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3.

midpoint of  (6, 12)  and  (0, -6)  =  \(\Big( \frac{6+0}{2},\frac{12+-6}{2}\Big)\ =\ \Big(\frac62,\frac62\Big)\ =\ (3,3)\)

sum of coordinates of  (3, 3)  =  3 + 3  =  6

Very nice, power   !!!!

1.

distance between  (1, 1)  and  (4, 7)  =  \(\sqrt{(4-1)^2+(7-1)^2}\ =\ \sqrt{9+36}\ =\ \sqrt{45}\ =\ 3\sqrt5\)

2.

Thanks!

For the 5 games they scored twice as many points in, they must score points that are a multiple of 2.

There are 5 multiple of 2 scores: 2,4,6,8,10

The opposing team would score 1, 2, 3, 4 and 5 points respectivly.

When the team scores 1, 3, 5, 7, and 9 points the other team scored 1 more point.

The oponant would score 2, 4, 6, 8 and 10 points in those games.

1+2+3+4+5+2+4+6+8+10= 45 points scored by the opponents.

10 yards = 30 ft

So....

2(W + L)   = Perimeter

2(6 + L)  = 30      divide both sides by 2

6 + L  = 15         subtract 6 from both sides

L = 9

And Area =  W * L  =  6 * 9   =   54 square feet

The x intercept of a graph is the point where y=0 so the point is (x,0)

To find the x intercept of a line, set y to 0 and solve for x.

0=(1/3)x+7

subtract 7

-7=(1/3)x

multiply by 3

-21=x

so the x intercept is (-21,0)

0=2x+5

subtract 5

-5=2x

divide by 2

-2.5=x

and the x intercept is (-2.5,0)

Add the x intercepts together:

-2.5+-21=\(\boxed{-23.5}\)

Thanks!

There are 6 vowels, 20 consonatns and 10 digits.

For the first character there are 20 options, the second character 6 options, the third 20 options and the last 10 options.

Using the multiplication principle of counting gets 20*6*20*1 = \(\boxed{2400}\) possible license plates.

The ratio of their side lengths is...

\(\sqrt{\frac{192}{80}}\ =\ \sqrt{\frac{12}{5}}\ =\ \frac{\sqrt{12}}{\sqrt5}\ =\ \frac{\sqrt{12}\,\cdot\,\sqrt5}{\sqrt5\,\cdot\,\sqrt5}\ =\ \frac{\sqrt{12\,\cdot\,5}}{\sqrt{5\,\cdot\,5}}\ =\ \frac{\sqrt{2\,\cdot\,2\,\cdot\,3\,\cdot\,5}}{\sqrt{5\,\cdot\,5}}\ =\ \frac{\sqrt{2\,\cdot\,2}\,\cdot\,\sqrt{3\,\cdot\,5}}{\sqrt{5\,\cdot\,5}}\ =\ \frac{2\sqrt{15}}{5}\)

Now it is in the simplified form  \(\frac{a\sqrt{b}}{c}\)  where  a,  b,  and  c  are integers.

a + b + c  =  2 + 15 + 5  =  22

We need to solve this

-16t^2 + 60t = 56     rearrange as

16t^2 - 60t + 56 = 0       divide through by 4

4t^2 - 15t + 14  = 0   factor

(4t - 7) (t - 2)  = 0

Set each factor to 0 and solve for t  and we get   7/4 sec  and 2 sec

7/4 sec is correct  = 1.75 sec

Thanks!

ahhh the formatting is scary but here we go! \( $\sqrt[3]{\frac{8}{\sqrt{27}}}\)  \(\frac{a\sqrt{b}}{c}, a+b+c?\)
Ok so first you need to simpify the first expression which is 2/3 because 
cube root of 8= 2
so next you would need to say that radical 27 is basically 27 to the power of 1/2 and put it under the cube root and simplify 
and you would get \(2\sqrt{3}/3 \) and then you need to add the 3 numbers so it would be 8.
 (´･ω･`) (´･ω･`) (´･ω･`)

Look at the following image:

I agree with the guest....the inner circle is not needed

In the circle,  the angles E and D are bisected by OE and OD....so the measure of angles OED and ODE = 37.5°....so angle DOE = 105°

So....each chord will span an arc of 105°

Note that.... 

3 chords span 3(105) = 315°  = - 45°    and we are at point "D"

6 chords span 6(105)  = 630° = - 90°   and we are at point "G"

So....every 3 chords will end up shifting us  a multiple of -45° from "A" 

So...we need      360 / 45 * (3)  =  8 * 3  = 24  chords to bring us back to "A"

no problem, hope it helped!

Thanks!

ok so first you need to find the line thats perpendicular to y=2x-2  and that is y=-1/2x+b 
next solve for the y intercept, and i got 3 so now the equation would be y=-1/2x+3 
now you need to find the point of intersection between the two points so you would use either subsitution or elimination or any other method you are comfortable with. 
I used substitution: 
2x-2=-0.5x+3
x=2 
y=2 
and then you would need to find the distance between the points (2,2) and (6.0) so you would use the distance formula:
\(\sqrt{(-2)^2+(4)^2}\)

\(\sqrt{4+16}\)

\(\sqrt{20 }\)

\(2\sqrt{5}\)
❀◕ ‿ ◕❀ ❀◕ ‿ ◕❀ ❀◕ ‿ ◕❀

Hello!

So when we distribute all the variables in (Ax+1)(Bx+5), we get ABx^2+5Ax+Bx+5. Therefore, AB has to equal 6, and 5A+B has to equal 17. So the answer is 6, and we can check this by finding the values of A and B. These come out to be 3 for A and 2 for B. Hope this helped!

ok so since there were 38 pizzas, and each had 8 slices, you would have to multiply those two and get 304!

welcome BasicMaths!  

Hi BasicMaths

I am always really pleased when I am told believable authentic about how someone has learnt from this site.

I am glad you have finally made your own account. It is so much nicer when we know who we are talking to. 

Have fun and continue to learn lots!

b)

You can try looking at that graph and moving the point until the y-value goes just above 15 .

But to find the answer without using that....

Let's find values of  t  which make  h(t)  =  15

\(15\ =\ -8\cos(\frac{\pi t}{10})+9\\~\\ 6\ =\ -8\cos(\frac{\pi t}{10})\\~\\ -\frac34\ =\ \cos(\frac{\pi t}{10})\)

There are two values of  \(\frac{\pi t}{10}\)  in the interval  [0, 2π)  and thus two values of  t  which make  \(\cos(\frac{\pi t}{10})=-\frac34\)

They are:

\(\begin{array}{} \frac{\pi t}{10}\ =\ \arccos(-\frac34)&\quad&\frac{\pi t}{10}\ =\ 2\pi-\arccos(-\frac34)\\~\\ t\ =\ \frac{10}{\pi}\arccos(-\frac34)&&t\ =\ \frac{10}{\pi}(2\pi-\arccos(-\frac34))\\~\\ t\ \approx\ 7.7&&t\ =\ 20-\frac{10}{\pi}\arccos(-\frac34)\\~\\ &&t\ \approx\ 20-7.7\\~\\ &&t\ \approx\ 12.3 \end{array}\)

The height is 15 meters 7.7 seconds after the starting position and again 7.7 seconds before the starting position.

So we can see that Bobby will be really nervous when  t  is in the interval  (7.7, 12.3)

Bobby will be really nervous again 20 seconds later when the Ferris wheel is back at the same spot, so

Bobby will be really nervous when  t  is in the interval  (27.7,  32.3)

^{What is 269278645298734569827634598264956384775628456298743 divided by 9865298746528945692873659827465245}

Well your answer is 27295538859730818.3446586092722013 

~Nickolas