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3 years ago

If g(x) = x3 - 5 and h(x) = 2x - 2, then h(g(-2))= ?

1 answer:

4 0

Please, write "x^3" for "the cube of x," not "x3." "^" denotes exponentiation.

Then you have g(x) = x^3 - 5 and (I assume) h(x) = 2x - 2.

1) evaluate g(x) at x = -2: g(-2) = (-2)^3 - 5 = -8 - 5 = -13

2) let the input to h(x) be -13: h(-13) = 2(-13) - 2 = -28 (answer)

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Solve for x: 4 over x plus 4 over quantity x squared minus 9 equals 3 over quantity x minus 3. (2 points) Select one: a. x = -4

Kay [80]

Answer:

Step-by-step explanation:

$\dfrac{4}{x}+\dfrac{4}{x^2-9}=\dfrac{3}{x-3}$

Domain:

$x\neq0\ \wedge\ x^2-9\neq0\ \wedge\ x-3\neq0\\\\x\neq0\ \wedge\ x\neq\pm3$

solution:

$\dfrac{4}{x}+\dfrac{4}{x^2-3^2}=\dfrac{3}{x-3}$

use <em>(a - b)(a + b) = a² - b²</em>

$\dfrac{4}{x}+\dfrac{4}{(x-3)(x+3)}=\dfrac{3}{x-3}$

multiply both sides by (x - 3) ≠ 0

$\dfrac{4(x-3)}{x}+\dfrac{4(x-3)}{(x-3)(x+3)}=\dfrac{3(x-3)}{x-3}$

cancel (x - 3)

$\dfrac{4(x-3)}{x}+\dfrac{4}{x+3}=3$

subtract $\frac{4(x-3)}{x}$ from both sides

$\dfrac{4}{x+3}=3-\dfrac{4(x-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x}{x}-\dfrac{(4)(x)+(4)(-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-\bigg(4x-12\bigg)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-4x-(-12)}{x}\\\\\dfrac{4}{x+3}=\dfrac{-x+12}{x}$

cross multiply

$(4)(x)=(x+3)(-x+12)$

use FOIL

$4x=(x)(-x)+(x)(12)+(3)(-x)+(3)(12)\\\\4x=-x^2+12x-3x+36$

subtract 4x from both sides

$0=-x^2+12x-3x+36-4x$

combine like terms

$0=-x^2+(12x-3x-4x)+36\\\\0=-x^2+5x+36$

change the signs

$x^2-5x-36=0\\\\x^2-9x+4x-36=0\\\\x(x-9)+4(x-9)=0\\\\(x-9)(x+4)=0$

The product is 0 if one of the factors is 0. Therefore:

$x-9=0\ \vee\ x+4=0$

$x-9=0$ <em>add 9 to both sides</em>

$x=9\in D$

$x+4=0$ <em>subtract 4 from both sides</em>

$x=-4\in D$

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In March 2007, the U.S. unemployment rate was 4.4 percent. In August 2008, the unemployment rate was 6.1 percent. Predict what

Luba_88 [7]

Answer:

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Step-by-step explanation:

In March 2007, the unemployment rate was 4.4 percent. In August 2008 was 6.1 percent. We need to remember that the unemployment rate equals the number of unemployed people divided by the people in the labor force.

Now, if we consider that the labor force remained constant during this period of time (according to the problem) then this would mean that the number of unemployed people actually increased during this period of 17 months.

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Tomtit [17]

Answer: 6.698

Step-by-step explanation:

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Cindy took her five grandchildren to the movies, where she offered to buy all of them popcorn and candy. A popcorn bag costs $4.

Svetradugi [14.3K]

Answer:

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Step-by-step explanation:

this is because 5 times 4.00 is 20$ and 2.50 times 6 is 15$

15 + 20 is 35

so your answer is 5 boxes of popcorn and 6 boxes of candy

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