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3 years ago

Need help finding the volumes of this pyramid please

Mathematics

1 answer:

o-na [289]3 years ago

7 0

Volume of pyramid = 1/3*AH, where A is the area of the base and H is the height

Since we are given three sides of the triangle (the base of the pyramid), we should use Heron formula: Area of a triangle = sq.root of(s(s - a)(s - b)(s - c)), where s is the semi-perimeter (ie. the perimeter divided by 2) and a, b and c are side lengths.
s = (5 + 12 + 13)/2
= 30/2 = 15
A = sq,root of(15(15 - 5)(15 - 12)(15 - 13))
= sq.root of (15*10*3*2)
= sq.root of 900
= 30 m^2

Volume = 1/3*AH
= 1/3*30*9
= 90 m^3

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Which expression is equivalent to...

torisob [31]

Answer:

$x^{\frac{2}{7} } y^{-\frac{3}{5} } \\$ i.e answer A.

Step-by-step explanation:

This question involves knowing the following power/exponent rule:

$\sqrt[n]{x^m} = x^\frac{m}{n} \\\\so \sqrt[7]{x^2} = x^\frac{2}{7} \\\\and \\\\ \sqrt[5]{y^3} = y^\frac{3}{5} \\$

Next, when a power is on the bottom of a fraction, if we want to move it to the top, this makes the power become negative.

so the y-term, when moved to the top of the fraction, becomes:

$y^{-\frac{3}{5} } \\$

So the answer is: $x^{\frac{2}{7} } y^{-\frac{3}{5} } \\$

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3 years ago

When Mischa filled her car's gas tank before beginning a trip, the car's odometer read 44,587 miles. When she stopped for gas ne

pantera1 [17]

Answer:

18.11 miles per gallon

Step-by-step explanation:

Get the miles traveled from the trip odometer, or subtract the original odometer reading from the new one.

Divide the miles traveled by the amount of gallons it took to refill the tank. The result will be your car’s average miles per gallon yield for that driving period.

44,895-44,587 = 308 miles

308/17 = 18.11

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3 years ago

James earns $2.20 less than twice gregs hourly wage. If james earns $16.50 per

Cerrena [4.2K]

Greg’s hourly wage is $9.35 per hour

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3 years ago

Read 2 more answers

Expand and combine like terms (3z^5 +7z^2)^2

AVprozaik [17]

Answer:

$\displaystyle{(3z^5+7z^2)^2 = 9z^{10}+42z^7 + 49z^4 }$

Step-by-step explanation:

Since it's a perfect square, we can simply use the formula:

$\displaystyle{(ax+by)^2 = a^2x^2+2abxy+b^2y^2}$

Given the perfect square expression $\displaystyle{(3z^5+7z^2)^2}$ . Apply perfect square formula:

$\displaystyle{(3z^5+7z^2)^2 = 3^2(z^5)^2+2(3)(7)(z^5)(z^2) + 7^2(z^2)^2 }$

Knowing laws of exponent is mandatory when it comes to algebra. Recall that:

$\displaystyle{(a^m)^n = a^{mn}}\\\\\displaystyle{a^m \cdot a^n = a^{m+n}}$

Apply laws of exponent to simplify the terms or expression:

$\displaystyle{(3z^5+7z^2)^2 = 9z^{10}+42z^7 + 49z^4 }$

Since there are no like-terms to do operation with (these terms have different degrees so they are not considered to be like-terms.) Therefore, the final answer is:

$\displaystyle{(3z^5+7z^2)^2 = 9z^{10}+42z^7 + 49z^4 }$

8 0

1 year ago

If g(x)= x=2 and h(x) = 4 - X, what is the value of (gºh)(-3)?

navik [9.2K]

The required value of (g°h)(-3) is 5.

Step-by-step explanation:

Given,

g(x)= x-2 and h(x) = 4 - x

To find (g°h)(-3)

Now,

(g°h)(x) = g(h(x))

= g(4-x)

= (4-x)-2 = 2-x

So,

(g°h)(-3) = 2-(-3) = 5 [ putting x=-3]

8 0

3 years ago