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3 years ago

-3(x + 5) + 8 = 2(x + 4) - 6

Mathematics

2 answers:

Elodia [21]3 years ago

6 0

-3x+(-15)+8=2x+8-6
45x+8=2x+2
not equal

AveGali [126]3 years ago

3 0

-3(x + 5) + 8 = 2(x + 4) - 6
-3x + (-15) + 8 = 2x + 8 - 6
-3x - 23 = 2x + 2
-3x - 2x - 23 = 2x - 2x + 2
-5x - 23 = 2
-5x - 23 + 23 = 2 + 23
-5x = 25
-5x/-5 = 25/-5
x = -5

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Given that the value of b can never be equal to -1, determine if the equations are intersecting, parallel, or coincident.

eimsori [14]

<h3>Answer: A) intersecting</h3>

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Work Shown:

Solve the first equation for y

x+y = ab

y = -x+ab

y = -1x + ab

slope = -1, y intercept = ab

-----------

Solve for y in the second equation

bx - y = a

bx - y - a = 0

bx-a = y

y = bx - a

Slope = b, y intercept = -a

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The first equation has a slope of -1. The second equation has a slope of b.

Since b cannot equal -1, this means the two equations have different slopes. It is impossible for these two lines to be parallel, because parallel lines have equal slopes. The different slope values tell us the lines cross at exactly one point.

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4 years ago

Find the remainder of (x4 – 2) ÷ (x + 1).

prisoha [69]

Please write (x4 – 2) ÷ (x + 1) as (x^4 – 2) ÷ (x + 1).

We can find the remainder using synth. div. as follows:

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-1 / 1 0 0 0 -2
-1 1 -1 1
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1 -1 1 -1 -1

The remainder is -1.

5 0

3 years ago

(1) (10 points) Find the characteristic polynomial of A (2) (5 points) Find all eigenvalues of A. You are allowed to use your ca

Yuri [45]

Answer:

Step-by-step explanation:

Since this question is lacking the matrix A, we will solve the question with the matrix

$\left[\begin{matrix}4 & -2 \\ 1 & 1 \end{matrix}\right]$

so we can illustrate how to solve the problem step by step.

a) The characteristic polynomial is defined by the equation $det(A-\lambdaI)=0$ where I is the identity matrix of appropiate size and lambda is a variable to be solved. In our case,

$\left|\left[\begin{matrix}4-\lamda & -2 \\ 1 & 1-\lambda \end{matrix}\right]\right|= 0 = (4-\lambda)(1-\lambda)+2 = \lambda^2-5\lambda+4+2 = \lambda^2-5\lambda+6$

So the characteristic polynomial is $\lambda^2-5\lambda+6=0$ .

b) The eigenvalues of the matrix are the roots of the characteristic polynomial. Note that

$\lambda^2-5\lambda+6=(\lambda-3)(\lambda-2) =0$

So $\lambda=3, \lambda=2$

c) To find the bases of each eigenspace, we replace the value of lambda and solve the homogeneus system(equalized to zero) of the resultant matrix. We will illustrate the process with one eigen value and the other one is left as an exercise.

If $\lambda=3$ we get the following matrix

$\left[\begin{matrix}1 & -2 \\ 1 & -2 \end{matrix}\right]$ .

Since both rows are equal, we have the equation

$x-2y=0$ . Thus x=2y. In this case, we get to choose y freely, so let's take y=1. Then x=2. So, the eigenvector that is a base for the eigenspace associated to the eigenvalue 3 is the vector (2,1)

For the case $\lambda=2$ , using the same process, we get the vector (1,1).

d) By definition, to diagonalize a matrix A is to find a diagonal matrix D and a matrix P such that $A=PDP^{-1}$ . We can construct matrix D and P by choosing the eigenvalues as the diagonal of matrix D. So, if we pick the eigen value 3 in the first column of D, we must put the correspondent eigenvector (2,1) in the first column of P. In this case, the matrices that we get are

$P=\left[\begin{matrix}2&1 \\ 1 & 1 \end{matrix}\right], D=\left[\begin{matrix}3&0 \\ 0 & 2 \end{matrix}\right]$

This matrices are not unique, since they depend on the order in which we arrange the eigenvalues in the matrix D. Another pair or matrices that diagonalize A is

$P=\left[\begin{matrix}1&2 \\ 1 & 1 \end{matrix}\right], D=\left[\begin{matrix}2&0 \\ 0 & 3 \end{matrix}\right]$

which is obtained by interchanging the eigenvalues on the diagonal and their respective eigenvectors

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3 years ago

Y= 4x + 2 put this on a graph please

nirvana33 [79]

....................................................

6 0

3 years ago

darcy likes to eat peanut butter and raisins on apple slices. on each apple slice she puts 1/16 cup of peanut butter and 8 raisi

netineya [11]

The answer is 7/10.

For one apple slice, Darcy needs 1/16 cup of peanut butter and 8 raisins. She has 2/5 cup of peanut butter. To compare how many butter she has and she needs we will divide 2/5 with 1/1

This means that Darcy needs 5/80 cup of peanut butter and 8 raisins.
If she has 32/80 cup of peanut butter, she will have it only fo 6 or 7 apple slices (32/80 ÷ 5/80 = 6.4) depending how it is rounded. If she prepares 6 apple slices, she will still have a little of peanut butter left (0.4 = 2/5 of cup). So, she will prepare 7 apple slices so the butter will be all gone.

For 7 apple slices, she needs 56 raisins (7 × 8 raisins).
That is 56 raisins out of 80 raisins, so fraction of the 80 raisins did she eat is:
 $\frac{56}{80} = \frac{7}{10}$

4 0

3 years ago