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5x+8y=16 --> 8y=-5x+16 --> y=-5/8x+2. To be perpendicular, slope has to be 8/5. So y=8/5x+b. We can plug in given coordinates to get 7=8/5*-5+b -->7=-8+b --> b=15. So eqn is y=8/5x+15 or in point-slope form, y=8/5x+15 --> 5y=8x+75 --> 5y-8x=75 

Thanks guest, I did not remember that one either.

It is actually very easy to prove,

You do have to start with the knowledge that 2 angles within a circle, both with their apex on the circumference, will be equal if they stand on the same arc.

And here is a you tube clip explaining it.

12 states joined from 1780 to 1789. Therefore, of his first 22 quarters, 12 of them are from this time period, making for $\frac{12}{22}$=$\frac{6}{11}$  of his coins being from this time period. If you didnt understandmy LaTeX the answer is 6/11. lol

You have to write a simple computer code to check all numbers from 1 to 1000 raised to 100 - 1. It would look like this: [a^100] - 1 mod 1000 =0. Here is a simple code that does just that:

a=1; p=0;c=(a^100) - 1;if(c%1000==0, goto4, goto6);printa,", ",;p=p+1; a++;if(a<=1000, goto2, 0);print"Total =",p

OUTPUT = 400 such numbers beween 1 and 1,000. Didn't want them listed, because they take a whole page.

If you wanted them listed, just let me know.

It would be 4 seconds. We want to find out how many seconds it will take until the ball hits the ground, making our h = 0. Adding \(-16t^2\)to both sides, we get \(16t^2 = 64t\). Dividing both sides by \(16t\) we get, \(t = 4\).

Logically, one would drop the lowest score, so (92+87+98+94+89)/2  = 92.

Instead of inches squared should be cubic inches  

I think there are some missing numbers... Could you put them in?

It would be (-2, -3). First, we use the distance formula to find the distance between the two endpoints. \(\sqrt{(-5 + 1)^2+(3 + 5)^2} = 4\sqrt{5}\) Since the line segment's length is \(4\sqrt{5}\), we know the distance from R to S is \(3\sqrt{5}\) as there is a 3:1 ratio in the line. Now to find the coordinates of point S. We can use Pythogorean Theorem to help solve this. In this case, \(3\sqrt{5}\) is the hypotenuse. Squaring it gives 45, meaning the two legs' sum must be 45. Using perfect squares and some trial and error, we find the two legs are lengths 6 and 3. It will not be 6 units to the right, 3 units down as that would not be close to on the line. Which only leaves, 6 units down and 3 units to the right. Starting from the coordinates of R, which are (-5, 3), going 6 units down and 3 units to the right gives us the coordinate point (-2, -3).

You are finding all positive integer solutions to $v+w+x+y+z=14$.

Imagine 14 balls. If you put 4 dividers in any of the in-between spaces (there are 13 in-between spaces for 14 balls right?), then you get the partition of 14 into 5 balls. 

So it's 13 choose 4 = $\frac{13!}{4!9!} = 13\cdot12\cdot11\cdot10/24=1430/2=715$

$4^x < 1^{x+2}+2^{x+1}+3^{x-1}+4^x = 1170$

Now $4^6=2^{12}=4096>1170$

So $x=1,2,3,4$ or $5$.

$x=1$ doesn't work.

Take mod 3 both sides and you get

$ 1+(-1)^{x+1}+0+1 \equiv 3 (mod 3)$

So $x$ must be odd.

Therefore $x=3$ or $x=5$. Then you can calculate both cases to get $x=5$

2. Kadin makes a snowman by stacking snowballs of radius 2 inches, 3 inches, and 5 inches. Assuming all his snowballs are spherical, what is the total volume of snow he uses, in cubic inches? Express your answer in terms of pi.

Total volume     V = (4/3*pi*2³) + (4/3*pi*3³) + (4/3*pi*5³)

                         V = 640 pi / 3             ( 670.206 inches squared)

If you use all 3 snowballs to make a single snowball, its radius will be 5.4288 inches.

                                                        V = 4*pi*5.4288³ / 3 = 670.206 inch³

  \( Solve\ for\ f(n)\ if\ n\in \mathbb N\)

 \(f(n)=\frac{n}{2} \)           \(If\ n\ is\ even\ then\)      \(f(n)\in \mathbb N\)

\(f(n)=3n+1 \)   \(If\ n\ is\ odd\ then\)       \(f(n) \in \{4,10,16,22\ …\}\)

  !

Since it is equiangular, it is also equilateral. Since one side is 6 inches, all 3 sides are also 6 inches. To find the height, we can use Pythorean Theorem. Since the hypotenuse is 6, and one leg is 3, c^2 - b^2 = a^2, 36 - 9 = 27. Which means a^2 = 27, and so simplifying to the nearest tenth gives us 5.2 inches.

I think asinus has a much cleaner explanation... check out theirs

Work out the the value of k.

Hello Guest!

\(\frac{a\sqrt{a}}{\sqrt[3]{a^2}}=a^k\)

\(a^{1+\frac{1}{2}-\frac{2}{3}}=a^k\)

\(k=1+\frac{1}{2}-\frac{2}{3}=\frac{6+3-4}{6}\)

\(k=\frac{5}{6}\)

  !

If we multiply cbrt(a) on both the denominator and numerator, we get (a*sqrt(a)*cbrt(a))/a. The a's cancel out and we are left with sqrt(a)*cbrt(a) = a^k. sqrt(a) can also be written as a^(1/2) and cbrt(a) can be written as a^(1/3). Because they are multiplying each other, we add the exponent to get k = 5/6

Using simple Pythagorean Theorm, we can find this. In this case, 4 meters is the hypotenuse and 3.5 meters is one of the legs. We know a^2 + b^2 = c^2, and we can reverse than for our need. c^2 - b^2 = a^2 turns into, 16 - 12.25 = a^2, simplifying, 3.75 = a^2. And so a is, rounded to the nearest hundredth, 1.94 meters.

I think x = 26/7... I will explain if it is correct

The answer would be B. 15. This is because the red triangle and the blue triangle are similar, and because 20/8 = 2.5, the red triangle is scaled to a factor of 2.5 in ratio to the blue triangle. Applying the same logic for the other leg, we get 6*2.5 = 15.

15 - 13 = 2 minutes x 60 =120 seconds that the bee spent flying back and forth.

a - Distance = Time x Speed

Time =Distance / Speed

D / 12  +  D / 8 = 120, solve for D

b - D = 576 feet from the hive to the flowerbed.

If I understand your sequence, then this is the "closed form" of the sequence:

a_n = 63 - 4 n

Sum = (59, 55, 51, 47, 43, 39, 35, 31, 27, 23, 19, 15, 11, 7, 3) = 465

Nu, yiu got scammedddddddd