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Ray Of Light [21]
3 years ago
14

The coefficient of xkyn-k in the expansion of (x+y)n equals (n/k) true or false

Mathematics
2 answers:
dexar [7]3 years ago
7 0

Answer:

The correct option is 1. The given statement is true.

Step-by-step explanation:

The binomial expansion is defined as

(x+y)^n=^nC_0x^{n-0}y^{1}+^nC_{1}x^{n-1}y^{2}+....+^nC_{n-1}x^{1}y^{n-1}+^nC_nx^{0}y^{n}

The rth term in a binomial expansion is defined as

\text{rth term}=^nC_rx^{n-r}y^{r}

Let the coefficient of x^ky^{n-k} be A. The power of x is k and the power of y is n-k. It means

k=n-r

n-k=r

The coefficient of x^ky^{n-k} is

^nC_{n-k}=\binom{n}{n-k}

Using the property of combination,

^nC_{n-r}=^nC_r

^nC_{n-k}=^nC_{k}=\binom{n}{k}

The coefficient of x^ky^{n-k} is \binom{n}{k}. Therefore the given statement is true.

RUDIKE [14]3 years ago
6 0
The answer to your question is
TRUE -Apex
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According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots?
HACTEHA [7]

Answer:

Option (1)

Step-by-step explanation:

Fundamental theorem of Algebra states degree of the polynomial defines the number of roots of the polynomial.

8 roots means degree of the polynomial = 8

Option (1)

f(x) = (3x² - 4x - 5)(2x⁶- 5)

When we multiply (3x²) and (2x⁶),

(3x²)(2x⁶) = 6x⁸

Therefore, degree of the polynomial = 8

And number of roots = 8

Option (2)

f(x) = (3x⁴ + 2x)⁴

By solving the expression,

Leading term of the polynomial = (3x⁴)⁴

                                                     = 81x¹⁶

Therefore, degree of the polynomial = 16

And number of roots = 16

Option (3)

f(x) = (4x² - 7)³

Leading term of the polynomial = (4x²)³

                                                    = 64x⁶

Degree of the polynomial = 6

Number of roots = 6

Option (4)

f(x) = (6x⁸ - 4x⁵ - 1)(3x² - 4)

By simplifying the expression,

Leading term of the polynomial = (6x⁸)(3x²)

                                                     = 18x¹⁰

Degree of the polynomial = 10

Therefore, number of roots = 10

3 0
3 years ago
HURRY PLEASE I WILL GIVE BRAINLIEST AND LOTS OF POINTS
Mrac [35]

Answer:

m =  \dfrac{3}{4}

Step-by-step explanation:

We would like to find the <u>s</u><u>l</u><u>o</u><u>p</u><u>e</u><u> </u> of the line of the given equation .

\longrightarrow y =\dfrac{3}{4}x -1

We know that <u>s</u><u>l</u><u>o</u><u>p</u><u>e</u><u> </u><u>i</u><u>n</u><u>t</u><u>e</u><u>r</u><u>c</u><u>e</u><u>p</u><u>t</u><u> </u><u>f</u><u>o</u><u>r</u><u>m</u><u> </u> of the line is given by ,

\longrightarrow y = mx + c

where ,

  • m is the slope
  • c is y intercept

Now we can compare the given equation with the slope intercept form to find the slope . You will see that 3/4 is present at the place of m .Therefore ,

\longrightarrow \underline{\underline{m=\dfrac{3}{4}}}

Hence <u>o</u><u>p</u><u>t</u><u>i</u><u>o</u><u>n</u><u> </u><u>C</u><u> </u> is correct choice .

4 0
2 years ago
At basketball practice, charlie makes 52 baskets out of 80 shots. What percentage of baskets did he make?
Mazyrski [523]
Charlie made 65% of the baskets at practice
8 0
2 years ago
Read 2 more answers
A biologist is comparing the growth of a population of flies per week to the number of flies a bullfrog will consume per week. S
Lubov Fominskaja [6]

Realize that since 2x and 3x - 1 are equal to each other, they are also equal to y. This means that we can craft two equations, y = 2x and y = 3x - 1.


When you want to solve a systems of equations via a graph, you need to plot both equations on a graph and determine the x- and y-value of where the lines intersect. In this case, we would plot both y = 2x and y = 3x - 1. These lines intersect at the point (1, 2).


Since we are trying to find the day the bullfrog will be able to eat the entire population, or x, we are going to use the x-value of our point as our answer. Thus, our answer is 1 day.

3 0
3 years ago
A home-made baseball diamond is in the shape of a square. The distance from base to base is 80 feet because of space constraints
Lelu [443]
Call x the distance from home plate to second base.

There is a right triangle formed by homeplate, first base and second base. The sides of this triangle are 80 feet and 80 feet. The hypothenuse meets Pythagoras theorem:

x^2 = 80^2 + 80^2 = 2(80)^2
x = 80√2

Then the answer is the option D.
3 0
3 years ago
Read 2 more answers
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