Write the equation of the function g(x) if g(x) = f(x+2) +4 and f(x) = x^3 -7

Answers

Answer 1

Answer: f(x) = x³ - 7
f(x + 2) = (x + 2)³ - 7
f(x + 2) = (x + 2)(x + 2)(x + 2) - 7
f(x + 2) = (x(x + 2) + 2(x + 2))(x + 2) - 7
f(x + 2) = (x(x) + x(2) + 2(x) + 2(2))(x + 2) - 7
f(x + 2) = (x² + 2x + 2x + 4)(x + 2) - 7
f(x + 2) = (x² + 4x + 4)(x + 2) - 7
f(x + 2) = (x²(x + 2) + 4x(x + 2) + 4(x + 2)) - 7
f(x + 2) = (x²(x) + x²(2) + 4x(x) + 4x(2) + 4(x) + 4(2)) - 7
f(x + 2) = (x³ + 2x² + 4x² + 8x + 4x + 8) - 7
f(x + 2) = (x³ + 6x² + 12x + 8) - 7
f(x + 2) = x³ + 6x² + 12x + 8 - 7
f(x + 2) = x³ + 6x² + 12x + 1

g(x) = f(x + 2) + 4
g(x) = (x³ + 6x² + 12x + 1) + 4
g(x) = x³ + 6x² + 12x + 1 + 4
g(x) = x³ + 6x² + 12x + 5

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Find the slope of the line that passes through (5,2) and (4,-1)

Which of these items is the better buy? A. An 8-pack of glue sticks for $3.99 or 1 glue stick for $0.54? B. A 12-pack of tape for $2.50 or 1 roll of tape for $0.19 c. A 100-pack of pencils for $4.88 or 1 pencil for $0.05 d. A 50-pack of paper clips for $0.89 or a 25-pack of paper clips for $0.45

Answers

Answer: A is the 8-pack, B is the single roll, C is the 100 pack, D is the 50 pack.

Step-by-step explanation:

For each of these, multiply the smaller number by a number that has a product of the bigger number, example D. multiply 25 by 2 to get 50, then compare the totals.

Answer:

the first one is an 8 pack of glue sticks

the second one is 1 tape roll for .19

the third one is 100 pack of pencils for 4.88

the fourth one is a 25 pack of paper clips

Step-by-step explanation:

Mrs. Quotient asked her students to simplify each of the expressions below. Which of the numbered choices represents the expressions which simplified to the same result? A 71 B 72 C 73

Answers

Answer:

A and B

Step-by-step explanation:

Mrs. Quotient asked her students to simplify each of the expressions below. Which of the numbered choices represents the expressions which simplified to the same result? A 126/2 B 23 × 3 C 3 × 21

When simplifying an algebraic expression, the following steps are needed to be taken.

Firstly, remove parenthesis by multiplying the constant with the term in the parenthesis or remove parenthesis using exponent rules for parenthesis in exponent form.

Secondly Combine terms by adding coefficients of terms with the same order and lastly sum all constant.

A) 126/2

Applying the division rule give:

126/2 = 63

B) 23 × 3

Applying multiplication rule gives:

23 × 3 = 69

C) 3 × 21

Applying multiplication rule gives:

3 × 21 = 63

Both the results of expression A and expression B are simplified to the same result

Simplify (3x - 5) + (3x + 6).

Answers

Since neither of the bracketed expressions is preceded by a minus sign, and neither one has a multiplier outside of it, all of the parentheses can simply be removed.

(3x - 5) + (3x + 6)

3x - 5 + 3x + 6

Combine the 'x'-terms: 3x + 3x = 6x
Combine the numbers: -5 + 6 = 1

The expression is equivalent to . . . . . 6x + 1

add like terms.
3x + 3x + -5 + 6

your final answer would be 6x + 1

What is the area of this polygon?

Answers

The middle is a square with side length of 12cm

Area of the square = 12 x 12 = 144 cm^2

There are 4 triangles with base of 13cm and height of 8 cm

Area of triangle = 1/2 x base x height

Area = 1/2 x 12 x 8 = 48cm^2 each

48 x 4 = 192 cm^2

Total area = 144 + 192 = 336 cm^2

Seth receives 100$ from his grandmother for his birthday he also saves 20$ every month tell whether the equation is linear or non-linear

Answers

Linear y=mx+b
100 is y intercept (b)
20 is your slope (m)
X would be equal to however many moths he saves

A tower casts a shadow 11 feet long the distance from the top of the tower to the end of the the shadow is 61 feet how many feet tall is the tower?

Answers

This is very easy!! I have attached a picture I have drawn if you are a visual learner... well, everything else like computations is here.
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This is the PYTHAGOREAN THEOREM!!
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If you don't know, it says that the lengths of the legs squared added together all equal the hypotenuse squared in a right triangle!!
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And if you want to know why the "triangle" has a right angle... well, are towers slanted? I mean, other than the Leaning Tower of Pizza. I mean Pisa.
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So... we plug it in!!
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Formula: a^2 + b^2 = c^2.
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Plug it in: 11^2+ 61^2 = c^2
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c^2 = 3842.
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So now what?
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SQUARE ROOT OF EVERYTHING!!
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c = √3842.
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So? c = approximately 61.984.
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Hope I helped!!

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For BRAINLY :)Triangle angle-sum theorem