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Now,
AD = √(AB² - BD²)
      = √(100 - 4(x)²)

      = √(100 - 4(3)²)
      = √(100 - 36)
      = √(64)
      = 8

AB = 10
AC = 17

BD : DC = 2 : 5 
BD = 2x
DC = 5x

√(AB² - BD²) = AD
⇒√(100 - 4x²)= AD
√(AC² - DC²) = AD
⇒√( - 25x²) = AD
Therefore,
√(100 - 4x²) = √(289 - 25x²)
⇒100 - 4x² = 289 - 25x²
⇒-189 = -21x²

⇒189 = 21x²

⇒21x² - 189 = 0
⇒ 21(x² - 9) = 0
⇒x² - 9 = 0
⇒ x = 3
 

Probability = 17

We can either use combinations:

Since there are 6 black balls and we're choosing 2, and there are a total of 9 balls, we calculate \(\frac{6 \choose 2}{9 \choose 2}\)which is 15/36 or 5/12.

Or multiplication principle:

The probability that the first ball is black is 6/9 = 2/3. Since both the black and the total have been reduced by 1, the probability that the second ball and the first ball are black is 2/3 * 5/8 = 10/24 = 5/12.

Without loss of generality, assume that the first number is 1. Then, x_2 can be any of 2, 3, 4, or 5 (assume it is 2, WLOG again), which is 4 possibilities. x_3 can thus be 1, 3, 4, or 5. It is apparent that the pattern of 4 possibilities continues throughout x_4, x_5, x_6, and x_7, so we have 5 possibilities for the first number, then 4 possibilities for the six following numbers, totaling to \(5 \cdot 4^6 = 20480.\)

Let the sides of the triangle be x and y, where x is the repeated side length. It follows that 2x+y = 60. Also, by the triangle inequality, 2x>y and x+y>x (which is trivial, since this simplifies to y>0.) Defining pairs of (2x,y) over 2x>y and \(x, y \in \mathbb{Z}\), we have (32,28), (34,26), ... (58,2) which totals to 14 pairs.

Please explain how that answer is wrong

(sorry if I am missing something very basic)

In 1 minute, the junior senator can work through 1/50 labyrinth.

The senior senator can work through 1/30 labyrinth in a minute.

Thus, if they work together, they will be done with 1/30 + 1/50 = 4/75 of a labyrinth in a minute. This means that they need to work for 75/4 minutes to finish the whole labyrinth. Multiply this by 12, getting 225 minutes.

(6a³+92a²-7)-(-7a³+5a²-7)

First, distribute the negative sign to the right parenthesis, and take away both parenthesis.

6a³+92a²-7+7a³-5a²+7

Combine like-terms.
13a³+87a²

Pull out an a².

a²(13a+87)

a²(13a + 87)

If each place value has to have a 2, 5, or 8, there are 3 possibilities for each place value.

3*3*3= 27

boy is going 11mph train is 8mph so boy is 3mph faster and so the time for a 3mph object to move 1 mile is 20m and so to move 1/4 a mile is 20/4 which is 5m

Angle QRC = 15 degrees!!! 

ABA₆+411₆=1215₆

Although there are other ways to do this, I would start by converting the two right values to base ten.

The now converted equation is:

ABA₆+151₁₀=299₁₀

If we then subtract 151 from both sides, we get:

ABA₆=148
We can then use the equation 36A+6B+A=148, which simplifies to 
37A+6B=148

The only non-extraneous values that work for this equation are A=4 and B=0

4-0=4, which makes the answer 4.

If a word consists of _ _ _ blanks, and A and B must be used once each,

there could be 6 different positions. (AB{}, A{}B, BA{}, B{}A, {}AB, {}BA)

the blank has four different values for each position (A, B, C, or D)

If we multiply the number of postions by what value could be filled in for each postion, we get 4x6=24

There are therefore 24 ways.

The area is 78 cm^2.

The answer is 6 minutes.

* S i m i l a r  T r i a n g l e s*

AQ => x             QZ => 42 - x

8 / 28 = x / (42 - x)

QZ = 32 ²/₃

The question is incomplete! 

The vertices of triangle ABC lie on the sides of the equilateral triangle DEF, as shown. If CD = 3, CE = BD = 2, and angle ACB = 90º, then find AE.

dang... thank you v much! really appericiate it 

Ill see if I can do this in like 11 hours its like 10:30 pm for me so i gotta sleep

Please tell me if this helped if you have time