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Paladinen [302]
2 years ago
14

The length of a rectangle is 5 cm more than twice a number. the width is 4cm less than the same number. if the area of the recta

ngle is 15cm2, find the number
​
Mathematics
1 answer:
lana [24]2 years ago
7 0
A = Lw (area of rectangle is length times width)
A = 15 (Area is 15)
L = 2x + 5 (length is 2 times a number plus another 5)
w = x - 4 (width is 4 less than that number

Plug in the values:
15 = (2x + 5)(x - 4)
FOIL
15 = 2x2 - 8x + 5x - 20
simplify:
15 = 2x2 - 3x - 20
Subtract 15
0 = 2x2 - 3x - 35
Factor out the quadratic. We know that one number has to be 7 and the other 5 so that they multiply together to make 35, and that one of them has to be negative so that it's actually -35.
That means we have m * n = -35
We also need it set up so that so that 2m + n = -3:
2 * -5 + 7 = -3
0 = (2x + 7)(x - 5)
So:
0 = 2x + 7, or 0 = x - 5
x = -7/2 or 5
We cannot have a negative length, so x = 5

Check:
15 = (2 * 5 + 5) (5 - 4)
15 = 15 * 1
15 = 15
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<img src="https://tex.z-dn.net/?f=5%20-%203x%20%3D%2011" id="TexFormula1" title="5 - 3x = 11" alt="5 - 3x = 11" align="absmiddle
const2013 [10]

Hi there! :)

<u>Answer:</u>

x = -2


Step-by-step explanation:

<u>5</u> - 3x = 11

Subtract "5" from each side of the equation → 11 - 5 = 6

<u>-3</u>x = 6

Divide each side of the equation by "-3" → 6 ÷ -3 = -2

<u>x = -2</u>


There you go! I really hope this helped, if there's anything just let me know! :)

5 0
3 years ago
Jennifer needs to use a ladder to clean a second floor window on a building. If the window is 13 ft above the ground and the bas
BigorU [14]

By using the Pythagoras theorem, the length of the ladder will be 13.6 feet.

<h3>What is a Pythagoras theorem?</h3>

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

Jennifer needs to use a ladder to clean a second-floor window on a building.

If the window is 13 ft above the ground and the base of the ladder is 4 ft from the building.

Then the length of the ladder will be

H² = 13² + 4²

H² = 169 + 16

H² = 185

H = 13.6 ft

More about the Pythagoras theorem link is given below.

brainly.com/question/343682

#SPJ1

7 0
2 years ago
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