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
sweet [91]
3 years ago
5

Rectangle ABCD is dilated to create rectangle A'B'C'D' . The width of rectangle ABCD is 8 feet. The width of rectangle A'B'C'D'

is 6 feet. The area of rectangle ABCD is 96 square feet.
What is the area of rectangle A'B'C'D' ? I NEED HELP PLEASE!!
Mathematics
1 answer:
likoan [24]3 years ago
5 0

Answer:

54 square feet

Step-by-step explanation:

The width of the rectangle ABCD is 8 feet and the area of the same rectangle is 96 square feet.

Hence, the length of the rectangle is (96 ÷ 8) = 12 feet.

Now, if the rectangle ABCD is dilated to rectangle A'B'C'D', then the length and the width of the new rectangle will be changed in the same ratio.

So, \frac{AB}{A'B'} = \frac{BC}{B'C'}  {Where AB is the length and BC is the width}

⇒ \frac{12}{A'B'} = \frac{8}{6}

⇒ A'B' = 9 feet

Therefore, the area of the dilated rectangle A'B'C'D' will be A'B' × B'C' = 9 × 6 = 54 square feet. (Answer)

You might be interested in
Find the probability that a randomly generated bit string of length 10 does not contain a 0 if bits are independent and if:a) a
lara31 [8.8K]

Answer:

A) 0.0009765625

B) 0.0060466176

C) 2.7756 x 10^(-17)

Step-by-step explanation:

A) This problem follows a binomial distribution. The number of successes among a fixed number of trials is; n = 10

If a 0 bit and 1 bit are equally likely, then the probability to select in 1 bit is; p = 1/2 = 0.5

Now the definition of binomial probability is given by;

P(K = x) = C(n, k)•p^(k)•(1 - p)^(n - k)

Now, we want the definition of this probability at k = 10.

Thus;

P(x = 10) = C(10,10)•0.5^(10)•(1 - 0.5)^(10 - 10)

P(x = 10) = 0.0009765625

B) here we are given that p = 0.6 while n remains 10 and k = 10

Thus;

P(x = 10) = C(10,10)•0.6^(10)•(1 - 0.6)^(10 - 10)

P(x=10) = 0.0060466176

C) we are given that;

P((x_i) = 1) = 1/(2^(i))

Where i = 1,2,3.....,n

Now, the probability for the different bits is independent, so we can use multiplication rule for independent events which gives;

P(x = 10) = P((x_1) = 1)•P((x_2) = 1)•P((x_3) = 1)••P((x_4) = 1)•P((x_5) = 1)•P((x_6) = 1)•P((x_7) = 1)•P((x_8) = 1)•P((x_9) = 1)•P((x_10) = 1)

This gives;

P(x = 10) = [1/(2^(1))]•[1/(2^(2))]•[1/(2^(3))]•[1/(2^(4))]....•[1/(2^(10))]

This gives;

P(x = 10) = [1/(2^(55))]

P(x = 10) = 2.7756 x 10^(-17)

3 0
3 years ago
Hey if you could help me with this it'd mean a lot I can't figure it out
Blababa [14]

Answer:

L = 12  S = 5

Step-by-step explanation:

L+S=17

3L+2S=46

Multiply the first equation by -2

-2L -2S = -34

Then add it to the second equation

-2L -2S = -34

3L+2S=46

------------------

L = 12

Now we can find S

L+S = 17

12 + S = 17

Subtract 12 from each side

S = 17-12

S = 5

6 0
3 years ago
Please help me<br> Show your work
GrogVix [38]

<u>ANSWER TO PART A</u>

The given triangle has vertices J(-4,1), K(-4,-2),L(-3,-1)


The mapping for rotation through 90\degree counterclockwise has the mapping


(x,y)\rightarrow (-y,x)


Therefore

J(-4,1)\rightarrow J'(-1,-4)


K(-4,-2)\rightarrow K'(2,-4)


L(-3,-1)\rightarrow L'(1,-3)


We plot all this point and connect them with straight lines.


ANSWER TO PART B


For a reflection across the y-axis we negate the x coordinates.


The mapping is



(x,y)\rightarrow (-x,y)


Therefore

J(-4,1)\rightarrow J''(4,1)


K(-4,-2)\rightarrow K''(4,-2)


L(-3,-1)\rightarrow L''(3,-1)


We plot all this point and connect them with straight lines.


See graph in attachment







7 0
3 years ago
A tree is 12 feet tall. A wire runs from the top of the tree to a point of 6 feet from its base. The wire is square root 180 fee
Artyom0805 [142]
13.42 is how long the wire is to the nearest hundredth of a foot
8 0
3 years ago
Find the slant height of this square pyramid
shutvik [7]
Lateral Surface Area of a square pyramid (4 isosceles triangles): For the isosceles triangle Area = (1/2)Base x Height. Our base is side length a and for this calculation our height for the triangle is slant height s. With 4 sides we need to multiply by 4. (hope this will help)
8 0
2 years ago
Read 2 more answers
Other questions:
  • There were twelve times more children then adults at the mantinee performance of the school play. There were 455 people at the p
    9·1 answer
  • Help lee figure out her score in some games she played with friends her score is always in between the lowest score and the high
    12·1 answer
  • Harmony baked 24 cookies with 4 scoops of flour. How many scoops of flour does Harmony need in order to bake 36 cookies? Solve u
    8·2 answers
  • Write the equation that the phrase represents, then solve the equation. The difference of a number and 1 2/7 is 5 1/2 ( with exp
    12·1 answer
  • (y+6)^2-(y-2)^2 <br><br> I got 16y+26 but it is wrong?
    15·1 answer
  • Find the exact value of sin A in simplest radical form. ​
    5·1 answer
  • The population of a bacterium doubles every hour. At 9 am, the population is 12 bacteria. The function P (t) = 12.2 models the b
    15·1 answer
  • How do you solve this using substitution method<br> 17x+7y=20 <br> Y=20x-42
    14·1 answer
  • Pls help asap
    7·1 answer
  • Solve the following simultaneous equations in ELIMINATION way​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!