When you draw a diagonal across a rectangle, you create two congruent right triangles that share the diagonal as the hypotenuse. The legs of the triangles are the lengths of the sides of the rectangle. You can use the
Pythagorean Theorem to find the length of the diagonal.
Let...

720, 540, and 180 are the degrees of different flips or spins. One full rotation = 360o.
720o = 360o*2= two full rotations
540o = 360o*1.5 = 1 1/2 rotations
180o = 360o*(1/2) = half a rotation

|-x| = x
Let x = -1:
|-(-1)| = -1
|1| = -1
1 = -1
Conjecture is false.

In 4 hours, the first employee uses (3/4 gallon per hour)*(4 hours) = 3 gallons
In 4 hours, the second employee uses (5/3 gallon per hour)*(4 hours) = 20/3 = 6 2/3 gallons
To find out how much they use together, add the results.

I assume we're talking Microsoft Excel here.
What formulas would you enter to add the values in cells B4, B5, and B6?
=B4+B5+B6
What function would you enter to achieve the same results?
...

Let s = team sack's score. Since team tackle beat team sack by 7 points, team tackle scored s+7 points. Their scores total 89 points, so let's add them:
s + s + 7 = 89
2s + 7 = 89
Solve for s.

You didn't tell us what the problem is, but I'm guessing you want the expression factored.
4x3 + 28x2 + 7x + 49
(4x3 + 28x2) + (7x + 49)
Factor the greatest common factor...

n(U) = n(A) + n(A') = 49 + 48 = 97
n(AUB) = n(A) + n(B) - n(A∩B) = 49 + 64 - 22 = 91
n((AUB)') = n(U) - n(AUB) = 97 - 91 = 6

For a parallelogram:
Area = base*height
Divide both sides of the equation by height:
Area/height = base
Since the area is 4x+16, substitute it for the Area:
...

The product of twenty nine and x means to multiply 29 by x = 29x
increased by the quantity x plus seven means to add (increase) x+7 = 29x + x + 7 = 30x + 7

(39/500)*(15) = 585/500 = 1 85/500 = 1 17/100 = 1.17 inches

Let x be the smallest integer. Since the integers are consecutive, the other two are (x+1) and (x+2). We want the sum of the first two (x + x+1) to equal three times the third (3(x+2))
x + x+1 = 3(x+2)
...

The perimeter of a rectangle is the distance around its sides. Since there are two length sides and two width sides, the formula is:
Perimeter = 2L + 2W
Where L is the length and W is the width. Since the perimeter is given...

45% 144
------- = -------
100% x
Where x is the total number of students. Solve for x.

n(AUB) = n(A) + n(B) - n(A∩B)
Since the sets A and B are disjoint, n(A∩B) = 0. Hence:
n(AUB) = n(A) + n(B) = 35 + 15 = 50
n((AUB)') = n(u) - n(AUB) = 70 - 50 = 20

Given f(x) = x2 – 4x – 2 and g(x) = 2x2 + 4x + 9, find (f – g)(x).
(f-g)(x) = f(x) - g(x)
= (x2 – 4x – 2) - (2x2 + 4x + 9)
= x2 - 4x - 2 - 2x2...

The circumference of the wheel is 2*pi*radius = 2*3.14*26 = 37.7 inches. This is how far the bike moves forward in one revolution of the wheel. The problem states that the bike is moving at 200 revolutions per minute (rpm). That equates to a linear speed of:
(200...

Let x be the unknown number:
The product of 5 and the sum of two and the number: 5*(2+x)
is five times the number = 5x
5(2+x) = 5x
Divide both sides by 5:
2 + x = x
Subtract x from both sides:
2 =...

Let x be the first unknown number. The second number is 5 more than x, or x+5. Their sum is 125:
x + (x+5) = 125
Combine like terms:
2x + 5 = 125
Subtract...

I'll do problem D) for you. The others are done the same way.
D) 2/x + 6/(1/y)
= 2/x + 6y (When you divide by a fraction (1/y), invert the fraction and multiply)
...