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EleoNora [17]
3 years ago
12

Multiply 3x^2 (5x^3)

Mathematics
2 answers:
never [62]3 years ago
8 0

Answer:

15x^5

Step-by-step explanation:

Multiply the integers and add the powers .

That’s

3 x 5 x^2+3

15x^5

tresset_1 [31]3 years ago
7 0

Answer:

Step-by-step explanation:

Here's what the multiplication looks like when it's done horizontally:

(4x2 – 4x – 7)(x + 3)

(4x2 – 4x – 7)(x) + (4x2 – 4x – 7)(3)

4x2(x) – 4x(x) – 7(x) + 4x2(3) – 4x(3) – 7(3)

4x3 – 4x2 – 7x + 12x2 – 12x – 21

4x3 – 4x2 + 12x2 – 7x – 12x – 21

4x3 + 8x2 – 19x – 21

That was painful! Now I'll do it vertically:

4x^2 – 4x – 7 is positioned above x + 3; first row: +3 times –7 is –21, carried down below the +3; +3 times –4x is –12x, carried down below the x; +3 times 4x^2 is +12x^2, carried down to the left of the –12x; second row: x times –7 is –7x, carried down below the –12x; x times –4x is –4x^2, carried down below the +12x^2; x times 4x^2 is 4x^3, carried down to the left of the –4x^2; adding down: 4x^3 + (+12x^2) + (–4x^2) + (–12x) + (–7x) + (–21) = 4x^3 + 8x^2 – 19x – 21

That was a lot easier! But, by either method, the answer is the same:

4x3 + 8x2 – 19x – 21

Simplify (x + 2)​(x3 + 3x2 + 4x – 17)

I'm just going to do this one vertically; horizontally is too much trouble.

Note that, since order doesn't matter for multiplication, I can still put the "x + 2" polynomial on the bottom for the vertical multiplication, just as I always put the smaller number on the bottom when I was doing regular vertical multiplication with just plain numbers back in grammar school.

x^3 + 3x^2 + 4x – 17 is positioned above x + 2; first row: +2 times –17 is –34, carried down below the +2; +2 times +4x is +8x, carried down below the x; +2 times 3x^2 is +6x^2, carried down to the left of the 8x; +2 times x^3 is +2x^3, carried down to the left of the +6x^2; second row: x times –17 is –17x, carried down below the +8x; x times +4x is +4x^2, carried down below the +6x^2; x times +3x^2 is +3x^3, carried down below the +2x^3; x times x^3 is x^4, carried down to the left of the +3x^3; adding down: x^4 + (+2x^3) + (3x^3) + (+6x^2) + (+4x^2) + (+8x) + (–17x) + (–34) = x^4 + 5x^3 + 10x^2 – 9x – 34

x4 + 5x3 + 10x2 – 9x – 34

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Answer:

1. The square root of 100

2.c=27.11

d=13.96

e=12.6

<u>Step</u><u> </u><u>by</u><u> </u><u>step</u><u> </u><u>explanation</u><u>:</u><u> </u>

1. 2×50=100 the geometric mean is the square root of 100

2. The diagram is made up of three right angled triangles the big outer one and two triangles inside the big one thus we can use the pythagorean theorem to come up with expressions which will help us in solving the unknown parts as below.

c²=30²-d²

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both the following add up to c² meaning they are equal:

c²=30²-d²

c²=e²+24²

thus

30²-d²=e²+24²

I want to remain with d² only thus;

30²-24²-e²=d²

900-576=324 (squareroot of 324=18) so

d²=18²-e² and d²=e²+6²

both the above add up to d² meaning they are equal thus;

18²-e²=e²+6²

18²-6²=e²+e²

324-36=2e²

318=2e²

159=e²

e=12.61

<em>Thus</em><em> </em><em>d</em><em>²</em><em>=</em><em>e</em><em>²</em><em>+</em><em>6</em><em>²</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>d</em><em>²</em><em>=</em><em>1</em><em>2</em><em>.</em><em>6</em><em>1</em><em>²</em><em>+</em><em>6</em><em>²</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>d</em><em>²</em><em>=</em><em>1</em><em>5</em><em>9</em><em>+</em><em>3</em><em>6</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>d</em><em>²</em><em>=</em><em>1</em><em>9</em><em>5</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>d</em><em>=</em><em>1</em><em>3</em><em>.</em><em>9</em><em>6</em>

<em>c</em><em>²</em><em>=</em><em>e</em><em>²</em><em>+</em><em>2</em><em>4</em><em>²</em>

<em>c</em><em>²</em><em>=</em><em>12.61</em><em>²</em><em>+</em><em>2</em><em>4</em><em>²</em>

<em>c</em><em>²</em><em>=</em><em>1</em><em>5</em><em>9</em><em>+</em><em>5</em><em>7</em><em>6</em>

<em>c</em><em>²</em><em>=</em><em>7</em><em>3</em><em>5</em>

<em>c</em><em>=</em><em>27.11</em>

<em> </em>

<em>I</em><em> </em><em>hope</em><em> </em><em>this</em><em> </em><em>helps</em>

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