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Alex787 [66]
3 years ago
7

Use the Binomial Theorem Which of the following is equivalent to the expression (m + 3)4​

Mathematics
1 answer:
kondor19780726 [428]3 years ago
3 0

Answer:

Step-by-step explanation:

(x+a)^n=nc0x^n+nc1x^{n-1}a+nc2x^{n-2}a^2+...+ncna^n

(x+3)^4=4c0m^4+4c1m^3(3)+4c2m^2(3)^2+4c3m(3)^3+4c4(3)^4

4c0=1

4c1=4/1=4

4c2=(4×3}/(2×1)=6

4c3=(4×3×2)/(3×2×1)=4

4c4=(4×3×2×1)/(4×3×2×1)=1

(m+3)^4=m^4+4m³(3)+6m²(3)²+4m(3)³+3^4

=m^4+12m³+54m²+108m+81

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(-a,b)

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3 years ago
The sum of 2 numbers is 46. One number is 12 more than the other. What are the numbers?
harkovskaia [24]

Answer:

two numbers are 29 and 17

Step-by-step explanation:

let the number be x

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What equation represents y=2x^2+24x+85 in vertex form
Andrej [43]
Y=a(x-h)^2+k

vertex form is basically completing the square

what you do is
for
y=ax^2+bx+c
1. isolate x terms
y=(ax^2+bx)+c
undistribute a
y=a(x^2+(b/a)x)+c
complete the square by take 1/2 of b/a and squaring it then adding negative and postive inside
y=a(x^2+(b/a)x+(b^2)/(4a^2)-(b^2)/(4a^2))+c
complete square
too messy \
anyway

y=2x^2+24x+85
isolate
y=(2x^2+24x)+85
undistribute
y=2(x^2+12x)+85
1/2 of 12 is 6, 6^2=36
add neagtive and postivie isnde
y=2(x^2+12x+36-36)+85
complete perfect square
y=2((x+6)^2-36)+85
distribute
y=2(x+6)^2-72+85
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vertex form is
y=2(x+6)^2+13
8 0
3 years ago
The height of a trapezoid is 6 in. and it’s area is 72 in to the 2nd power. One base of the trapezoid is 6 inches longer than th
Vitek1552 [10]

Given:

The height of the given trapezoid = 6 in

The area of the trapezoid = 72 in²

Also given, one base of the trapezoid is 6 inches longer than the other base

To find the lengths of the bases.

Formula

The area of the trapezoid is

A=\frac{1}{2} (b_{1} +b_{2} )h

where, h be the height of the trapezoid

b_{1} be the shorter base

b_{2} be the longer base

As per the given problem,

b_{2}=b_{1}  +6

Now,

Putting, A=72, b_{2}=b_{1}+6 and h=6 we get,

\frac{1}{2} (b_{1} +b_{1}+6)(6) = 72

or, b_{1}+b_{1}+6 = \frac{(72)(2)}{6}

or, 2b_{1}+6 = 24

or, 2b_{1}=24-6

or, b_{1}= \frac{18}{2}

or, b_{1}=9

So,

The shorter base is 9 in and the other base is = (6+9) = 15 in

Hence,

One base is 9 inches for one of the bases and 15 inches for the other base.

5 0
3 years ago
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