Algebra Word Problem Solutions

The opposite of squaring a number is division. False or True

Simplify $-<!--\; -\; -->3(x+3{)}^2-<!--\; -\; -->3+3x$

Prove that $⟨<!--\; ⟨\; -->[a]⟩<!--\; ⟩\; -->=⟨<!--\; ⟨\; -->[b]⟩<!--\; ⟩\; -->$ in ${\mathbb{Z}}_n$ iff $gcd(a,n)=gcd(b,n)$

Natalie's Nail Salon has 2 locations: Natalie's Downtown, and Natalie's By-the-Beach. The two salons combined performed 320 pedicures in the first quarter of 2011, and 400 pedicures in the second quarter. Pedicures cost $8.50 at both locations in Q1 and Q2. Natalie notices that in Q1, 30% of pedicures are performed at By-the-Beach but in Q2, 55% of the total were performed there. Natalie's sales goals for Quarter 3 are 6% growth in each location compared to Quarter 2. Natalie is considering raising pedicures prices to $11 at both locations in Q3 to increase revenue.
What was the overall pedicure growth rate from Q1 to Q2?

Find the global maximum and minimum for the function on the closed interval. Show your work and justify your answer. A calculator answer is not acceptable.
$f(x)=x-<!--\; -\; -->2\ln <!--\; \; -->(x+1),\text{ where }0\le <!--\; \le \; -->x\le <!--\; \le \; -->2$

For the function $32/x+3$ , find $(g-<!--\; -\; -->1?g)(5).$

Which set of ordered pairs in the form (x,y) does not represent a function of x?
A. $(-<!--\; -\; -->1,2),(3,-<!--\; -\; -->2),(0,1),(5,2)$
B.$(-<!--\; -\; -->1,2),(3,2),(-<!--\; -\; -->2,2),(0,2)$
C.$(-<!--\; -\; -->1,2),(3,-<!--\; -\; -->2),(0,1),(3,5)$
D.$(-<!--\; -\; -->1,2),(2,3),(3,-<!--\; -\; -->2),(-<!--\; -\; -->2,0)$

What is the measure of a straight line angle?
A.90 degrees
B.360 degrees
C.270 degrees
D.180 degrees

How many endpoints does a ray have?
A)0.0
B)1
C)2
D)3

How to make a 80 degree angle using compass and scale

What is the value of n in the equation $5^n=5^{11}\times <!--\; \times \; -->5^3$

Which of the following statements is/are true? (5 points)
1.If f '(x) exists and is nonzero for all x, then f(1) $f(1)\ne <!--\; \ne \; -->f(0)$ f(0)
2.If f is differentiable for all x and f (-1) = f(1), then there is a number c, such that |c| < 1 and f '(c) = 0.
3.If f '(c) = 0, then f has a local maximum or minimum at x = c.

What number is $60\%$ of $200$?

$\cos ({\tan }^{-1}x)=?$
A$1+x^2$
B$\frac{1}{1}$
C$1+x^2$
D None of these

The fraction $\frac{25}{6}$ when expressed as a mixed fraction equals. <br.1) $4\frac{1}{6}$
2) $4\frac{1}{3}$
3) $8\frac{1}{3}$
4) $3\frac{1}{6}$

Find the square root of the following decimal number: 7.29

Simplify the expression: $\sin <!--\; \; -->x(1+{\cot }^2<!--\; \; -->x)$

All polygons are quadrilaterals, but not every polygon is a quadrilateral.
True or False

How do you find the general form of an equation?