The volume of a prism changes from 20 to 540 after a dilation. what was the scale factor of the dilation?

Answers

Answer 1

Answer: Scale factor is used by architects or engineers to transfer their prototype idea to large-scale use. If the volume of a prism is 20, you need to multiply its dimensions with a scale factor to find the new volume which is 540. For example, if the volume is doubled, this means you used a scale factor of 2. Hence, you just have to divide the new volume by the smaller volume.

Scale factor = 540/20
Scale factor = 27

Answer 2

Answer:

Answer:

The scale factor is 3 : 1.

Step-by-step explanation:

We know that,

The scale factor of the dilation of a prism is the cube root of the ratio of the volume of resultant prism after dilation and the volume of the given prism,

Here, the volume of prism before dilation = 20 cube unit,

And, the volume of the prism after dilation = 540 cube unit,

Thus, by the above statement,

$\text{The scale factor of dilation}=\sqrt[3]{(540)/(20)}$

$=\sqrt[3]{27}$

$=3$

Hence, the scale factor is 3 : 1.

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What is the name of the relationship between 4 and 8?A.
adjacent

B.
alternate interior

C.
alternate exterior

D.
corresponding

Answers

4 and 8 are corresponding angles.

The easiest way to tell is to look at the two groupings: 1, 2, 3, 4 and 5, 6, 7, 8. 4 and 8 are in the same position in both groupings (bottom right corner). This makes them corresponding.

Adjacent angles would have a common side and vertex. This would be like 4 and 2 or 1 and 3 or 5 and 7 or 8 and 6.

Alternate interior angles would be opposite angles inside the parallel lines. This would be like 4 and 5 or 3 and 6.

Alternate exterior angles would be opposite angles outside the parallel lines. This would be like 2 and 7 or 8 and 1.

No it's alternate exterior corresponding is the angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.

Draw the shape!
Find the volume!
PLEASE INCLUDE WORK!

Answers

okay i gotchu hold up

What is the volume of this sphere?Use 3.14 for pi and round to the nearest hundredth when necessary.

113.04 cm³

678.24 cm³

904.32 cm³

7234.56 cm³

Answers

Answer:

The volume of the sphere is $904.32\ cm^(3)$

Step-by-step explanation:

we know that

The volume of the sphere is equal to

$V=(4)/(3)\pi r^(3)$

In this problem we have

$D=12\ cm$ -----> given problem

Find the radius

$r=12/2=6\ cm$ ----> the radius is half the diameter

substitute

$V=(4)/(3)(3.14)(6^(3))=904.32\ cm^(3)$

Given the parent functions f(x) = log3 (5x − 5) and g(x) = log3 (x − 1), what is f(x) − g(x)?. . a. f(x) − g(x) = log3 (4x − 4). b.f(x) − g(x) = log3 (4x − 6). c. f(x) − g(x) = log3 5. d. f(x) − g(x) = = log3 1/5.

Answers

$f ( x ) = log _(3) ( 5 x - 5 ), g ( x ) =log _(3) ( x - 1 ); \n f ( x ) - g ( x ) = log _(3)( 5 x - 5 ) - log _(3)( x - 1 ) = \n log _(3) (5(x-1))/(x-1) = log _(3) 5$
Answer: C ) f ( x ) - g ( x ) = log3 5

If f(x)=x^2+3x-10, then f(10)=?

Answers

Answer:

f(10) = 120

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Function Notation

Step-by-step explanation:

Step 1: Define

f(x) = x² + 3x - 10

f(10) is x = 10

Step 2: Evaluate

Substitute: f(10) = 10² + 3(10) - 10
Exponents: f(10) = 100 + 3(10) - 10
Multiply: f(10) = 100 + 30 - 10
Add: f(10) = 130 - 10
Subtract: f(10) = 120

In the next 3 hours, the crew was digging at a rate of -2.5 feet each hour. During the last 2 hours, the crew slowed to a rate of -2.25 feet each hour. What number would they record for the location after the 8 hours?

Answers

To calculate the location after 8 hours of digging at different rates, you can sum up the distances they dug during each time period.

In the first 3 hours, they dug at a rate of -2.5 feet per hour, so they dug a total of:
3 hours * (-2.5 feet/hour) = -7.5 feet

In the next 2 hours, they dug at a rate of -2.25 feet per hour, so they dug a total of:
2 hours * (-2.25 feet/hour) = -4.5 feet

Now, add these two distances together to find their location after 8 hours:
-7.5 feet + (-4.5 feet) = -12 feet

So, they would record a location of -12 feet after 8 hours of digging.

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