12. A carpenter made two tables. The first table is 4 feet
1 answer:
Answer:
a. True
b. True
c. False
d. False
Step-by-step explanation:
<u>First Table</u>
Length=10 feet, Width=4 feet
Area =10 X 4=40 Square Feet
<u>Second Table</u>
The second table is half as long as the first table.
Length =0.5 X 10 =5 feet
Area=5 X Width= 5w
The area of the second table is one fourth the area of the first table.
Area of Second Table = X Area of first table
5w= X 40
5w=10
Width of the Second table, w=2 feet
The following are true.
(a)The width of the second table is 2 feet.
(b) The area of the second table is 10 square feet.
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Assuming a diagram similar to the one I've attached, ∠<em>YVZ</em> is a vertical angle to ∠<em>WVX</em>, which means they have an equal measure. Additionally, ∠<em>WVZ</em> and ∠<em>WVX</em> form a linear pair, which means they are supplementary (sum to 180°). That means we start out with the equation
We combine our like terms (the <em>x</em>'s get combined, then the constants get combined) and have:
Cancel the 9 first by subtraction:
Cancel the 19 by division:
Since we know that our angle we're looking for, ∠<em>YVZ</em>, is the same measure as ∠<em>WVX</em>, we substitute 9 in for <em>x</em>:
8(9)+28=72+28=100°
We combine our like terms (the <em>x</em>'s get combined, then the constants get combined) and have:
Cancel the 9 first by subtraction:
Cancel the 19 by division:
Since we know that our angle we're looking for, ∠<em>YVZ</em>, is the same measure as ∠<em>WVX</em>, we substitute 9 in for <em>x</em>:
8(9)+28=72+28=100°