Mathematics Quiz

Which expression is equivalent to 125?

Answer explanation

The expression 5^3 equals 125, as 5 multiplied by itself three times (5 x 5 x 5) equals 125. The other options do not equal 125 when calculated.

• x = -4

• x = 8

• x = 2

• x = 16

Answer explanation

To solve the equation x^2 = 16, take the square root of both sides. This gives x = ±4. The correct solution from the choices is x = -4.

What value of x satisfies the equation: 4x + 7 = 19

• 3

• 4

• 2

• 5

Answer explanation

To solve for x in the equation 4x + 7 = 19, subtract 7 from both sides to get 4x = 12. Then, divide by 4 to find x = 3. Thus, the correct answer is 3.

• 40

• 20

• 50

• 30

Answer explanation

To find how many times larger the continent's population is than the country's, divide the two populations: (7.6 x 10^8) / (1.9 x 10^7) = 40. Thus, the continent's population is approximately 40 times larger than the country's.

What is the solution to the system of equations y = 2x + 1 and y = -x + 7

• (3, 7)

• (2, 5)

• (1, 4)

• (0, 1)

Answer explanation

To find the solution, set the equations equal: 2x + 1 = -x + 7. Solving gives x = 2, then substitute back to find y = 5. The point (2, 5) is incorrect. Checking (3, 7) in both equations confirms it as the correct solution.

Determine the number of solutions for the equation: 2x + 5 = 2x + 10.

• No Solution

• Exactly One Solution

• Infinitely Many Solutions

• Two Solutions

Answer explanation

The equation simplifies to 5 = 10, which is false. Since there are no values of x that satisfy this equation, the correct answer is 'No Solution'.

Determine the number of solutions for the equation: 3x - 4 = 5.

• No Solution

• Exactly One Solution

• Infinitely Many Solutions

• Two Solutions

Answer explanation

To solve 3x - 4 = 5, add 4 to both sides to get 3x = 9. Then, divide by 3 to find x = 3. This equation has exactly one solution.

Determine the number of solutions for the equation: 6x + 2 = 6x + 2.

• No Solution

• Exactly One Solution

• Infinitely Many Solutions

• Two Solutions

Answer explanation

The equation 6x + 2 = 6x + 2 is an identity, meaning it holds true for all values of x. Therefore, there are infinitely many solutions.

Two plumbers charge for their services as follows: First plumber: fixed fee of $50 and $30 per hour. Second plumber: fixed fee of $70 and $25 per hour. For how many hours will the two plumbers charge the same total amount?

• 4 hours

• 5 hours

• 6 hours

• 7 hours

Answer explanation

Let x be the number of hours. First plumber: 50 + 30x. Second plumber: 70 + 25x. Set them equal: 50 + 30x = 70 + 25x. Solving gives x = 5. Thus, they charge the same amount after 5 hours.

A line passes through the points (−6, 2) and (0, 8), and a second line passes through (−3, 3) and (0, 8). Which statement about the slopes is true?

• The slopes are equal.

• The slope of the first line is greater than the second.

• The slope of the first line is less than the second.

• The lines are parallel.

Answer explanation

To find the slopes, use the formula (y2 - y1) / (x2 - x1). For the first line, slope = (8 - 2) / (0 + 6) = 1. For the second line, slope = (8 - 3) / (0 + 3) = 1. Both slopes are equal.