If a storm window is 315 square inches, what are the dimensions if the window is 6 inches higher than it is wide

1 answer:

3 0

$\bf \textit{area of a rectangle}\\\\ A=Lw~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=\stackrel{\textit{6 more than \underline{w}}}{w+6}\\ A=315 \end{cases}\implies 315=(w+6)(w) \\\\\\ 315=w^2+6w\implies 0=w^2+6w-315 \\\\\\ (w+21)(w-15)=0\implies w= \begin{cases} -21\\ \boxed{15} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill w=15\qquad \stackrel{w+6}{L=21}~\hfill$

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Colt1911 [192]

1/8 + 6/8 = 7/8
17 11/13 - 9 7/13 = 8 4/13
2/8 + 4/8 = 6/8 = 3/4
8/4 + 1/4 = 9/4 = 2 1/4
9/10 + 3/10 = 12/10 = 1 1/5
2 - 3/5 = 10/5 - 3/5 = 7/5 = 1 2/5
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3 years ago

Using the quadratic formula, solve the equation: 5.1x^2-1.7x-3.2

CaHeK987 [17]

There's no equation to solve, until you tell us
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3 years ago

If the outliers are not included, what is the mean of the data? 76,79,80,82,50,78,83,79,81,82.

natta225 [31]

50 is the only outlier so take 50 out of the set then add the other 9 data points and divide by 9.
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3 years ago

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

Tju [1.3M]

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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seropon [69]

 The answer is 0.75.Hope this will help u....

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