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7nadin3 [17]
3 years ago
12

Both triangles are similar. The area of the smaller triangle is about 270 ft^2. What is the best approximation for the larger tr

iangle?
Mathematics
1 answer:
Ugo [173]3 years ago
4 0
Ratio of the sizes of the smaller triangle to the sizes of the bigger triangle is 15 : 35 = 3 : 7 = 1 : 7/3

Area of triangle = 1/2bh
Ratio of the area of the smaller triangle to the area of the bigger trfiangle is 1/2bh : 1/2(7/3b)(7/3h)
1/2bh : 49/9(1/2bh)
270ft^2 : 49/9(270ft^2)

The best approximation of the area of the larger triangle is 1,470 ft^2
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Which is the value of the expression (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed?
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Answer:

The value to the given expression is 8

Therefore \left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=8

Step-by-step explanation:

Given expression is (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed

Given expression can be written as below

\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3

To find the value of the given expression:

\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=\frac{((10^4)(5^2))^3}{((10^3)(5^3))^3}

( By using the property ((\frac{a}{b})^m=\frac{a^m}{b^m} )

=\frac{(10^4)^3(5^2)^3}{(10^3)^3(5^3)^3}

( By using the property (ab)^m=a^mb^m )

=\frac{(10^{12})(5^6)}{(10^9)(5^9)}

( By using the property (a^m)^n=a^{mn} )

=(10^{12})(5^6)(10^{-9})(5^{-9})

( By using the property \frac{1}{a^m}=a^{-m} )

=(10^{12-9})(5^{6-9}) (By using the property a^m.b^n=a^{m+n} )

=(10^3)(5^{-3})

=\frac{10^3}{5^3} ( By using the property a^{-m}=\frac{1}{a^m} )

=\frac{1000}{125}

=8

Therefore \left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=8

Therefore the value to the given expression is 8

3 0
3 years ago
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Area of this circular plate=π(5.5 in)²=30.25π in²=30.25 * 3.141592... in²≈
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