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guapka [62]
3 years ago
15

In an older television set, the screen height is 0.75 times the screen width.

Mathematics
1 answer:
natima [27]3 years ago
5 0
The television set has a rectangular shape. The diagonal of this rectangle along with its width and length together form a right angular triangle.
This means that we can apply the Pythagorean theorem which states that:
(diagonal)^2 = (length)^2 + (width)^2

Let the width be w. We know that the length is 0.75 times the width, this means that: length = 0.75 w

Substitute in the above equation:
(20)^2 = (0.75w)^2 + (w)^2
400 = 0.5625 w^2 + w^2
400 = 1.5625 w^2
w^2 = 256
w = 16

This means that the width of the screen is 16 in. 
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The formula of an area of a rectangle:

A = wl

We have l = w - 4 and A = 21.

Substitute:

w(w - 4) = 21       <em>use distributive property</em>

(w)(w) + (w)(-4) = 21

w² - 4w = 21     <em>subtract 21 from both sides</em>

w² - 4w - 21 = 0

w² - 7w + 3w - 21 = 0

w(w - 7) + 3(w - 7) = 0

(w - 7)(w + 3) = 0 ↔ w - 7 = 0 ∨ w + 3 = 0

w = 7 ∨ w = -3 < 0

l = w - 4 → l = 7 - 4 = 3

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4 0
2 years ago
What is the value of the expression below? 8 + 24 / 2 X 6 - 4
umka21 [38]

8 + 24 / 2 X 6 - 4

following order of operations divide 24 by 2:

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8 + 72 -4

Add 8 and 72:

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Subtract to get 76

6 0
3 years ago
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576 is what percent of 800?
aleksley [76]
72 percent.
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the cost of a family membership at a health club $58 per month plus a one time 129 start up fee . if a family spent 651 , how ma
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Answer:

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Step-by-step explanation:

651=58x+129

-129         -129

522=58x  divide 522 by 58

=9

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