Improve Your Algebra Skills with Practice Problems

To find:
The ratio of $16 to $12 whole numbers using fractional notation in simplest form.

To identify that the given proportion, ${\displaystyle \frac{gal}{min}=\frac{gal}{min}}$ is correct or not.

Find the ratios in lowest terms of 5 ounces to 15 ounces.

To find:
The required amount of ingredient for apple pie.
Given: For an apple recipe, 12 cups sliced apples and ${\displaystyle \frac{1}{4}}$ teaspoon salt is required.

On a black sheet of paper (lined or not), write any two different positive integers less than 10. In other words, two different single digit positive whole numbers. (Yes, that is redundant because whole numbers are positive.)
Use those two numbers to create two factors, ${\displaystyle (x-a)}$ and ${\displaystyle (x-b)}$, where a and b are your two numbers.
(If you work together with others on this, which is ok for this assignment, be sure each of you chooses different numbers.)
Multiply your factors to create a quadratic in standard form. Next write as a function:
${\displaystyle f\left(x\right)=x^2-bx+c}$.
Now create a quadratic equation by changing f(x) to zero: ${\displaystyle 0=x^2-bx+c}$.

Perform the indicated operation, and simplify if possible. Assume any factors you cancel are not zero.
${\displaystyle \frac{\frac{5}{x}+\frac{8}{x^2}}{\frac{3}{x^2}-\frac{5}{x}}}$

Evaluate ${\displaystyle \left(\frac{3}{14}\right)-\left(\frac{2}{21}\right)}$

A polynomial P is given (a) Factor P into linear and irreducible quadratic factors with real coefficients. (b) Factor P completely into linear factors with complex coefficients.
${\displaystyle P\left(x\right)=x^6-64}$

Use least commin multiple or greatest common divisor to solve the problem.
Rob can complete his bus route in 6 hours. Joan can complete her bus route in 4 hours. If they both left the terminal at 3:00 am and after each completed route returned to the terminal, determine the next time they would leave the terminal at the same time.
A) 9:00 am
B) 7:00 am
C) 3:00 pm
D) Not enough information given to tell.

${\displaystyle X^4=16-x^3}$ - Find all real solutions of the equation, rounded to two decimals.

To evaluate: the proportions ${\displaystyle \frac{1,6}{b}=\frac{8}{25}}$ by cross products property.

In the following exercises, determine if the given number is prime or composite.
Given: 481

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2,3,4,5,6 and 10.
Given: 1080

The Universal Set, U, consists of the natural numbers from 20 to 60 incluive
a. Define or describe in words the following three (3) sets: factors of 64, prime numbers, and multiples of 3.
b. List the elements in each of your sets:
${\displaystyle A=\{}$
${\displaystyle B=\{}$
${\displaystyle C=\{}$
c. Determine the probability of each of the following:
${\displaystyle I.P\left(C\right)}$
${\displaystyle II.P(A\cup B)}$
${\displaystyle III.P(A\cap B\cap C)}$
${\displaystyle IV.P\left(BC\right)}$
${\displaystyle V.P(\left(AB\right)\cap C)}$

Exponential and Logarithmic Equations solve the equation. Find the exact solution if possible. otherwise, use a calculator to approximate to two decimals.
${\displaystyle \ln (x-2)+\ln 3=\ln (5x-7)}$

A restaurant mixes sugar and cinnamon together to sprinkle on desserts. The cost of sugar is $1.10 kg and the cost of cinnamon is $3.60 kg What mass of each is needed to make 50 kg of mixture that costs $1.85 kg. Solve using elimination.

Solve Equations with Decimal Coefficients In the following exercises, solve the equation by clearing the decimals.
${\displaystyle 0.10d+0.25(d+7)=5.25}$