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Answers by Philip P.

Math question (answer)

let the length of the three sides be a, b, and c.  The volume is:        V = abc   Now let's double side a so it's 2a.  The new volume is:        Vnew = 2abc = 2V   where V is the original volume...

I assume they want you to simplify the expression.   (10m6n3)/(20m3n7)   (10m6-3n3-7)/20   (10m3n-4)/20   m3/2n4

Assuming * is a multiplication, then:        (3n)*5 + (1/2) * 2(3n-1)   Distribute the 2 across the terms in parentheses        5*3n + (1/2)(2*3n - 2)   Distribute the 1/2 across the terms in parentheses:       ...

Standard form:  Ax + By = C   To find the equation of the line, use the point-slope form:   y - y1 = m(x - x1) y - (-6) = (-2)(x - (-4)) y + 6 = -2x - 8   y + 2x = -14    This is in Standard From

Let j = cost of a pair of jeans, d = cost of a dress, s = cost of a shirt.   3j + 5d + 6s = $888 j + d = $128   (so d = 128 - j) d = s + $20    (since d = 128 - j, then 128-j = s + 20 so 108 - j = s)   3j + 5d +...

Finding angles (answer)

Let x and y be the two unknown angles: Two angles are adjacent and form an angle of 160°:  x + y = 160 Their difference is 34°:  x - y = 34   x + y = 160 x - y  =  34 -------------- 2x     = 194   x = 97o   x...

Let x = acres of corn planted and y = acres of oats.  The revenue is:         R = $127x + $51y   The profit is revenue minus costs. The costs will be capital costs plus labor costs:   C = $36x + $18y + $8*(8x +...

1. 4 = 3√(2x - 8)      43 = 2x - 8      64 = 2x - 8      72 = 2x      36 = x 2. (x2-1)2/3 +2 = 6      (x2-1)2/3 = 4      x2 - 1 = 43/2     ...

U = {1, 2, 3, 4, 5, 6, 7} A = {1, 2, 4, 5} B = {1, 3, 5, 7}   B' = U - B = {1, 2, 3, 4, 5, 6, 7} - {1, 3, 5, 7} = {2, 4, 6}   A U B' = {1, 2, 4, 5} + {2, 4, 6} = {1, 2, 4, 5, 6}   (A U B')' = U - (A U B') = {1, 2, 3, 4, 5, 6, 7} - {1, 2, 4, 5, 6}...

Use the point-slope form for the equation of a line:   y - y1 = m(x - x1)   where: (x1,y1) is a known point on the line = (3,36) m is the line's slope = 12   y - 36 = 12(x - 3)   Now convert it to the slope-intercept form, y = mx +...

Linear program (answer)

Let s = the number of soldiers produced each week and t = the number of trains,  The Profit equation is:   P = $4s + $2.5t   The constraints are:   3s + 2t ≤ 120  (No more than 120 hours of finishing labor available per week) 2s +...