Factor 40x + 64.
Write your answer as a product with a whole number greater than 1.

Answer:

(a) The average rate of change is 0

(b) The values of x are: [tex]x =4\ or\ x = -4[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 16 - x^2; [-4,4][/tex]

Solving (a): The average rate of change (m)

This is calculated using:

[tex]m = \frac{f(b) - f(a)}{b - a}[/tex]

Where

[tex][a,b] = [-4,4][/tex]

So:

[tex]m = \frac{f(4) - f(-4)}{4 - -4}[/tex]

[tex]m = \frac{f(4) - f(-4)}{8}[/tex]

Solve f(4) and f(-4)

[tex]f(4) = 16 - (4^2) = 16 - 16 = 0[/tex]

[tex]f(-4) = 16 - (-4^2) = 16 - 16 = 0[/tex]

So:

[tex]m = \frac{f(4) - f(-4)}{8}[/tex]

[tex]m = \frac{0 - 0}{8}[/tex]

[tex]m = \frac{0}{8}[/tex]

[tex]m = 0[/tex]

Solving (b): All values of x where [tex]f(x) = m[/tex]

In (a), we have:

[tex]m = 0[/tex]

So:

[tex]f(x) = 0[/tex]

So, we have:

[tex]f(x) = 16 - x^2[/tex]

[tex]16 - x^2=0[/tex]

Express 16 as [tex]4^2[/tex]

[tex]4^2 - x^2=0[/tex]

Apply difference of two squares

[tex](4 - x)(4 + x) = 0[/tex]

Split

[tex]4 - x =0; 4 + x = 0[/tex]

Solve for x

[tex]x =4\ or\ x = -4[/tex]

We will find that the average of the function over the given interval is 0, and the two values of x such that the function is equal to the average are x = -4 and x = 4.

To find the average of a function f(x) over an interval [a, b] we need to compute:

[tex]\frac{f(b) - f(a)}{b -a}[/tex]

In this case we have:

f(x) = 16 - x^2

And the interval is:

[-4, 4]

We will get:

[tex]\frac{(16 - (4)^2) - (16 - (-4))^2}{4 - (-4)} = \frac{0}{8} = 0[/tex]

So the function has an average of 0 over that interval.

B) Here we just need to solve:

f(x) = 16 - x^2 = 0

We will get:

16 - x^2 = 0

16 = x^2

±√16 = x

±4 = x

So the solutions are x = 4 and x = -4.

If you want to learn more about averages of functions, you can read:

https://brainly.com/question/16033358

Answer: A

Step-by-step explanation:

The equation sin²(2π)+ cos²(2π) = 1 will be 0² + 1² = 1. Then the correct option is A.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The equation is given below.

sin²(2π)+ cos²(2π) = 1

We know that the value of sin 2π is 0 and the value of cos 2π is 1.

Then the equation will be

0² + 1² = 1

Then the correct option is A.

More about the Pythagoras theorem link is given below.

https://brainly.com/question/343682

#SPJ2

Answer:

Model A

Step-by-step explanation:

Given the table :

___________M 1 ____ M 2 ____ M 3 ____M 4

Multiple R _ 0.993 ___ 0.991 ___0.936__ 0.746

R Square __0.987___ 0.982 ___0.877 __0.557

Adj R² ____ 0.982___ 0.978 __ 0.849 ___0.513

S E_______ 4,043 __ 4,463 ___11,615 __20,878 Observations_ 12 _____ 12 _____ 12 ____12

Based on the detains of the model given, we could use the R value, R² and standard error values to evaluate the performance of the different models.

The best model will be one with Correlation Coefficient (R value) closet to 1. The model with the highest R value will also have the highest Coefficient of determination, R² value. The a best model is one which has a low a standard error value.

From the table, Model A has the highest R and R² values. It also has the lowest standard error value. Hence, we can conclude that model A provides the best fit.

Answer:

the answer is 3/8

Step-by-step explanation:

Answer:

HAHAHAHAHAHHAHAHAHHAAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA

Step-by-step explanation:

Answer:

Step-by-step explanation:

y= -1/4x

Answer:

14322 * 10¹²

1.4322 * 10¹⁶

Step-by-step explanation:

14322000000000000

14322 * 10¹²

1.4322 * 10¹⁶

Answer:

hope this help you look it once

(-b±√(b²-4ac))/(2a)

Answer:

x=120±6434−−−√

x=−4.996

x=244.996

Find the Solution for

−125x2+30000x+153000=0

using the Quadratic Formula where

a = -125, b = 30000, and c = 153000

x=−b±b2−4ac−−−−−−−√2a

x=−30000±300002−4(−125)(153000)−−−−−−−−−−−−−−−−−−−−−√2(−125)

x=−30000±900000000−−76500000−−−−−−−−−−−−−−−−−−−√−250

x=−30000±976500000−−−−−−−−√−250

The discriminant b2−4ac>0

so, there are two real roots.

Simplify the Radical:

x=−30000±1500434−−−√−250

x=−30000−250±1500434−−−√−250

Simplify fractions and/or signs:

x=120±6434−−−√

which becomes

x=−4.996

x=244.996

Answer:

68

Step-by-step explanation:

I literally just used a calculator LOL

Answer:

After 30 years

Step-by-step explanation:

population×2=20 years

population×2×1.5=20×1.5 years

population×3=30 years

Answer:

D

Step-by-step explanation:

Tust me Plz

Answer:

D

Step-by-step explanation:

5+6 then multiply by 3

(5+6) x 3 or 3 x (5+6)

Answer:

4 Zebras

Step-by-step explanation:

I can only see that she have 5 elephants, possibly more, however it's cut off. If that's true. Then:

If she has 5 elephants (which is currently what she has the most of) and 2 zebras. She needs 4 more zebras. Then she will have 6 zebras. More then any other animal.

Answer:

assuming the elephant has the most dots, as i cant see the full picture, then she needs to collect 4 more because she has 2 already.

Step-by-step explanation:

The elephant has 5 dots

the zebra has 2 dots

4+2=6

Answer:

running

Step-by-step explanation:

Answer:

0.42

Step-by-step explanation:

they are both multiples of 0.06

think of it like 6 x 6= 36 and 6 x 8 = 48

6 x 7 = 42 would be halfway

Answer:

0.42

Step-by-step explanation:

To find the half, add da numbers and divide by 2. So 0.36 and 0.48 added together is 0.84. That divided by 2 is 0.42.

Answer:

95% of the confidence interval for q is

(0.05809 , 0.1183)

Step-by-step explanation:

Step:1

Given that the random sample of 340 electronic components manufactured by a certain process is tested, and 30 are found to be defective.

sample proportion

                   [tex]q^{-} = \frac{x}{n} = \frac{30}{340} = 0.0882[/tex]

Step:2

95% of the confidence interval is determined by

[tex](q - Z_{0.05} \sqrt{\frac{pq}{n} } , q + Z_{0.05} \sqrt{\frac{pq}{n} } )[/tex]

[tex]((0.0804 -1.96 \sqrt{\frac{0.0804 X0.9118}{340} } ,0.0804 +1.96 \sqrt{\frac{0.0804 X0.9118}{340})[/tex]

[tex]( 0.0882- 1.96 \sqrt{0.000236} , 0.0882 + 1.96 \sqrt{0.000236} )[/tex]

(0.0882 - 0.03011 , 0.0882+0.03011)

(  0.05809 , 0.1183)

Final answer:-

95% of the confidence interval for q is

(0.05809 , 0.1183)

9514 1404 393

Answer:

  3 ft

Step-by-step explanation:

The formula for the area of a trapezoid is ...

  A = 1/2(b1 +b2)h

Filling in the given information, we can solve for h.

  15 ft² = 1/2(4 ft +6 ft)h

  15 ft² = (5 ft)h

  h = (15 ft²)/(5 ft) = 3 ft

The height of the trapezoid is 3 feet.

Answer:

93 becouse you add 75 plus 2x10 is 20 so 75 plus is 105 so 14.75 plus .20 is 15.05

Step-by-step explanation:

Answer:

Is there any other information?

Step-by-step explanation:

Answer:

c is the answer

Step-by-step explanation:

Answer:

B. 4x ≤ 320

Step-by-step explanation:

Not sure how to explain my thinking. However, 4x must be smaller than 320 because she cannot spend more than that.

Answer:

Step-by-step explanation:

b

Answer:

If you have 2 decks of 52, it would be 1/52 chance per card, so since there are two, add it up, its 2/104

Step-by-step explanation:

Answer:

1/16

Step-by-step explanation:

:))

Answer:

200

Step-by-step explanation:

Answer:

x midpoint 5

y midpoint 2

(5,2)

Answer:

11 c12 cyfiddiddjkssjksajusaahogsyi of

Answer:

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Step-by-step explanation:

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