1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Andrews [41]
3 years ago
5

A circle with a radius of 1/2ft is dilated by a scale factor of 8. Which statements about the new circle are true? Check all tha

t apply. The length of the new radius will be 4 feet. The length of the new radius will be 32 feet. The new circumference will be 8 times the original circumference. The new circumference will be 64 times the original circumference. The new area will be 8 times the original area. The new area will be 64 times the original area. The new circumference will be feet. The new area will be square feet.

Mathematics
1 answer:
otez555 [7]3 years ago
3 0

Answer:

A) The length of the new radius will be 4 feet

C) The new circumference will be 8 times the original circumference

F) The new area will be 64 times the original area

H) The new area will be 16π square feet

Step-by-step explanation:

<u><em>Verify each statement</em></u>

see the attached figure to better understand the problem

Part A) The length of the new radius will be 4 feet

The statement is true

Because

we know that

The radius of the original circle is r=1/2 ft

The scale factor is 8

so

To find out the length of the new radius multiply the radius of the original circle by the scale factor

(1/2)(8)=4 ft

Part B)  The length of the new radius will be 32 feet.

The statement is false

Because, the length of the new radius is 4 ft (see part A)

Part C) The new circumference will be 8 times the original circumference

The statement is true

Because

The original circumference is equal to

C=\pi (\frac{1}{2})

C=\frac{1}{2}\pi\ ft

The new circumference is equal to

C=\pi (4)

C=4\pi\ ft

Divide \frac{4\pi}{(1/2)\pi}=8

so

the new circumference will be the original circumference multiplied by 8

Part D) The new circumference will be 64 times the original circumference

The statement is false

Because, the new circumference will be 8 times the original circumference (see part C)

Part E) The new area will be 8 times the original area

The statement is false

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

The scale factor is 8

so

The scale factor squared is 8²=64

therefore

The new area will be 64 times the original area

Part F) The new area will be 64 times the original area

The statement is true

(see Part E)

Part G) The new circumference will be 8π feet

The statement is false

Because, the new circumference will be 4π feet (see part C)

Part H) The new area will be 16π square feet

The statement is true

Because

The area of a circle is

A=\pi r^{2}

we have

r=4\ ft

substitute

A=\pi (4)^{2}

A=16\pi\ ft^{2}

You might be interested in
One eighth of Tony's books are mystery books He has 3 Mystery books how many books does Tony have in all
kolezko [41]
The answer to <span>One eighth of Tony's books are mystery books He has 3 Mystery books how many books does Tony have in all is 24

</span>
5 0
2 years ago
Read 2 more answers
Find the value of x.<br><br><br><br><br> 36<br><br><br> 21<br><br><br> 42<br><br><br> 18
Degger [83]
The answer for this is 42. just subtract 152 from 68 and then divide that by 2. 
5 0
3 years ago
Read 2 more answers
Calculate the slope of the line that passes through (12,15) and (10, 21). Reduce answer to lowest terms if
gulaghasi [49]

Answer:

-3

Step-by-step explanation:

Slope is rise divided by run. Y2-Y1 Divided by X2-X1

You get 6 divided by -2

-3

3 0
2 years ago
A biker traveled 24 miles in 6 hours. A unit rate to describe this would be 4 miles per hour. What is another unit rate in this
padilas [110]

Answer:

(1/4) hr/mile

Step-by-step explanation:

4 mph can be rewritten using other units of measurement:

Suppose we convert 'miles' to 'feet:'

Then:

4 miles     5280 ft

---------- * ------------- = 21120 ft/hr

     1 hr        1 mile

Note that we could invert 4 mph and obtain

 1 hr

-------- or (1/4) hr/mile

4 mi

4 0
3 years ago
Read 2 more answers
Derrick earned $1472during the 4 weeks he had his summer job.if he earned the same amount each week,how much did he earn each we
valkas [14]
You take $1472 and divide it by 4 

$1472 divided by 4 = $368 per week or $52.57 a day 
hope this helps!!
8 0
3 years ago
Other questions:
  • Solve using the system using elimination for x - y= -5 and 3x + y= 1
    11·2 answers
  • The Gonzalez family is taking a cruise that costs e,082.24 for a family of four. How much does it cost per person?
    15·2 answers
  • F(x)=7x+7 and g(x)=6x^2<br> find (fg)(x)
    10·2 answers
  • Explain how to estimate 524 divide 9
    5·1 answer
  • The process of finding such equations to describe​ real-world phenomena is called mathematical​ _______. Such​ equations, togeth
    6·1 answer
  • Answer the following
    14·1 answer
  • The $120 repair bill included $36 for parts and rest for labor. What percent of the bill was for labor?​
    7·1 answer
  • How do you find a total surface area of a triangular prism
    10·1 answer
  • Find the slope of the line of best fit shown below.​
    6·1 answer
  • Select The correct Description giving brainliest PLZ HELP
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!