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suter [353]
2 years ago
12

The coefficient of x^ky^n-k in the expression of (x+y)^n equals (n-k/k) true or false

Mathematics
1 answer:
gulaghasi [49]2 years ago
3 0

Answer:

False

Step-by-step explanation:

The given statement is:

The coefficient of x^ky^n-k in the expression of (x+y)^n equals (n-k/k)

This is a false statement

Reason:

When we do expansion of (x+y)^n by binomial theorem we get the following solution:

(x+y)^n = nCk x^k y^n-k

This shows that the coefficient of  x^ky^n-k  is nCk which is equivalent to n!/(n-k)! k!

Therefore it is a false statement....

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Nana76 [90]
1.five hundred and three thousand six hundred seventy-two
2. 500000+3+600+70+2
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3 years ago
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If the sales tax rate is 8%, how much tax would Louis pay for a pair of pants for $18 and two shirts for $9.99 each?
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You’d pay $19.44 for the pants! And you’d pay $10.7892 for each shirt!
8 0
2 years ago
Solve x2+4x+6=0 by graphing
klemol [59]

Answer: x = -2±√2 i or no real roots. See the explanation below.

Step-by-step explanation:

If you draw the graph, you will notice that there are no common points or you can say that there are no x-intercepts.

This means that the equation doesn't have any real roots.

If there are 2 common points (2 x-intercepts) then there are 2 real roots (answers.)

If there is only one common point (vertex is on x-axis) then there is only 1 real root.

If there aren't any common points (no x-intercepts) then there are no real roots.

So first, I'm gonna convert the equation into function and convert the standard form to vertex form.

x^2+4x+6=0\\y=x^2+4x+6\\y=(x^2+4x+4)-4+6\\y=(x+2)^2+2

We notice that the vertex is at (-2,2), the graph doesn't have x-intercepts (Graph below)

So the answer is clearly complex.

If you solve this by solving the equation then it'll be.

x^2+4x+6=0\\x= \frac{-b+-\sqrt{b^2-4ac}}{2a} \\x=\frac{-4+-\sqrt{16-24} }{2}\\x=\frac{-4+-\sqrt{-8} }{2}\\\\x=\frac{-4+-2\sqrt{2}i }{2}\\\\x={-2+-1\sqrt{2}i }\\\\

The answer is complex.

However, you can find the value of x easily by graphing. For example.

x^2+6x+5=0

Factor then you get

(x+5)(x+1)=0\\x=-5,-1

Or you can convert it to vertex form then graph.

y=x^2+6x+5

y=(x^2+6x+9)-9+5\\y=(x+3)^2-4

The vertex is at (-3,-4) then graph parabola (x-intercepts determine the roots of quadratic equation. For the graph, parabola intercepts x at (-5,0) and (-1,0) that means both -5 and -1 both are the value of x.

Note:

From the standard form, y=ax^2+bx+c The graph is called Parabola, and it's Quadratic Function.

a is how the graph is, for example. If a>0, the graph is supine parabola and if a<0 then the graph is inverted parabola.

|a| is determined if the graph is wide or narrow, the more the value of a is, the more narrow it will be. The less the value of a is, the more wide it will be.

b is what determined the change of graph (likely vertex). Without b, then it'd be ax^2+k which only move y-axis and not x-axis.

c is what determined the y-intercept and y-axis. If there is no b or the value of b is 0 then the vertex is at (0,c). If there is the value of b then c is only determined the y-intercept.

4 0
3 years ago
Peter shot 40 free throws. He made 80% of his shots. Which fraction is equivalent to
DaniilM [7]

Answer:

B equals 4/5

how I do Not Know

6 0
2 years ago
HELP QUICK!!!!!!!!!!
Mama L [17]

Answer:

Option is right

Step-by-step explanation:

Given that bella want to know what the students at her school think of her show. which is the BEST group to survey to find this information

For getting accurate results she must select a random sample without bias

For this option a will not serve since she selects only students she recognizes.

Option B may not be right, as during show on the face they may not give correct opinion

C is right as a random sample is taken

D is wrong as the first 30 students may not be at random.

So option C is right

8 0
3 years ago
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