Algebra Word Problem Solutions

How do you find the general form of an equation?

Solve each of the quadratic equations $3x=0.5x^2$ and $0=5x^2-<!--\; -\; -->2x+6$
a. x = -6 or x = 0
b. x = -4 or x = 3
c. x = -2 or x = 1.5
d. x = 0 or x = 6

Factor $x^2–8x+15$. Which pair of numbers has a product of ac and a sum of b?

Classify the equation as separable, linear, exact, or none of these.
$x^{2}ydx+5dy=0$

Question 4(i)
Find the multiplicative inverse of the following: -13

It is function is odd function?
$y=2x^3-<!--\; -\; -->3x^2$

Express the following fractions as mixed fractions: $\frac{29}{7}$

Which statement is true for the function $f(x)=\ln <!--\; \; -->(\tan <!--\; \; -->x)$ on the openinterval $\mathrm{\pi <!--\; \pi \; -->}<x<\frac{5\mathrm{\pi <!--\; \pi \; -->}}{4}$?
a. f(x) is increasing at an increasing rate.
b. f(x) is increasing at a decreasing rate.
c. f(x) has a point of symmetry in the open interval.
d. f(x) has an absolute maximum in the open interval
e. f(x) has a point of inflection in the open interval.

Kialani sells orchid and lily plants at the farmers' market.
Each plant sells for a different price. 8 orchid and 12 lily plants sell for $362. 12 orchid and 8 lily plants sell for $388.
How much does Kialani charge for the lily plant?

A spinner is divided into 5 sections of equal size. You spin it 4 times, with the following results: 1, 5, 3, 2. Which of the following is Talse?
a The theoretical probability of a 1 is 20%.
b The expernimental probability of a 2 is 25%.
c. If you spin the spinner again and get different results, the theoretical probability will change.
d. All of the above are true

A spherical balloon is being inflated at the rate of $35cc/min$. The rate of increase of the surface area of the balloon, when its diameter is $14cm$, is $7sqcm/min$,$10sqcm/min$,$17.5sqcm/min$,$28sqcm/min$

How to find period of a real function f given the functional equation $\sqrt{3}f(x)=f(x-<!--\; -\; -->1)+f(x+1)$?
If a periodic function satisfies the equation $\sqrt{3}f(x)=f(x-<!--\; -\; -->1)+f(x+1)$ for all real x then prove that fundamental period of the function is 12.
Here fundamental period means the smallest positive real for which function repeats its value for all x.
I tried replacing x by $x\pm <!--\; \pm \; -->1$ then try to find f(x) in terms of other but always end up with it in terms of sum of other two arguments in the function eg $f(x+2)$ etc.
Please provide a general method and also especially do give the thought process or reasoning for all the steps ie why you are doing these particular steps or what led you to thinking that doing these steps would give you the period of f.

Convert $\frac{1}{6}$ to percentage.

A cubic monomial is which of the following?
1) $4x^3+2x+6$
2) $x+5$
3) $9x^3$
4) $2x^2+2x+7$

what is the following sum?
$\frac{1}{1\cdot <!--\; \cdot \; -->2}+\frac{1}{2\cdot <!--\; \cdot \; -->3}+\frac{1}{3\cdot <!--\; \cdot \; -->4}+...+\frac{1}{(n-<!--\; -\; -->1)\cdot <!--\; \cdot \; -->n}$

$\frac{-3}{8}$ is a ____ rational number.

What's the greatest common factor of twenty-eight and forty-two?

Which rational functions is graphed below

The WRT Corporation makes collections on sales according to the following schedule: 15% in month of sale 75% in month following sale 5% in second month following sale 5% uncollectible The following sales have been budgeted: Sales April $ 198,000 May $ 117,000 June $ 159,000 Budgeted cash collections in June would be:

Use natural logarithms to solve the equation. Round to the nearest thousandth. $6e^{4x}-<!--\; -\; -->2=3$
–0.046
0.327
–0.448
0.067