Math - Pre-Algebra | Practice Hub

What is the area of a triangle with a base of and a height of ?

Explanation

The formula for the area of a triangle is $A=\frac{1}{2}b*h$ .

Plug in our given values.

$A=\frac{1}{2}b*h$

$A=\frac{1}{2}5*12$

$A=\frac{1}{2}*60$

What is the circumference of a circle with a radius of ?

$30\pi$

$15\pi$

$225\pi$

Explanation

To find the circumference of a circle given the radius we must first know the equation for the circumference of a circle which is

We then plug in the number for the radius into the equation yielding

$Cicumference=2(15)\pi$

We multiply to find the value for the circumference is $30\pi$ .

The answer is $30\pi$ .

Rojo Salsa is on sale at a price of for jars of ounces each. Verde Salsa is on sale at a price of for jars of ounces each. Which of the following statements is true?

An ounce of Rojo Salsa is the same price as an ounce of Verde Salsa.

An ounce of Verde Salsa costs more than an ounce of Rojo Salsa.

A jar of Verde Salsa costs more than a jar of Rojo Salsa.

Verde salsa sells at per ounce.

An ounce of Rojo Salsa costs more than an ounce of Verde Salsa.

Explanation

The statement "A jar of Verde Salsa costs more than a jar of Rojo Salsa" can be tested by comparing the price per jar of each salsa.

$\frac{$9}{3 \ jars \ Rojo} = $3 \ per \ jar$ versus $\frac{$8}{4 \ jars \ Verde} = $2 \ per \ jar$

The statement is false since the price of Rojo per jar is greater.

The remaining statements above can all be proven true or false by finding the price per ounce of each salsa.

Rojo Salsa is on sale at a price of for jars of ounces each. The following operations can be used to determine the cost of Rojo Salsa per ounce:

$3 \ jars \times 12 \ ounces \ per \ jar =36 \ ounces \ sold \ per \ $9$

$\rightarrow $9 = 36 \ ounces \rightarrow $ \frac{9}{36} = 1 \ ounce \rightarrow $ \frac{1}{4} \ per \ ounce$

$\rightarrow $0.25 \ per \ ounce$ for Rojo Salsa.

Verde Salsa is on sale at a price of for jars of ounces each. The following operations can be used to determine the cost of Verde Salsa per ounce.

$4 \ jars \times 8 \ ounces \ per \ jar =32 \ ounces \ sold \ per \ $8$

$\rightarrow $8 = 32 \ ounces \rightarrow $ \frac{8}{32} = 1 \ ounce \rightarrow $ \frac{1}{4} \ per \ ounce$

$\rightarrow $0.25 \ per \ ounce$ for Verde Salsa.

The only true statement is "An ounce of Rojo Salsa is the same price as an ounce of Verde Salsa."

Which of the following is equivalent to ?

$X^{10}$

$X^{7}$

$X^{5}$

$X^{3}$

$X^{25}$

Explanation

When an exponent expression is raised by another exponent, you can multiply the exponents:

$(X^{2})^{5}=X^{2 \cdot 5}=X^{10}$

A farmer has units of fence. If he uses this to build a square fence, what will be the length of each side?

Explanation

If this is a square fence, then each of the four sides will be equal.

The fence in question will become the perimeter of that square.

Since when working with a square, for this problem .

$\frac{100}{4}=s$

What is the circumference of a circle with a radius of ?

$70\pi$

$35\pi$

$1225\pi$

Explanation

To find the circumference of a circle given the radius we must first know the equation for the circumference of a circle which is

We then plug in the number for the radius into the equation yielding

$C=2(35)(\pi)$

We multiply to find the value for the circumference is $70\pi$ .

The answer is $70\pi$ .

What is the perimeter of a square with a side length of ?

Explanation

To find the perimeter of a square you must multiply the side length by .

To do this we plug the side length into the equation

Then multiply the side length by ,

The answer is .

Solve for .

Explanation

Subtract from both sides.

If , what is ?

Explanation

Let's start with our equation, .

Subtract from both sides:

Combine our s:

Divide both sides by :

However, the problem is asking for not , so multiply both sides by :

What is the perimeter of a square with a side length of ?

Explanation

To find the perimeter of a square, you must multiply the side length by .

To do this we plug the side length into the equation .

Then multiply the side length by .

The answer is .

Pre-Algebra

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