High School Math

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Questions 1 - 10

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

Explanation

To find the perimeter of a polygon, add the lengths of all sides together. For a square, since all side lengths are the same. simply multiply the side length by the number of sides.

$Perimeter=12\cdot4$

If the surface area of a cube equals 96, what is the length of one side of the cube?

Explanation

The surface area of a cube = 6a2 where a is the length of the side of each edge of the cube. Put another way, since all sides of a cube are equal, a is just the lenght of one side of a cube.

We have 96 = 6a2 → a2 = 16, so that's the area of one face of the cube.

Solving we get √16, so a = 4

Solve using the quadratic formula:

$a=\frac{5 \pm i\sqrt{7}}{4}$

$a=\frac{6 \pm i\sqrt{7}}{4}$

$a=\frac{4 \pm i\sqrt{7}}{4}$

$a=\frac{3 \pm i\sqrt{7}}{4}$

$a=\frac{7 \pm i\sqrt{7}}{4}$

Explanation

Use the quadratic formula to solve:

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$a = \frac{-(-5) \pm \sqrt{(-5)^2-4(2)(4)}}{2(2)}$

$a = \frac{5 \pm \sqrt{-7}}{4}$

$a = \frac{5 \pm i\sqrt{7}}{4}$

One side of a square is inches long. What is the perimeter of the square?

inches

Explanation

The perimeter of a square is the sum of all of the sides of the square. In this case, each side is inches long. Since a square has four equal sides, we get a perimeter of inches.

What is the derivative of $2x^4+\frac{1}{2}x$ ?

$8x^{3}+\frac{1}{2}$

$8x^2+\frac{1}{2}x$

$\frac{2}{5}x^5+\frac{1}{4}x^2+c$

Explanation

To take the derivative of this equation, we can use the power rule. The power rule says that we lower the exponent of each variable by one and multiply that number by the original exponent.

$\frac{\mathrm{d} }{\mathrm{d} x}(2x^4+\frac{1}{2}x)=(4*2x^{4-1})+(1*\frac{1}{2}x^{1-1})$

Simplify.

$\frac{\mathrm{d} }{\mathrm{d} x}(2x^4+\frac{1}{2}x)=(4*2x^{3})+(\frac{1}{2}x^{0})$

Remember that anything to the zero power is equal to one.

$\frac{\mathrm{d} }{\mathrm{d} x}(2x^4+\frac{1}{2}x)=(8x^{3})+(\frac{1}{2}*1)$

$\frac{\mathrm{d} }{\mathrm{d} x}(2x^4+\frac{1}{2}x)=8x^{3}+\frac{1}{2}$

A shirt costs $12 after a 15% discount. What was the original price of the shirt?

$\$14.12$

$\$14.50$

$\$10.20$

$\$15.00$

Explanation

Convert 15% to a decimal.

Let the original price equal $\small x$ . The discount will be 15% of $\small x$ . Subtracting the discount from the original price will equal the amount paid, $12.