Help! Emergency Pre Calc Questions?

Question

I need to solve 4 of these:

1. If the reciprocal of x+1 is x-1, determine x.

2. In rectangle ABCD, AB = 4 cm and BC = 5 cm. Extend BD past D to E so that DE = BD. How long is AE?

3. A township's population increased from x thousand to x + y thousand. Find the percent of the population increase.

4. How many perfect squares are divisors of the product 1!*2!*3!*...*9!?

5. A merchant paid $30 for an article. He wishes to place a price tag on it so that he can offer a 10 percent discount on the price marked on the tag and still make a profit of 20 percent on the cost. What price should he mark on the tag?

6. Find two fractions that are evenly spaced between these two: (3/a) and (7/2a).

7. Find the ordered pair of numbers (x,y) for which 123x+321y = 345 and 321x+123y = 543.

8. For a given arithmetic sequence, the sum of the first fifty terms is 200, and the sum of the next fifty terms is 2700. What is the first term of the sequence? PLEASE HELP

Answer 1

The answers are posted below:
1.) 1/(x+1) = x-1
x= +2^1/2 and -2^1/2 ( this is + or - the square root of 2)

2.) If you draw the picture as you described it, then
AE = the square root of (4 squared + 10 squared)
you need to drop a straight line down from point E and connect a horizontal line to that from A, this will give you a right triangle and then you can use Pythagorean theorem to get AE = 10.7703 or 2 x square root of 29

5.) You need to take the price he paid and multiply it by 1.2 to get the original price + a 20% profit. This gives the price to be $36.00.

7.) If you solve these two equations simultaneously, you will get (3/2 , 1/2). Solve one equation for x, and then plug this function into the other equation to get y, then all you have to do is plug the value of y into either equation to get the value of x.

I hope this helps. You said that you only needed four answers, so I chose the four that were the fastest to me. Good luck.

Answer 2

a) The $2.50 to $3 in 3 years would mean 50centincrease/3yrs or 100centsincrease/6years(fromNOW); end result: $4, 6years from NOW. b) [3 -4] / (-a million -a million) ==> m(slope) is -a million/(-2) or a million/2. f(x) =(a million/2)x +3.5 regardless of the reality that (pt-slope variety): y - 4 =(a million/2)(x - a million) ======= For the two issues ?y/?x determines the slope of the linear function; the numerator ?y is the exchange in the based variable; and ?x is the corresponding exchange in the self sustaining variable. One based formula from this wide assessment must be [very final state -preliminary state of based variable]/[very final state self sustaining variable -preliminary state indep. var.] it incredibly is only a skeleton instruction manual; you're able to flesh out the assumption so as which you will own each and all of the certainty as your guy or woman.