geno3141

(32/35) ÷ (27/7)

To divide, multiply by the reciprocal:

(32/35) x (7/27)

Now, multiply the numerator times the numerator (32 x 7) and the denominator times the denominator (35 x 27):

224 / 945

This can be reduced; divide both the numerator and the denominator by 7.

In scientific notation, you want the decimal point to be after the first (non-zero) digit. You will need to move the decimal point  5  places to the left:

3.587 x 10^5

12x(x + 1)  =  -3

MUltiply out the left side (distributive property):

12x² + 12x  = -3

12x² + 12x + 3  =  0

Divide by 3 to get a simpler equation:

4x² + 4x + 1  =  0

You can now finish this by factoring, by completing the square, or by using the quadratic formula.

Since you didn't tell me that I had to use long division and since  a² - 11a + 30  can be factored, I'm going to factor it:  (a - 6)(a - 5).

Now, the problem is:  (a - 6)(a - 5) / (a - 5)  which reduces to  a - 6.

First: write it as a single common fraction:  1/2 + 3/4  ==>  2/4 + 3/4  ==>  5/4

5/4  as a ratio is  5:4

A common denominator is 12; multiply each term times 12:

  12(2x/3) + 12(x/2) - 3(12) = 12(3x/4) + 2(12)

  8x + 6x - 36 = 9x + 24

  14x - 36 = 9x + 24

    5x  =  60

      x  =  12

cos = adj/hyp           sin = opp/hyp 

1)  For angle B, adj = 7 and hyp = 25; so cos B  =  7/25  = .28  

     This works; but A = 90 - B.

2)  Isn't correct; cos B = .28 not .96

3)  For angle A, opp = 7 and hyp = 25; so sin A  = 7/25 = .28 and B is found by 90 - A.

By FOIL,  (a - 4b)(a + 4b)  =  a² + 4ab - 4ab - 16b²  =  a² - 16b²

Draw a right triangle from the plane (point A) parallel to the ground to a point right above the airport (point C) and from point C down to the airport (point B) and then from point B back to point A.

There is a right angle at point C.

AC = 4 miles 

angle A is 6.5 degrees (the angle of elevation is the same as the angle of depression)

In right triangle ACB, you know angle A and its adjacent side, AC. You need to know its opposite side CB.

tan = opp/adj    --->    tan 6.5  =  x / 4   --->  x = 4 · tan(6.5)

Solve for x.

If you can read 11 pages in 1/2 hour, then you should be able to read 22 pages in 1 hour (twice the number of pages in twice the time).

The rate is 22 pages per hour.