<span>Since the number of nail boxes is 6 less than the number of yards of wood, the right expression to use is x-6. (x being the number of yards of wood)
Now let us calculate the number of nail boxes she bought.
Cost of x yards of wood at $27 per yard = 27x.
Cost of x-6 boxes of nails at $4 per box = 4(x-6) = 4x - 24
Therefore 27x +4x - 24 = 193
31x -24 = 193
31x = 193 + 24
31x = 217
x = 217/31
= 7
So she bought 7 yards of wood and 7-6 boxes of nail. That is, she bought only one box of nail.</span>
Answer:
151
Step-by-step explanation:
Answer:
![x=\pm\sqrt{2}i\text{ (or) }x=\pm i](https://tex.z-dn.net/?f=x%3D%5Cpm%5Csqrt%7B2%7Di%5Ctext%7B%20%28or%29%20%7Dx%3D%5Cpm%20i)
Step-by-step explanation:
We have been given an equation
. We are asked to find the solutions of our given equation using u-substitution.
We can rewrite our given equation as:
![(x^2)^2+3x^2+2 = 0](https://tex.z-dn.net/?f=%28x%5E2%29%5E2%2B3x%5E2%2B2%20%3D%200)
Let us assume that
.
![u^2+3u+2 = 0](https://tex.z-dn.net/?f=u%5E2%2B3u%2B2%20%3D%200)
![u^2+2u+u+2 = 0](https://tex.z-dn.net/?f=u%5E2%2B2u%2Bu%2B2%20%3D%200)
![u(u+2)+1(u+2) = 0](https://tex.z-dn.net/?f=u%28u%2B2%29%2B1%28u%2B2%29%20%3D%200)
![(u+2)(u+1) = 0](https://tex.z-dn.net/?f=%28u%2B2%29%28u%2B1%29%20%3D%200)
![(u+2)=0\text{ (or) }(u+1) = 0](https://tex.z-dn.net/?f=%28u%2B2%29%3D0%5Ctext%7B%20%28or%29%20%7D%28u%2B1%29%20%3D%200)
![u=-2\text{ (or) }u=-1](https://tex.z-dn.net/?f=u%3D-2%5Ctext%7B%20%28or%29%20%7Du%3D-1)
Upon substituting back the value of u, we will get:
![x^2=-2\text{ (or) }x^2=-1](https://tex.z-dn.net/?f=x%5E2%3D-2%5Ctext%7B%20%28or%29%20%7Dx%5E2%3D-1)
![x=\pm\sqrt{-2}\text{ (or) }x=\pm\sqrt{-1}](https://tex.z-dn.net/?f=x%3D%5Cpm%5Csqrt%7B-2%7D%5Ctext%7B%20%28or%29%20%7Dx%3D%5Cpm%5Csqrt%7B-1%7D)
![x=\pm\sqrt{-1\cdot 2}\text{ (or) }x=\pm\sqrt{-1}](https://tex.z-dn.net/?f=x%3D%5Cpm%5Csqrt%7B-1%5Ccdot%202%7D%5Ctext%7B%20%28or%29%20%7Dx%3D%5Cpm%5Csqrt%7B-1%7D)
Now we will use imaginary unit i. We know that
.
![x=\pm\sqrt{i^2\cdot 2}\text{ (or) }x=\pm\sqrt{i^2}](https://tex.z-dn.net/?f=x%3D%5Cpm%5Csqrt%7Bi%5E2%5Ccdot%202%7D%5Ctext%7B%20%28or%29%20%7Dx%3D%5Cpm%5Csqrt%7Bi%5E2%7D)
![x=\pm\sqrt{2}i\text{ (or) }x=\pm i](https://tex.z-dn.net/?f=x%3D%5Cpm%5Csqrt%7B2%7Di%5Ctext%7B%20%28or%29%20%7Dx%3D%5Cpm%20i)
Therefore, the solutions for our given equation are
.
Answer: 11
Step-by-step explanation:
275% × 4 =
(275 ÷ 100) × 4 =
(275 × 4) ÷ 100 =
1,100 ÷ 100 = 11
Let
be the amount (gal) of the 40% slime solution you end up using. You want to end up with 120 gal of the 50% solution, so that you would use
gal of the 70% solution.
You want the final solution to consist of 50% slime, or 60 gal of slime. Each gal of the 40% solution contributes 0.4 gal of slime, while each gal of the 70% solution contributes 0.7 gal of slime. This means
![0.4x+0.7(120-x)=0.5\cdot120=60](https://tex.z-dn.net/?f=0.4x%2B0.7%28120-x%29%3D0.5%5Ccdot120%3D60)
![\implies0.4x+84-0.7x=60](https://tex.z-dn.net/?f=%5Cimplies0.4x%2B84-0.7x%3D60)
![\implies24=0.3x](https://tex.z-dn.net/?f=%5Cimplies24%3D0.3x)
![\implies x=80](https://tex.z-dn.net/?f=%5Cimplies%20x%3D80)
so the answer is B.