Use the Exemption amounts in Figure 2.2 on page 132 to find the
(a) amount for exemptions and (b) annual state income taxes.
11. Jeff Falls, a heating system
salesman, is single with 3
dependents. He earns $57,900
annually, and his state's tax rate
is 3%.
13. Rick Delgado earns $43,500
annually as an automobile
mechanic. He is married but
has no dependents. The state
tax rate is 4.6%.
12. Sara Moon is a video editor
who earns $63,840 annually.
She is married, has 2 dependents,
and her state tax rate is 4%.
14. Julie Bookwalter is single,
claims 1 dependent, and
earns $32,300 annually. The
state tax rate is 2.5%.

Answer:

x = ± 3

Step-by-step explanation:

given y varies as [tex]\frac{1}{x^2}[/tex] , then

y = k × [tex]\frac{1}{x^2}[/tex] = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation

to find k use the condition x = 2 , y = 1

1 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )

4 = k

y = [tex]\frac{4}{x^2}[/tex] ← equation of variation

when y = [tex]\frac{4}{9}[/tex] , then

[tex]\frac{4}{9}[/tex] = [tex]\frac{4}{x^2}[/tex] ( cross- multiply )

4x² = 36 ( divide both sides by 4 )

x² = 9 ( take square root of both sides )

x = ± [tex]\sqrt{9}[/tex] = ± 3

Answer:

16c+7d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

(14x + 18) and 116 are corresponding angles and are congruent, then

14x + 18 = 116 ( subtract 18 from both sides )

14x = 98 ( divide both sides by 14 )

x = 7

The ratio of the number of girls to the number of adults is 5 : 1.

Ratio is used to compare two or more values together. Ratio shows the frequency of one number compared to the frequency of another number. The sign that is used to represent ratio is :.  

The ratio of the number of girls to the number of adults = number of girls : number of adults

number of girls = 100

number of adults = 20

The ratio of the number of girls to the number of adults = 100 : 20

Express the ratio in its simplest form. To do this, divide both numbers by the greatest common factor of 100 and 20. The greatest common factor of 100 and 20 is 20.

The ratio of the number of girls to the number of adults = 5 : 1

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Perimeter = side 1 + side 2 ´+ side 3.

Triangle 1

Perimeter = 6 + 8 + 10

= 24

Triangle 2

Perimeter = 9 + 12 + 15

= 36

Ratio

24/36 = 2/3

The ratio of the perimeters is also 2/3

yes,  5^x a polynomial. a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

In the given expression 5^x x is a variable and 5 is a real number.

5^x is a finite polynomial or infinite polynomial. It depends upon the value of x. If x is finite then 5^x is a  finite polynomial  and if x is infinite then  5^x is a  infinite polynomial.

Hence If x is finite then 5^x is a finite polynomial  and if x is infinite then  5^x is a  infinite polynomial.

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Answer:

Step-by-step explanation:I don’t know

Answer Las raíces de la ecuación x2 − 6x + 7 = 0 son α y β. Encuentra la ecuación con raíces α + 1 β y β + 1 α. Deduzco que α + β = − b a = 6 1 = 6 y que αβ = c a = 7 1 = 7.

Step-by-step explanation:

Formular for total surface area of a cylinder

S = 1231.5 sq ft

a. Using the equation of the relationship, the temperature outdoor would be 67.5 °F.

b. 140 chirps in a minute.

c. 60 chirps at that temperature is expected.

d. The graph for the relationship is given below.

e. 1/4 is the unit rate or slope = in 1/4°F per chirp.

f. 40 represents the starting or initial temperature.

The graph of a linear equation, y = mx + b, will have a slope value of m, and an initial value or y-intercept of b, which is the point on the y-axis that the line intercepts.

Given the equation, f = ¼c + 40, where:

f = temperature in degrees Fahrenheit

c = number of chirps

1/4 represents the temperature in °F per chirp

40 represents the initial temperature

a. Substitute c = 110 into the equation, f = ¼c + 40:

f = ¼(110) + 40

f = 67.5

The outdoor temperature is predicted to be 67.5 °F.

b. Substitute f = 75 into the equation, f = ¼c + 40:

75 = ¼c + 40

75 - 40 = ¼c

35 = 1/4c

4(35) = c

c = 140

140 chirps would be heard in a minute.

c. Substitute f = 55 into the equation, f = ¼c + 40:

55 = ¼c + 40

55 - 40 = ¼c

15 = c/4

4(15) = c

c = 60

Expect to hear 60 chirps at that temperature.

d. The graph for f = ¼c + 40 is in the attachment.

e. 1/4 is the unit rate or slope, which is the temperature in °F per chirp.

f. 40 tells us about the equation of the relationship that the initial temperature where we can start expecting the crickets to chirp starts from 40 °F.

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The value of x + y in the system of equations is  0.82125.

Given system of equations:-

8x + 9y = 4.92  ...(1)

9x + 14y = 6.93 ...(2)

We have to find the value of x + y in the system of equations.

Multiplying (1) by 9 and (2) by 8, we get,

72x + 81y = 44.28  ...(3)

72x + 112y = 55.44 ...(4)

(4) - (3), we get,

0x + 31y = 11.16

31y = 11.16

y = 11.16/31

y = 0.36

Putting the value of y in (1), we get

8x + 9*(0.36) = 6.93

8x + 3.24 = 6.93

8x = 6.93 - 3.24

8x = 3.69

x = 0.46125

Hence,

x + y = 0.46125 + 0.36 = 0.82125

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Given:

Height of triangular base = 8 cm

Length of traingular base = 6cm

Height of pyramid = 12 cm

Let's determine the volume of Valeria's pyramid.

To find the volume of the triangular pyramid, apply the formula:

Where A is the area of the triangular base and h is the height of the pyramid

To find the area of the triangular base, apply the area of a triangle formula:

To find the volume of the pyramid, substitute 24 for A and 12 for h in the formula above.

Thus, we have:

Solving further:

Therefore, the volume of Valeria's pyramid is 96 cubic centimeters.

ANSWER:

Answer:

70

Step-by-step explanation:

So 175% of 40 is the amount in april so we can split it up into 2 problems

100% of 40? 40

75% of 40? 30

Then you add the 2 to get 175% of 40 which will be 70!

The general form of an equation in intercetp form is:

Where m is the change of y in function of x and b is the value of b when x is 0

In this situation you have:

y=C

x=r

m= 1.75 ( C increase 1.75 each r)

b= 7 (When there is not ride r=0 the admission fee is 7)

The factors of the given equation 4x^2-x-5 are 5/4 and -1.

For the given question, the expression is given as;

= 4x^2-x-5

as, 4×5 = 20, break the number such that on subtraction we will get -1.

=  4x^2 - 5x + 4x -5

Taking x common from first two digit.

= x(4x - 5) + (4x - 5)

Taking common again.

= (4x - 5)(x + 1)

Put the equation equal zero to find the factor.

4x - 5 = 0

x = 5/4

and, x + 1 = 0

x = -1

Thus, the factors are found as 5/4 and -1.

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Answer:

Step-by-step explanation:

The spending is the cost plus expenses:

Net income is the difference of money made and spent:

Answer:

a=1

Step-by-step explanation:

Answer:

Step-by-step explanation:

4 and 2/5 inches by 8 and 3/5 inches.

60 and 6 feet by 120 and 9 feet.

66 by 129 feet

8514 feet squared

When b²−4ac=0 there is one real root.

When b²−4ac>0 there are two real roots.

When b²−4ac<0 no real roots or two complex roots

First equation

-x²-4x+7

b²−4ac>0, then equation -x²-4x+7 has two real roots.

Second equation

-2x²+9x-11

b²−4ac<0, then equation -2x²+9x-11 has two complex roots.

Third equation

3x²-6x+3

b²−4ac=0, then equation 3x²-6x+3 has one root.

The coordinates of the trapezoid  RSTU with vertices R(-13, 7), S(-1, 7), T(-1, -5), and U(-13,-9) after dilation with scale factor of k= 1/4 are

Data gotten from the question

Dilation refers to an increment or reduction in dimension and location of a preimage to get a new image

The coordinate of the image of dilation is gotten using the formula

x₂ = kx₁ - x₀(k - 1) for x coordinate

y₂ = ky₁ - y₀(k - 1) for y coordinate

definition of terms

terms with subscript 2 is corresponding to the image

terms with subscript 1 is corresponding to the preimage

terms with subscript 0 is corresponding to the center of dilation

\k = scale factor

R(-13, 7) ⇒ R'(-7, -2)

x₂ = 1/4 * -13 - -5(1/4 - 1) = -7

y₂ = 1/4 * 7 - -5(1/4 - 1) = -2

S(-1, 7)  ⇒ S' (-4, -2)

x₂ = 1/4 * -1 - -5(1/4 - 1) = -4

y₂ = 1/4 * 7 - -5(1/4 - 1) = -2

T(-1, -5) ⇒ T' (-4, -2.5)

x₂ = 1/4 * -1 - -5(1/4 - 1) = -4

y₂ = 1/4 * -5 - -5(1/4 - 1) = -2.5

U(-13,-9) ⇒ U' (-7, -6)

x₂ = 1/4 * -13 - -5(1/4 - 1) = -7

y₂ = 1/4 * -9 - -5(1/4 - 1) = -6

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I think

Answer:

23

Step-by-step explanation:

Isolate the variable. Divide each variable

The ratio 5:12 means that we have 5 orange marbles for 12 black marbles (5 to 12) and the orange marbles will be 30 if the container has 72 black marbles.

According to the question,

We have the following information:

A container full of marbles has a ratio of orange marbles to black marbles of 5:12.

It means that we have 5 orange marbles when the number of black marbles is 12.

Now, let's take the number of orange marbles to be 5x and the number of black marbles to be 12x.

Now, we have the number of black marbles as 72.

So ,we have:

12x = 72

x = 72/12

x = 6

Now, we will put the value of x in 5x to find the number of orange marbles:

5x

5*6

30

Hence, the number of orange marbles in the container when it has 72 black marbles is 30.

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The solution for the given linear equation is z = 6

Here we have the following linear equation:

10 = z/2 + 7

To solve it, we need to isolate the variable in one of the sides of the equation.

First, we can subtract 7 in both sides:

10 - 7 = z/2 + 7 - 7

3 = z/2

Now we can multiply both sides by 2 to get:

2*3 = 2*(z/2)

6 = z

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The expression which can be rewritten using a common factor is [tex]\frac{xy}{14} (x^{2} +3y)[/tex].

According to the question,

We have the following information:

One fourteenth times x cubed times y plus three fourteenths times x times y squared.

(We know that 'times' has to be replaced with multiplication.)

Now, we will change this into mathematical expression:

[tex]\frac{x^{3} y}{14} +\frac{3xy^{2} }{14}[/tex]

Now, from these two terms, the common factor can be [tex]\frac{xy}{14}[/tex].

(Common factor means that the number and the variables taken as a common factor should be able to completely divide the terms given any expression.)

Now, taking it as a common factor, we have the following expression:

[tex]\frac{xy}{14} (x^{2} +3y)[/tex]

Hence, the required expression is [tex]\frac{xy}{14} (x^{2} +3y)[/tex].

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Answer:

Step-by-step explanation:

First, we need to find the rate. miles/hours. 3000/75 = 40mph (miles per hour). to find the answer we need to divide the rate by the distance they want us to find. to see a deeper explanation of why scroll past the answer.  4000/40 = 100 hours.

deeper explanation:

we can set the numbers given to us equal to what we are looking for.

miles/hour

3000/75 = 4000/x            x being the time we are looking for

cross multiply          3000x=300000

divide by 3000          x=100 hours

Answer: 899.998434785 times more than the loser.

PLUG IN THE VALUES IN THE RIGHT POSITIONS AND SIMPLIFY.

[tex] = 2( \frac{1}{2} + \frac{3}{4} ) + 6 \\ = 2( \frac{5}{4} ) + 6 \\ = \frac{10}{4} + 6 \\ = \frac{5}{2} + 6 \\ = \frac{17}{2} [/tex]

THE ANSWER IS OPTION C.

Model P televisions made up 12 of the 40 televisions when Quick Sell outlet sold a total of 40 television, each of which was either a model P television or a model Q television.

Price plus quantity equals revenue.

Let x be the quantity of sold TVs of model p.

40 - x units of the model q TV would have been sold.

Profits from model p TV sales are

px

Sales of the type q TV bring in money.

(40 - x)q

Total income equals px plus (40 - x)q

The average price calculation formula is written as

Total revenue / total number of TVs sold equals average price.

The 40 televisions sold for an average (arithmetic mean) price of $141. It follows that

141 = (px + (40 - x)q)/40

141 × 40 = px + (40 - x)q

5640 = px + (40 - x)q

p = q - 30

5640 = x(q - 30) + (40 - x) (40 - x)

q

30x + 40q - xq = 5640

5640 = - 30x + 40q

Since q = 120,

5640 = - 30x + 40 × 120

5640 = - 30x + 4800

5640 - 4800 = - 30x

840 = - 30x

x = 840/- 30 = - 28

Q cannot equal 120 since x cannot be negative.

Again,

5640 = px + (40 - x)q

If q = 30 + p, then

5640 = px + (40 - x)(30 + p)

5640 = px + 1200 + 40p - 30x - px

5640 = 1200 + 40p - 30x

Therefore,

If p = 120, then

5640 = 1200 + 40 × 120 - 30x

5640 = 6000 - 30x

30x = 6000 - 5640

30x = 360

x = 360/30

x = 12

Therefore, out of 40 televisions 12 tv are of model p

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