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3 years ago

15

If h(x) = f

le" class="latex-formula"> ° $g) (x)$ and $h(x) = \sqrt[3]{x+3}$ , find $g(x)$ if $f(x) = \sqrt[3]{x +2}$ ·

1 answer:

sertanlavr [38]3 years ago

7 0

Answer:

g(x) = x+1

Step-by-step explanation:

f(x) = $\sqrt[3]{x+2}$

h(x) = $\sqrt[3]{x+3}$

h(x)= (fog)(x)= f(g(x))= $\sqrt[3]{g(x)+2}$

so $\sqrt[3]{x+3}$ = $\sqrt[3]{g(x)+2}$

cubing both sides ,we get

x+3 = g(x) +2

solving for g(x) ,we get

g(x) = x+1

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The vertices of ΔABC are A(−3,4), B(−2,4), and C(−5,2). If ΔABC is reflected across the line y=−2 to produce the image ΔA'B'C

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The coordinates of vertex B' is $P'(x,y) = (-2, -8)$ .

<h3>How to calculate the coordinate of point by reflection</h3>

A point if reflected across the line $y = -2$ by means of the following formula:

$P'(x,y) = P(x,y)+2\cdot [(x_{P}, -2)-P(x,y)]$ (1)

Where:

$P(x,y)$ - Original point
$x_{P}$ - x-Coordinate of point P
$P'(x,y)$ - Resulting point

If we know that $P(x,y) = (-2,4)$ and $x_{P} = -2$ , then the coordinates of the vertex is:

$P'(x,y) = (-2, 4) + 2\cdot [(-2,-2)-(-2,4)]$

$P'(x,y) = (-2, 4) +2\cdot (0, -6)$

$P'(x,y) = (-2, 4) + (0,-12)$

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The coordinates of vertex B' is $P'(x,y) = (-2, -8)$ . $\blacksquare$

To learn more on reflections, we kindly invite to check this verified question: brainly.com/question/1878272

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3 years ago

1. The manager of FrozonAir Refrigerator factory notices that on Monday it cost the company a total of $25,000 to build 30 refri

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Answer:

The fixed costs per day for the factory is $10,000 and marginal cost of one refrigerator for $500

Step-by-step explanation:

Let

Cost per refrigerator (marginal cost) = r

Fixed costs per day for the factory = f

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Monday

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Tuesday

30,000 = 40r + f

Using Monday,

f = 25000 -30r

Substitute f = 25000 - 30r into Tuesday

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30,000 = 40r + (25,000 -30r)

30,000 = 40r + 25,000 - 30r

Collect like terms

30,000 - 25,000 = 40r - 30r

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Divide both sides by 10

r = 5,000 / 10

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r = $500

Substitute r= 500 into Monday equation

f = 25,000 -30r

= 25,000 - 30(500)

= 25,000 - 15,000

= 10,000

f = $10,000

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Answer:

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b)At least one product will be launched?

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