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oee [108]
3 years ago
12

The length of a rectangle is 13 centimeters less than three times its width. Its area is 56 square centimeters. Find the dimensi

ons of the rectangle. Use the​ formula, area=length*width.
Mathematics
2 answers:
tatuchka [14]3 years ago
4 0

Answer:

Area = length  x width

Area = (3width - 13) x width

Area = 3 width^2 -13width

56 = 3width^2 -13 width

Width = 7

Length = (3 *7) -13 = 8

Step-by-step explanation:

Katyanochek1 [597]3 years ago
4 0

Answer:

The dimensions of the rectangle are 8 by 7 centimeters.

Step-by-step explanation:

The length of a rectangle is 13 centimeters less than three times its width. In other words:

\ell = 3w-13

Given that the area of the rectangle is 56 square centimeters, we want to determine its dimensions.

Recall that the area of a rectangle is given by:

A = w \ell

Substitute in known values and equations:

(56)=w(3w-13)

Solve for <em>w</em>. Distribute:

3w^2-13w=56

Isolate the equation:

3w^2-13w-56=0

Factor. We want to find two numbers that multiply to 3(-56) = -168 and that add to -13.

-21 and 8 suffice. Hence:

3w^2 - 21w + 8w - 56 = 0 \\ \\ 3w(w-7) + 8(w-7) = 0 \\ \\ (3w+8)(w-7) = 0

Zero Product Property:

3w+8=0\text{ or } w-7=0

Solve for each case:

\displaystyle w = -\frac{8}{3} \text{ or } w=7

Since the width cannot be negative, we can ignore the first solution.

Therefore, the width of the rectangle is seven centimeters.

Thus, the length will be:

\ell = 3(7) - 13 = 8

Thus, the dimensions of the rectangle are 8 by 7 centimeters.

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Answer:

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2 years ago
The circumference of a circle is 15π ft. What is the area, in square feet? Express your answer in terms of π.
DerKrebs [107]

Answer:

  • Area of the circle is 56.25π square feet.

Step-by-step explanation:

<u>Given that</u>:

  • The circumference of a circle is 15π ft.

<u>To Find</u>:

  • What is the area, in square feet?

<u>We know that</u>:

  • Circumference of a circle = 2πR
  • Area of a circle = πR²

Where,

  • Radius is denoted as R.

<u>Finding the radius of the circle</u>:

Circumference of a circle = 15π

⟶ 2πR = 15π

⟶ 2πR = 2π × 7.5

Cancelling 2π.

⟶ R = 7.5

∴ Radius of the circle = 7.5 ft.

<u>Finding the area of the circle</u>:

⟶ Area = πR²

⟶ Area = π(7.5)²

⟶ Area = π × 7.5 × 7.5

⟶ Area = π × 56.25

⟶ Area = 56.25π

∴ Area of the circle = 56.25π ft.²

7 0
3 years ago
Jane must get at least three of the four problems on the exam correct to get an A. She has been able to do 80% of the problems o
NISA [10]

Answer:

a) There is n 81.92% probability that she gets an A.

b) If she gets the first problem correct, there is an 89.6% probability that she gets an A.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the answer is correct, or it is not. This means that we can solve this problem using binomial distribution probability concepts.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And \pi is the probability of X happening.

For this problem, we have that:

The probability she gets any problem correct is 0.8, so \pi = 0.8.

(a) What is the probability she gets an A?

There are four problems, so n = 4

Jane must get at least three of the four problems on the exam correct to get an A.

So, we need to find P(X \geq 3)

P(X \geq 3) = P(X = 3) + P(X = 4)

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

P(X = 3) = C_{4,3}.(0.80)^{3}.(0.2)^{1} = 0.4096

P(X = 4) = C_{4,4}.(0.80)^{4}.(0.2)^{0} = 0.4096

P(X \geq 3) = P(X = 3) + P(X = 4) = 2*0.4096 = 0.8192

There is n 81.92% probability that she gets an A.

(b) If she gets the first problem correct, what is the probability she gets an A?

Now, there are only 3 problems left, so n = 3

To get an A, she must get at least 2 of them right, since one(the first one) she has already got it correct.

So, we need to find P(X \geq 2)

P(X \geq 3) = P(X = 2) + P(X = 3)

P(X = 2) = C_{3,2}.(0.80)^{2}.(0.2)^{1} = 0.384

P(X = 4) = C_{3,3}.(0.80)^{3}.(0.2)^{0} = 0.512

P(X \geq 3) = P(X = 2) + P(X = 3) = 0.384 + 0.512 = 0.896

If she gets the first problem correct, there is an 89.6% probability that she gets an A.

3 0
3 years ago
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Phoenix [80]

Answer:

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Step-by-step explanation:

5 0
3 years ago
Subtract -2k3 + k2 - 9 from 5k3 - 3k + 7.
tankabanditka [31]
5k3-3k+7-(-2k3+k2-9)
basically rewrite with simple algebra principles
15k-3k+7-(-6k+2k-9)
split up the parenthesis
15k-3k+7+6k-2k+9
sort them
15k-3k+6k-3k+7+9
short down by adding up the similar factors
answer: 18k+18
factorise
18(k+1)
both forms are right
8 0
3 years ago
Read 2 more answers
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