Which relation represents a function?

Substitution method - the points are (-6, -11/2),(-4,-3), (-8/5,0), (0,2) and (4,7)

what is the substitution method?

To solve many simultaneous linear equations, use the substitution method in algebra. The value of a variable from one equation is substituted in the second equation in this procedure, as the name implies.

we are given the equation,

5x - 4y = -8

case I

when x = -6

5(-6) - 4y  = -8

-30 - 4y = -8

-4y = -8 + 30

-4y = 22

y = -(22/4)

y = -11/2

(x,y) = (-6, -11/2)

case II

when y = -3

5x - 4(-3) = -8

5x + 12 = -8

5x = -8 -12

5x = -20

x = -20/5

x = -4

(x,y) = (-4,-3)

case III

when y = 0

5x - 4y = -8

5x - 4(0) = -8

5x = -8

x = -8/5

(x,y) = (-8/5,0)

case III

when x = 0

5(0) - 4y = -8

0 - 4y = - 8

y= 8/4

y = 2

(x,y) = (0,2)

case IV

when x = 4

5(4) - 4y = -8

20 - 4y = -8

-4y = -8-20

-4y = -28

y = 28/4

y = 7

(x,y) = (4,7)

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The problems in the test are 16.

In the given case a student missed four problems on a test.

The test happened to be a mathematics test and the student scored a total percentage of 75%.

It is mentioned that every question has of same score values.

To find out how many problems were actually on the test we need to solve the problem by following the steps.  

Let,

Questions not attempted ( x ) = 4

Percentage gained ( y ) = 75%

The percentage lost is 25%

The total questions in the test are;

         → A = (100/25) * 4

            A = 16

Therefore, the questions in the test are 16.

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According to a government study among adults the percent of the adults spend more than $2,775 per year on reading and entertainment is

Given data form the question

the mean amount spent per year on reading and entertainment is $1,875

standard deviation of $640

what percent of the adults spend more than $2,775 per year on reading and entertainment

Definition of variables

mean sample, μ = $1,875

standard deviation, σ =  $640

measure X = $2,775

For normal distribution, the z-score of a measure X with mean μ and standard deviation σ  is given by as follows:

Z = ( X - μ ) / σ

Z = (2775 - 1875) / 640

Z = 1.40625 gives p-value of 0.0798250014

This is equivalents to 7.98%

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For this following function by evaluating f(5)-f(4) we get -19.

What is evaluate?

Finding the value of an algebraic expression when a given number is used to replace a variable is known as evaluating the expression. When evaluating an expression, we change the variable in the expression to the given number and then use the order of operations to simplify the expression.

Sol- f(5)-f(4)

f(5)-f(4)= (-2.5^2-5+3)-(-2.4^2-4+3)

Calculate the power

(-2×25-5+3)-(-2×4^2-4+3)

Calculate the product or quotient

(-50-5+3)-(-2×16-4+3)

Calculate the sum

-52-(-32-4+3)

=-52-(-33)

determine the sign

=-52+33

By calculating the sum of difference we are get

-19.

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Answer: 9 square inches

Step-by-step explanation:

The height of a the given shape which has a volume of 7/8, length of 5/8, width of 7/9 is 9/5

Volume = Length × width × height

7/8 = 5/8 × 7/9 × x

7/8 = 35/72x

x = 7/8 ÷ 35/72

= 7/8 × 72/35

= 9/5

So therefore, the height of the given shape is 9/5

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Answer:

Step-by-step explanation:

-6x-11=19/+11 <=>

<=> -6x=30/:(-6) <=>

<=> x=-5

Answer:

Step-by-step explanation:

The reasonable price of the car after 4 years will be $8618.

What is regression analysis?

Regression analysis is a group of statistical procedures used in statistical modelling to determine the associations between a dependent variable and one or more independent variables.

Given that a dealership tracks the correlation between the age of its used cars and asking price for a car. The regression line is y = 12,338 – 930x, where x is the age of the car, in years.

The price of the car after 4 years will be calculated as follows:-

y = 12338 - 930x

y = 12338 - ( 930 x 4 )

y = 12338 - 3720

y = $8618

Therefore, the reasonable price of the car after 4 years will be $8618.

Answer:

B - For every one year in age, the price is predicted to decrease by $930

C- If the Car is new, the car is predicted to cost $12,338.

Step-by-step explanation:

correct on edge 2022

Based on the fact that Aster Inc. paid salaries to its employees, the effect on the balance sheet and the income statement is A. Assets ↓ Expenses ↑.

When the salaries were paid by Aster Inc. to its employees, the effect was that the assets decreased. This is because cash was used to pay the salaries and cash is an asset.

Expenses will increase because when there is a payment of expenses to employees, it is recorded as a debit to the relevant asset account so this is an increase that will decrease income.

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If the number of cups of water w, needed for f cups of flour is described by the equation w = 0.75f, 0.75 represents the number of cups of water needed for one cup of flour

The equation is

w = 0.75f

Where w is the number of cups waters needed for f cups of flour.

Here w is is dependent variable and f is the independent variable

We can see that w is proportional to the f, the 0.75 is the constant.

w = 0.75f

Move the f to left hand side of the equation

w/f = 0.75

Hence, If the number of cups of water w, needed for f cups of flour is described by the equation w = 0.75f, 0.75 represents the number of cups of water needed for one cup of flour

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Answer:

54.4 %

Explanation:

The percent change in net sales can be calculated as:

Where the final number is the net sales in quarter 2 and the initial number is the net sales in quarter 1. Replacing the values by 170 and 110, we get:

Therefore, the answer is:

percent change = 54.5 %

Step-by-step explanation:

E = (-8, 2)

reflected across the y axis means that there is kind of a mirror along the y-axis.

and when you look into that mirror, you see point D as point E all the way on the other side of the mirror, at the same distance from the mirror as point D is. and point E has the same "height" (y) as point D.

since the other side of the mirror represents the negative numbers, the same distance to the mirror means the same amount of negative units away from the mirror for E, as we have positive units away from the mirror for D.

Answer:

135

Step-by-step explanation:

two interior angles of a triangle equal to the exterior of the angle that is neither of the interior angles

so in this case

p + t = 135

The three responses that can show a number of friends Wes could divide his tokens among evenly include:

25 tokens each for 2 friends.

5 tokens each for 5 friends.

10 tokens for 5 friends.

From the information, Wes wants to treat his friends to some arcade games. He has 50 game tokens.

It should be noted that this information simply wants you to illustrate the factors of 50.

Therefore, the factors are 2, 5, 10, 25 and 50.

Therefore, 25 for 2 friends will be 50. Same with 5 for 10 friends. In this case, it should be noted that 25 × 2 = 50 and 5 × 10 = 50. This gives the original value and shows how he can divide the game tokens equally.

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The starting point is 1,365 miles .

Given :

→ initial time of plane = 1.7 hours

→ initial speed = 140 mph

→ final time of plane = 9.6 hours

→ final speed = same = 140 mph

The initial displacement of the plane is :

distance = speed × time

= 1.7 × 140

= 238 miles

The final displacement of the plane is :
distance = 9.6 × 140

= 1,344 miles

The angles between initial and final displacement is :

100° - 10 ° = 90 °

The distance of the plane from its starting point is calculated as follows

d = [tex]\sqrt{238^{2}+ 1344^{2} }[/tex]

d  = [tex]\sqrt{56644 + 1806336}[/tex]

   = [tex]\sqrt{1862980}[/tex]

    = 1364.9 miles ≈ 1,365 miles

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Answer:

-1/4

Explanation:

To write the decimal -0.25 as a fraction we need to multiply and divide by 100 as follows:

We multiply by 100 because there are 2 digits after the decimal point.

Then, we need to simplify the fraction, so we can divide the numerator and the denominator by 25 as:

So, the fraction in its simplest form is -1/4

The relationship has no relation to continental drift theory, as it is a relation between distance and time, not distance and elevation.

The continental drift theory states that the world's tectonic plates are in constant motion over time.

This is supported by the fact that some millions of years ago, there was only one continent, named Pangea, and now we have the continents as we know. These continents are also moving a small amount a year.

In this problem, the elevation decreases and the distance increases, however, the continental drift theory should have the distance increasing or decreasing over time, hence the graph relationship has no relation to the continental drift theory.

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Answer: [tex]\frac{\sqrt{x}^3 }{3}[/tex]

Step-by-step explanation:

Step 1: Insert f(x) in for the x in g(x). This will give you [tex]\sqrt{x^3}[/tex]

Step 2: Insert [tex]\sqrt{x^3}[/tex] into the x in h(x) giving you [tex]\frac{\sqrt{x}^3 }{3}[/tex]

The probability that the mean age of a sample of 36 vehicles is between 98 and 100 months is 15.71%.

For the given question;

The data for the vehicles registered in the united states is given as-

The formula for the z score is-

z = (x - μ)/(σ/√n)

Put the values.

√n = √36 = 6

For x = 98 months

z = (98 - 96)/(15/6)

z = 0.8

p(z < 0.8) = 0.7881

For x = 100 months

z = (100 - 96)/(15/6)

z = 1.6

p(z < 1.6) = 0.9452

P(0.8<x<1.6) = 0.9452 - 0.7881

P(0.8<x<1.6) = 0.1571

Thus, the probability that the mean age of a sample of 36 vehicles is between 98 and 100 months is 15.71%.

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The unknown angles are as follows:

An angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.

In other words, a line that splits an angle into two equal angles.

Therefore, a bisector of an angle 120 degrees bisect the angle into 60 degrees.

Hence, FH bisect ∠EFG into the angles m∠EFH  and  m∠GFH .

Therefore,  m∠GFH  and m∠EFH are congruent.

m∠EFG = 119°

Hence,

m∠EFH = m∠GFH

Therefore,

m∠EFH  = 119 / 2

Hence,

m∠EFH  = 59.5°

m∠GFH  = 59.5°

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The monomial in standard form is 6x¹¹y¹⁸.

The given expression is

[tex](-3xy^{2})^{3} .(-\frac{2}{3}x^{2} y^{3} )^{4}[/tex]

We to write the expression as a monomial in standard form

Monomial is an expression having a single term. It can be represented as kxⁿ, where k is any integer often known as the coefficient, x represents the variable/s in the given expression and n denotes the power.

In the expression

[tex](-3xy^{2})^{3} .(-\frac{2}{3}x^{2} y^{3} )^{4}[/tex]

we first need to multiply the powers

using the formula

(mn)ˣ = mˣnˣ

[tex](-3xy^{2})^{3} .(-\frac{2}{3}x^{2} y^{3} )^{4}\\(-3x^3y^{2.3}) .(-\frac{2}{3}x^{2.4} y^{3.4} )\\(-3x^3y^{6}) .(-\frac{2}{3}x^{8} y^{12} )\\[/tex]

Now, we need to multiply both the terms

The following formula is used

xᵃ . xᵇ = xᵃ+ᵇ

[tex](-3x^3y^{6}) .(-\frac{2}{3}x^{8} y^{12} )\\\\-3(-\frac{2}{3})x^{3+8} y^{6+12} \\\\6x^{11}y^{18}[/tex]

Therefore the monomial in standard form is 6x¹¹y¹⁸.

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Answer:

=(3x - 2y( (4x - 3y)

Step-by-step explanation:

We have,

12x2 – 17xy + 6y2

The coefficient of x2 is 12

The coefficient of x is -17y

Constant term is 6y2

So, we express the middle term -17xy as -9xy – 8xy

12x2 -17xy+ 6y2 = 12x2 – 9xy – 8xy + 6y2

= 3x (4x – 3y) – 2y (4x – 3y)

= (3x – 2y) (4x – 3y)

Considering the situation with the parallel lines being cut by the two transversal lines, the measures of the angles are given as follows:

12. m<14 = 66º (option C).

13. m<12 = 86º (option D).

Angles 4 and 15 are alternate exterior angles, as they are on different sides of the same transversal line, hence they are congruent, that is:

m<15 = 114º.

Angles 14 and 15 are consecutive interior angles, meaning that they are supplementary, hence the measure of angle 14 is calculated as follows:

m<14 + m<15 = 180º

m<14 + 114º = 180º

m<14 = 66º.

Angles 5 and 10 are alternate interior angles, as they are on the opposite internal sides of the same transversal line, hence they are congruent and the measure of angle 10 is given as follows:

m<10 = 86º.

Angles 10 and 12 are equivalent angles, as they are on the same position, just relative to different transversal lines, hence they are also congruent, and the measure of angle 12 is given as follows:

m<12 = 86º.

The diagram with these lines is given by the image at the end of the answer.

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The correct answer is [b] ΔHGF and ΔABC.

In geometry, the two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

In geometry, the two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Formally speaking, two sets of points are said to be congruent if—and only if—they can be changed into the one another by an isometry, which is a combination of rigid motions like translation, rotation, and reflection. This indicates that either object may be precisely aligned with the other object by moving and reflecting it, but not by resizing it. So if we can cut out and then perfectly match up two separate plane figures on a piece of paper, they are congruent. The paper may be turned over.

Triangles with two pairs of congruent sides and an included congruent angle are said to be congruent by ASA.

According to the graph, sides TU, FG, and BC are congruent, as well as sides TV, HG, and AB. Additionally, it shows that angles G and B are congruent as well as angles U, F, and C. Triangle TUV is eliminated because ASA cannot find another triangle that is equivalent to angle U of triangle TUV using the information provided.

The only triangles left are FGH and ABC. These triangles are congruent by ASA since it is clear that angles G and B are included angles.

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Transformations that maps ∆ABC to ∆A''B''C'' is [tex]A^{''}(8,-2)\\B^{''}(5,-2)\\C^{''}(7,0)[/tex]

A coordinate plane is a two-dimensional surface made up of two number lines. It is produced when a horizontal line crosses the origin, which is the location where the X-axes and Y-axes meet. The numbers on a coordinate grid are used to find points. Using a coordinate plane, you may graph points, lines, and many other things. It functions as a map and gives precise driving instructions between two spots.

Reflection about x - axes (x,y)→(x,-y)

Reflection about y - axes (x,-y)→(-x,-y)

combined reflection is reflection about origin.

[tex]A^{'}(5,-3) \\B^{'}(2,-3)\\[/tex]

[tex]C^{'}(4,-1)[/tex]

Shift upward by 1 unit and on right hand side by 3 units

(x,y)→(x+3;y+1)

=[tex]A^{''}(8,-2)\\B^{''}(5,-2)\\C^{''}(7,0)[/tex]

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Using algebraic identities, we found that for B=2 and B= -2 , the trinomial x² + Bx +1  makes a perfect square.

Algebraic identities are the identities which aids in solving products or powers of algebraic expressions. Most common identities are :

(a+ b)² = a² + 2ab + b²

(a- b)² = a² - 2ab + b²

a² -b² = (a+ b) (a- b), where a and b can be variable or constants or algebraic expressions.

Let the perfect square of the trinomial be (x +a)²

x² + Bx +1 = (x+ a)² = x² + 2xa + a² (using identity (a+ b)² = a² + 2ab + b²)

⇒ x² + Bx +1  = x² + 2xa + a²

⇒ Bx = 2xa , a² =1

⇒B = 2a , a =± 1

if a =1 ⇒ B = 2

If a = -1 , B = -2

For B = 2 , x² + Bx +1  = x² + 2(1)x +1² = (x+1)² ( ∵(a+ b)² = a² + 2ab + b²)

For B = -2 , x² + Bx +1  = x² -2x + (-1)² = x² -2x +1 = ( x-1)²  (∵(a- b)² = a² -2ab  

                                                                                                                 + b²)

Thus, the given trinomial x² + Bx +1  is perfect square when B =2 or -2

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Answer: bean

Step-by-step explanation:

bean chd china bean poopies beans

26 = (110 - x)/2

52 = 110 - x

x = 110 - 52

x = 58°

a computer randomly selects 800 names from a list of all registered voters. Then option C  is correct  that is Simple random sampling

A simple random sample in statistics, is a subset of individuals chosen from a larger set. Each individual is chosen randomly and entirely by chance, such that each individual has the same probability for the entire larger set.

the complete question is

Identify the sampling method as simple random​ sampling, systematic​ sampling, convenience​ sampling, or stratified sampling. A computer randomly selects 800 names from a list of all registered voters. Those selected are surveyed to predict who will win the election for Mayor.

Choose the correct sampling technique below.

A. Systematic sampling

B. Convenience sampling

C. Simple random sampling

D. Stratified sampling

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