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$\tan C = \boxed{\frac{5}{4}}$.

If (3,6) is on the graph of y = g(x), then g(3) = 6.

we know that h(x) = (g(x))2

that means h(3) = (g(3))2

so h(3) = (6)2

h(3) = 36

therefore, the point (3, 36) is on the graph of y = h(x)

36 + 3 = 39

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\(16 + 9 = 25\\ 25 - 5 = 20\)

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Express the distance as a function. The distance between any point (x,y) and the origin is √(x^2 + y^2). Since y = 1/2(x^2-3), we have to minimize √(x^2 + (1/2(x^2-3))^2), or 1/2 √(x^4 - 2 x^2 + 9). To minimize the expression inside the radical, we let a=x^2, and find the minimum value/vertex of the parabola that results from its graph. Completing the square, we have a^2-2a+9 --> a^2-2a+1 + 8, or (a-1)^2 + 8. This makes the vertex (1,-8), so 1 = x^2, and x = ±1. Inputting this into our expression (x^2-1)^2 + 8, we get 8, so our answer is 1/2*√8 = 1/2 * 2√2 = √2.

Let:

x = the number of games Bucky can bowl

y = the total price

y = 2.50x + 4

(The total price is equal to the price of each game times the number of games plus the cost to rent a pair of shoes)

> If Bucky has $20 how many games can he bowl?

y = 20, solve for x

20 = 2.50x + 4

16 = 2.50x

x = 6.4

Bucky can play 6 games (not 6.4 because he can't play 0.4 of a game and not 7 because then it will cost over $20)

10!  =  10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

27  =  3 x 3 x 3 

When you divide 10! by 27 (and cancel out the corresponding 3s) you get:  10 x 8 x 7 x 2 x 5 x 4 x 3 x 1 

with no remainder; remainder = 0.

Take the number of people who own cats.

Add to this, the number of people who own dogs.

From this total, subtract the number of people who own both cats and dogs.

AB = 13 ¹/₃

Arc AB = 14.59455312   or    ≈ √213

BC = 3CD => BD + CD = 3CD => BD = 2CD

AC/CD = AB/BD => AC/CD = AB/2CD => AB = 2AC

Perimeter = AC + BC + AB = AC + 3CD + 2AC = AC + CD + 2(AC + CD) = 3(AC + CD) = 3(12) = 36 cm.

 What is the radius of the circle?

HelloGuest!

The middle of the points (-3,2) and (-2, -2) is the point (-2.5,0). The vertical has a gradient of m = 1/4.

\(y=m(x-x_1)+y_1\\ y=0.25(x+2.5)+0\\ y=0.25x+0.625\ |\ \color{blue}x_c=0 \\ \color{blue}y_c=0.625\)

\(r^2=(2-0.625)^2+|-3\ |^2\\ r=\sqrt{10.891}\)

\(r=3.3\)

\(The\ radius\ of\ the\ circle\ is\ {\color{blue}3.3}\ . \)

  !

Fun fact: sum of powers of 2 starting from 2^0 up to 2^n = 2^n-1

It’s probably not fun if it’s not a fact.... But it’s definitely NOT a fact.

The formula for the sum of powers of (2) is \(2^{(n+1)}-1 \text { where (n) is an integer}\)

... now I get the trick (think about it).

OK, I’ve thought about it... 

Your formula (2^n – 1) gives the correct number of games played when (n=8), but how does the problem solver find the (8)? ...And after finding it, how does it help in solving the problem?

This is a binary question. There are 256 Players. Each game eliminates one player. How many players must be eliminated until only one remains? Answer: 255. Because 256 – 255 = 1

For this kind of question, the answer is always one less than the number of players. 

4

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With on the circle do you mean on the circumference of the circle or inside the circle?

Just a guess: 0.5

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Find the distance AB.  

Along the circumference, or a straight line between them? 

The school mascot is rectangular in nature.

Perimeter P = 2(L+W)

L is the length = 4feet

W is the width = 12 feet

Perimeter = 2(4+12)

Perimeter = 2(16)

Perimeter  = 32 feet

Convert to inches

12 in = 1feet

x = 32 feet

Cross multiply

x = 12 * 32

x = 384in

Hence the perimeter of the school mascot is 384 in

If it is to be completely framed using a single row of square tiles each 2 inches on an edge

2 inches = 1 tiles

384 inches = y tiles

Cross multiply

2y = 384

y = 384/2

y = 192 tiles

The number of tiles needed is 192 tiles

Get the cost of 192tiles

If the tiles are $010 each. 192 tiles will cost 192 * 0.1 = $19.2

Hence the cost of the tiles needed is $19.2

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1 book is in the library, 1 book is checked out.

That leaves 4 books that can either be checked out or in the library.

Thus, there are 2⁴ = 16 ways for the books to by arranged.

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6r^2 + 7r + 8 = 6 + 3r + 9r^2       rearrange  as

3r^2  -  4r   -  2   =  0       

Using  the Quadratic Formula.....the largest  value  of  r  =

4  +  sqrt ( 4^2  - 4 (3)(-2)  ]                    4  +  sqrt  [ 40 ]          4  + 2sqrt [10]              

_______________________  =            _____________  =   _____________  =       

                2 * 3                                                 6                                6   

2  +  sqrt [10]

_____________

          3                           

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6,000 x 0.05  x  2 years ==$600 - interest due in 2 years.

On a roll of 2 dice, there are 15 ways of getting a prime number. But, there are only 2 ways of getting the sum of 3, and that is: 1+ 2 and 2+1: 

Therefore, the probability is: 2 / 15

(1, 1) ,  (1, 2) ,  (1, 3) ,  (1, 4) ,  (1, 5) ,  (1, 6) ,  (2, 1) ,  (2, 2) ,  (2, 3) ,  (2, 4) ,  (2, 5) ,  (2, 6) ,  (3, 1) ,  (3, 2) ,  (3, 3) ,  (3, 4) ,  (3, 5) ,  (3, 6) ,  (4, 1) ,  (4, 2) ,  (4, 3) ,  (4, 4) ,  (4, 5) ,  (4, 6) ,  (5, 1) ,  (5, 2) ,  (5, 3) ,  (5, 4) ,  (5, 5) ,  (5, 6) ,  (6, 1) ,  (6, 2) ,  (6, 3) ,  (6, 4) ,  (6, 5) ,  (6, 6) ,  Total == 36

I don't think that this is the full question.

The probability is 3/5.

The area of triangle ACE is 45.

5% of 6000= 30 :)

Smaller cube area = 24 cm²                (Area of a single side = 4 cm²)

Larger cube area = 54 cm²

Area of a solid = 78 - 8 = 70 cm²