Let JD = Distance drilled in joist
<span>JD = 3 - 1 1/3 </span>
<span>JD = 9/3 - 4/3 </span>
<span>========================== </span>
<span>JD = 5/3 or 1 2/3 in ◄ Ans
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8 inches
Divide 56 by 7 which equals 8 so Fred's frog jumped 8 inches.
Answer:
Step-by-step explanation:
f(x) =2x - 7
f( - 3) = 2( - 3) - 7 = - 13
f(3) = 2(3) - 7 = - 1
f(a) = 2a - 7
- f(a) = - (2a - 7) = 7 - 2a
f(a + h) = 2(a + h) - 7 = 2a + 2h - 7
Answer:
Yes they are
Step-by-step explanation:
Given
![a\sqrt{x+b}+c=d](https://tex.z-dn.net/?f=a%5Csqrt%7Bx%2Bb%7D%2Bc%3Dd)
we have
![\sqrt{x+b}=\dfrac{d-c}{a}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%2Bb%7D%3D%5Cdfrac%7Bd-c%7D%7Ba%7D)
Squaring both sides, we have
![x+b=\dfrac{(d-c)^2}{a^2}](https://tex.z-dn.net/?f=x%2Bb%3D%5Cdfrac%7B%28d-c%29%5E2%7D%7Ba%5E2%7D)
And finally
![x=\dfrac{(d-c)^2}{a^2}-b](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B%28d-c%29%5E2%7D%7Ba%5E2%7D-b)
Note that, when we square both sides, we have to assume that
![\dfrac{d-c}{a}>0](https://tex.z-dn.net/?f=%5Cdfrac%7Bd-c%7D%7Ba%7D%3E0)
because we're assuming that this fraction equals a square root, which is positive.
So, if that fraction is positive you'll actually have roots: choose
![a=1,\ b=0,\ c=2,\ d=6](https://tex.z-dn.net/?f=a%3D1%2C%5C%20b%3D0%2C%5C%20c%3D2%2C%5C%20d%3D6)
and you'll have
![\sqrt{x}+2=6 \iff \sqrt{x}=4 \iff x=16](https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%2B2%3D6%20%5Ciff%20%5Csqrt%7Bx%7D%3D4%20%5Ciff%20x%3D16)
Which is a valid solution. If, instead, the fraction is negative, you'll have extraneous roots: choose
![a=1,\ b=0,\ c=10,\ d=4](https://tex.z-dn.net/?f=a%3D1%2C%5C%20b%3D0%2C%5C%20c%3D10%2C%5C%20d%3D4)
and you'll have
![\sqrt{x}+10=4 \iff \sqrt{x}=-6](https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%2B10%3D4%20%5Ciff%20%5Csqrt%7Bx%7D%3D-6)
Squaring both sides (and here's the mistake!!) you'd have
![x=36](https://tex.z-dn.net/?f=x%3D36)
which is not a solution for the equation, if we plug it in we have
![\sqrt{x}+10=4 \implies \sqrt{36}+10=4 \implies 6+10=4](https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%2B10%3D4%20%5Cimplies%20%5Csqrt%7B36%7D%2B10%3D4%20%5Cimplies%206%2B10%3D4)
Which is clearly false