Question

what happened to the shark who swallowed a bunch of keys? write the letter of each answer in the box containing the exercise number. solve the literal equation for y. 1. y + 5x = 17 2. 4y - 36x = 28 3. 8x - 11 = 13 + 8y 4. 6 + \frac{1}{3}y = 10 + 12x solve the literal equation for x. 5. y = 9x - 2x 6. d = 5x + 10xf 7. rx - sx = p 8. 3j = 4kx + 7mx + n solve the formula for the indicated variable. 9. volume of a cone: v = \frac{1}{3}\pi r^{2}h; solve for h. 10. perimeter of a rectangle: p = 2l + 2w; solve for w. 11. area of a rectangle: a = lw; solve for l. 12. the surface area of a right - circular cylinder is given by the formula s = 2\pi rh+2\pi r^{2}. solve the equation for h. answers: o. y = x - 3 w. x = \frac{3j - n}{4k + 7m} t. x = \frac{d}{5 + 10f} o. y = 9x + 7 e. y = - 5x + 17 g. h = \frac{3v}{\pi r^{2}} k. y = 36x + 12 h. x = \frac{p}{r - s} l. l = \frac{a}{w} a. x = \frac{1}{7}y c. w = \frac{p - 2l}{2} j. h = \frac{s - 2\pi r^{2}}{2\pi r}

Explanation:

Step1: Solve $y + 5x=17$ for $y$

Subtract $5x$ from both sides: $y=17 - 5x=-5x + 17$

Step2: Solve $4y-36x = 28$ for $y$

Add $36x$ to both sides: $4y=36x + 28$. Then divide by 4: $y = 9x+7$

Step3: Solve $8x-11=13 + 8y$ for $y$

First, subtract 13 from both sides: $8x-24 = 8y$. Then divide by 8: $y=x - 3$

Step4: Solve $6+\frac{1}{3}y=10 + 12x$ for $y$

Subtract 6 from both sides: $\frac{1}{3}y=4 + 12x$. Multiply by 3: $y = 36x+12$

Step5: Solve $y = 9x-2x$ for $x$

Combine like - terms: $y = 7x$. Then $x=\frac{1}{7}y$

Step6: Solve $d = 5x+10xf$ for $x$

Factor out $x$: $d=x(5 + 10f)$. Then $x=\frac{d}{5 + 10f}$

Step7: Solve $rx-sx=p$ for $x$

Factor out $x$: $x(r - s)=p$. Then $x=\frac{p}{r - s}$

Step8: Solve $3j=4kx+7mx + n$ for $x$

Factor out $x$: $3j=x(4k + 7m)+n$. Subtract $n$: $3j - n=x(4k + 7m)$. Then $x=\frac{3j - n}{4k+7m}$

Step9: Solve $V=\frac{1}{3}\pi r^{2}h$ for $h$

Multiply both sides by 3: $3V=\pi r^{2}h$. Then $h=\frac{3V}{\pi r^{2}}$

Step10: Solve $P = 2\ell+2w$ for $w$

Subtract $2\ell$ from both sides: $P - 2\ell=2w$. Then $w=\frac{P - 2\ell}{2}$

Step11: Solve $A=\ell w$ for $\ell$

Divide both sides by $w$: $\ell=\frac{A}{w}$

Step12: Solve $S = 2\pi rh+2\pi r^{2}$ for $h$

Subtract $2\pi r^{2}$ from both sides: $S - 2\pi r^{2}=2\pi rh$. Then $h=\frac{S - 2\pi r^{2}}{2\pi r}$

Answer:

1. E. $y=-5x + 17$
2. K. $y = 9x+7$
3. O. $y=x - 3$
4. O. $y = 36x+12$
5. A. $x=\frac{1}{7}y$
6. T. $x=\frac{d}{5 + 10f}$
7. H. $x=\frac{p}{r - s}$
8. W. $x=\frac{3j - n}{4k+7m}$
9. G. $h=\frac{3V}{\pi r^{2}}$
10. C. $w=\frac{P - 2\ell}{2}$
11. L. $\ell=\frac{A}{w}$
12. J. $h=\frac{S - 2\pi r^{2}}{2\pi r}$