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Artyom0805 [142]
3 years ago
6

The area of a rectangle is 63ft ^2 and the length of the rectangle is 5ft more than double the width. Find the dimensions of the

rectangle.
Mathematics
1 answer:
Tasya [4]3 years ago
4 0
---------------------------------------------------------------------------------
Define Length and Width
---------------------------------------------------------------------------------
Let the width be x
Width = x
Length = 2x + 5

---------------------------------------------------------------------------------
Form equation and solve for x
---------------------------------------------------------------------------------
x(2x + 5) = 63
2x² + 5x = 63
2x² + 5x - 63 = 0
<span>(x+7)(2x-9) = 0
</span>x = -7 (rejected, length cannot be negative) or 2x - 9 = 0
2x - 9 = 0
2x = 9
x = 9 ÷ 2 
x = 4.5 ft

---------------------------------------------------------------------------------
Find Length and Width
---------------------------------------------------------------------------------
Width = x = 4.5 ft
Length = 2x + 5 = 2(4.5) + 5 = 14 ft

---------------------------------------------------------------------------------
Answer: Width = 4.5 ft , Length = 14 ft
---------------------------------------------------------------------------------


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A multiple-choice standard test contains total of 25 questions, each with four answers. Assume that a student just guesses on ea
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Answer:

a)  8*88*10⁻⁶ ( 0.00088 %)

b) 0.2137 (21.37%)

Step-by-step explanation:

if the test contains 25 questions and each questions is independent of the others, then the random variable X= answer "x" questions correctly , has a binomial probability distribution. Then

P(X=x)= n!/((n-x)!*x!)*p^x*(1-p)^(n-x)

where

n= total number of questions= 25

p= probability of getting a question right = 1/4

then

a) P(x=n) = p^n = (1/4)²⁵ = 8*88*10⁻⁶ ( 0.00088 %)

b) P(x<5)= F(5)

where F(x) is the cumulative binomial probability distribution- Then from tables

P(x<5)= F(5)= 0.2137 (21.37%)

7 0
3 years ago
An item that was selling for $80 is reduced to $42. Find the percent decrease in
Westkost [7]

Answer:

47.5%

Step-by-step explanation:

You have to first subtract 80 and 42 to find the decrease first. This is 38. Now, you have to divide this by the original number which is 80. So 38 divided by 80 is 0.475.

Now multiply this by 100.

You can easily move the decimal point to the right.

So you would get 47.5%

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3 0
3 years ago
Solve the system of equations. y = x − 5 and y = x2 − 5x + 3 A. (-4,-9) and (-2,-7) B. (4,-9) and (2,-7) C. (4,-3) and (2,-1) D.
larisa [96]

Answer:

D

Step-by-step explanation:

Given the 2 equations

y = x - 5 → (1)

y = x² - 5x + 3 → (2)

Substitute y = x² - 5x + 3 into (1)

x² - 5x + 3 = x - 5 ← subtract x - 5 from both sides

x² - 6x + 8 = 0 ← in standard form

(x - 2)(x - 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 4 = 0 ⇒ x = 4

Substitute each of these values into (1) for corresponding values of y

x = 2 → y = 2 - 5 = - 3 ⇒ (2, - 3 )

x = 4 → y = 4 - 5 = - 1 ⇒ (4, - 1 )

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