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2 years ago

How many ways can nick choose 5 pizza toppings from a menu of 11 toppings

Mathematics

2 answers:

Stells [14]2 years ago

6 0

Answer:

462

Step-by-step explanation:

Using choosing, we can choose 5 pizza topping out of 11. 11!/5!/(11-5)! = 462.

Can I have Brainiest if I'm correct?

Maksim231197 [3]2 years ago

4 0

462 will be you answer

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Use Synthetic substitution to find f(3) and f(-4) for f(x)=x^4-8x-11

brilliants [131]

Answer:

46 and 277

Step-by-step explanation:

Given

f(x) = $x^{4}$ - 8x - 11 ← substitute x = 3, x = - 4 into f(x)

f(3) = $3^{4}$ - 8(3) - 11 = 81 - 24 - 11 = 81 - 35 = 46

f(- 4) = $(-4)^{4}$ - 8(- 4) - 11 = 256 + 32 - 11 = 288 - 11 = 277

4 0

2 years ago

1.What is the solution to the system of equations?

Ludmilka [50]

1. x=4, y=0
3. x=2.6666, y=0.3333

8 0

2 years ago

Given a leading coefficient of 8, polynomial roots of 1 & 2, and the known point on the graph (4,5). Write an equation that

m_a_m_a [10]

Given:

The leading coefficient of a polynomial is 8.

Polynomial roots are 1 and 2.

The graph passes through the point (4,5).

To find:

The 3rd root and the equation of the polynomial.

Solution:

The factor form of a polynomial is:

$y=a(x-c_1)(x-c_2)...(x-c_n)$

Where, a is a constant and $c_1,c_2,...,c_n$ are the roots of the polynomial.

Polynomial roots are 1 and 2. So, $(x-1)$ and $(x-2)$ are the factors of the polynomial.

Let the third root of the polynomial by c, then $(x-c)$ is a factor of the polynomial.

The leading coefficient of a polynomial is 8. So, a=8 and the equation of the polynomial is:

$y=8(x-1)(x-2)(x-c)$

The graph passes through the point (4,5). Putting $x=4,y=5$ , we get

$5=8(4-1)(4-2)(4-c)$

$5=8(3)(2)(4-c)$

$5=48(4-c)$

Divide both sides by 48.

$\dfrac{5}{48}=4-c$

$c=4-\dfrac{5}{48}$

$c=\dfrac{192-5}{48}$

$c=\dfrac{187}{48}$

Therefore, the 3rd root on the polynomial is $\dfrac{187}{48}$ .

8 0

2 years ago

The first steps in writing f(x) = 3x^2 -24x+10 in vertex form what is the function written in vertex form

Vika [28.1K]

F(x) = 3(x-4)^2-38 because finding the perfect square would get you f(x)+38=3(x^2-8x+16) and then finding the squareroot of that and moving the constant on the left back to the right would leave u with f(x)=3(x-4)^2-38

4 0

3 years ago

Read 2 more answers

(x+12) (3x+2)<br> Find the value of X

KatRina [158]

Step-by-step explanation:

Equation at the end of step 1

(3x2 - 38x) + 24 = 0

STEP2:Trying to factor by splitting the middle term

2.1 Factoring 3x2-38x+24

The first term is, 3x2 its coefficient is 3 .

The middle term is, -38x its coefficient is -38 .

The last term, "the constant", is +24

Step-1 : Multiply the coefficient of the first term by the constant 3 • 24 = 72

Step-2 : Find two factors of 72 whose sum equals the coefficient of the middle term, which is -38 .

-72 + -1 = -73 -36 + -2 = -38 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -36 and -2

3x2 - 36x - 2x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

3x • (x-12)

Add up the last 2 terms, pulling out common factors :

2 • (x-12)

Step-5 : Add up the four terms of step 4 :

(3x-2) • (x-12)

Which is the desired factorization

Equation at the end of step2:

(x - 12) • (3x - 2) = 0

STEP3:Theory - Roots of a product

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

3.2 Solve : x-12 = 0

Add 12 to both sides of the equation :

x = 12

Solving a Single Variable Equation:

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3 years ago

Read 2 more answers