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9966 [12]
3 years ago
9

Coefficient of x^2 in expansion of the binomial theorem (2x-1)^4 show your work

Mathematics
1 answer:
tekilochka [14]3 years ago
4 0

Answer:

24

Step-by-step explanation:

If you use Pascal's triangle, which I did, you will look at the 5th row of the triangle which contains the numbers 1, 4, 6, 4, 1

If we expand using a = 2x and b = -1, then the expansion looks like this:

1(2x)^4(-1)^0+4(2x)^3(-1)^1+6(2x)^2(-1)^2+4(2x)^1(-1)^3+1(2x)^0(-1)^4

If you simplify all that down by multiplying, you'll get

16x^4-32x^3+24x^2-8x+1

If you don't know how to use Pascal's triangle, you need to learn.  It's so very cool!

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The average income, I, in dollars, of a lawyer with an age of x years is modeled with the following function: I = -425x^2 + 45,5
lord [1]

We are given

The average income, I, in dollars is

I=-425x^2+45500x-650000

(a)

now, we are given

average income is $275000

so, I=275000

now, we can set them equal

and then we can solve for x

275000=-425x^2+45500x-650000

-425x^2+45500x-925000=0

we will have to use quadratic formula

x=\frac{-45500+\sqrt{45500^2-4\left(-425\right)\left(-925000\right)}}{2\left(-425\right)}:\quad \frac{-\sqrt{45500^2-1572500000}+45500}{850}

x=\frac{-45500-\sqrt{45500^2-4\left(-425\right)\left(-925000\right)}}{2\left(-425\right)}:\quad \frac{\sqrt{45500^2-1572500000}+45500}{850}

we get

x=27.28199

x=79.776

we need to find youngest age

It means that we need to choose smallest value

so,

x=27............Answer

(b)

we are given

x=40

so, we can plug it and find I

I=-425(40)^2+45500(40)-650000

I=490000..............Answer

6 0
3 years ago
Mr. Sarpy went to shoot some hoops on the basketball court. For every shot that he made within the three-point line he earned 2
Lostsunrise [7]

Answer:

x + y = 50 (1) and 2x + 3y = 115 (2); x = 35, y = 15

Step-by-step explanation:

Since x represents the number of 2 point shots and y represents the number of 3 point shots. If the total number of shots is 50, then x + y = 50 (1)

Also, the total 2 point shots is number of 2 point shots × points per shot = 2x and the total 3 point shots is number of 3 point shots × points per shot =  3y. Since the total number of points is 115, then

2x + 3y = 115 (2)

So, the system of equations are

x + y = 50 (1) and 2x + 3y = 115 (2)

We can solve for x and y by substituting x = 50 - y into (2)

So, 2(50 - y) + 3y = 115

100 - 2y + 3y = 115

100 + y = 115

y = 115 - 100

y = 15

So, x = 50 - y

= 50 - 15

= 35

6 0
3 years ago
How many different digits are needed for the base 6 system?​
lorasvet [3.4K]

Answer:

0, 1, 2, 3, 4 and 5

Step-by-step explanation:

In a nutshell, base six  is a number system that employs the numbers 0 through 5 instead of 0 through 9 in each digit. As a result, a number that would be stated as 6 in base ten is written as 10. We count one, two, three, four, five, ten, eleven, twelve, thirteen, fourteen, fifteen, twenty, and so on.

6 0
3 years ago
Find the first five terms of the sequence described.
kipiarov [429]

Answer:

I dont think i dont know this but its 10?

5 0
2 years ago
Help help help math math
kiruha [24]

Answer:

add x to both sides. once you do this, you will get x+y=15

3 0
2 years ago
Read 2 more answers
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