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the first one has no solutions, I will show you how, by step

1) we rewrite the equations : x+y=−1;3x=−3y+4

2) in the x+y=-1, we solve for x

x+y=−1

x+y+−y=−1+−y(Add -y to both sides)

x=−y−1

3)Substitute−y−1for x in 3x=−3y+4:

3x=−3y+4

3(−y−1)=−3y+4

−3y−3=−3y+4(Simplify both sides of the equation)

−3y−3+3y=−3y+4+3y(Add 3y to both sides)

−3=4

−3+3=4+3(Add 3 to both sides)

0=7

and so there are no solution

the second one:

1)Solve3x−4y+2=0 for x:

3x−4y+2=0

3x−4y+2+4y=0+4y(Add 4y to both sides)

3x+2=4y

3x+2+−2=4y+−2(Add -2 to both sides)

3x=4y−2

3x/3 = (4y-2)/3

(Divide both sides by 3)

x=4/3y + -2/3

Problem 2: Substitute 4/3y + -2/3 for x in -10y+10=15x-10

−10y+10=15x−10

−10y+10=15(4/3y+-2/3)-10

−10y+10=20y−20(Simplify both sides of the equation)

−10y+10+−20y=20y−20+−20y(Add -20y to both sides)

−30y+10=−20

−30y+10+−10=−20+−10(Add -10 to both sides)

−30y=−30

-30y/-30 = -30/-30, (Divide both sides by -30)

and Y=1

Now we solve for X

x=4/3y+-2/3

x=4/3(1) +-2/3

x=2/3

so x=2/3 and y=1

The X-axis is the perpendicular bisector of the line segment joining the points (3,12) & (x,y). Find (x,y). 

Perpendicular means at right angles.

Bisector means cuts exactly in half.

Here is the pic :)

Mmm

Well I could see that the key numbers were going to be 2 and 16  can you see why?

I actually draw a rough number line and marked 2 and 16 on it.  Then I had to work out each of the 3 sections seperately.

for instance.  

try x=0     x-2=-2   so  |x-2|  must be  -(x-2) which is 2-x        at x=0 x-16 is already positive so  |x-16|=x-16

So when x is less than 2   the value will  be  2-x   +  x-16  etc.

Do you understand that?

You just need to think about that for each of the 3 sections of the graph and you will have your full answer.

Since he can deliver to 130 houses, in a 2.5 hour period you should

figure out how many he can deliver in 1/2 an hour, which is 26

divide 234 by 26, 

and you get 9

9  x 1/2 is equal to 9/2

which is equal to 4.5 hours

\(\text{assuming constant acceleration}\\ v(t) = a t+ v_0\\ 80~m/s = a~m/s^2 \cdot 20~s+0~m/s\\ a = \dfrac{80~m/s}{20~s} = 4~m/s^2\)

Since, the player cost 400, and the video-game enthusiast has $750, then he only has $350 left to spend for the games. 

Round 49 to 50

50 goes into 350 7 times

minus 7 because of the rounding,

7 games can be bought

I have drawn it. I just have issues with noticing where. I did a whole Midpoint eq too, got (0,0) and 4 but I don't think I'm right

Thank you very much! I had already solved the [2,16]: f (x)= 14 but for some reason I couldn't put my head around the other two! Is there any suggestions you can give in order to remember the steps easier? I always freeze when this comes up in any quiz

Try drawing it on a rough graph. You should be able to see the answer easily.

I think that this is what you mean

 f(x)=|x−2|+|x−16|

When x is less then 2 then  x-2 and x-16  will both be negative SO

f(x)= 2-x+16-x = 18-2x

When x is between 2 and 16  x-2 will be positive and x-16 will be negative SO

f(x)=x-2+16-x = 14

When x is greater than 16   both expressions will be positive   SO

f(x)=x-2+x-16 = 2x-18

Not only that, but a triangle is 180°

therefore a triangle is half a circle.

The postman delivers to 130 houses in 2.5 hours

Divide 130 houses by 2.5 hours and his rate of delivery is 130/2.5 = 52 houses per hour

To deliver to 234 houses, divide 234 by the rate 52 houses/hour and you get 4.5 hours

Tip:  the word "per" always means "divide by"

240 up to sea level then  8000 feet higher still.

You can do the addition!  :)

I guess I am meant to assume Bill spends every cent of hims money so that his ONLY soruce of income his his Mickey D job.

If he works 40 hours a week, for 52 weeks a year then he earns $20million/(40*52) = $9615 per hour or $160 per minute.

I would take less than half a minute to pick up the note so yes it is probably worth his while - so long as he does not have  back problem that is. 

Does he get to keep the money?

acceleration is    change in speed/time      = 80m/s divided by 20sec 

    \( = \frac{80m}{sec}\times \frac{1}{20sec}\\ =\frac{80m}{sec*20sec}\\ =\frac{4m}{sec^2}\\ =4m/s^2\)

It is a joke noobie :)

When 11^4 is written out in base 10, the sum of its digits is 16=2^4. What is the largest base b such that the base-b digits of 11^4 do not add up to 2^4? (Note: here, 11^4 in base b means that the base-b number 11 is raised to the fourth power.)

Mmm I have to work out what is being asked first.

\((11_b)^4\\=((b+1)_{10})^4\\=(b^4+4b^3+6b^2+4b+1)_{10}\\ \qquad If \;\;b>6 \;\;then\\ =14641_b \)

1+4+6+4+1 = 16

If b =6 or less than 6  this would equal a different number and the digits would not add to 16

SO the largest b  where the digits DO NOT add to 16 is b=6

how many times does the moon rotate around the world

You need to add in how much time.

Like how many tiems does the moon go arouind the Earth in an Earth year for example.

See the RHS of this link for all details on the Moon: https://en.wikipedia.org/wiki/Moon

180 / (13 + 2) =12 bands of 15 students each.

Since 2 from each band are sidelined, then:

12 x 2 = 24 - number of students on the sidelines, so that:

13 x 12 + 24 =180 - total number of students.

You have to set up 2 simultaneous equations as follows:

3=F^2 / (1 - r^2), 2 = F / (1 - r), solve for r, F

This gives r =1/7 and F =12/7

YES!. It is correct. The common ratio is 1/7 and the first term 1 5/7 which all sum up to 2. And their squares sum up to 3. Here are the first 10 terms:

(1.714285714, 0.2448979592, 0.03498542274, 0.004997917534, 0.0007139882192, 0.000101998317, 0.00001457118815, 0.000002081598307, 0.000000297371186 7, 0.000000042481598 1, 0.000000006068799 728)