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Answer:

The rate of change of the function at x = 0.6 is approximately -0.72

Step-by-step explanation:

The given information from the graph are;

Points (0, 0) and (1, -0.5)

We have that the graph is that of a cubic function, therefore;

f(x) = ax³ + bx² + cx + d

At f'(x) at  (0, 0) and (1, -0.5) = 0 gives;

3ax² + 2bx + c = 0

∴ c = 0

Also

ax³ + bx² + cx + d = 0

d = 0

We have

3a(1)² + 2b(1) + 0 = 0

3·a + 2·b = 0..............(1)

a(1)³ + b(1)² + c(1) + d = -0.5

a + b + 0×(1) + 0 = -0.5

a + b = -0.5..........(2)

Multiplying equation (2) by 2 and subtracting it from equation (1) gives;

2 × (a + b = -0.5) = 2·a + 2·b = -1

3·a + 2·b - (2·a + 2·b) = 0 - (-1) = 0 + 1 = 1

a = 1

From

a + b = -0.5, we have;

1 + b = -0.5 = 0

b = -0.5 - 1 = -1.5

The equation becomes

f(x) = x³ - 1.5·x²

The rate of change of the function at x = 0.6 is therefore given as follows;

f'(x) = 3 × x² - 2 × (1.5)·x = 3·x² - 3·x

At x = 0.6, we have;

f'(0.6) = 3·(0.6)² - 3·(0.6)

f'(0.6) = 3×0.6² - 3×0.6 = -0.72

The rate of change of the function at x = 0.6 ≈ -0.72

Answer:

Seven days

Step-by-step explanation:

From the information given, you know that you drink in a day 1.25 cups of the tea in the morning morning and 1.5 cups of the tea in the evening which is equal to:

1.25+1.5=2.75 cups a day

Now that you know the amount of cups that you drink in a day, you can divide  the amount of cups in the pitcher by the amount of cups you drink in a day:

19.25/2.75= 7

According to this, the answer is that you will run out of iced tea after seven days.

Answer:

7

Step-by-step explanation:

Step 1:

18 - 5w + 7w - 4 = 28

Step 2:

14 + 2w = 28

Step 3:

2w = 14

Answer:

w = 7

Hope This Helps :)

In 3(x+2)=18,  X=4

Divide both sides by the numeric factor on the left side, then solve.

Answer:

52

Step-by-step explanation:

I'm pretty sure that it would be 52 mi because it is the same said that the angel ST is. Angels NM and ST are congruent. Therefore, the answer is 52 mi.

Answer:

mesosphere

The air in the mesosphere has extremely low density: 99.9 percent of the mass of the atmosphere is below the mesosphere. As a result, air pressure is very low.

Answer:

A,

Step-by-step explanation:

because the whole number 144 is a perfect square and the square root of 144 is also a whole number

Answer:

B,C,D,E,A

Step-by-step explanation:

Btw, Mr. Stokes from RTMS?

Step-by-step explanation:

Equation of a line is y = mx + b

where

m is the slope

b is the y intercept

First question

y = 3x - 4

Comparing with the general equation above

Slope / m = 3

The y intercept / b = - 4

Second question

4x - 5y = 15

First we must write the equation in the general equation above by making y the subject

That's

5y = 4x - 15

Divide both sides by 5

That's

[tex] \frac{5y}{5} = \frac{4}{5} x - \frac{15}{5} [/tex]

We have

[tex]y = \frac{4}{5} x - 3[/tex]

Comparing with the general equation above

Slope = 4/5

Y intercept = - 3

Hope this helps you

Answer:

167

Step-by-step explanation:

Answer:

167

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Their are 9 in the first row and their are 5 rows all together so 9 times 5 is 45.

Answer:

Susie rounded to the nearest thousandth.

Step-by-step explanation:

since the 100th place is 0 it would round down to 39,000 when you are rounding to the nearest thousand.

Answer:

60

Step-by-step explanation:

The angle measures in a triangle always add up 180 degrees. 180-80-40=60

16x⁴y⁶

(4x²y³)² =

= 4²x²ˣ²y³ˣ²

= 16x⁴y⁶

Ammera's sweet= A

Dhabia's sweet= B

Dana's sweet= C

Ax2=B+2=C

Answer:

45 minutes

Step-by-step explanation:

We want to know how long it takes to an airplane to fly a distance of 375 miles, if the speed of the airplane is 500 miles per hour.

For this, we should divide the distance/speed to get the time that the plane needs.

T = 375mi/(500mi/h) = 0.75 hours

The plane needs 0.75 hours or 0.75*60 = 45 minutes to fly that distance.

Answer:

To solve for the problem above, let x be the regular price of the shoe.

1/2x is the one-half price of the shoe then we add 6 for the pair of socks,

1/2x + 6, then lola has 32 left so we add that too, 1/2x + 6 + 32 = 75. The total amount of lola spent is 75 - 32, which is 1/2x + 6.

Step-by-step explanation:

Answer: yes it is

Step-by-step explanation:

Common difference -2

Answer:

x = 75

Step-by-step explanation:

X/5=15

Multiply each side by 5

x/5 * 5 = 15*5

x = 75

Answer:

Step-by-step explanation:

15*5=75

therefore answer is x=75

Answer:-$208

Step-by-step explanation:

Answer:

Step-by-step explanation:

-40 - 5 = -45

answer is D

Answer:

[tex]r=199[/tex]

Step-by-step explanation:

hopefully that was the answer you were looking for

Answer:

1.34117647059

Step-by-step explanation:

114 divided by 85 =1.34117647059

hope this helps

Answer:

  26 square units

Step-by-step explanation:

Reflection and translation are rigid motions that do not affect the size or shape of the triangle. It has the same area as the original: 26 units².

Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by using the formula

[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-6,-8) and (-2,0)

The distance between them is

[tex]d = \sqrt{ ({ - 6 + 2})^{2} + ({ - 8 - 0})^{2} } \\ = \sqrt{ ({ - 4})^{2} + ({ - 8})^{2} } \\ = \sqrt{16 + 64} \\ = \sqrt{80} [/tex]

We have the final answer as

[tex]4 \sqrt{5} \: \: \: units[/tex]

Hope this helps you

Answer:

4 3/4

Step-by-step explanation:

Just multiply 1 3/4 and 3 = 4 3/4