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ankoles [38]
2 years ago
7

The length of a rectangle is 5 inches less than 4 times the width. The perimeter is 110 inches. Find the length and the width.

Mathematics
1 answer:
nataly862011 [7]2 years ago
6 0

Answer:

  • Length = 43 inches
  • Width = 12 inches

Step-by-step explanation:

Perimeter of a rectangle = 2 * ( L + W)

The length of a rectangle is 5 inches less than 4 times the width.

Assume the width is x. Length is:

4x - 5

Equation is therefore:

2 * (4x - 5 + x) = 110

4x - 5 + x = 110/2

5x - 5 = 55

5x = 55 + 5

x = 60/5

x = 12 inches

If width is 12 inches, then length is:

= 4x - 5

= 4 * 12 -5

= 43 inches

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Answer:

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Step-by-step explanation:

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dezoksy [38]

Answer:

45% of students are female or 15/32

Step-by-step explanation:

We find out their is 72 Boys and 60 Girls

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5 0
3 years ago
How do you do this question?
likoan [24]

Answer:

a) -7/9

b) 16 / (n² + 15n + 56)

c) 1

Step-by-step explanation:

When n = 1, there is only one term in the series, so a₁ = s₁.

a₁ = (1 − 8) / (1 + 8)

a₁ = -7/9

The sum of the first n terms is equal to the sum of the first n−1 terms plus the nth term.

sₙ = sₙ₋₁ + aₙ

(n − 8) / (n + 8) = (n − 1 − 8) / (n − 1 + 8) + aₙ

(n − 8) / (n + 8) = (n − 9) / (n + 7) + aₙ

aₙ = (n − 8) / (n + 8) − (n − 9) / (n + 7)

If you wish, you can simplify by finding the common denominator.

aₙ = [(n − 8) (n + 7) − (n − 9) (n + 8)] / [(n + 8) (n + 7)]

aₙ = [n² − n − 56 − (n² − n − 72)] / (n² + 15n + 56)

aₙ = 16 / (n² + 15n + 56)

The infinite sum is:

∑₁°° aₙ = lim(n→∞) sₙ

∑₁°° aₙ = lim(n→∞) (n − 8) / (n + 8)

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8 0
2 years ago
Prove that:- (1-sinA)(1+sinA)÷(1+cosA)(1-cosA)=cot^2A​
astraxan [27]

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

sin²x + cos²x = 1 , then

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Consider the left side

\frac{(1-sinA)(1 + sinA)}{(1+cosA)(1-cosA)} ← expand numerator/denominator using FOIL

= \frac{1-sin^2A}{1-cos^2A}

= \frac{1-(1-cos^2A)}{1-(1-sin^2A)}

= \frac{1-1+cos^2A}{1-1+sin^2A}

= \frac{cos^2A}{sin^2A}

= cot²A = right side , thus proven

6 0
2 years ago
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