Name
(Score for Question 2:
of 4 points)
2. Jaxon bought a cell phone. The cell phone's down payment is $35. There is a monthly cost of $20.
A. Write an equation that gives the total cost (in dollars) of paying a down payment for a cell
phone and paying a monthly payment as a function of the number of months needed to pay
off the phone in full. Write the equation in slope-intercept form.
-
Date
y=mx+b
Math 4.10 | Unit 4 Test, Part 2 | Lines | Page 2 of 4
B. Find the total cost if it takes 10 months to pay off the cell phone in full. Show your work.

The vertical line intercept the the graph more than once, the graph is of a relation but it is not a function

Hence, the vertical line intercept the the graph more than once, the graph is of a relation but it is not a function.

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52.7gk. 1mok/39.1gk= 1.347 mol k/1133y=1 kci

The measure of the second largest angle in (6x-17) (4x-12) (2x+5) is 56°.

It should be noted that the value of the angle in a triangle is equal to 180°. Therefore, we will add the angle and add them to equate 180°

This will be:

(6x-17) + (4x-12) + (2x+5) = 180

6x - 17 + 4x - 12 + 2x + 5 = 180

12x -24 = 180

Collect like terms

12x = 180 + 24

12x = 204

Divide

x = 204 / 12

x = 17

First angle = 6x - 17 = 6(17) - 17 = 85°

Second angle = 4x - 12 = 4(17) - 12 = 68 - 12 = 56°

Third angle = 2x + 5 = 2(17) + 5 = 39°

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The volume of the entire shape, given that the figure is a solid shape, and the unit cubes, is d. 32 cubic units.

The volume for the shape can be found by the formula:

= Length  Width x Height

Each small cube is a unit cube which means that the measurements of the dimensions are:

Length = 4 units because there are 4 unit cubs along the length

Width = 4 units for the same reason

Height = 2 units because there are 2 unit cubes needed to get the height

The volume would therefore be:

= 4 x 4 x 2

= 32 cube units

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The total cost per yard is $4

How do we calculate the total cost?

The average total cost formula shows the cost per unit of the quantity produced and is calculated by taking two figures where the first one is total production cost and the second one is the quantity produced in numbers and then the total cost of production is divided by the total quantity produced in numbers.

Average Total Cost = Total Cost of Production / Quantity of Units Produced

Given,

Gloria bought fabric which is = 6 3/4 yards or 27 / 4 yards

Total cost was = $27

Cost per yard is = 27 / (27/4)

                           = $4 per yard

Therefore, the total cost per yard is $4

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Answer:

Do 2007-1979

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

She will have to pay 1,500

a) An equation to describe the relationship between time and the number of restaurants in the United States, with 2012 as the base, is Y = 980 + 16.5x.

b) Using this equation, we can predict that the number of restaurants in 2018 will be 1,079 thousand.

An equation is a mathematical statement or function claiming that two mathematical expressions that may combine numbers, variables, and constants are equal or equivalent.

Equations are depicted with the equation symbol (=) to establish the equality of expressions.

The number of thousands of restaurants in the United States:

2012 = 980

2016 = 1,046

4 years (2016 - 2012) = 66 more restaurants (1,046 - 980)

In 1 year = 16.5 more restaurants (66/4)

(0, 980) and (4, 1,046)

Y = 980 + 16.5x

Where Y = the number of thousands of restaurants in the year

x = the number of years past.

In 2018, the number of restaurants, Y = 980 + 16.5x

The number of years between 2018 and 2012 = 6 years

The expected number of restaurants Y = 980 + 16.5(6)

= 1,079.

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The height of Liberty School  in ordinary form is 8850 m and of Festus school is 5890 m , the difference of the height values is 2960 m.

In the question ,

it is given that the height of the Liberty  school is 8.85 × 10³ m.

we have to convert this height in the ordinary form ,

8.85 × 10³ = (885/100) × 1000

= 885 × 10

= 8850 m

The height of the Festus school is 5.89 × 10³ m

in ordinary form it is

= 5.89 × 10³

= (589/100) × 1000

= 589 × 10

= 5890 m

The difference in the height of the school = height of liberty school - height of Festus school .

difference = 8850 - 5890

= 2960 m

Therefore , the height of liberty school is 8850 m and height of Festus school is 5890 m, the difference of the height values is 2960 m.

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The cost function, C(x) = x² - 20·x + 340, where x is the units sold, indicates;

The person should sell 10 units of tacos to minimize the costs. The minimum cost is $240

A function is the definition of the relationship between the input and output variables of an ordered pair, such that each input has one output.

The daily cost function for the sale of Tacos is, C(x) = x² - 20·x + 340

Where;

C(x) = The cost of selling x tacos

x = The number of units of tacos sold

The function in the question is a quadratic function and the positive coefficient of x² indicates that the graph of the function which is a parabola, is concave upwards.

The vertex of the parabola, of the equation, f(x) = a·x² + b·x + c,  is at the point where, x = b²/(2·a)

Comparison with the equation, C(x) = x² - 20·x + 340, indicates that we have;

a = 1

b = -20

c = 340

The x-coordinate of the vertex, which is the minimum point of a concave up parabola is; x = (20)/(2×1) = 10

The number of units sold that yields minimum cost is; x = 10

The number of units the person should sell to minimize the cost is 10.

The minimum cost is therefore;

C(10) = 10² - 20 × 10 + 340 = 240

The minimum cost is $240

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The value of angles in triangle are ,

1) x=60°.

2) y = 15°.

3) Angle of C=45°

4) Angle of DBC=  105°.

5)Angle of CBA = 75°

What is triangle ?

 Three-sided polygons with three sides are known as triangles, however this term is not particularly common. Every triangle has three sides and three angles, some of which might be the same. Having three sides and three vertices, a triangle is a polygon. There is a 180 degree angle created inside the triangle. This indicates that a triangle's interior angles add up to 180°. Having the fewest sides of all polygons, it is that.

Here the given diagram DA is the straight line.

In straight line angle at any point is 180°. then

=>7y°+5y°=180°

=> 12y = 180

=> y = 180/12

=> y = 15°.

Then angle of DBC = 7y= 7*15 = 105°.

Now angle of CBA = 5y = 5*15 =75°.

And angle C = 3y=3*15=45°.

Now consider the triangle ABC , we know that sum of all angles in triangle is add upto 180°.

=> ∠A+∠B+∠C=180°

=> x+75+45=180

=> x= 180 - 120

=> x = 60°.

There fore the value of angles in triangle are ,

1) x=60°.

2) y = 15°.

3) Angle of C=45°

4) Angle of DBC=  105°.

5)Angle of CBA = 75°

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The cost for each pound of chocolate chips and each pound of walnuts is: $1.25 and $9.75

Given,A store is having a sale on chocolate chips and walnuts.

For 3 pounds of chocolate chips and 5 pounds of walnuts, the total cost is 18.00 .

For 12 pounds of chocolate chips and 2 pounds of walnuts, the total cost is 45.

we are asked to determine the cost for each pound of chocolate chips and each pound of walnuts.

let x=cost/lb of walnuts

let y=cost/lb of chocolate chips

we frame the equations as:

3x+5y=16

6x+2y=22

Multiply eq 1 by 2.

we get:

6x+10y=32

6x+2y  = 22

subtract now,

8y = 10

y = 10/8

y=1.25

x = x=16-5y=9.75

cost/lb of walnuts=$1.25

cost/lb of chocolate chips=$9.75

Hence we get the required cost.

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Answer:

n = 49

Step-by-step explanation:

We can find the value of n by completing the square.  The general form of the quadratic equation is ax^2 + bx + c and the formula for completing the square is (b / 2)^2.  

In the question, -14 is the b value so we can do:

[tex](-14/2)^2=(-7)^2=49[/tex]

Answer: 40 $

Step-by-step explanation:

Answer:

$40

Step-by-step explanation:

Since the discount is 25% off the original price, and 100% - 25% = 75%, then the sale price of $30 is 75% of the original price.

75% of x = $30

0.75x = 30

x = 30/0.75 = 30/(3/4)

x = 30 × 4/3

x = 40

Answer: $40

Answer: 17/25

Step-by-step explanation:

This equals 68%, which equals 68/100.

Let's divide both sides by 2.

68/2 = 34

100/2 = 50

This gives us 34/50.

We can simplify even more!

34/2 = 17

50/2 = 25.

This gives us 17/25.

We can no longer simplify, which means 17/25 is our final answer.

The point-slope form of the equation is y - 2 = -(x + 2)

From the graph, we have the following points

(-2, 2) and (2, -2)

Start by calculating the slope of the points

This is calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

This can be rewritten as

m = (y₂ - y₁)/(x₂ - x₁)

Where

slope = m

(x, y) = (-2, 2) and (2, -2)

So, we have

m = (-2 - 2)/(2 + 2)

Evaluate the expression

m = -1

From the question, we understand that:

(x₁, y₁) = (-2, 2)

The equation of the line is then calculated as

y - y₁ = m(x - x₁)

Substitute the known values in the above equation, so, we have the following representation

y - 2 = -1(x + 2)

Evaluate

y - 2 = -(x + 2)

Hence, the equation of the line is y - 2 = -(x + 2)

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On a given map each unit represnts= 100 miles

Given that the airports are located at coordinates p(1,17) and q(12,10) in this puzzle, the distance between them is given by: Since 100 miles are represented by each unit, the distance in miles is calculated as follows: D = 13.03 x 100 = 1303 miles.

Therefore the distance to the nearest whole mile between the two airports= 1303 miles.

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Answer:

1. [tex]\frac{3}{7}[/tex] × [tex]\frac{4}{5}[/tex] = [tex]\frac{12}{35}[/tex]

2. [tex]2\frac{6}{8}[/tex] × [tex]\frac{2}{3}[/tex] = [tex]\frac{11}{4}[/tex] × [tex]\frac{2}{3}[/tex]

             = [tex]\frac{11}{6}[/tex]

             = [tex]1\frac{5}{6}[/tex]

3. [tex]\frac{12}{5}[/tex] ÷ [tex]\frac{3}{7}[/tex] = [tex]\frac{12}{5}[/tex] × [tex]\frac{7}{3}[/tex]

             = [tex]\frac{28}{5}[/tex]

             = [tex]5\frac{3}{5}[/tex]

4. [tex]\frac{8}{18}[/tex] ÷ [tex]\frac{4}{6}[/tex] = [tex]\frac{8}{18}[/tex] × [tex]\frac{6}{4}[/tex]

             = [tex]\frac{2}{3}[/tex]

Springfield's population in the year 2026, based on the population in 2019, and the growth rate, would be 251, 940 people

As at the year 2019, the population of Springfield was estimated to have been 202, 628 people. This number is also growing by the year, at a rate of 0. 81%.

This means that in the year 2046, the population of Springfield can be estimated using the future value formula which is:

= Current population x ( 1 + population growth rate) ^ number of years

Find the number of years as:

= 2046 - 2019

= 27 years

The population would be:

= 202, 628 x ( 1 + 0.81 % ) ²⁷

= 251, 940 people

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The gross income of each month will be 2500/month and 30,000/year. And the net income will be 1850/month and 22,200/year.

We got 30000 a year to budget our expenses.

And the year has 12 months.

So, our monthly gross income will be 30,000/12

= 2500

Now, the tax rate is 15%

So, the tax will be,

=2500×15/100

=2500×.0.15

=375/month

And our insurance is 200 a month

Now,

we put 3% of our income for our retirement every month

so, the retirement fund will be

=2500×3/100

=2500×0.03

=75

Therefore,

The net income will be

=2500-375-200-75

=2500-650

=1850

Hence, our gross income will be 2500/month and 30000/year

And our net income will be 1850/month and 22,200/year

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a) The value of (g/f)(-3) is  -1/2

b)  -5 and -2 are the values that are not in the domain of g(x)/f(x)

What are domain and range of a function ?

The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

g(x)=x+4

f(x)=(x+5)(x+2)

a) g(x)/f(x) = (x+4)/ (x+5)(x+2)

(g/f)(-3) = (-3+4)/(-3+5)(-3+2)

            = 1/(2*-1)

           = 1/-2

           = -1/2

b)  

Set denominator to zero

(x+5)(x+2) = 0

=> (x+5)=0 or (x+2)=0

=> x = -5 and x=-2

=> -5 and -2 are the values that are not in the domain of g(x)/f(x)

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Answer: 100 x 1.05^(15x12) = $651739.184097

Step-by-step explanation:

The four sided figure formed by opposite pairs of parallel lines is called a parallelogram.

In the attached figure we can see that the quadrilateral ABCD has the following aspects:

AB || CD

AD || BC

Which states that the opposite sides are parallel.

Now ∠A + ∠B = 180° co interior angles are supplementary.

Therefore , ∠A = 180° - ∠B

Again ∠C + ∠B = 180° co interior angles are supplementary.

And , ∠C= 180° - ∠B

Therefore from the above two statements we can say that  ∠C = ∠B.

A unique sort of quadrilateral made up of parallel lines is called a parallelogram. According to definition, a parallelogram is a shape with opposite sides that are parallel and any angle between the sides on each side.

If the opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. If both pairs of opposite sides of a quadrilateral remain parallel and equal, the shape is referred to as a parallelogram.

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The compound interest rate is 54.23% for investment that triples in 2 years.

What is compound interest?

The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is calculated by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.

When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:

A = P (1 + r/4)4t

Given investment triples in 2 years

3p = [tex]e^{rt}[/tex]

rt = ln(3)

r = ln(3)/2 = 0.54

Which is 54.23%

Hence the interest rate is 54.23% for investment that triples in 2 years.

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Answer:

20

Step-by-step explanation:

Let x = number of members.

Let y = number of chairs.

75% of x = 5/6 of y

3x/4 = 5y/6

x/y = 5/6 × 4/3

x/y = 20/18

x/y = 10/9

The ratio of members to chairs is 10/9.

We need the smallest numbers in the ratio of 10/9 for which 75% of the first number and 5/6 of the second number are whole numbers.

Try 10:9; 75% of 10 = 7.5; not a whole number

Try 20/18; 75% of 20 = 15; 5/6 of 18 =  15 both whole number. This is the answer.

Answer: 20

The smallest possible number of people in the club is 20

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Let x = number of members.

Let y = number of chairs.

Therefore,

75% of x = 5/6 of y

3x/4 = 5y/6

x/y = 5/6 × 4/3

x/y = 20/18

x/y = 10/9

The ratio of members to chairs is; 10/9.

We want the smallest numbers in the ratio of 10/9 for which 75% of the first number and 5/6 of the second number are whole numbers.

10:9;

75% of 10 = 7.5; not a whole number

20/18;

75% of 20 = 15;

5/6 of 18 =  15 both whole number.

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The range of the function y= [tex]x^2-4[/tex] is (-4,∞)

What is range?

 The set of every output from a function is its range. Example: Let's have a look at the function f: AB, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output. Set of even natural numbers is the range.

Here the given function is ,

=> y= [tex]x^2-4[/tex]
Now we know that x>0

Then , square on both sides

=> [tex]x^2[/tex] > 0 now add -4 thwn ,

=> [tex]x^2[/tex] -4> -4

=> y > -4

We note that value of y is greater than -4 , (not including -4)

Then range of the function is ,

=> (-4,∞)

Hence the range of the function is (-4,∞).

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