How do you simply these expressions?<br> a. (1/2)^-3 b. (3/5x)^-1

Question number five answer

kiruha [24]

Answer:

D

Step-by-step explanation:

5 0

2 years ago

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Garcia's Grill offers 77 side dishes, 55 types of steak, and 88 toppings. How many different smothered steak dinners can be made

svet-max [94.6K]

Answer:

Therefore the total number of ways that the customer can order the smothered steak dinner is 9800.

Step-by-step explanation:

There are 7 side dishes, and types of stake and 8 toppings.

The customer will have a smothered steak dinner.

The smothered steak dinner will consist of steak and 3 different toppings and 4 $\binom{8}{3} = \frac{8!}{3! \times 5!} = 56$ different side dishes.

The number of ways steak can be selected is = $\binom{5}{1} = \frac{5!}{1! 4!} =5$

The number of ways toppings can be chosen is = $\binom{8}{3} = \frac{8!}{3! 5!} = 56$

The number of ways side dishes can be chosen = $\binom{7}{4} = \frac{7!}{4!3!} = 35.$

Therefore the total number of ways that the customer can order the smothered steak dinner is

= 5 × 56 × 35 = 9800.

7 0

2 years ago

Finding an Equation of a tangent Line in Exercise, find an equation of the tangent line to the graph of the function at the give

frutty [35]

Answer:

$y=\dfrac{3x}{e}+\dfrac{4}{e}$

this is the equation of the tangent at point (-1,1/e)

Step-by-step explanation:

to find the tangent line we need to find the derivative of the function g(x).

$g(x) =e^{x^3}$

we know that $\frac{d}{dx}(e^{f(x)})=e^{f(x)}f'(x)$

$g'(x) =e^{x^{3}}(3 x^{2})$

$g'(x) =3 x^{2} e^{x^{3}}$

this the equation of the slope of the curve at any point x and it also the slope of the tangent at any point x. hence, g'(x) can be denoted as 'm'

to find the slope at (-1,1/e) we'll use the x-coordinate of the point i.e. x = -1

$m =3 (-1)^{2} e^{(-1)^{3}}\\m =3e^{-1}\\m=\dfrac{3}{e}$

using the equation of line:

$(y-y_1)=m(x-x_1)$

we'll find the equation of the tangent line.

here (x1,y1) =(-1,1/e), and m = 3/e

$(y-\dfrac{1}{e})=\dfrac{3}{e}(x+1)\\y=\dfrac{3x}{e}+\dfrac{3}{e}+\dfrac{1}{e}\\$

$y=\dfrac{3x}{e}+\dfrac{4}{e}$

this is the equation of the tangent at point (-1,1/e)

3 0

2 years ago

What are the numbers called in a multiplication

mart [117]

The numbers that are called in multiplication are called factors. Multiplying factors together will create a product.

3 0

3 years ago

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What can be concluded about the line represented in the table? Check all that apply. x y –6 –7 2 –3 8 0 The slope is 2. The slop

Stels [109]

The first thing we must do for this case is to find the equation of the line.
$y-yo = m (x-xo)
$
We have then:
$m = (y2 - y1) / (x2-x1)

m = (-3 - 0) / (2-8)

m = 1/2$
We choose an ordered pair:
$(xo, yo) = (8, 0)
$
Substituting values:
$y-0 = (1/2) (x-8)

y = (1/2) x - 4$

From here we conclude:

Intersection with y:
We evaluate x = 0 in the function:
$y = (1/2) (0) - 4

y = -4$

Slope of the line:
$m = 1/2
$

Point (-2, -5):
We evaluate the value of x = -2 and the value of y = -5
$-5 = (1/2) (- 2) - 4

-5 = -1 - 4

-5 = - 5$
The equation is satisfied.

Point (8, 0):
It is part of the table, therefore belongs to the line.

Answer:
The slope is 1/2
The y-intercept is -4.
The points (-2, -5) and (8, 0) are also on the line.

7 0

2 years ago

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How do you simply these expressions? a. (1/2)^-3 b. (3/5x)^-1