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Naily [24]
2 years ago
15

Which two points in the graphed function have an average rate of change of 5?

Mathematics
1 answer:
photoshop1234 [79]2 years ago
6 0

First of all, a positive average rate of change means that the function is increasing, so the answer can only be A->B or B->C.

The average rate of change is defined as

A = \dfrac{f(b)-f(a)}{b-a}

i.e. as the ratio between the vertical and horizontal gain.

In order to go from point A to point B, you gain 1 unit horizontally and 5 units vertically. So, the average rate of change is 5/1=5.

In order to go from point B to point C, you gain 1 unit horizontally and 3 units vertically. So, the average rate of change is 3/1=3.

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In a shoe store window, Sandy sees a sign announcing twenty-five percent off all sandals in stock. She finds a pair she likes th
katovenus [111]
Step 1) Convert $25 to a decimal:

0.25

Step 2) Multiply that by the amount the sandals cost.

$0.25×$45=$11.25

Step 3) Subtract from the amount you last got.

$45-$11.25=

$33.75

And there we have it! Our answer came out to $33.75.
So, with the 25% off, Sandy is now only paying $33.75 instead of $45.
3 0
3 years ago
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Suppose x=c1e−t+c2e3tx=c1e−t+c2e3t. Verify that x=c1e−t+c2e3tx=c1e−t+c2e3t is a solution to x′′−2x′−3x=0x′′−2x′−3x=0 by substitu
Harrizon [31]

The correct question is:

Suppose x = c1e^(-t) + c2e^(3t) a solution to x''- 2x - 3x = 0 by substituting it into the differential equation. (Enter the terms in the order given. Enter c1 as c1 and c2 as c2.)

Answer:

x = c1e^(-t) + c2e^(3t)

is a solution to the differential equation

x''- 2x' - 3x = 0

Step-by-step explanation:

We need to verify that

x = c1e^(-t) + c2e^(3t)

is a solution to the differential equation

x''- 2x' - 3x = 0

We differentiate

x = c1e^(-t) + c2e^(3t)

twice in succession, and substitute the values of x, x', and x'' into the differential equation

x''- 2x' - 3x = 0

and see if it is satisfied.

Let us do that.

x = c1e^(-t) + c2e^(3t)

x' = -c1e^(-t) + 3c2e^(3t)

x'' = c1e^(-t) + 9c2e^(3t)

Now,

x''- 2x' - 3x = [c1e^(-t) + 9c2e^(3t)] - 2[-c1e^(-t) + 3c2e^(3t)] - 3[c1e^(-t) + c2e^(3t)]

= (1 + 2 - 3)c1e^(-t) + (9 - 6 - 3)c2e^(3t)

= 0

Therefore, the differential equation is satisfied, and hence, x is a solution.

4 0
2 years ago
(a+b-c)-(b-a-c)<br><br> I NEED IT RN FOR A TEST OR ELSE I AM DEAD FOR LIFE
Zepler [3.9K]

Answer:

<h2><em><u>2a</u></em></h2>

Step-by-step explanation:

(a+b-c)-(b-a-c)

= a + b - c - b + a + c

= a + a + b - b - c + c

= <em><u>2a (Ans)</u></em>

5 0
2 years ago
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Explanatory writing that explores the relationship between an action and its consequence ____________
yawa3891 [41]
Explanatory research is research conducted in order to explain any behaviour
6 0
3 years ago
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Raj tried to solve the system below.
jekas [21]

Answer: Option C) Raj forgot the negative when substituting -15+9x for y.


Solution:

(1) 9x-y=15

(2) 2x+8y=28

Isolating y in the first equation. Subtracting 9x both sides of the equation:

(1) 9x-y-9x=15-9x

Subtracting:

(1) -y=15-9x

Multiplying both sides of the equation by -1:

(1) (-1)(-y)=(-1)(15-9x)

(1) y=-15+9x

Then Raj found the value of y. It's not option D.

Substitutng y by -15+9x in the second equation:

(2) 2x+8(-15+9x)=28

Then option C) is the answer: Raj forgot the negative when substituting -15+9x for y.

Eliminating the parentheses applying the distributive property in the multiplication:

(2) 2x-120+72x=28

Adding similar terms:

(2) 74x-120=28

Solving for x. Adding 120 both sides of the equation:

(2) 74x-120+120=28+120

Adding:

(2) 74x=148

Dividing both sides of the equation by 74:

(2) 74x/74=148/74

Dividing:

(2) x=2

Solving for y: Replacing x by 2 in the first equation:

(1) y=-15+9x

(1) y=-15+9(2)

Multiplying:

(1) y=-15+18

Subtracting:

(1) y=3  

3 0
3 years ago
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