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3 years ago

Expand the following using either the Binomial Theorem You must show

1 answer:

n200080 [17]3 years ago

4 0

<h2><u><em>Answer:</em></u></h2><h2><em>A Pascal triangle is the triangular way of expanding a binomial. So the best way in expanding that function is thru Binomial Theorem and the expanded for of it is 8x^3+48x^2+98x+64 </em></h2><h2><em></em></h2><h2><u><em>Step-by-step explanation:</em></u></h2><h2><em>Before even trying to put this into the binomial form, we must figure out the coefficients. If we go by the Pascal's Triangles way we should end up with: </em></h2><h2><em> </em></h2><h2><em> 1 </em></h2><h2><em> </em></h2><h2><em> 1 1 </em></h2><h2><em> </em></h2><h2><em> 1 2 1 </em></h2><h2><em> </em></h2><h2><em>1 3 3 1 </em></h2><h2><em> </em></h2><h2><em>Going by the last level (which is the third level) we get 3C0:1, 3C1:3, 3C2:3, 3C3:1. </em></h2><h2><em> </em></h2><h2><em>Now with the equation: (a+b)^3 = 3C0a^3 + 3C1a^2 b + 3C2a b^2 + 3C3b^3 we just plug in all the values and simplify </em></h2><h2><em> </em></h2><h2><em>(2x+4)^3 = 2x^3 + 3(2x)^2 (4) + 3(2x) (4)^2 + (4)^3 </em></h2><h2><em> </em></h2><h2><em>(2x+4)^3 = 8x^3 + (3)(4x^2)(4) + (3)(2x)(16) + 64 </em></h2><h2><em> </em></h2><h2><em>Then we finally end with: (2x+4)^3 = 8x^3 48x^2 + 96x +64 </em></h2>

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Veronica drove 294 miles and used 12 gallons of gasoline, how many gallons of gas would it take her to drive 490 miles?

Alekssandra [29.7K]

Answer:

Step-by-step explanation:

u make a proportion and solve for x:

294/12 = 490/x

12 x 490 = 5880

5880/294 = 20

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4 years ago

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Describe a mathematical idea or philosophy that came out of the Vitruvian Man.

iragen [17]

Answer:

provides a procedure to hand-draw a square and a circle of equal area

Step-by-step explanation:

According to Vitruvian Man, an arm span and height have a nearly perfect correspondence in the human body. As a result, the body is placed perfectly inside a square. Buildings and other works of man should also occur depending on these proportions. All of this ties in with the problem of finding a procedure to hand-draw a square and a circle of equal area.

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3 years ago

FACTORISE :4a^2 + a<br> FACTORISE: FOUR A SQUARED PLUS A

Helen [10]

Answer:

First we will select all terms in the expression

Terms=4a²,a

Then factor

Factor=4a²=4,a²

=a=a

Step-by-step explanation:

Pls mark as branliest thanks

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3 years ago

Mina tossed two number cubes labeled 1 to 6.What is the probability that the sum is equal to 5

valentinak56 [21]

Hello there!

Firstly, let's figure out the total number of possible outcomes there are.
6 x 6 = 36

Therefore, the answer would be something out of 36.

The possible our comes that would make the sum of 5 would be:
1+4
2+3
3+2
4+1

So there are 4 possible outcomes that would make the sum of 5.

The answer would be 4/36.
However, you have to simplify the answer.
4/36 = 1/9

Thus, the final answer is 1/9

Hope this helped :D

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4 years ago

Santiago wants the lateral surfaces of the ramp to be painted red. how many squares feet of the ramp will be painted red?

Annette [7]

Answer:

262 square feet

Step-by-step explanation:

The lateral surface is the side surfaces, except top and bottom.

There are 3 lateral surfaces.

The 2 sides are triangles with length 20 and height 8.5

And

The back is a rectangle with length 12 and height 8.5

We sum up all the 3 surface areas, that will give us the answer.

Area of triangle is (0.5) * length * height

So,

Area of 1 triangle = 0.5 * 20 * 8.5 = 80

Area of 2 triangles = 80 * 2 = 160

Area of rectangle = length * height

so,

Area of back rectangle = 12 * 8.5 = 102

Total Lateral Surface Area = 160 + 102 = 262 square feet

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3 years ago