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3 years ago

Which of the binomials below is a factor of this trinomial? x2 - x-12 A) x+6 B) x+4 C) x-4 D) x-6

Mathematics

1 answer:

andre [41]3 years ago

8 0

Start by setting up your two sets of parenthses.

X² breaks down into x and x.

What we are looking for is factors of the constant term

that add to the coefficient of the middle term.

The question is, what is the coefficient of the middle term

in this problem if there is nothing written in front of the x.

Well if there is nothing written there,

the coefficient is understood to be 1.

So what we are looking for are factors of -12 that add to -1.

<em><u>Factors of -12</u></em>

+12 · -1

-12 · +1

+6 · -2

-6 · +2

+4 · -3

-4 · + 3

We can see that -4 and +3 add to -1.

So they go in the second position of each binomial.

This gives us (x - 4)(x + 3) as our answer.

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Students in a zoology class took a final exam. They took equivalent forms of the exam at monthly intervals thereafter. After t

juin [17]

Answer:

a. 73; b. 48.9; c. 2; d. 33.8; e. 73

Step-by-step explanation:

Assume the function was

S(t)= 73 - 15 ln(t + 1), t ≥ 0

a. Average score at t = 0

S(0) = 73 - 15 ln(0 + 1) = 73 - 15 ln(1) = 73 - 15(0) =73 - 0 = 73

b. Average score at t = 4

S(4) = 73 - 15 ln(4 + 1) = 73 - 15 ln(5) = 73 - 15(1.61) =73 - 24.14 = 48.9

c. Average score at t =24

S(24) = 73 - 15 ln(24 + 1) = 73 - 15 ln(25) = 73 - 15(3.22) =73 - 48.28 = 24.7

d. Percent of answers retained

At t = 0. the students retained 73 % of the answers.

At t = 24, they retained 24.7 % of the answers.

$\text{Percent retention} = \dfrac{\text{24.7}}{\text{73}} \times 100 \, \% = \text{33.8 \%}\\\\\text{The students retained $\large \boxed{\mathbf{33.8 \, \%}}$ of their original knowledge after two years.}$

e. Maximum of the function

The maximum of the function is at t= 0.

Max = 73 %

The graph below shows your knowledge decay curve. Knowledge decays rapidly at first but slows as time goes on.

6 0

3 years ago

What is the answer to this?

rusak2 [61]

Answer:

y = 28x

Step-by-step explanation:

To find the answer, we need to divide the number of bushels by the number of acres. If the quotient is the same for all three divisions, then the quotient is how many times x is multiplied to get y.

140 / 5 = 28

224 / 8 = 28

420 / 15 = 28

Therefore, y = 28x is our answer.

6 0

3 years ago

Can you tell me if this equation I made for a project is correct?

Schach [20]

Yes, your answer is correct

5 0

3 years ago

Read 2 more answers

Suppose that, in addition to edge capacities, a flow network has vertex capacities. That is each vertex has a limit l./ on how m

storchak [24]

Answer:

See explanation and answer below.

Step-by-step explanation:

The tranformation

For this case we need to construct G' dividing making a division for each vertex v of G into 3 edges that on this case are $v_1, v_2 and l(v)$ .

We assume that the edges from the begin are the incoming edges of $v_1$ and all the outgoing edges from v are outgoing edges from $v_2$

We need to construct $G' = (V', E')$ with capacity function a' and we need to satisfy the follwoing:

For every $v \in V$ we create 2 vertices $v_1, v_2 \in V'$

Now we can add a new edge asscoiated to $v_1, v_2 \in E'$ with the condition $a' (v_1,v_2) = l(v)$

Now for each edges $(u,v)\in E$ we can create the following edge $( u_r, v_1) \in E'$ and the capacity is given by: $a' (u_r, v_1) = a (u,v)$

And for this case we can see this:

$|V'| = 2|V|, |E'|= |E| +|V|$

Now we assume that x is the flow who belongs to G respect vertex capabilities. We can create a flow function x' who belongs to G' with the following steps:

For every edge $(u,v) \in G$ we can assume that $x' (u_r ,v_1) = x(u,v)$

Then for each vertex $u \in V -t$ and we can define $x\(u_1,u_r) = \sum_{v \in V} x(u,v)$ and $x' (t_1,t_2) = \sum_{v \in V} x(v,t)$

And after see that the capacity constraint on this case would be satisfied since for every edge in G' on the form $(u_r, u_1)$ we have a corresponding edge in G because: