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This is not an equation as there is no equal sign but

sqrt(250) = sqrt(25*10) = sqrt(25)*sqrt(10) = 5sqrt(10)

(7x+10)=(26x+5)

\(7x+10=26x+5\\ 7x+10-7x=26x+5-7x\\ 10=19x+5\\ 10-5=19x+5-5\\ 5=19x\\ x=\frac{5}{19}\)

sqrt3(2)+sqrt8(2) = 2.3504287825601308  simplify by collecting radical terms

I am not sure what you mean ://

\(\sqrt3+\sqrt8\\ =\sqrt3+\sqrt{4*2}\\ =\sqrt3+2\sqrt{2}\\ \)

= approx  

sqrt(3)+sqrt(8 = 4.5604779323150674

---------------------------------

sqrt3(2)+sqrt8(2)

\(\sqrt[3]{2}+\sqrt[8]{2} = can't \;be\;simplified\)

2^{1/3}+2^{1/8} =  2.3504287825601309

I guess this is what you meant.

You should have expressed it as 

The third root of 3 + the eight root of 2  :)

I'll just play with it a bit more

\(2^{1/3}+2^{1/8}\\ 2^{8/24}+2^{3/24}\\ 2^{3/24}(2^{5/24}+1)\\\)

2^(3/24)*(2^(5/24)+1 = 2.3504287825601308

you can do this but it is not helpful !

5.32

The LONGEST side of a RIGHT triangle.

Here is one way:

8 / [1 - 1/5] =10

What is the AMOUNT of the loan?????????????

Sorry CPhill: Square root is NOT allowed according to the question!. Thanks.

[ √ (5 -1) ] / 1   + 8   =

[ √4 ] / 1   +  8  =

[2] / 1 + 8   =

2 + 8   =

10

No.....by the triangle inequality we must have that a + b > c   .......if a + b = c, then we have a "degenerate" triangle  [ just a  line segment of length c, the hypotenuse ]

bull s**t n***a

x- 1/3 > 1/8    add 1/3 to both sides

x >  1/8 + 1/3

x >  3/24 + 8/24 

x >  11/24    which we can also denote as (11/24, infinity )

I'm assuming that we're talking about  the quadratic 2x^2 + bx + c

If the roots are   3 ±sqrt5........then , by the quadratic formula   -b/2a  = 3 →  -b = 2a* 3   = 2(2) * 3  = 12.......so.....b = -12

And since the irrational part of the root = sqrt(5).....we have that that this = 4sqrt(5)/[2a]   =

4sqrt(5)/[2*2]  = sqrt (16*5)/ 4   =   sqrt (80) / 4

So.....this implies that    b^2  - 4ac  = 80    →   144 - 4(2)c  = 80  →   64  = 8c  →   c  = 8

So....our function  is

y = 2x^2 -12x + 8 

The x coordinate of the vertex = -b/2a  = 12/ (2 *2)   = 12/4   = 3

And we can find the y coordinate by subbing the previous result into the function....so we have

2(3)^2 - 12(3) + 8  =  18 - 36 + 8   =  26 - 36   = -10

So....the vertex is  (3, -10)

P.S.  -  if the function is supposed to be  -2x^2 + bx + c with the same roots, then  b = 12 and c = -8   and IMAWESOME's answer is correct

Here's the graph of both functions : https://www.desmos.com/calculator/ewtfjezite

5.The local theater has one ticket window. In how many ways can 6 people line upto buy a ticket?

The total number of ways  = 6!  =  720

6.In how many ways can you order 7 different colored hats in a row?

This is similar to (5).......7!   =  5040   ways

7. Our basketball team has 12 members, each of whom can play any position. In how many ways can we choose a starting lineup consisting of a center, a power forward, a shooting foward, a point guard, and a shooting guard?

We have 12 ways to choose the center, 11 to choose a power forward, 10 to choose a shooting forward, etc........so     12* 11 * 10 * 9 * 8   =   P(12,5)   =  95040 ways

4. How many 3-letter combinations can be formed if the second letter must be a vowel(A,E,I,O,or U), and the third letter must be different from the first letter?

The frist letter can be selected in 26 ways

The second letter  can be selected in 5 ways

And since the third letter must be different from the first, we have 25 choices left for it

So.....the total number  =  26 * 5 * 25   = 26 * 125  = 3250 combinations

3.You have 5 shirts, 6 pairs of pants, and 8 hats. How many outfits can you make consiting with 1 shirt, 1 pair of pants, and 1 hat?

We want to choose 1 of 5 shirts = 5 choices

And 1 of 6 pairs of pants = 6 choices

And 1 of 8 hats  = 8 choices

So....the total number of different outfits = 5 * 6 * 8   =  30 * 8   = 240

2.Mr.Stewarts class has 16 boys, and 22 of his studentsbring thier calculators to class. If 13 of thestudentswith calculators are girls, then how many boys did not bring thier calculators?

The number of boys who brought their calculators to class must be  22 - 13  = 9

And if there are 16 boys, then  16 - 9   = 7 did not bring their calculators

1.There are 20 people in my club. 8 of them are left-handed. 15 of them like jazz music. 2 of them are right handed and dislike jazz music. How many club members are left handed and like jazz music?

If 8  are left-handed, then  20 - 8 =  12 must be right-handed........assuming that all the right-handed people have a preference for either liking or disliking jazz music, then 12 - 2 = 10 of the right-handed people must like it.......which means that 15 - 10   = 5 left-handed people like jazz music

please explain so I can understand it

I think you must want the number of terms in this series.........we can find this as follows :

a_n  = a₁ + d(n - 1)      where a_n is the last term  = 83.5, a₁ is the first term = 2.5, d is the common difference between terms = 3,   and n is the number of terms........so we have

83.5  = 2.5 + 3(n - 1)      subtract 2.5 from each side

81   = 3(n - 1)        divide both sides by 3

27 = n  -  1        add 1 to both sides

28 = n  = the number of terms

15000000000

he has 2 apples left

a1 = 1.111 m/s² 

a2 = -.90909 m/s²

The vertiz is (3,10)

You can also go to google and type in the search bar "graph" plus your equation, e.g. "graph y = -2/3x+2" . Limited graph functionality but for a quick look its great