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tester [92]
3 years ago
13

What is the area of the composite shape?

Mathematics
1 answer:
Lelu [443]3 years ago
3 0

Answer:

84 sq. inches

Step-by-step explanation:

When you section off each, you can find the area of each shape and add together to make composite.

Triangle on left is 6 sq. inches

Rectangle on right (5x10) is 50 sq. inches

Rectangle on bottom (7x4) is 28 sq. inches

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What is the factorization of 729^15+1000?
igomit [66]

Answer:

The factorization of 729x^{15} +1000 is (9x^{5} +10)(81x^{10} -90x^{5} +100)

Step-by-step explanation:

This is a case of factorization by <em>sum and difference of cubes</em>, this type of factorization applies only in binomials of the form (a^{3} +b^{3} ) or (a^{3} -b^{3}). It is easy to recognize because the coefficients of the terms are <u><em>perfect cube numbers</em></u> (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).

Let's solve the factorization of 729x^{15} +1000 by using the <em>sum and difference of cubes </em>factorization.

1.) We calculate the cubic root of each term in the equation 729x^{15} +1000, and the exponent of the letter x is divided by 3.

\sqrt[3]{729x^{15}} =9x^{5}

1000=10^{3} then \sqrt[3]{10^{3}} =10

So, we got that

729x^{15} +1000=(9x^{5})^{3} + (10)^{3} which has the form of (a^{3} +b^{3} ) which means is a <em>sum of cubes.</em>

<em>Sum of cubes</em>

(a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})

with a= 9x^{5} y b=10

2.) Solving the sum of cubes.

(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )

(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)

.

8 0
3 years ago
4x+2y+9+3y+12x+20=<br> How do you solve this expression?
balu736 [363]

Answer:

5y+16x+29

Step-by-step explanation:

3 0
3 years ago
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yKpoI14uk [10]

I gather you're supposed to compute the integral of G(x,y,z)=z over a surface S that is the part of the parabolic cylinder y=z^2 with 0\le x\le2 and 0\le z\le\frac{\sqrt{15}}2.

We can parameterize S by

\vec s(x,z)=x\,\vec\imath+z^2\,\vec\jmath+z\,\vec k

with the given constraints on x and z. Take the normal vector to S to be

\vec s_x\times\vec s_z=-\vec\jmath+2z\,\vec k

so that the surface element is

\mathrm dS=\|\vec s_x\times\vec s_z\|\,\mathrm dx\,\mathrm dz=\sqrt{1+4z^2}\,\mathrm dx\,\mathrm dz

Then in the integral, we have

\displaystyle\iint_Sz\,\mathrm dS=\int_0^2\int_0^{\sqrt{15}/2}z\sqrt{1+4z^2}\,\mathrm dz\,\mathrm dx=\boxed{\frac{21}2}

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Simplify these expressions<br> 2a + 5a <br> 12x-3x<br> 3p+2p-p
Novosadov [1.4K]

Step-by-step explanation:

1.solution

=2a+5a

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2.solution

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3.solution

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Hope it helps you.

6 0
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What the fraction of 0.13
Kay [80]

Answer:

13/100 sorry thats the simplest its kind of obvious..

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2 years ago
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