All categories

2 years ago

Simplify. x-2/(x^2+4x-12)

Mathematics

1 answer:

Serhud [2]2 years ago

6 0

In order to solve this you need to factor the denominator.
x^2 +4x - 12
I see that 12 is a product of 6 and 2 and 4 and 3 and 1 and 12.
I pick the two products that, when added together, give me the 4x term.
Here it's 6 and two I just need to make one of them a negative.
now put them in this form:
(x + 6)(x-2)
In the fraction I see that there is an x-2 in the numerator. This can cancel out with the x-2 in the denominator. Now you have 1/x-6 but remember you can never have a zero in the denominator so x can't equal -6.
And you're done!

You might be interested in

Nora invested $1,500 in a bond at a simple interest rate of 3%. How much will the bond be worth in total after 10 years?

attashe74 [19]

<h2>The bond will be worth in total after 10 years is =$1,950</h2>

Step-by-step explanation:

Given,

Nora invested $1,500 in at a bond simple interest rate of 3%

here P= $1500 R= 3% and t = 10year

Simple interest(I) = $\frac{P\times R \times t }{100}$

=$ $\frac{1500\times 3 \times 10}{100}$

=$ 450

<h3>The bond will be worth in total after 10 years is = $1,500+ $450</h3><h3> =$1,950</h3>

8 0

2 years ago

4. There are seven days in a week. How many days are there in 16 weeks?

lesya692 [45]

Answer:

There are 112 days in 16 weeks

8 0

2 years ago

All vectors are in Rn. Check the true statements below:

Oduvanchick [21]

Answer:

A), B) and D) are true

Step-by-step explanation:

A) We can prove it as follows:

$Proy_{cv}y=\frac{(y\cdot cv)}{||cv||^2}cv=\frac{c(y\cdot v)}{c^2||v||^2}cv=\frac{(y\cdot v)}{||v||^2}v=Proy_{v}y$

B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that $||Ax||=\sqrt{(A_1 x)^2+\cdots (A_n x)^2}$ . Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then $||Ax||=\sqrt{(x_1)^2+\cdots (x_n)^2}=||x||$ .

C) Consider $S=\{(0,2),(2,0)\}\subseteq \mathbb{R}^2$ . This set is orthogonal because $(0,2)\cdot(2,0)=0(2)+2(0)=0$ , but S is not orthonormal because the norm of (0,2) is 2≠1.

D) Let A be an orthogonal matrix in $\mathbb{R}^n$ . Then the columns of A form an orthonormal set. We have that $A^{-1}=A^t$ . To see this, note than the component $b_{ij}$ of the product $A^t A$ is the dot product of the i-th row of $A^t$ and the jth row of $A$ . But the i-th row of $A^t$ is equal to the i-th column of $A$ . If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then $A^t A=I$

E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.

In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set $\{u_1,u_2\cdots u_p\}$ and suppose that there are coefficients a_i such that $a_1u_1+a_2u_2\cdots a_nu_n=0$ . For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then $a_i||u_i||=0$ then $a_i=0$ .

5 0

2 years ago

What is the rate of change for y=2x+10

Tanzania [10]

Answer:

its 2

The general rate of change can be found by using the difference quotient formula. To find the average rate of change over an interval, enter a function with an interval

8 0

2 years ago

In order to avoid staying after work, a quality control analyst inspects the first 100 items produced that day. Which sampling m

Elanso [62]

The sampling method used in the situation of the quality control analyst in his attempt to avoid staying after work would be a non-probability sampling method. He used a nonprobability sampling called convenience sampling wherein the person gets a sample for easy and convenient results.

7 0

2 years ago