Algebra 1 Quiz

Solve the equation 3x + 5 = 17

• x = 10

• x = 7

• x = 2

• x = 4

Answer explanation

To solve the equation 3x + 5 = 17, subtract 5 from both sides to get 3x = 12. Then divide both sides by 3 to find x = 4. Therefore, the correct choice is x = 4.

Find the value of y when x = 2 in the equation y = 2x - 3

• y = 2(2) - 3 = -1

• y = 2(2) - 3 = 5

• y = 2(2) - 3 = 4 - 3 = 1

• y = 2(2) - 3 = 2

Answer explanation

When x = 2, substituting the value in the equation y = 2x - 3 gives y = 2(2) - 3 = 4 - 3 = 1. Therefore, the correct choice is y = 2(2) - 3 = 4 - 3 = 1.

Graph the linear function y = 2x + 4

• Graph the linear function y = 2x + 4 by plotting the y-intercept at (4, 0) and using the slope of 2 to find another point. Connect the two points to draw the line.

• Graph the linear function y = 2x + 4 by plotting the y-intercept at (0, 4) and using the slope of 2 to find another point. Connect the two points to draw the line.

• Graph the linear function y = 2x + 4 by plotting the y-intercept at (0, 2) and using the slope of 4 to find another point. Connect the two points to draw the line.

• Graph the linear function y = 2x + 4 by plotting the y-intercept at (0, 4) and using the slope of 2 to find another point. Then draw a curve instead of a straight line.

Answer explanation

Graph the linear function y = 2x + 4 by plotting the y-intercept at (0, 4) and using the slope of 2 to find another point. Connect the two points to draw the line.

Find the slope of the line passing through the points (3, 5) and (1, 2)

• 2.5

• 1.5

• 0.75

• 3.5

Answer explanation

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). In this case, the slope is (2 - 5) / (1 - 3) = 1.5. Therefore, the correct answer is 1.5.

Solve the system of equations: 2x + 3y = 10 and 4x - y = 5

• x = 2, y = 2

• x = 5, y = 2

• x = 1, y = 3

• x = 3, y = 4

Answer explanation

To solve the system of equations, substitute x = 2 and y = 2 into both equations. The resulting equations are true, confirming that x = 2 and y = 2 is the correct solution.

Determine the solution to the system of equations: 3x - 2y = 7 and 2x + y = 4

• The solution to the system of equations is x = 5, y = 1.

• The solution to the system of equations is x = 0, y = 4.

• The solution to the system of equations is x = 3, y = -2.

• The solution to the system of equations is x = -2, y = 3.

Answer explanation

The solution to the system of equations is x = 3, y = -2.

Factor the quadratic expression x^2 + 5x + 6

• (x + 2)(x + 3)

• (x + 4)(x + 2)

• (x + 1)(x + 6)

• (x + 3)(x + 3)

Answer explanation

To factor the quadratic expression x^2 + 5x + 6, we look for two numbers that multiply to 6 and add up to 5. The correct choice is (x + 2)(x + 3) because 2 * 3 = 6 and 2 + 3 = 5.

Solve the quadratic equation x^2 - 9x + 20 = 0

• x = 6 or x = 7

• x = 2 or x = 10

• x = 4 or x = 5

• x = 3 or x = 8

Answer explanation

The correct choices are x = 4 or x = 5 because they satisfy the quadratic equation x^2 - 9x + 20 = 0.

A rectangle has a length 3 times its width. If the perimeter is 28, find the dimensions of the rectangle using algebra

• Width: 3, Length: 10

• Width: 5, Length: 15

• Width: 6, Length: 8

• Width: 4, Length: 12

Answer explanation

The correct choice is Width: 4, Length: 12 because when the width is 4, the length is 3 times the width, which is 12. This gives a perimeter of 28.

A sum of money is divided between two persons in the ratio 5:3. If the difference of their shares is $400, find the total sum of money using algebra

• $800

• $1600

• $2000

• $1200

Answer explanation

The total sum of money is $1600 because the difference between the shares is $400 and the ratio is 5:3.