Acc2 3A Geometry Figures Quiz

On a map, 1 inch represents 5 miles. If the distance between two towns on the map is 3 inches, what is the actual distance between the towns?

Answer explanation

The map’s scale of 1 inch : 5 miles means the real distance is 5 times the map distance.

We set up a proportion or simply multiply:

3 inches × 5 = 15 miles

In general, a scale drawing uses a constant ratio of drawing length to actual length.

For example, a scale of 1:100,000 means the real distance is 100,000 times the drawing length.

Here, the actual distance is 15 miles.

Tags

CCSS.6.RP.A.3B

Determine whether each statement is True or False about angle relationships:

1. Complementary angles can be supplementary. ​

2. Vertical angles must be supplementary. ​

3. 3. Adjacent angles can be complementary.​

• False

• False
• True

Answer explanation

- Adjacent angles can be complementary if they share a common ray and sum to 90°.

- Vertical angles (opposite each other when two lines intersect) are always equal, not necessarily supplementary.

- Complementary angles sum to 90° by definition, so they cannot be supplementary because supplementary angles sum to 180°.

Solve the equation: 3(2x – 1) = 5x + 7

Answer explanation

Explanation:

We need to isolate the variable x by using inverse operations on both sides of the equation.

Step 1: Distribute 3 on the left side:

3(2x – 1) = 6x – 3

Step 2: Rewrite the equation:

6x – 3 = 5x + 7

Step 3: Subtract 5x from both sides:

6x – 5x – 3 = 7

x – 3 = 7

Step 4: Add 3 to both sides to isolate x:

x = 7 + 3

x = 10

Step 5: Check the solution by substituting x = 10 into the original equation:

Left side:

3(2(10) – 1) = 3(20 – 1) = 3(19) = 57

Right side:

5(10) + 7 = 50 + 7 = 57

Since both sides are equal, x = 10 is the correct solution.

Tags

CCSS.8.EE.C.7B

Tags

CCSS.7.G.B.5

Triangle Inequality Theorem

**Explanation:** Imagine you are building a triangle with ​ sticks. You have **​ (a)   sticks** of different lengths. To make a triangle, two of the sticks **​ (b)   ** to reach and connect the third stick. If two sticks are too short, they won’t touch, and you won’t have a triangle!

• three
• four
• five
• must be long enough
• must be short enough

Triangle Inequality Theorem

**Key Rule:** If the **sum of any two sides** is **​ (a)   ** the third side, you can make a triangle!

• bigger than
• smaller than
• same as

Triangle Inequality Theorem

**Example:** - **Can make a triangle:** If you have sticks that are **3 inches, 4 inches, and 5 inches**, you can form a triangle because: - 3 + 4 = 7 (​ ​ (a)   ) - 3 + 5 = 8 (​ (b)   ) - 4 + 5 = 9 (​ (c)   )

• which is bigger than 5
• which is bigger than 4
• which is bigger than 3

Lerato is solving the following linear equation:
5 + 2x - 3 = 6x + 8 - 4x
After several steps, Lerato arrives at the following equation:
2 + 2x = 2x + 10
Lerato's final step is:
2 = 10

What is the meaning of Lerato's final solution?

• The solution to the equation is x = 5

• The solution to the equation is x = -4.

• There is no solution since 2 = 10 is a false statement.

• There are infinitely many solutions since 2 = 10 is a false statement.

• The false statement indicates there is no solution to the original equation.