Which of the following are examples of rational numbers? Select all that apply

Answer:

(3, 0) and (5, 0)

Step-by-step explanation:

we have

[tex]y=x^{2}-8x+15[/tex]

we know that

The x-intercepts are the values of x when the value of y is equal to zero

so

For y=0

[tex]x^{2}-8x+15=0[/tex]

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2}-8x+15=0[/tex]  

so

[tex]a=1\\b=-8\\c=15[/tex]

substitute in the formula

[tex]x=\frac{-(-8)\pm\sqrt{-8^{2}-4(1)(15)}} {2(1)}[/tex]

[tex]x=\frac{8\pm\sqrt{4}} {2}[/tex]

[tex]x=\frac{8\pm2} {2}[/tex]

[tex]x=\frac{8+2} {2}=5[/tex]

[tex]x=\frac{8-2} {2}=3[/tex]

so

x=3, x=5

therefore

The x-intercepts are (3,0) and (5,0)

Answer:

2 grams

Step-by-step explanation:

multiply by 1000

Answer:

9+10-1+4+1

25

Step-by-step explanation:

The range is the value of y in the graph so the range of the function graphed below is -∞ < y ≤ 2.

We have,

The range of a function on a graph is the y-values the graph touches.

Now,

From the graph,

There are two parts the graph touches the y-values.

- From -∞ to 0

- From 0 to 2

This can be written in an interval as:

(-∞, 2]

Thus,

The range of the function is (-∞, 2].

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Answer:473

Step-by-step explanation:

Final answer:

To determine how many cans are needed to hold 2,367 tennis balls, with each can holding 5 balls, you divide the total number of tennis balls by 5 and round up to the nearest whole number, resulting in 474 cans.

Explanation:

The subject of the question is Mathematics, as it involves a division problem. The question entails calculating the number of cans needed to hold 2,367 tennis balls, given that each can hold 5 tennis balls. To determine the number of cans required, we divide the total number of tennis balls by the number of balls that can fit in each can.

To find the solution:

Divide 2,367 by 5, which equals 473.4.

Since you can't have a fraction of a can, you would need to round up because you will need part of another can to hold the remaining balls. So, rounding 473.4 up, you get 474 cans.

Therefore, the Tennis Teams of Atlanta need to purchase 474 cans to hold 2,367 tennis balls.

Both the friends stayed for 2 hours. Each one paid $12.

Step-by-step explanation:

Given,

Amount paid by Ronald = $12

Amount paid by Tyler upfront = $4

Amount per hour = $4

Let,

x be the number of hours.

R(x) = 12

T(x) = 4x+4

As both the friends paid same;

T(x) = R(x)

[tex]4x+4=12\\4x=12-4\\4x=8[/tex]

Dividing both sides by 4

[tex]\frac{4x}{4}=\frac{8}{4}\\x=2[/tex]

Putting x=2 in T(x)

T(2) = 4(2) + 4 = 8+4 = 12

Both the friends stayed for 2 hours. Each one paid $12.

Keywords: function, division

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To make an educated decision between the two job offers, you need to consider factors such as the number of hours worked, additional benefits, potential for overtime, job satisfaction, career growth opportunities, and work-life balance.

To make an educated decision, there are a few factors to consider when comparing these two job offers. First, you need to know the number of hours you will be working in a year for both jobs. Second, you need to know if there are any additional benefits, such as health insurance or retirement plans, offered with each job. Third, you need to consider the potential for overtime hours and how often you would work them.

Let's assume that the first job pays $45,000 for working 40 hours a week, 52 weeks a year, with no overtime. The second job pays $15 per hour for 40 hours a week, 52 weeks a year, and you can potentially earn time and a half for any hours worked beyond the 40 hours.

If the second job offers consistent overtime hours, then it could potentially provide a higher income compared to the first job. However, if the overtime hours are not guaranteed or if you prefer the stability of a fixed salary, then the first job with a salary of $45,000 would be a better option. Other factors to consider when finding work include job satisfaction, career growth opportunities, and work-life balance.

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Final answer:

To determine which apartment Mrs. Cooper should choose, first list all available apartments with two bedrooms and a parking space. Next, compare the monthly rents to her income, aiming to spend no more than 30% on rent, and then consider other monthly expenses before making a final decision.

Explanation:

The student's question relates to determining which apartment Mrs. Cooper should choose based on her monthly income and her specific requirements of having a two-bedroom apartment and a parking space. Unfortunately, the question does not provide a list of available apartments with their respective rents, so I can't provide a specific recommendation. However, I can guide the student on how to make the decision.

First, Mrs. Cooper should list each available apartment that meets her criteria of having two bedrooms and a parking space. Next, she should determine the monthly rent for each of these apartments. Having this, she should compare the rent prices against her monthly income of $2,960 keeping in mind that a general rule of thumb is not to spend more than 30% of one's income on rent, which in her case would be $888 per month.

It is also important for Mrs. Cooper to account for additional monthly expenses (like utilities, groceries, and any other recurring payments) when determining affordability. If there are any apartments that fit these financial parameters, Mrs. Cooper can then choose the one that best fits her other personal preferences or needs.

The second robot working alone would spend 7.5 minutes to do the task.

Equation is used to show the relationship between two or more numbers and variables.

Let y represent the rate at which the first robot work and x represent the rate that the second robot work.

Two robots can do a task in 5 min, working together. Hence:

The first robot, working alone, can for the task in 15 min. hence y = 15 min.

(1/x + 1/15)5 = 1

5/x + 1/3 = 1

x = 7.5 minutes

The second robot working alone would spend 7.5 minutes to do the task.

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The second robot working alone would spend 7.5 minutes to do the task.

To find the time it takes for the second robot to complete the task alone, we can utilize the concept of rate. Here's how:

Define rates:

Let R be the combined rate of both robots working together. We know they can complete the task in 5 minutes, so their combined rate is R = 1/5 tasks per minute (since rate = work done / time taken).

Let R1 be the rate of the first robot working alone. We know it takes him 15 minutes to complete the task, so R1 = 1/15 tasks per minute.

Relate rates:

The second robot's rate (R2) can be found by subtracting the first robot's rate from the combined rate: R2 = R - R1.

Calculate R2:

Substituting the known values: R2 = (1/5) - (1/15) = 2/15 tasks per minute.

Find time taken by second robot:

To find the time (T2) it takes for the second robot to complete the task alone, we can use the formula: T2 = 1 / R2.

Substituting the calculated rate: T2 = 1 / (2/15) = 15/2 = 7.5 minutes.

Therefore, the second robot will take 7.5 minutes to do the task alone.

Answer:

the second one

Step-by-step explanation:

Answer:

The numbers are 6 and 9

Step-by-step explanation:

Let the two numbers be x and y.

Given :

The sum of two numbers [tex]x+y=15[/tex]  equation:1

Also the difference of x and y  [tex]x-y= -3[/tex] equation:2

On solving equation:2  

                                      [tex]x=y-3[/tex]    equation:3

Putting this value of x in equation 1.

                      [tex]x+y=15\\\\(y-3)+y=15\\2y-3=15\\2y=15+3\\2y=18\\y=18/2\\y=9[/tex]

     Putting value of y in equation:3 to find x

                     [tex]x=y-3\\x=9-3\\x=6[/tex]

Paul bought  23 / 15 pounds of bananas.

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

Given that,

The total quantity of bananas and apples bought by Paul = 3 ¹/₃

Also, Paul bought 1 ⁴/₅ pounds of apples.

To find the quantity of bananas that Paul bought.

Use subtraction property,

Quantity of bananas = total quantity - quantity of apples

=  3 ¹/₃ -  1 ⁴/₅

= 10 / 3 - 9 / 5

= 50 - 27 / 15

= 23 / 15

The required quantity of bananas is 23 / 15.

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Answer:

1759

Step-by-step explanation:

multiply, then add

Answer:

1759

Step-by-step explanation:

5*354=1725

1725+34=1759

Answer:

30 years old.

Step-by-step explanation:

Here's what we know.

B=5J

M+2=8J+16

M=3B

So now let's solve using substitution.

M+2=8J+16

M=8J+14

But we know that M=3B

3B=8J+14

And we know B=5J

3*5J=8J+14

15J=8J+14

7J=14

J=2

Now, we can plug it into the M+2=8J+16

M+2=2*8 +16

M+2=16+16

M+2=32

M=30

Hope you enjoyed.

Answer:

30 years old

Step-by-step explanation:

look at the person above me he is right

Answer:

Echo can plant a maximum of 8 shrubs.

The total cost for Echo's shrubs is  = 8 [tex]\times[/tex] $15.32 = $122.56

Step-by-step explanation:

i) Garden is 36 feet wide

ii) Each shrub is 4.5 feet wide.

iii) therefore the maximum number of shrubs that can be planted are

[tex]= \frac{36}{4.5} = 8[/tex]

 Therefore Echo can plant a maximum of 8 shrubs.

Therefore the total cost for Echo's shrubs is  = 8 [tex]\times[/tex] $15.32 = $122.56

Answer:

The height of the pole is 40 feet.

Step-by-step explanation:

Answer:

Step-by-step explanation:

37.5 feet

Answer:(-2+0)(3+10)

Step-by-step explanation:

Answer:

y = 2x + 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (3, 10)

m = [tex]\frac{10-0}{3+2}[/tex] = [tex]\frac{10}{5}[/tex] = 2, thus

y = 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 2, 0), then

0 = - 4 + c ⇒ c = 0 + 4 = 4

y = 2x + 4 ← equation of line

Answer:

5

Step-by-step explanation:

2(x+3)=4(x-1)

2x+6=4x-4

6=4x-2x-4

6=2x-4

2x=6+4

2x=10

x=10/2

x=5

The maximum amount that can be financed is $156,250.

Minimum down payment required by the lender = 16% of the value of home

Available cash in hand = $25,000

Now,

the  maximum amount of down payment that can be paid = $25,000

let the maximum amount that can be financed is 'x'

also,

16% of x = $25,000

or

0.16 × x = $25,000

or

x = [tex]\frac{\$ 25,000}{0.16}[/tex]

or

x = $156,250.

Hence, the maximum amount that can be financed is $156,250.

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Answer:

52 sides

Step-by-step explanation:

The only way I know how to do this is to create one fraction which is a combination of 2 steps used when 1 of the interior angles is known.

Formula

360/(180 - 9000/s ) = s

Multiply denominator and numerator on the left by s.

360 * s

=======                  = s        

s* (180 - 9000/s)

Remove the brackets on the denominator

360s

================    =s

180s - 9000

Cancel the numerators s's.

360 / (180s - 9000) = 1

Multiply both sides by 180s - 9000

360 =180s - 9000

Add 9000 to both sides

360 + 9000 = 180s

9360 = 180s

Divide by 180

9360/180 = 180/180 s

s = 52

Answer:

n = 24 - 8.

Step-by-step explanation:

n + 8 = 24

Subtract 8 from each side:

n + 8 - 8 = 24 - 8

n = 24 - 8.

Answer:

Option D.) [tex]100 \textdegree[/tex] is correct.

Step-by-step explanation:

In a quadrilateral, ABCD, opposite angles are supplementary.

[tex]\angle BCD + \angle BAD = 180\textdegree[/tex]

therefore [tex]\angle BCD = 180\textdegree - \angle BAD = 180\textdegree - 80\textdegree = 100 \textdegree[/tex]

therefore option D.) [tex]100 \textdegree[/tex] is correct.

Answer:

Answe is 100

Step-by-step explanation:

The area of the figure PQRS can be found by applying the rule of areas in proportional shapes. The area of PQRS equals 32 square centimeters after rounding the calculated value.

The given problem involves the calculation of area and the application of ratios. It mentions two figures, ABCD and PQRS, along with certain dimensions and the area of the first figure. To find the area of the figure PQRS, we apply a rule of ratios used in geometry that states the areas of two similar figures is equal to the square of the ratio of their corresponding sides.

The corresponding sides here are DC and SR. So the ratio of their areas would be (DC/SR)². Plugging in the values we get = (10 centimeters/15 centimeters)² which simplifies to 0.444 (after rounding).

Then, to find the area of PQRS, we multiply the area of ABCD (which is 72 square centimeters) with the calculated square of the ratio. Therefore, the area of figure PQRS is 72 * 0.444 which equals 31.968 square centimeters (rounded to 32 square centimeters).

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Answer:

The constant of proportionality is equal to 4

Step-by-step explanation:

The picture of the question in the attached figure

Let

y ----> the total cost in dollars

x ----> the number of bags of peanuts

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

To find out the constant of proportionality, we need to take one point from the graph

take the point (1,4)

Find the value of k

[tex]k=\frac{y}{x}[/tex]

substitute the value of x and the value of y

[tex]k=\frac{4}{1}=\$4\ per bag[/tex]

Answer:

4

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

5x-2y=3  when: y=2x

1. Plug in the y-value (y=2x) into the equation (5x-2y=3). The equation should then look like 5x-2(2x)=3

2. Simplify:

5x-2(2x)=3

5x-4x=3

1x=3

x=3

Check:

5x-2(2x)=3 (plug in the x-value you solved for: 3)

5(3)-2×2(3)=3

15-2×6=3

15-12=3

3=3

Hope this helped !

Cheers, Z

Answer:

c = 6.5, a = 11.6

Step-by-step explanation:

2a + 3c = 42.7

3a + 5c = 67.3

Elimination

(2a+3c = 42.7)*3

(3a+5c = 67.3)*2

(1) 6a+9c = 128.1

(2) 6a+10c = 134.6

(2) - (1)

c = 6.5

Substitue 'c' in any of the equation

2a + 3(6.5) = 42.7 or 3a + 5(6.5) = 67.3

2a + 19.5 = 42.7 3a + 32.5 = 67.3

2a = 42.7 - 19.5 3a = 67.3 - 32.5

2a = 23.2 3a = 34.8

a = 11.6 a = 11.6

Answer:

Therefore [tex]x =\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]\frac{7}{8} x+\frac{3}{4} x+\frac{7}{16} x-\frac{1}{16} =\frac{5}{8}[/tex]

[tex]\Leftrightarrow \frac{7}{8} x+\frac{3}{4} x+\frac{7}{16} x =\frac{5}{8}+\frac{1}{16}[/tex]

[tex]\Leftrightarrow \frac{14x+12x+7x}{16} =\frac{10+1}{16}[/tex]         [ L.C.M of 8,4,16 =16 and  L.C.M of 8,16 =16]

[tex]\Leftrightarrow \frac{33x}{16} =\frac{11}{16}[/tex]

[tex]\Leftrightarrow x =\frac{11\times 16}{16\times 33}[/tex]

[tex]\Leftrightarrow x =\frac{1}{3}[/tex]

Therefore [tex]x =\frac{1}{3}[/tex]