All Answers 356601 Answers

Or, you could factor:

\((x+5)(y+4)=1\)

When y = -4, the left-hand side will always equal zero, so \(\boxed{y=-4}\) is the solution.

Clearly we'll have an equation of the form $ax+b=ax+c$. So $y=-4$, so $-4x+4x=1$, impossible.

Ans: $\boxed{-4}$.

a) $\frac{15}{12}=\frac{5}{4}$

b) $12\left(\frac{4}{5}\right)^3=\frac{768}{125}$

c) $12*\left(\frac{5}{4}\right)^{16}\approx 426.32$

$5\ge -3\implies  f(5)=7+4*5=\boxed{27}$

$2x^2-x+11=0$

$r^2+s^2=(r+s)^2-2rs$

By Vieta: $r+s=\frac{1}{2}, rs=\frac{11}{2}$

Answer: $\frac{1}{4}-11=\boxed{\frac{-43}{4}}$.

Firstly, you can always put it on a grid - use coordinates.

My Solution is synthetic, and uses the mass points method:

Suppose $C$ has mass $1$. We get $A$ to have mass $1$ as well. Therefore, $B$ has mass $2$, and $D$ has mass $2$. Since $A$ has mass $1$ and $D$ has mass $2$, $FD=\frac{1}{2}AF\implies FD=\frac{1}{3}AD$, or the height of $\triangle FDE$ is $\frac{1}{3}$ of the height of the big triangle. The base is $\frac{1}{2}$ of the big triangle. Therefore, the area is $\frac{1}{2}*\frac{1}{3}=\frac{1}{6}$ of the big triangle. The big triangle has area $\frac{1}{2}\cdot 14\cdot 18=126$, so the answer is $\boxed{21}$.

4/8 x 4/7= 2/7 probability of an odd then even number. 4/8 is the probability of the odd number, 4/7 is the probability of an even number after the odd card has been drawn.

8 = 2^3

15 = 3 * 5

LCM(8, 15) = 2^3 * 3 * 5 = 120

It's pretty clear that $\boxed{x=1}$ works.

Notice that \(25^x - 9^y = (5^x + 3^y)(5^x - 3^y)\). Hope this gets you started.

120       is the LCM

sin pi/3  =  sqrt 3/2

cos pi/3 = 1/2                      so tan pi/3 = sqrt 3

cos 5pi/6 =  - sqrt3/2

                       sqrt 3  - sqrt3/2  = sqrt 3/ 2

sqrt3 /2 * -sqrt2/2 =  - sqrt 6  / 4

$(a+c+e)+(b+d+f)i=-3i\implies (a+c-a-c)+(7+d+f)i=-3i\implies (d+f+7)i=-3i\implies d+f+7=-3\impies d+f=-\boxed{-10}$.

P ==10.97226185

10.97226185 = Log_a(b)

b =a^10.97226185

a ==2   and   b==2009

Or use Wolfram|Alpha

Here we go.

a) $\frac{17\pi}{5}$ is in the third quadrant, and the angle is $\frac{7\pi}{5}-\pi=\boxed{\frac{2\pi}{5}}$.

b) $614$ is in the third quadrant, and the angle is $614-360-180=\boxed{74}$

c) $\frac{21\pi}{4}$ is in the first quadrant, so the angle is $\boxed{\frac{\pi}{4}}$

d) $240$ is in the third quadrant, so the angle is $240-180=\boxed{60}$.

$18^2=18*18=324$

$324-140=\boxed{184}$.

You should have: 9 x 5 x 10 x 5 ==2,250 such numbers

Incorrect.

I'll leave you to find the correct answer with the fact that reflecting $(x,y)$ across $y=-x$ yields $(-y,-x)$. 

$x=1\pmod{3}, x=2\pmod{4}, x=1\pmod{5}$.

If $x=1\pmod{3,5}$, $x=1\pmod{\text{lcm}(3,5)=15}$.

Now $x=15k+1=4j+2$. Taking the equation modulo $4$, $1-k=2\pmod{4}\implies k=3\pmod{4}$. So minimum $x$ is $15*3+1=45+1=\boxed{46}$.

Nice one.