons:

The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1

Therefore, we have;

(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2

The x-intercept of the above function are, x = √2, and x = -√2

Which gives;

The domain = [-√2, √2]

The range = [0, 2]

(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3

At the x–intercepts, we have;

-3·x² + 3 = 0

x = ±1

The domain = [-1, 1]

The maximum value of y is given at x = 0, therefore;

= -3 × 0² + 3 = 3

The range = [0, 1]

(c) y = -f(x) = -(-x² + 1) = x² - 1

At the x–intercepts, x² - 1 = 0

x = ± 1

The domain = [-1, 1]

The minimum value of y is given at x = 0, which is y = -1

The range = [0, -1]

(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x

At the x–intercepts, we have;  -x² + 2·x = 0, which gives;

(-x + 2)·x = 0

Which gives, x = 0, or x = 2

The domain = [0, 2]

The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1

y = f(1) =  -1² + 2×1 = 1

Therefore;

The range = [0, 1]

(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2

At the x–intercepts, we have;  -x² - 4·x - 2 = 0, which gives;

x = -(2 + √2) or x = x = √2 - 2

The domain = [-(2 + √2), (√2 - 2)]

The maximum value of y is given when x = -4/(2)) = -2

Which gives;

-(-2)² - 4·(-2) - 2 = 2

The range = [0, 2]

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The mean is 20 and standard deviation for the number of patients that experience side effects in such groups of 100 is 4.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The number of patients experiencing side effects in a sample of 100 patients as a binomial distribution with n = 100 and p = 0.20.

The mean of a binomial distribution is given by:

μ = np

Substituting n = 100 and p = 0.20, we get:

μ = 100 × 0.20 = 20

Therefore, the mean is 20.

The variance of a binomial distribution is given by:

σ²= np(1 - p)

Substituting n = 100 and p = 0.20, we get:

σ² = 100 × 0.20 × (1 - 0.20) = 16

Therefore, the variance of the number of patients experiencing side effects in a sample of 100 patients is 16.

The standard deviation of a binomial distribution is the square root of its variance:

σ =√Variance

=√16

= 4

Hence, the mean is 20 and standard deviation for the number of patients that experience side effects in such groups of 100 is 4.

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The baseball team won 87.5% of their games in that month.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation contains one or more variables, which are unknown values that can vary or change. The variables are usually represented by letters such as x, y, or z. The expressions on either side of the equals sign can be constants, variables, or functions of variables.

The simplest form of an equation is a linear equation, which can be represented as ax + b = c, where a, b, and c are constants and x is a variable. To solve a linear equation, we need to find the value of the variable that makes the equation true. This is done by performing arithmetic operations on both sides of the equals sign to isolate the variable.

Equations can also be more complex, involving multiple variables, powers, and functions. In such cases, algebraic techniques such as factoring, substitution, and solving systems of equations may be required to find the solution.

Equations are used to describe relationships between variables in many fields of study, including physics, chemistry, economics, and engineering. They are also used in everyday life, such as in calculating the cost of a purchase after applying a discount, or determining the amount of time it takes to travel a certain distance

To find the percentage of games won, we need to divide the number of games won by the total number of games played and multiply by 100%:

percentage of games won = (number of games won / total games played) x 100%

total games played = number of games won + number of games lost = 21 + 3 = 24

percentage of games won = (21 / 24) x 100%

percentage of games won = 87.5%

Therefore, the baseball team won 87.5% of their games in that month.

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The percentage of the decrease in the value of the XYZ Company stock is 16%.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
The decrease in the value of the stock is $25 - $21 = $4.

To find the percent decrease, we need to divide the decrease by the original value and then multiply by 100:

Percent decrease = (Decrease / Original value) x 100

In this case, the original value is $25, so:

Percent decrease = (4 / 25) x 100 = 16%

Therefore, the percentage of the decrease in the value of the XYZ Company stock is 16%.

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The stem and leaf for the split between hundreds place and the tens place is 74 and 5 respectively.

A stem and leaf plot also called a stem and leaf diagram is a way of organizing data into a form that makes it easy to observe the frequency of different types of values. It is a graph that shows numerical data arranged in order. Each data value is broken into a stem and a leaf.

Given that, 600, 600, 600, 610, 610, 610, 610, 610, 610, 610, 610, 610, 610, 610, 612, 620, 620, 625, 629, 631, 635, 638, 640, 640, 645, 646, 650, 651, 660, 660, 665, 671, 671, 674, 680, 693, 700, 705, 706, 707, 707, 715, 715, 719,  720,  725, 727, 732, 738, 739 and 745.

a) Split between hundreds place and the tens place.

60|  0   0   0

61|  1    1    1    1    1    1    1    1    1    1    1    2

62|  0   0   5   9

63|   1    5   8  

64|  0    0   5   6

65|  0    1

66|  0    0   5

67|   1     1    4

68|  0

69|  3

70|  0  5   6   7   7

71 |   5  5  9

72|   0  5  7

73|   2  8  9

74|   5

b) Split between the tens place and the ones place.

6|   00  00   00  10   10  10   10   10   10  10  10  10  10  10   12   20   20   25 29   31   35   38   40   40   45   46   50   51   60   60   65   71   71   74   80   93

7|    00   05   06   07   07   15   15   19  20  25  27  32  38  39  45

Therefore, stem and leaf for the split between hundreds place and the tens place is 74 and 5 respectively.

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