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andrey2020 [161]
3 years ago
11

Ally is making a scale diagram of her classroom. She uses a scale factor of 3 centimeters per foot to draw the diagram. The actu

al length of the classroom is 18 feet, and its width is 20 feet. What is the area of the scale drawing of the classroom?
Mathematics
1 answer:
Soloha48 [4]3 years ago
6 0

18*3 = 54

20*3 = 60

so the scale drawing would be 54cm x 60cm

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The roots of 2x^2-3x=4 are a and b. Find the simplest quadratic equation which has roots 1/a and 1/b
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Find the roots

solve
we use hmm, completing the suare
2(x²-1.5x)=4
divide both sides by 2
x²-1.5x=2
take 1/2 of linear coeiftn and square it
-1.5/2=-0.75, (-0.75)²=0.5625
add that to both sides
x²-1.5x+0.5625=2+0.5625
factor perfect squaer trinomial
(x-0.75)²=2.5625
square root both sides, remember to take positive and negative square roots
x-0.75=+/-√2.5625
add 0.75 to both sides
x=0.75+/-√2.5625

the roots are x=0.75+√2.5625 and x=0.75-√2.5625

1/a and 1/b
1/(0.75+√2.5625) and 1/(0.75-√2.5625)

if the roots of a quadratic equation are r1 and r2 then it factors to
(x-r1)(x-r2)
so then we can factor our equation to be
(x-\frac{1}{0.75+\sqrt{2.5625}})(x-\frac{1}{0.75-\sqrt{2.5625}})

if we were to try and expand it, we would get
x²+0.75x-0.5
that's the simpliest equation with roots 1/a and 1/b where a and b are he roots of 2x²-3x=4


x²+0.75x-0.5 is answer
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3 years ago
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