Rectangle ABCD is dilated to create rectangle A'B'C'D' . The width of rectangle ABCD is 8 feet. The width of rectangle A'B'C'D'
1 answer:
Answer:
54 square feet
Step-by-step explanation:
The width of the rectangle ABCD is 8 feet and the area of the same rectangle is 96 square feet.
Hence, the length of the rectangle is (96 ÷ 8) = 12 feet.
Now, if the rectangle ABCD is dilated to rectangle A'B'C'D', then the length and the width of the new rectangle will be changed in the same ratio.
So, {Where AB is the length and BC is the width}
⇒
⇒ A'B' = 9 feet
Therefore, the area of the dilated rectangle A'B'C'D' will be A'B' × B'C' = 9 × 6 = 54 square feet. (Answer)
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Answer:
18 kilograms of 30% copper alloy is mixed with 72 kilograms of 55% copper alloy to makes 90 kg of a 50% copper alloy .
Step-by-step explanation:
Let us assume that the kilogram of 30% copper used to make alloy be x .
Let us assume that the kilogram of 55% copper used to make alloy be y .
As given
A metalworker has a metal alloy that is 30% copper and another alloy that is 55% copper.
The metalworker combine to create 90 kg of a 50% copper alloy .
Equation becomes
x + y = 90
30% is written in the decimal form .
= 0.30
55% is written in the decimal form .
= 0.55
50% is written in the decimal form .
= 0.50
Equation becomes
Concentration of 30% copper alloy × Number of kilograms of 30% copper alloy used + Concentration of 55% copper alloy × Number of kilograms of 55% copper alloy used = Concentration of 50% copper alloy × Number of kilograms of 50% copper alloy .
0.30x + 0.55y = 0.50 × 90
Simplify the above equation
30x + 55y = 4500
Two equation becomes
x + y = 90
30x + 55y = 4500
Multiply x + y = 90 by 30 and subtracted form 30x + 55y = 4500 .
30x - 30x + 55y - 30y = 4500 - 2700
25y = 1800
y = 72 kilograms
Putting the value of y in the equation .
x + 72 = 90
x = 90 - 72
x = 18 kilograms
Therefore 18 kilograms of 30% copper alloy is mixed with 72 kilograms of 55% copper alloy to makes 90 kg of a 50% copper alloy .
Answer:
x = 14.4
Step-by-step explanation:
Similar means that the figures are proportional to each other. Because of this, we can form a problem. (the short side lengths) =
(the long side lengths). Now we can solve this by cross-multiplying. If we multiply 9 · 8 we get 72, and 5 · x is 5x. 72 = 5x. Now divide both sides by 5. 72 ÷ 5 = 14.4. Therefore, x should be equal to 14.4. Does this make sense?