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3 years ago

Simplify (2/3)^2∙81 please explain 2

Mathematics

1 answer:

SVETLANKA909090 [29]3 years ago

8 0

Answer:

Step-by-step explanation:

Simplify the following:

(2/3)^2 81

Hint: | Simplify (2/3)^2 using the rule (p/q)^n = p^n/q^n.

(2/3)^2 = 2^2/3^2:

2^2/3^2 81

Hint: | Evaluate 2^2.

2^2 = 4:

4/3^2 81

Hint: | Evaluate 3^2.

3^2 = 9:

4/9×81

Hint: | Express 4/9×81 as a single fraction.

4/9×81 = (4×81)/9:

(4×81)/9

Hint: | In (4×81)/9, divide 81 in the numerator by 9 in the denominator.

81/9 = (9×9)/9 = 9:

4×9

Hint: | Multiply 4 and 9 together.

4×9 = 36:

Answer: 36

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Solve the inequality. p – 9 < –9

il63 [147K]

I hope this helps you

p-9 < -9

p-9+9 < -9+9

p <0

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2 years ago

The shelf is 4 feet wide and 2/3 feet deep. what is the area of the shelf?

steposvetlana [31]

Answer:

Area of the self will be $=4\times \frac{2}{3}=\frac{8}{3}=2.666ft^2$

Step-by-step explanation:

We have given that self is 4 feet wide and $\frac{2}{3}$ feet deep

So length pf the shelf l = $\frac{2}{3}$ feet

And width = 4 feet

We have to find the area of the self

We know that area is given by

Area = length × width

So area of the self will be $=4\times \frac{2}{3}=\frac{8}{3}=2.666ft^2$

6 0

3 years ago

A university is building a new student center that is two- thirds the distance from the arts center to the residential complex.

Natasha2012 [34]

Answer:

$C = (\frac{21}{5},\frac{33}{5})$

Step-by-step explanation:

Given

Points: (1, 9) and (9, 3)

Ratio = 2/3

Required

Determine the coordinate of the center

Represent the ratio as ratio

$Ratio = 2:3$

The new coordinate can be calculated using

$C = (\frac{mx_2 + nx_1}{n + m},\frac{my_2 + ny_1}{n + m})$

Where

$(x_1,y_1) = (1, 9)$

$(x_2, y_2) = (9, 3)$

$m:n = 2:3$

Substitute these values in the equation above

$C = (\frac{2 * 9 + 3 * 1}{3 + 2},\frac{2 * 3 + 3 * 9}{2 + 3})$

$C = (\frac{18 + 3}{5},\frac{6 + 27}{5})$

$C = (\frac{21}{5},\frac{33}{5})$

Hence;

The coordinates of the new center is $C = (\frac{21}{5},\frac{33}{5})$

7 0

3 years ago

Total profit P is the difference between total revenue R and total cost C. Given the following total-revenue and total-cost fu

gavmur [86]

Answer:

The profit function is:

$P(x)=-x^2+1280x-3300$

The maximum value is 406, 300 occurring when x = 640.

Step-by-step explanation:

The revenue function is:

$R(x)=1300x-x^2$

And the cost function is:

$C(x)=3300+20x$

Then the total profit function will be:

$P(x)=R(x)-C(x)=(1300x-x^2)-(3300+20x)=-x^2+1280x-3300$

This is a quadratic function.

Therefore, the maximum value of the total profit will occur at its vertex point.

The vertex of a quadratic is given by:

$\displaystyle \Big(-\frac{b}{2a}, f\Big(-\frac{b}{2a}\Big)\Big)$

In this case, a = -1, b = 1280, and c = -3300.

Then the point at which the maximum profit occurs is at:

$\displaystyle x=-\frac{1280}{2(-1)}=640$

And the maximum profit will be:

$P(640)=-(640)^2+1280(640)-3300=406300$

5 0

3 years ago

Read 2 more answers

the area of a square sandbox is 83 square feet. to the nearest foot, what is the perimeter of sandbox?

vagabundo [1.1K]

$Area=bh$
$b=base$
$h=height$

Since a square has 4 equal sides, we can √83 to give us each side. This being $9.11 feet$

$perimeter=9.11+9.11+9.11+9.11=36.44$

$Answer: 36$ to the nearest foot

7 0

3 years ago