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3 years ago

The surface area of a rectangular prism is increased by a factor of 16.

Mathematics

1 answer:

Orlov [11]3 years ago

8 0

Answer:

$64$

Step-by-step explanation:

It was given that, the surface area of a rectangular prism is increased by a factor of 16.

Let k be the scale factor:

${k}^{2} = 16$

$\implies \: k = \sqrt{16} = 4$

To determine the factor by which the volume of the figure is increased,we cube the scale factor to get:

${k}^{3} = {4}^{3} = 64$

Therefore the volume is increased by a factor of 64

You might be interested in

Is x = -3 a solution to the inequality below?<br><br> -5 ≤ <br> x

alekssr [168]

Answer:

it can be any number equal to or greater than -5

Step-by-step explanation:

technically -3 would be correct

4 0

3 years ago

What is (-100)a×56 and thanks

Stella [2.4K]

Hey there!
First, we will multiply -100 by a.
-100 x a = -100a
Now we have:
-100a x 56
Let’s multiple this as well.
-100a x 56 = -5600a
Your answer is -5600a.
Hope this helps!

4 0

3 years ago

Find the fourth point of a parallelogram given the first three (more than one correct answer is possible): (0,6), (5, -1) and (3

inysia [295]

Answer:

The fourth point of the parallelogram is one point among (-2,2), (2,10) and (8,-12).

Step-by-step explanation:

Given information: The first three vertices of parallelogram are (0,6), (5, -1) and (3,-5).

Let fourth point of the parallelogram is (a,b).

Diagonals of a parallelogram bisect each other. It means midpoint of both diagonals are same.

Midpoint formula:

$Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Case 1: If the point (0,6), (5, -1) and (3,-5) are consecutive, then pairs of opposite vertices are (0,6) and (3,-5), (5,-1) and (a,b).

$(\frac{0+3}{2},\frac{6-5}{2})=(\frac{5+a}{2},\frac{-1+b}{2})$

$(\frac{3}{2},\frac{1}{2})=(\frac{5+a}{2},\frac{-1+b}{2})$

On comparing both sides, we get

$\frac{3}{2}=\frac{5+a}{2}$

$3=5+a$

$a=-2$

$\frac{1}{2}=\frac{-1+b}{2}$

$1=-1+b$

$b=2$

It means the fourth point of the parallelogram is (-2,2).

Case 2: If the point (0,6), (5, -1) and (3,-5) are not consecutive, then pairs of opposite vertices are (0,6) and (5,-1), (3,-5) and (a,b).

$(\frac{0+5}{2},\frac{6-1}{2})=(\frac{3+a}{2},\frac{-5+b}{2})$

$(\frac{5}{2},\frac{5}{2})=(\frac{3+a}{2},\frac{-5+b}{2})$

On comparing both sides, we get

$\frac{5}{2}=\frac{3+a}{2}$

$5=3+a$

$a=2$

$\frac{5}{2}=\frac{-5+b}{2}$

$5=-5+b$

$b=10$

It means the fourth point of the parallelogram is (2,10).

Case 3: If the point (0,6), (5, -1) and (3,-5) are not consecutive, then pairs of opposite vertices are (5,-1) and (3,-5), (0,6) and (a,b).

$(\frac{5+3}{2},\frac{-1-5}{2})=(\frac{0+a}{2},\frac{6+b}{2})$

$(\frac{8}{2},\frac{-6}{2})=(\frac{a}{2},\frac{6+b}{2})$

On comparing both sides, we get

$\frac{8}{2}=\frac{a}{2}$

$8=a$

$\frac{-6}{2}=\frac{6+b}{2}$

$-6=6+b$

$b=-12$

It means the fourth point of the parallelogram is (8,-12).

5 0

4 years ago

By selling a table for sh.56, gain is as much as percent as its cost in dollars. What is the cost price? By selling a table for

sergij07 [2.7K]

The cost price of the table is $40.

Gain is the amount gain by selling the product at a higher price than its cost.

Let the cost of the table is $ x

The percentage gain is x% (as given in the question)

Cost price = ?

It is known that

Step 1 : Gain = ( selling Price - Cost Price) * 100 / Cost Price

Selling price = 56

Cost Price = $ x

Therefore substituting the value

x = (56 - x) * 100 / x

x² = 5600 - 100x

x² +100x -5600 = 0

Step 2 : Factorizing

x² + 140x - 40 x -5600 = 0

x( x+14 ) -40( x +14) = 0

( x - 40)(x +14) = 0

x = $40

Therefore the cost price of the table is $40.

To know more about Gain

brainly.com/question/23385214

#SPJ1

3 0

2 years ago

Use the Distributive Property to simplify the expression.

katovenus [111]

Multiply the equation by 4 to get rid of the fraction, the result is
4(10) + 4(4y) 4(1/4)
(40 + 16y) 1
40 +16y
8(5+2y)

7 0

3 years ago