geno3141

Using (x1, y1) = (-1, 3) and (x2, y2) = (2, -.5), find the slope of the line:

slope  =  m  =  (y2 - y1) / (x2 - x1)

Then use the slope-intercept form of a line to get the equation:  y - y1  =  m(x - x1)

Replace x1, y1, and m in the equation; simplify what you get so you have an equation with y alone on one side and an x-term and another number on the other side.

A possible answer:  the number of feet in a mile.

If you compare ratio of the distance jogged to the distance walked, you get the ratio:  1/2  :  3/4

But, you want the comparison when the the distance walked is 1; so you want the second number to be 1.

To get 1 as the second number, multiply that number by its reciprocal, 4/3  because 3/4 x 4/3  = 1.

However, if you multiply the second number by 4/3, you must also multiply the first number by 4/3.

Doing this will give you the ratio that you want and the number of miles jogged per unit miles walked.

Multiply the numbers together and add the exponents of teh factors that have the same base:

2·4 = 8         b·b^2  =  b^3     c^3·c^7  =  c^10

answer:  8b^3·c^10

If you're supposed to show that (11^-4)^-6 = 11; it doesn't.

If you're supposed to find the exponent on 11 to make it true:  since you have an exponent to an exponent, multiply the exponents together:  -4 x -6  =  24.       11^24 is the simplified expression.

N = 7·L·H

2310  =  7·30·H

2310  =  210·H                      (now, divide both sides by 210)

2310 ÷ 210  =  11

H = 11 feet

There are ten digits:  0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

The probabiliy of guessing the first digit correctly is 1 in 10, or 1/10.

That is also the probability of guessing the second digit correctly, and also the third digit correctly, and also the last digit correctly.

Since you must get the first digit correct AND the second digit correct AND the third digit correct AND the last digit correct, multiply 1/10 x 1/10 x 1/10 x 1/10 to get 1/10000.

(You multiply when you have 'and' and when the different parts are independent. In this case, the different parts are independent because guessing the first digit correctly does not affect guessing the second digit correctly, etc.)

Or, another way:  there are 10000 numbers starting with 0000 and 9999. Guessing any one of these 10000 numbers correctly is 1/10000.

Interesting problems ...

1)  x > -3   --->   (-3, ∞)           x ≤ 3    --->   (-∞, 3]          or:  union:      (-3, ∞)  ∪  (-∞, 3]  =  (-∞, ∞)

2)  4x + 3 ≤ 11   --->   x ≤ 2   --->   (-∞, 2]

     6x > 25   --->   x > 4 1/6   --->   (4 1/6, ∞)         or:  union:    (-∞, 2]  ∪  (4 1/6, ∞)

3)  3x - 9 < -18     --->  x < -3   --->   (-∞, -3)

     -6x + 2 > -28   --->   x < 5   --->   (-∞, 5)         and:  interesect:  (-∞, -3)  ∩  (-∞, 5)  =   (-∞, -3)   

The 'r' stands for the length of the radius of the circle.

If you are to simplify this by multiplying out, use FOIL -- First, Outside, Inside, Last ---

(7x - 4)(2x - 5)

=  (7x)(2x) + (7x)(-5) + (-4)(2x) + (-4)(-5)

=  14x² - 35x - 8x + 20

=  14x² - 43x + 20