All categories

3 years ago

What are the roots of this function? f(x) = x2 – 8x + 12

Mathematics

1 answer:

pishuonlain [190]3 years ago

3 0

Answer:

Step-by-step explanation:

We can find the roots of this function by factoring the trinomial and setting each factor equal to 0 to solve for x.

Trinomials are three term algebraic expressions typically featuring variables to exponent powers. To break these trinomials down we factor them using the diamond method or GCF. The diamond method states that for a trinomial $ax^2+bx+c$ multiply a*c then find two numbers which multiply to this number and add to b. When you find those numbers, write them as $(x-/+ number)(x-/+number)$ .

$x^2-8x+12$

a=1, c=12

ac=12 and add to b=-8 which are -2 and -6

So (x-2)(x-6) are the factors. We set each equal to 0 and solve for x.

(x-2)=0

x=2

(x-6)=0

x=6

{2,6} are the roots of the function.

You might be interested in

Help!!!!! What’s the answer

Olegator [25]

D because is the equal to the other side but added allá together

5 0

3 years ago

What’s 20 divided by 20 im tired

MaRussiya [10]

Answer:

The answer to 20 ÷ 20 is 1

7 0

3 years ago

Read 2 more answers

Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and

Brums [2.3K]

Answer:

$t=\frac{51.6-48}{\frac{1.1}{\sqrt{10}}}=10.349$

$p_v =P(t_9>10.349)=1.34x10^{-6}$

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=51.6$ represent the sample mean

$s=1.1$ represent the standard deviation for the sample

$n=10$ sample size

$\mu_o =48$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean score is higher than 48, the system of hypothesis would be:

Null hypothesis: $\mu \geq 48$

Alternative hypothesis: $\mu > 48$

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{51.6-48}{\frac{1.1}{\sqrt{10}}}=10.349$

Calculate the P-value

First we find the degrees of freedom:

$df=n-1=10-1=9$