Question

1. which equation verifies that the value of x in the diagram is equal to 10? options: 4 = \frac{1}{2}(x + 7), x = \frac{1}{2}(4 + 7), 7 = \frac{1}{2}(8 + 4) + (7 + 14), 7 = \frac{1}{2}(x + 4)

Explanation:

Step 1: Analyze the Diagram

The diagram appears to show a trapezoid (or a figure with parallel sides) where the midline (or midsegment) length is related to the lengths of the two parallel sides. The midline length of a trapezoid is the average of the lengths of the two parallel sides. Here, one side is \( x \), another is composed of \( 4 + 7 \) (from the segments shown), and the midline (or the segment of length 7?) Wait, actually, looking at the options, we can test each equation by plugging \( x = 10 \) and see which one holds.

Step 2: Test Each Option

• Option 1: \( 4=\frac{1}{2}(x + 7) \). Plug \( x = 10 \): \( \frac{1}{2}(10 + 7)=\frac{17}{2}=8.5

eq4 \).

• Option 2: \( x=\frac{1}{2}(4 + 7) \). \( \frac{1}{2}(11)=5.5

eq10 \).

• Option 3: \( 7=\frac{1}{2}(x + 4) \). Plug \( x = 10 \): \( \frac{1}{2}(10 + 4)=\frac{14}{2}=7 \). This works.
• Option 4: \( 7=\frac{1}{2}(x + 4)+(7 + 14) \). This is too large, no need to calculate as the left side is 7 and right side would be way bigger.

The Final Answer

The equation that verifies \( x = 10 \) is \( 7=\frac{1}{2}(x + 4) \), so the correct option is the one with \( 7=\frac{1}{2}(x + 4) \) (the third option in the list as per the image labels).

Answer:

Step 1: Analyze the Diagram

The diagram appears to show a trapezoid (or a figure with parallel sides) where the midline (or midsegment) length is related to the lengths of the two parallel sides. The midline length of a trapezoid is the average of the lengths of the two parallel sides. Here, one side is \( x \), another is composed of \( 4 + 7 \) (from the segments shown), and the midline (or the segment of length 7?) Wait, actually, looking at the options, we can test each equation by plugging \( x = 10 \) and see which one holds.

Step 2: Test Each Option

• Option 1: \( 4=\frac{1}{2}(x + 7) \). Plug \( x = 10 \): \( \frac{1}{2}(10 + 7)=\frac{17}{2}=8.5

eq4 \).

• Option 2: \( x=\frac{1}{2}(4 + 7) \). \( \frac{1}{2}(11)=5.5

eq10 \).

• Option 3: \( 7=\frac{1}{2}(x + 4) \). Plug \( x = 10 \): \( \frac{1}{2}(10 + 4)=\frac{14}{2}=7 \). This works.
• Option 4: \( 7=\frac{1}{2}(x + 4)+(7 + 14) \). This is too large, no need to calculate as the left side is 7 and right side would be way bigger.

The Final Answer

The equation that verifies \( x = 10 \) is \( 7=\frac{1}{2}(x + 4) \), so the correct option is the one with \( 7=\frac{1}{2}(x + 4) \) (the third option in the list as per the image labels).