gibsonj338

$4\times7y+9+1=10$

$28y+9+1=10$

$28y+10=10$

$28y+10-10=10-10$

$28y+0=10-10$

$28y=10-10$

$28y=0$

$\frac{28y}{28}=\frac{0}{28}$

$\frac{1y}{1}=\frac{0}{28}$

$1y=\frac{0}{28}$

$y=\frac{0}{28}$

$y=0$

Now put the answer you came up with and put back into the original equation and solve to see if the answer you came up with is the correct answer.

$4\times7y+9+1=10$

$4\times7\times0+9+1=10$

$28\times0+9+1=10$

$0+9+1=10$

$9+1=10$

$10=10$

Because you came up with $10=10$, that means that $y=0$ is the correct answer.

$4(x+1)>-4$ or $2x-4≤-10$

Firstly solve for x in the first inequality.

$4(x+1)>-4$

$4x+4>-4$

$4x-4+4>-4-4$

$4x-0>-4-4$

$4x>-4-4$

$4x>-8$

$\frac{4x}{4}>\frac{-8}{4}$

$\frac{1x}{1}>\frac{-8}{4}$

$1x>\frac{-8}{4}$

$x>\frac{-8}{4}$

$x>-\frac{8}{4}$

$x>-\frac{2}{1}$

$x>-2$

Secondly solve for x in the second inequality.

$2x-4≤-10$

$2x-4+4≤-10+4$

$2x-0≤-10+4$

$2x≤-10+4$

$2x≤-6$

$\frac{2x}{2}≤\frac{-6}{2}$

$\frac{1x}{1}≤\frac{-6}{2}$

$1x≤\frac{-6}{2}$

$x≤\frac{-6}{2}$

$x≤-\frac{6}{2}$

$x≤-\frac{3}{1}$

$x≤-3$

Thirdly put both answers together with the word "or" in between.

$x>-2$ or $x≤-3$

Forthly, put answer in interval notation.

$(-2,∞)$ or $(-∞,-3]$

$(-∞,-3]$ or $(-2,∞)$

Lastly, look at the list of A. B. C. and D. and figure out which one matches the answer.

A.  (-∞,-3] or $(-2,∞)$

$x$ = cubic yards of cement the first truck can hold at one time

$y$ = cubic yards of cement the second truck can hold at one time

$f$ = number of trips of the first truck

$s$ = number of trips of the second truck

$f+s$ = the combined number of trips between the first and second trucks

$x+y$ = the combined cubic yards of cement that can be held between the first and second trucks

$xf+sy$ = the combined cubic yards of cement delivered between the first and second trucks

If you are using a PC, press and hold the alt button and then type the number 248.  If you are using a mac, press and hold the option and shift buttons together and then type the number 8.  You can also copy and paste the degree sign from a PC and a mac.

happygal wants the exact answer, not a decimal answer.  If you look at my answer, you will see an exact answer in fraction form.

$\sqrt{37.6765}$

$\sqrt{37\frac{6765}{10000}}$

$\sqrt{\frac{376765}{10000}}$

$\sqrt{\frac{75353}{2000}}$

$\frac{\sqrt{75353}}{\sqrt{2000}}$

$\frac{\sqrt{75353}}{\sqrt{400}\sqrt{5}}$

$\frac{\sqrt{75353}}{20\sqrt{5}}$

$\frac{\sqrt{75353}}{20\sqrt{5}}\times\frac{\sqrt{5}}{\sqrt{5}}$

$\frac{\sqrt{75353}\sqrt{5}}{20\sqrt{5}\sqrt{5}}$

$\frac{\sqrt{376765}}{20\sqrt{5}\sqrt{5}}$

$\frac{\sqrt{376765}}{20\sqrt{25}}$

$\frac{\sqrt{376765}}{20\times5}$

$\frac{\sqrt{376765}}{100}$

Is the answer a, b, c, or d?

To answer the question, first figure out the equaton of the line. To do that first find the slope.  The formula for the slope of a line is

$m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$ where m = slope, ${y}_{2}$ = y-coordinate in the second point, ${y}_{1}$ = y-coordinate in the first point, ${x}_{2}$ = x-coordinate in the second point, and ${x}_{1}$ = x-coordintate in the first point.

$m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$

m = ?

${y}_{2}$ = 10

${y}_{1}$ = -2

${x}_{2}$ = 5

${x}_{1}$ = 1

$m=\frac{10-(-2)}{5-1}$

$m=\frac{10+2}{5-1}$

$m=\frac{12}{5-1}$

$m=\frac{12}{4}$

$m=\frac{3}{1}$

$m=3$

Now that we know that the slope of the line is 3, put that in the equation for a line.  The equation for a line is

$y=mx+b$ where $y$ = y-coordinate, $m$ = slope, $x$ = x-coordinate, and $b$ = y intercept (where line crosses the y axis).  Take one of the points and susitute $x$ and $y$ in the equation so we can solve for b.

$y=mx+b$

$y$ = 10

$m$ = 3

$x$ = 5

$b$ = ?

$10=3\times5+b$

$10=15+b$

$10-15=15+b-15$

$-5=15+b-15$

$-5=b-0$

$-5=b$

$b=-5$

Now fill in what you know leaving $y$ and $x$ as $y$ and $x$.

$y=3x-5$

To figure out at which point the line crosses the y-axis, subsitute $x$ for 0 and solve for $x$.

$y=3x-5$

$y=3\times0-5$

$y=0-5$

$y=-5$

The point that the line crosses the y-axis is at point $(0,-5)$ which means that the answer is neither a, b, c, or d.

I did just type in the numbers. :D.  By the way, not to sound criticizing, you did not graph the answer as per the question.

                          $|\frac{12}{x}+3|=2$

$\frac{12}{x}+3=2$                    $-(\frac{12}{x}+3)=2$

$\frac{12}{x}+3-3=2-3$     $-\frac{12}{x}-3=2$

$\frac{12}{x}+0=2-3$             $-\frac{12}{x}-3+3=2+3$

$\frac{12}{x}=2-3$                    $-\frac{12}{x}+0=2+3$

$\frac{12}{x}=-1$                        $-\frac{12}{x}=2+3$

$\frac{12}{x}\times x=-1\times x$        $-\frac{12}{x}=5$

$12=-1\times x$                 $-\frac{12}{x}\times x=5\times x$

$12=-x$                        $-12=5\times x$

$\frac{12}{-1}=\frac{-x}{-1}$                        $\frac{-12}{5}=\frac{5x}{5}$

$-12=\frac{-x}{-1}$                      $-\frac{12}{5}=\frac{5x}{5}$

$-12=x$                          $-\frac{12}{5}=x$

$x=-12$                          $x=-\frac{12}{5}$