Two trucks leave a warehouse at the same time, traveling in opposite directions. The rate of the faster truck exceeds that of the slower truck by 2 miles per hour. After 5 hours, they are 315 miles apart. What are the rates of the trucks?

a. Ryan's rate of change is $15 per month;

Taylor's rate of change is $20 per month

b. Ryan's starting balance is $50;

Taylor's starting balance is $25.

Recall:

Ryan's Savings Plan Function:

s = 15m + 50

Thus, the starting value (starting balance) modelled by this function is $50

The slope/rate of change is $15 per month

Taylor's Savings Plan:

Given the table, the starting value will be the amount saved (initial value) at 0 number of months.

Using (0, 25) and (1, 45) find the rate of change:

In summary:

a. Ryan's rate of change is $15 per month;

Taylor's rate of change is $20 per month

b. Ryan's starting balance is $50;

Taylor's starting balance is $25.

Learn more about linear function on:

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Answer:

B, y=X. Hope it works

Step-by-step explanation:

Answer: a

Step-by-step explanation:

u do 1+1

Answer:

8÷5 = 1 . 6

Step-by-step explanation:

They will divide the pizzas into 5 pieces further

Answer:

m=2

Step-by-step explanation:

Answer:

3:2

Step-by-step explanation:

42:28

21:14

3:2

Answer:

y=-9

Step-by-step explanation:

7+y=-2

subtract 7 on both sides

Answer:

y= -9

Step-by-step explanation:

This is a one-variable equation.

7+y= -2

We can subtract 7 from both sides to isolate y

7 + y - 7= -2 - 7

After simplifying, we get

y= -9

Answer:

15/4

Explanation:

To find the reciprocal of a fraction, switch the denominator and the numerator, which will give you the reciprocal of a fraction.

Hoped this helped.

[tex]GeniusUser[/tex]

[tex]\huge \bf༆ Answer ༄[/tex]

Here's the solution ~

Value of x is 64

Answer:

3.25

Step-by-step explanation:

13÷4=3.25

Everyone gets 3.25 kg of chocolate

Answer:

3 1/4 kilograms

Step-by-step explanation:

13 ÷ 4 = 3.25 = 3 1/4

Answer:

N||M, K||J

Step-by-step explanation:

N and M are both parallel to each other and || symbolizes that, same goes for K and J

Answer:

Olivia's puppy is linear i know this because after applying to the graph i got a straight line.

Step-by-step explanation:

Answer:

When looking at the table you can see that for every increase of 1 in the x value it results in an increase of 1 in the y value. The rate of change is constant.

Rate of change is calculated by the change in y/change in x

For the points (1,2), (3,3) and (5,4) the rate of change calculation would be as follows:

(1, 2)(3, 3)

3-2 / 3-1= 1/2

(3, 3)(5, 4)

4-3 / 5-3= 1/2

Since both equal 1/2 the rate of change is constant therefore making it linear.

Step-by-step explanation:

Answer: what’s the question I would love to help but there’s no question maybe try to post it again and I will see if I can answer?

Answer:

No question so no answer (just getting points i guess)

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

smallest slope

Answer:

[tex]8^6[/tex]

Step-by-step explanation:

Powers are defined as the number of times you multiply a number by itself. For example, 2 to the 3rd power is 2 multiplied by itself 3 times. 2 * 2 * 2 = 8. You also know that if you multiply two powers of the same base, you add the exponent, and if you raise a power to a different power, you multiply the exponents.

e.g:

[tex]2^2\cdot2^2=2^{2+2}=2^4\\(2^2)^3=2^{2\cdot3}=2^6[/tex]

Now, we are asking to use grouping to write 2 to the power 18 as a power of 8. We know 2 to the power 8 is 2 to the power 3, so we have the following equation:

[tex]2^{18}=(2^3)^x[/tex]

We know this is now 2 to the power 3x = 2 the power 18, and therefore x = 6, because 3 times 6 is equal to 18. Now, we can just simplify 2 to the third as 8 and we now have:

[tex]8^6[/tex]

Answer:

noun

1.

a surface of which one end or side is at a higher level than another; a rising or falling surface.

Step-by-step explanation:

steepness

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x)

step one: identify two points on the line

step two: select one to be (x1,y1) and the other to be (x2,y2)

step three: use the slope equation calulate slope

2x-3=8+7(+3)

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

2y=8x+10

----- --------

2y=8x+10

y=4x+5

Answer:

m=4

The different programs (in terms of order) that can be arranged is 120 different ways

Since we are dealing with arrangements, this is a permutation problem.

If there are three bands and two comics performing at a show, the total band will be 5 bands

The number of different programs that can be arranged will be 5!

5! = 5 * 4 * 3 * 2

5! = 60 * 2

5! = 120 ways

Hence the different programs (in terms of order) that can be arranged is 120 different ways

Learn more on permutation here: https://brainly.com/question/9253208

a.

The volume of the box V = 4x³ - 72x² + 324x

Since the dimensions of the square piece of paper are 18 inches each, and we cut out a length x from each side to give a total length of 2x cut from each side. So, each dimension is L = 18 - 2x.

Since the height of the open box is x and its base is a square, the volume of the open box ix V = L²x

= (18 - 2x)²x

= (324 - 72x + 4x²)x

= 324x - 72x² + 4x³

The volume of the box V = 4x³ - 72x² + 324x

b.

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

Since the volume of the box is 432 cubic inches,

V = 324x - 72x² + 4x³

324x - 72x² + 4x³ = 432

4x³  - 72x² + 324x - 432 = 0

x³  - 18x² + 81x - 108 = 0

A factor of the expression is x - 3

So, x³  - 18x² + 81x - 108 ÷ x - 3 = x² - 15x + 36

So,  x³  - 18x² + 81x - 108 = (x² - 15x + 36)(x - 3) = 0

Factorizing the expression x² - 15x + 36 = 0

x² - 3x - 12x + 36 = 0

x(x - 3) - 12(x - 3) = 0

(x - 3)(x - 12) = 0

So,  x³  - 18x² + 81x - 108 = (x - 3)(x - 3)(x - 12) = 0

So, (x - 3)²(x - 12) = 0

(x - 3)² = 0 and (x - 12) = 0

x - 3 = √0 and x - 12 = 0

x - 3 = 0 and x - 12 = 0

x = 3 twice and x = 12

Since x = 3 is the minimum value, the minimum value of x = 3.

Since the length of the box, L = 18 - 2x

= 18 - 2(3)

= 18 - 6

= 12 inches

The width of the box = L = 12 inches

The height of the box = x = 3 inches.

So,

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

Learn more about volume of a box here:

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[tex](5xy ^{2} {)}^{3} \\ = {5}^{3} \times {x}^{3} \times y ^{2 \times 3} \\ = 125 {x}^{3} {y}^{6} [/tex]

Answer:

[tex]125 {x}^{3} {y}^{6} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

125x^3y^6

Step-by-step explanation:

Distribute the 3 exponent on the outside to the 5, x^1 and y^2

5^3 = 125

1 * 3 = 3

2 * 3 = 6

125x^3y^6

Answer:

50/50

Step-by-step explanation:

Im not completly sure but when flipping a coin there is only two sides so theoretically if you are flipping a coin there is a 50/50 percent chance you will get heads

Answer:

1,771,470

Explanation:

10(3^n-1)

Answer:

$388.50

Step-by-step explanation:

9.25 *  42  = $388.50

Answer: B, or 824(1.03)^n-1

824 is the base we are starting off with, and when you multiply something by 1.03, the product will be +3% of the original number :)

Hope this helps!

Answer:

29/4

Step-by-step explanation:

7 x 4 = 28

28 + 1

hope that helps!

Answer:

29/4

Step-by-step explanation:

Step 1

Multiply the denominator by the whole number

4 × 7 = 28

Step 2

Add the answer from Step 1 to the numerator

28 + 1 = 29

Step 3

Write answer from Step 2 over the denominator

29/4

Hope this helps!:)

Answer:

y=1/2x+4

Step-by-step explanation:

y-y1=m(x-x1)

y-5=1/2(x-2)

y=1/2x-2/2+5

y=1/2x-1+5

y=1/2x+4

Note that the slope-intercept form is y=mx+b where m=slope and b=y-intercept.

If you're satisfied with the answer, then please mark me as Brainliest. Thank you.

Step-by-step explanation:

the description is very difficult to understand with special characters and potential typing errors.

I suspect the definition is

function(x) = 32 - x²

function(-5)function(-5) is then very easily calculated.

we need to calculate function(-5) and then square the result, as function(-5)function(-5) is just a simple multiplication of the function results.

function(-5) = 32 - (-5)² = 32 - 25 = 7

so,

function(-5)function(-5) = 7 × 7 = 49