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julsineya [31]
1 year ago
13

The number of ducks to geese in Miller's Pond last year was 2:3. This year the ratio of ducks to geese is 5:9. The number of gee

se stayed the same. Did the number of ducks increase or decrease? Explain
Mathematics
1 answer:
My name is Ann [436]1 year ago
4 0
No decreased-

Set up equaivalent ratioo. It started out 2 duck to every 3 geese, continue the pattern and see for a change

ducks   2    4   6
geese   3   6   9

but now its 5 ; 9 instead of 6 to 9, therefore the number of ducks decreased
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Write the equation of the line that passes through the points (7, —4) and (—1 , 3) , first in point -slope form , and then slope
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Answer:

The slope of the line is -7/8

The point slope-form is y+4=(-7/8)(x-7)

The slope-intercept form is y=(-7/8)x+(17/8)

Step-by-step explanation:

You have to find the slope first using m=y2-y1 divided by x2-x1. After you found the slope of the line, you use one of the points to plug it into the point-slope form which is y-y1=m(x-x1). After you have done that, you would have convert this equation into slope-intercept form which is y=mx + b. In order to convert it, you have to multiply m with x and x1. Then you would have to get rid of y1 by doing the opposite of what y1 is. Finally, you would take the opposite of y1 and add it to the other side of the equation.

Really hope this helps! :)

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Polygon ABCD is plotted on a coordinate plane.If the polygon translates 3 units to the left and 1 unit down,the length of diagon
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What is the binomial expansion of (x + 2)4? x4 + 4x3 + 6x2 + 4x + 1 8x3 + 24x2 + 32x x4 + 8x3 + 24x2 + 32x + 16 2x4 + 8x3 + 12x2
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<u>Answer-</u>

\boxed{\boxed{(x+2)^4=x^4+8x^3+24x^2+32x+16}}

<u>Solution-</u>

Given expression is (x+2)^4

Applying Binomial Theorem

\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i

Here,

a = x, b = 2 and n = 4

So,

\left(x+2\right)^4=\sum _{i=0}^4\binom{4}{i}x^{\left(4-i\right)}\cdot \:2^i

Expanding the summation

=\dfrac{4!}{0!\left(4-0\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(4-1\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(4-2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(4-3\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(4-4\right)!}x^0\cdot \:2^4

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=1\cdot x^4\cdot \:1+4\cdot x^3\cdot \:2+6x^2\cdot \:4+4\cdot x\cdot \:8+1\cdot 1\cdot \:16

=x^4+8x^3+24x^2+32x+16

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2 years ago
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