geno3141

What are the two points?

The formula for slope is:  m  =  (y2 - y1) / (x2 - x1)

For problem #1, let (x1, y1) = (2, -3) and (x2, y2) = (5, 8).

         --->   x1 = 2          y1 = -3          x2 = 5          y2 = 8

         ---> Substitute into the slope formula:  (8 - -3) / (5 - 2)  =  11/3

Use this example to work the other three problems.

There are 4 right parentheses but only 1 left parenthesis.

Is there a question here?

Enter that expression into the calculator just as it is; the answer is approximately 23000.

12 / [2(2)^(1/2)(2^(1/2) + 6)^2]

Since (2)^(1/2) = √2:

12 / [2√2(2^(1/2) + 6)^2]

Substituting again:

12 / [2√2(√2 + 6)^2]

Using FOIL on (√2 + 6)^2  =  2 + 12√2 + 36  =  12√2 + 38

Substituing:

12 /  [2√2(12√2 + 38)]

=  12 / [48 + 76√2]

Dividing top and bottom by 4:

=  3 / [12 + 19√2]

To write into reduced radical form, multiply both the numerator and the denominator by 12 - 19√2:

=  3[ 12 - 19√2 ] / [ (12 + 19√2)(12 - 19√2)]

=  (36 - 57√2) / -578  

=  (57√2 - 36) / 578

8²  =  64

Using the distributive law:

(x + 6)²  =  x² + 12x + 36

(x + 3)²  =  x² + 6x + 9

(x + 6)²  =  8² + (x + 3)²

x² + 12x + 36  =  64 + x² + 6x + 9

Subtract x² from both sides:

12x + 36  =  64 + 6x + 9

Subtract 6x from both sides:

6x + 36  =  64 + 9

Subtract 36 from both sides and simplify:

6x  =  37

Divide by 6:

x  =  37/6

f  =  (9/5)c + 32

Subtract the 32:

f - 32  =  (9/5)c

multiply both sides by 5/9, the reciprocal of 9/5:

(5/9)(f - 32)  =  (5/9)(9/5)c

(5/9)(f - 32)  =  c

Bus + Train + Taxi  =  16.

Train = 5·Bus

Taxi  = 2·Bus

Substituting:  Bus + 5·Bus + 2·Bus  =  16

Simplifying:                         8·Bus  =  16

Dividing by 8:                         Bus  =  2

Train  =  5·Bus  =  5·2  =  10

Taxi    =  2·Bus  =  2·2  =  4

The reason for the discrepancy is that happy7 assumed that the 14 and 35 referred to percenages while anonymous assumed that they were dollars. Since the question wasn't clear what the 14 and 35 were, each one is correct for its assumption.

Area  =  L · W  =  77

L = 2W + 3

Substituting:  (2W + 3)(W)  =  72

     2W² + 3w  =  77

     2W² + 3w - 77  =  0

     (2W - 11)(w + 7)  =  0

Either 2W - 11  =  0  --->   2W  =  1   --->   W  =  5.5   --->   L  =  2(5.5) + 3   --->   L  =  14

Or:     w + 7  =  0   --->   w  =  -7   (impossible)