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2x^2-x+5,g(x)=x+1    assuming that the first function is f(x)

[f+g](x) means that we just add the functions together  = 2x^2 + 6

[f + g](6)  means that we "plug" 6 into what we've just found in the first part......so we have...... 2(6)^2 + 6  = 2(36) + 6 = 72 + 6 = 78

f(x)  =  2x² - x + 5                 g(x)  =  x + 1

(f + g)(x)  =  f(x) + g(x)  =   (2x² - x + 5) + (x + 1)  =  2x² + 6

(f + g)(6)  = 2(6²) + 6  =  78

That IS excellent....very clever !!!!!!

Remove the negative exponent:  x^(-2/3)  =  1 / x^(2/3)

1 /  x^(2/3)  =  -1/9

Cross multiply:  9  =  -x^(2/3)

-9  =  x^(2/3)          This means the cube root of x squared, so

cube both sides:

(-9) ^3  =  x^2

-729  =  x^2

If you are restricted to real numbers, this is impossible. However, if you can use complex numbers:

Find the square root of both sides:

x  =  ±√(-729)  =  ±27i

That is excellent 

these brackets are identical.

If you take something away from itself then the answer is always 0

3. P=(1.2w)/h^2, find h.

Multiply both sides by h^2

h^2*P = 1.2w

Divide both sides by P

h^2 = (1.2w)/P

Take the positive root of both sides...since h is a positive quantity

h =√[1.2w/P]

4. 9/10g=7+2/3k, find k

Multiply both sides by the LCM of 3 and 10, i.e., 30

27g = 210 + 20k

Subtract 210 from both sides

27g - 210 = 20k

Divide both sides by 20

[27g - 210 ]/ 20 = g

5. 2-3/4p=5/6r+5, find r.

Multiply through by the LCM of 4 and 6, i.e., 12

24 - 9p = 10r + 60   

Subtract 60 from both sides

24 - 9p - 60 = 10r

Divide both sides by 10

[24 - 9p - 60 ] / 10  = r

Notice that the trick of multiplying through by the LCM first allows us to get rid of those nasty fractions in our work !!!

Can you correct the "$n.16"?

P = (1.2w) / h²                 (Cross-multiply:)

Ph²  =  1.2w                     (Divide by P:)

h²  =  1.2w/ P                   (Find the square root:)

h  =  ±√(1.2w/P)

(9/10)g =  7 + (2/3)k                   (Subtract 7:)

(9/10)g - 7  =  (2/3)k                   (Multiply by 3/2:)

(3/2)[( 9/10)g - 7 ]  =  k               (Distribute:)

(27/20)g - 21/2  =  k

2 - (3/4)p  =  (5/6)r + 5        (Subtract 5:)

-3 - (3/4)p  =  (5/6)r            (Multiply by 6/5:)

(6/5)[ -3 - (3/4)p ]  =  r        (Distribute:)

-18/5 - (9/10)p  =  r

150% = 1.5     "of" means multiply ......so we have

1.5 x 74 =  111

Make certain that the calculator is in radian or degree mode; whichevery you want (Lower left of screen).

Hit the 2nd key, then the acosh key, then enter the number.

For example, the answer to invCosh( 2 ) = 1.31695...

Can you also answer the other part that I posted?

Notice that 

40.8  =   40  + .8  ......and dividing each thing by 8  =   5 + .1    =  5.1

1)  Get all the terms that contain an 'a' to the left side; get all the other terms to the right side:

          ax + z  =  aw - y           (Subtract aw from both sides.)

          ax - aw + z =  -y           (Subtract z from both sides.)

          ax - aw  =  -y - z           (Factor a out of the left side.)

          a(x - w)  =  -y - z          (Divide both sides by x - w.)

          a  =  (-y - z) / (x - w)

2)  Get all the terms that contain an 'n' to the lift side; get all the other terms to the right side:

          -14n + q  =  rt - 4n          (Add 4n to both sides.)

          -14n + 4n + q  =  rt         (Subtract q from both sides.)

          -10n  =  rt - q                  (Divide both sides by -10.)

               n  =  (rt - q) / -10

               n  =  (q - rt) / 10

That settles it....... 117 is the Most Common Multiple (answer)........

3 = 3 x 1

39 =13 x 3

117 = 3² x 13

So taking each different factor with the higest power, we have

3² x 13  = 117   = LCM

39=3*13

117=3*3*13=3*39

so 117 is a multiple of 39

9=3*3  so 117 is a multiple of 9

so the lowest common multiple is 117

And to add to that sorry. 

3. P=(1.2w)/h^2, find h.

4. 9/10g=7+2/3k, find k

5. 2-3/4p=5/6r+5, find r. 

THANKS!

Write each number in factored form:

39  =  3 x 13

9  =  3 x 3

117  =  3 x 39  =  3 x 3 x 13

Take each factor the greatest number of times in each number;  3 x 3 x 13  =  117.

Each number, 13, 3, and 117 will divide into 117 without a remaider (and, no smaller number will work) ; therefore, it is the least common multiple.

To separate  40.8  gallons of paint into  8  containers, calculate:  40.8 ÷ 8  =  5.1 gallons each.

For  f(x)  =  (3/4)x²,

when  x = -6,  f(-6)  =  (3/4)(-6)²  =  27

when  x = -4,  f(-4)  =  (3/4)(-4)²  =  12

when  x =  2,  f(2)  =  (3/4)(2)²  =  3

The range consists of the values for f(x):   {27, 12, 3}.

OK...I misread that....so we have....

A =  [a (v_f  - v_i ) ] / t       multiply both sides by t

At = [a (v_f  - v_i ) ]           divide by a

(At) / a =  v_f  - v_i             add v_i to each side

[(At) / a ] + v_i =  v_f

If you are talking about graphing equations,

parallel lines have the same slope (for example y = 2x + 9 is parallel to y = 2x - 7 because both have the same slope, 2)

and perpendiculr lines have slopes that are negative reciprocals (for example y = 2x + 9 is perpendicular to y = (-1/2)x - 7, because the slopes are negative reciprocals).

Please send more complete information and we can answer the question more fully.

We could also use the Law of Cosines to find this. Note that the supplementary angle to "15° northward" is 165°

So we have

√[80² + 60² - 2(80)(60)cos(165°)] = 138.83 miles

I said that I wanted to solve for v with the small f