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The missing angle in the left triangle has value 40^o.

Therefore, its vertical angle in the right triangle is also 40^o.

This leaves 50^o for the missing angle.

The domain is the set of all real numbers that are allowable replacements for x.

The only number not allowed is -1, because this number makes the denominator zero.

So the domain is:  (-infinity, -1)  union  (-1, infinity).

In that case we have the following:

I'll leave you to calcuate the numerical value of c.

Thanks!

If the two circles are externally tangent, the distance between the centers is  8.

If they are internally tangent, the distance is 2.

Check if 60 is correct

x=60 degrees

2x-5≤-x+12

3x≤17

x≤17/3

(-∞, 17/3]

A rough sketch shows a square, of side L, with 5 rectangles inside, each L by L/5

Perimeter of rectangles = 2L +2(L/5) = 2.4 L = 36,,,,L= 15
Perimeter of square = 4*L=4*15 = 60 units

I fixed the question.

Is my answer correct? 60

I meant to say 

Let x be number of total enrolled then 20% of the OD, out of district, students would be 0.2x. The number is increased by 50%, 1.5 so (0.2x)(1.5)=0.3x, so 30% of the total enrolled is out of district.

1.  The probability your first ticket matches one of the white balls is 3/10.  Then the second ticket has a probability of matching of 2/9 (since there are only 9 white balls left). Then the probability of the third ticket matching is 1/8.  The probability of matching the red ball is 1/10.  Hence, the overall probability is (3/10)*(2/9)*(1/8)*(1/10) = 1/1200.

2.  I think this is as follows:

p(exactly 3 white) = (3/10)*(2/9)*(1/8) =  1/120

p(exactly 2 white) = (3/10)*(2/9)*(7/8) = 7/120

p(1 red) = 1/10

So probability(at least 2 white or 1 red) =  1/120 + 7/120 + 1/10= 1/6

Let number of children be c, and number of adults be a.  Then

c + a = 314

5c + 6a = 1740

Can you use these two equations to find a and c?

This doesn't have any meaning as written!

In the expansion of what?

There are an infinite number of solutions to this.  For example, just set y = -x and set z = 2.

log_x²

Let 'x' be her usual hourly wage

     then 1.6 x   is her ovetime wage

         she worked 6 hours overtime   (6 hours past 40 hours)

          40 x    +    1.6x ( 6)  = 644.80       Solve for 'x' her regular wage....

Not clear what you intend the first one to be!  Does it have log_x2 or log_x(something²) ?

2x-5 >= -x +12      add 'x' to both sides of the equation

3x -5  >=   +12    add 5 to both sides

3x  >= 17

x >=  17/3

[ 17/3 , +inf)

Hello, for 1., the answer was 1/1200, and for 2., the answer was not 2/19. I don't understand where you did it wrong, and if you would like to re-try or if anyone else can attempt it, that would be great. Thank you for trying!

Hi, I think you read the question wrong. For part a), there are 9 balls in total, not 10. Therefore, both of your answers were wrong. However, thank you so much for trying to help! (If you would like to reattempt the questions or if anyone else could, that would be greatly appreciated!)
Also, for 2., the question should be: 

From a standard deck of 52 cards, the four Aces, four 2's, and four 3's are drawn, forming a smaller deck of 12 cards. All 12 cards are dealt at random to four players, so that each player gets three cards. What is the probability that each player's hand consists of an Ace, a 2, and a 3?

Sorry about the formatting errors. I will double check them in future.