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S_A_V [24]
3 years ago
15

What is the coefficient of x^2 y^3 in the expansion of (2x+y)^5

Mathematics
1 answer:
Anna35 [415]3 years ago
4 0

If it's x²y³ then we know it's the second term of the expansion, that known we can use the combination

C(5, 2) = 5!/(2!.3!) = 10

Then if we had something like

(a + b)^5 our second term would be 10a²b³ but as we can see it's "a²"

And in our case we have 2x as a

So we must do 2² too

2² = 4

10 . 4 = 40

Then our second term of the expansion would be

40x²y³

You might be interested in
11. The rectangle has a width of 8 in, a length of x-5 in, and an area of 16 in). Solve for x.
Angelina_Jolie [31]

Use the area of rectangle formula which is:

\displaystyle \large \tt{A = width \times length}

Given that:

  • area of rectangle = 16
  • width = 8
  • length = x-5

Substitute in the formula:

\displaystyle \large{16 = 8 \times (x - 5)} \\  \displaystyle \large{16 = 8(x - 5)}

Distribute 8 in the expression:

\displaystyle \large{16 = (8 \times x) + (8 \times ( - 5))} \\  \displaystyle \large{16 = 8x - 40}

Move -40 to another side and change from -40 to 40.

\displaystyle \large{16 + 40 = 8x} \\    \displaystyle \large{56= 8x} \\

Then move 8 to divide 56, leaving only x.

\displaystyle \large{ \frac{56}{8} = x} \\    \displaystyle \large{7 = x} \\

Hence, the answer is:

\displaystyle \large \boxed{x = 7} \\

3 0
2 years ago
Triangle TRI has a base of m centimeters and a height of n centimeters. Rectangle REC and a width of m centimeters. Use complete
vichka [17]

Answer:Given a rectangle, the general equation for the perimeter is P=2l+2w and area is A=lw where l is the length and w is the width.

Let x = width and x+10 = length

So the equation to solve becomes 40=2x+2(x+10) so x=5 thus the width is 5m and the length is 15m.

Thus the area is 5⋅15=75m2

Step-by-step explanation:

3 0
2 years ago
Pls help being timed and I don’t understand
shepuryov [24]

Answer:

f ( -2 ) = 30

g ( -2 ) = 3

Step-by-step explanation:

when it says f(x) and then has f(-2) - you fill in all x's in the equation with -2.. like this:

f(x) = -7(-2-2) +2                         g(x) = 2(-2)^2 -5

f(x) = -7(-4) +2                             g(x) = 2(4) -5

f(x) = 28 + 2                                g(x) = 8 - 5

f(x) = 30                                      g(x) = 3

hope this helps!!

6 0
3 years ago
A 5-pound bag of sugar costs $3.90. What is the unit rate?
Dimas [21]
0.78 per pound is unit rate

Since 5lbs is $3.90, 0.78 is the cost of one pound.

3.90 divided by 5 is 0.78
7 0
2 years ago
Please help anyone know how to do this.
dexar [7]

sides of right angle triangle follows Pythagoras theorem

a^2 + b^2 = c^2

where a, b and c are sides of triangle

if you check, option 3 follow this. so answer is option 3

6 0
3 years ago
Read 2 more answers
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