Answer:
x = 5
Step-by-step explanation:
here's the solution in attached image
Answer:
Step-by-step explanation:
<u>We know that</u>
- The diagonals of a rectangle are of equal length
- The diagonals bisect each other
<u>Considering the above we have:</u>
<u>Substitute the given values and solve for x:</u>
- 24x - 8 = 2*(8x + 4)
- 24x - 8 = 16x + 8
- 24x - 16x = 8 + 8
- 8x = 16
- x = 16/2
- x = 2
Answer:
100 cm³
Step-by-step explanation:
If you use 3 for π, then the factors of 3 cancel in the formula for volume, and you have ...
V = r²h
The radius is half the diameter, so is (10 cm)/2 = 5 cm. Filling in the given values, you find the volume to be ...
V = (5 cm)²(4 cm) = 100 cm³
Answer: The length of the rectangle is 35 in.
The width of the rectangle is 28 in.
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Explanation:
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The formula for the area, "A", of a rectangle:
Area (A) = length (L) * width (w) ;
that is: " A = L * w " ;
A = 980 in² (given);
ratio of the length to the width is: " 5 : 4 " (given);
→ Find the length (L) and the width (w).
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→ 980 in² = (5x) * (4x) ;
in which: " 980 in² " is the area of the triangle;
" 5x" = the length (L) of the rectangle, for which we shall solve;
" 4x" = the width (w) of the rectangle, for which we shall solve.
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If we find solve for "x" ; we can solve for "5x" and "4x" (the "length" and the "width", respectively); by plugging in the solved value for "x" ;
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→ 980 in² = (5x) * (4x) ;
↔ (5x) * (4x) = 980 in² ;
→ (5x) * (4x) = (5) * (4) * (x) * (x) = 20 * x² = 20x² ;
→ 20x² = 980 ;
Divide each side by "10" ; by canceling out a "0" on each side of the equation:
→ 2x² = 98 ;
Now, divide each side of the equation by "2" ;
→ 2x² / 2 = 98 / 2 ;
to get:
→ x² = 49 ;
Now, take the "positive square root" of each side of the equation; (since a "length or width" cannot be a "negative value") ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ ⁺√(x²) = √49 ;
to get:
→ x = 7 ;
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Now, we can solve for the "length" and the "width" ;
→ The length is: "5x" ;
5x = 5(7) = " 35 in " ;
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→ The width is: "4x" ;
4x = 4(7) = "28 in."
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Let us check our answer:
→ A = L * w ;
→ 980 in² = ? 35 in. * 28 in. ?? ;
Using a calculator: "35 * 28 = 980" . Yes! ;
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{ Also note: " in * in = in² " ? Yes! } .
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180-24=5
180-56=34
Both are equal
D
