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3 years ago

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

1 answer:

4 0

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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3 years ago

Write equation of the line containing (4,2) and (3,5) in slope-intercept form.

11Alexandr11 [23.1K]

Answer:

The equation of the line containing (4,2) and (3,5) in the slope-intercept form will be:

y=-3x+14

Step-by-step explanation:

Given the points

(4, 2)

(3, 5)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(4,\:2\right),\:\left(x_2,\:y_2\right)=\left(3,\:5\right)$

$m=\frac{5-2}{3-4}$

$m=-3$

We know that the slope-intercept form of the line equation is

$y=mx+b$

where m is the slope and b is the y-intercept

substituting m=-3 and the point (4, 2) to get the y-intercept i.e. b

$y=mx+b$

2=(-3)4 + b

2 = -12 + b

b = 2+12

b = 14

Now, substituting b=14 and m=-3 in the slope-intercept form to determine the equation of a line in the slope-intercept.

$y=mx+b$

y=(-3)x+(14)

y=-3x+14

Thus, the equation of the line containing (4,2) and (3,5) in the slope-intercept form will be:

y=-3x+14

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3 years ago

A sandwich shop sells sandwiches for $5.95 each, including tax. the shop received a total of $71.40 from the sales of sandwiches

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The equation for determine the cost of sandwiches one afternoon is y=5.95*x
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The equation for determine the number of sandwiches sold one afternoon is x=y/5.95

We have that

y=71.40
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Answer:

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Step-by-step explanation:

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2 years ago

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Dahasolnce [82]

Answer:

$\large\boxed{\sqrt{300x^{15}}=10x^7\sqrt{3x}}$

Step-by-step explanation:

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