Simplify. Show your work.

(x−1)(2x^2+2x+2)

Answers

Answer 1

Answer: Here is the answer :)

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What is the rate of increase for the function f(x)= 1/3(^3 sqr root 24)^2x

Answers

The rate of increase for the function $f (x) = (1)/(3)( \sqrt[3]{24}) ^(2x)$ by using formula and identity are,

⇒ $f ' (x) = \frac{4}{\sqrt[3]{3} }$

Using formula and identity are,

$(dx^n)/(dx) = nx^(n - 1)$

And, $(a^x)/(a^y) = a^(x - y)$

Given that,

The function is defined as,

⇒ $f (x) = (1)/(3)( \sqrt[3]{24}) ^(2x)$

We have to find the rate of increase of the given function.

⇒ $f (x) = (1)/(3)( \sqrt[3]{24}) ^(2)x$

Differentiate the function with respect to x,

⇒ $f' (x) = (1)/(3)( \sqrt[3]{24}) ^(2)$

Then, we get;

⇒ $f ' (x) = (1)/(3) (\sqrt[3]{2* 2* 2* 3} )^2$

⇒ $f' (x) = (1)/(3) (2)^2 (3)^{(2)/(3) }$

Using the identity $(a^x)/(a^y) = a^(x - y)$ ,

So, the rate of increase of function is,

⇒ $f ' (x) = \frac{4}{\sqrt[3]{3} }$

To learn more about the function visit:

brainly.com/question/11624077

#SPJ4

You must simplify the function first until the exponent becomes a flat x. Step 1 Leave 1/3 only that is the value a, initial value. You are looking for the base Step 2 Deal with the parentheses. Factor 24 and you get 2 and the cube of 3. Step 3 Separate the exponent (2) (x) Step 4 Now square each term in parentheses 2 squared and cube 3 squared 2 2 will be 4, the other expression means cube of 3 times cube of 3 and that is cube of 9 Step 5 Your base should be (4 cube of 9)

Which of these points lies on the line described by the equation below?y - 4 = -2(x - 6)

A. (-6, -4) B. (-4,-6) C. (6,4) D. (4,6)

Answers

Answer:

Option C is correct.i.e., ( 6 , 4 ) lie on given line.

Step-by-step explanation:

Given Equation, y - 4 = -2 ( x - 6 )

Option A:

From given point, x = -6 and y = -4

LHS = y - 4 = -4 - 4 = -8

RHS = -2 ( x - 6 ) = -2 ( -6 - 6 ) = -2 × ( -12 ) = 24

LHS ≠ RHS

⇒ This point does not lie on given line.

Option B:

From given point, x = -4 and y = -6

LHS = y - 4 = -6 - 4 = -10

RHS = -2 ( x - 6 ) = -2 ( -4 - 6 ) = -2 × ( -10 ) = 20

LHS ≠ RHS

⇒ This point does not lie on given line.

Option C:

From given point, x = 6 and y = 4

LHS = y - 4 = 4 - 4 = 0

RHS = -2 ( x - 6 ) = -2 ( 6 - 6 ) = -2 × ( 0 ) = 0

LHS = RHS

⇒ This point lie on given line.

Option D:

From given point, x = 4 and y = 6

LHS = y - 4 = 6 - 4 = 2

RHS = -2 ( x - 6 ) = -2 ( 4 - 6 ) = -2 × ( -2 ) = 4

LHS ≠ RHS

⇒ This point does not lie on given line.

Therefore, Option C is correct.i.e., ( 6 , 4 ) lie on given line.

c.) (6,4)...................

144 miles on 4.5 gallons

Answers

Answer:

32 miles per gallon.

Step-by-step explanation:

We are supposed to find unit rate for the given scenario.

144 miles on 4.5 gallons.

To find unit rate, we will divide 144 by 4.5 as:

$\text{Unit rate}=\frac{144\text{ miles}}{\text{4.5 gallons}}$

$\text{Unit rate}=\frac{32\text{ miles}}{\text{gallon}}$

Therefore, unit rate for our given situation is 32 miles per gallon.

144 miles on 4.5 gallons
Solution: 144mi 4.5 32mi
------------ divided by = -------------
4.5gal 4.5 1 gal

How many ounces are equivalent to 25 pounds?

Answers

since a pound is 16 ounces multiply 16 and 25 to get 400 ounces. A pound is 400 ounces

400 ounces is equivalent to 25 pounds because 16 times 25 gives you 400

What is the greatest common factor of 9 21 60?

Answers

The greatest common factor (GCF) of 9, 21 and 60 is: 3

Factors of 9: 1, 3, 9
Factors of 21: 1, 3, 7
Factors of 60: 1, 2, 3, 4, 5, 6

The common factors between the three numbers are 1 and 3, but since 3 is the highest number, it is considered the GCF.

2x^3+17x^2+23x-42; 2x+7