Solving Equations, Transformations, and Angles Review

Answer explanation

To solve for x, subtract 2x from both sides: 3x - 2x + 5 = 9. This simplifies to x + 5 = 9. Next, subtract 5 from both sides: x = 4. Thus, the correct answer is x = 4.

Tags

NC.MA.NC.8.EE.7

Which of the following systems of equations has no solution?

Tags

NC.MA.NC.8.EE.8

A triangle is dilated by a scale factor of 2. Which of the following statements is true?

• The dilated triangle is congruent to the original.

• The dilated triangle is similar to the original.

• The dilated triangle is neither similar nor congruent to the original.

• The dilated triangle is smaller than the original.

Answer explanation

The dilated triangle is similar to the original because dilation preserves the shape of the triangle while changing its size. A scale factor of 2 means the new triangle is larger, but both triangles have the same angles.

Tags

NC.MA.NC.8.G.4

If two parallel lines are cut by a transversal, which of the following angle pairs are congruent?

• Corresponding angles

• Alternate interior angles

• Alternate exterior angles

• All of the above

Answer explanation

When two parallel lines are cut by a transversal, corresponding angles, alternate interior angles, and alternate exterior angles are all congruent. Therefore, the correct answer is 'All of the above'.

Tags

NC.MA.NC.8.G.5

Which transformation changes the size of a figure?

• Dilation

• Rotation

• Reflection

• Translation

Answer explanation

Dilation changes the size of a figure by scaling it up or down, while rotation, reflection, and translation maintain the figure's size and shape. Therefore, the correct answer is Dilation.

Tags

NC.MA.NC.8.G.2

Answer explanation

To find the solution, set the equations equal: 2x + 1 = -x + 4. Solving gives x = 1. Substituting x back into either equation, y = 2(1) + 1 = 3. Thus, the solution is (1, 3).

Tags

NC.MA.NC.8.EE.8

Which sequence of transformations will show that two figures are similar?

• Translation followed by rotation

• Rotation followed by dilation

• Reflection followed by translation

• Dilation followed by reflection

Answer explanation

The correct choice, 'Rotation followed by dilation', shows similarity because rotation preserves shape and size, while dilation changes size but maintains the shape. Together, they confirm that the figures are similar.

Tags

NC.MA.NC.8.G.4

In a triangle, if one angle measures 50 degrees and another measures 60 degrees, what is the measure of the third angle?

• 70 degrees

• 80 degrees

• 90 degrees

• 100 degrees

Answer explanation

In a triangle, the sum of the angles is always 180 degrees. Here, 50 + 60 = 110 degrees. Therefore, the third angle is 180 - 110 = 70 degrees, which is the correct answer.

Tags

NC.MA.NC.8.G.5

Which transformation will result in a figure that is congruent to the original?

• Dilation

• Rotation

• Enlargement

• Reduction

Answer explanation

A rotation is a transformation that turns a figure around a fixed point without changing its size or shape, making the figure congruent to the original. Dilation, enlargement, and reduction change the size.

Tags

NC.MA.NC.8.G.2

Answer explanation

To solve the equation, distribute: 4x - 8 = 2x + 8. Then, subtract 2x from both sides: 2x - 8 = 8. Add 8 to both sides: 2x = 16. Finally, divide by 2: x = 8. The correct answer is x = 2.

Tags

NC.MA.NC.8.EE.7