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Paraphin [41]
3 years ago
8

If a polynomial function f(x) has roots 3+ V5 and -6, what must be a factor of f(x)?

Mathematics
1 answer:
Mkey [24]3 years ago
5 0

Answer:

Step-by-step explanation:

Radicals and imaginary numbers ALWAYS come in pairs when it comes to factors of polynomials. This is the called the conjugate theorem. If we are given a solution/root/zero that is

x = 3 + √5, then its conjugate is x = 3 - √5. Going backwards from the solution to the factor, we utilize the Zero Product Property and get

(x - (3 - √5)) which simplifies to (x - 3 + √5). if you are looking for the conjugate of the given zero, the choice you want is the second one down.

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Toothbrushes are $4.00 each. there is a 10% discount but also 6% sales tax. What is the new price?
Katena32 [7]
Multiply 4 by 10%.
10% ⇒ 0.1

4 × 0.1 = 0.4
Subtract 0.4 from 4.
4 - 0.4 = 3.6 (price with discount)

Multiply 3.6 by 6%.
6% ⇒ 0.06
3.6 × 0.06 = 0.216

Add 0.216 to 3.6.
0.216 + 3.6 = 3.816

Round 3.816 to the hundredths.
3.816 ⇒ 3.82 (price with tax)

The new price of toothbrushes is $3.82.
6 0
3 years ago
Juan will put fencing around the outside of the enclosure. How much fencing does he need for the enclosure?
adell [148]
If Juan intends to put fencing around the enclosure, that means that we are looking at the perimeter of the image (the outside). We can count the amount of lines between the dots to determine how much fencing he will need. After counting the perimeter of this figure, we see that the total is 22. We do not know what the units are, so for now we can just say that he will need 22 units of fencing to fully enclose this shape.
3 0
3 years ago
What is the equivilent of +367 on a numberline?
Mama L [17]

Answer:

367

Step-by-step explanation:

367 because it is positive

8 0
3 years ago
Sample methods that embody random sampling are often termed probability sampling methods. OTrue False
stepan [7]

Answer:

The answer is true.

Step-by-step explanation:

Sample methods that embody random sampling are often termed probability sampling methods.

Yes this is a true statement.

Random sampling means picking up the samples randomly from a whole population with each sample having an equal chance of getting selected.

For example- selecting randomly 10 students from each class of a school, to survey for the food quality in school's cafeteria.

And this is a type of probability sampling methods. Other types are stratified sampling, cluster sampling etc.

3 0
3 years ago
Determine all values of h and k for which the system S 1 -3x - 3y = h -4x + ky = 10 has no solution. k= ht
Lana71 [14]

Answer:

h\neq 7.5

k = -4

Step-by-step explanation:

Given system of equations are,

-3x-3y = h

-4x + ky = 10

We have to find the values of h and k such that system of equations has no solution.

The standard form of system of equation in two variables can be given by,

a_1x+b_1y+c_1=0

a_2x+b_2y+c_2=0

And condition for the system of equations has no solution is given by,

\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}

So, by comparing the standard form of equations with given equations, the condition such that system has no solution can be written as,

\dfrac{-3}{-4}=\dfrac{-3}{k}\neq \dfrac{h}{10}

=>\dfrac{-3}{-4}=\dfrac{-3}{k}

=> k = -4

and \dfrac{-3}{-4}\neq \dfrac{h}{10}

    =>\ \dfrac{-3\times 10}{-4}\neq h

    =>\ h\neq \dfrac{30}{4}

    =>\ h\neq 7.5

So, the value of h and k for above given system of equations is

h\neq 7.5 and k = -4.

7 0
3 years ago
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