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3 years ago

Which number line shows the solution to the inequality? y - 2 < -5

Mathematics

2 answers:

xxMikexx [17]3 years ago

6 0

Answer: is the first option .

Step-by-step explanation:

Tatiana [17]3 years ago

5 0

For this case we have the following inequality:
$y - 2 \ \textless \ -5
$
We will solve the inequality algebraically.
We have then:
We add 2 to both sides of the inequality:
$y - 2 + 2 \ \textless \ -5 + 2
$
Rewriting we have:
$y \ \textless \ - 3
$
Therefore the solution is:
(-inf, -3)
Answer:
(-inf, -3)
See attached image.

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7 0

2 years ago

Let the matrix below act on C². Find the eigenvalues and a basis for each eigenspace in C².

forsale [732]

Hello, let's note A the matrix, we need to find $\lambda$ such that A $\lambda$ = $\lambda$ I, where I is the identity matrix, so the determinant is 0, giving us the characteristic equation as

$\left|\begin{array}{cc}1-\lambda&3\\-3&1-\lambda\end{array}\right|\\\\=(1-\lambda)^2+9\\\\=\lambda^2-2\lambda+10\\\\=0$

We just need to solve this equation using the discriminant.

$\Delta=b^2-4ac=2^2-40=-36=(6i)^2$

And then the eigenvalues are.

$\lambda_1=\dfrac{2-6i}{2}=\boxed{1-3i}\\\\\lambda_2=\boxed{1+3i}$

To find the basis, we have to solve the system of equations.

$A\lambda_1-\lambda_1 I=\left[\begin{array}{cc}3i&3\\-3&3i\end{array}\right] \\\\=3\left[\begin{array}{cc}i&1\\-1&i\end{array}\right] \\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}ai+b=0\\-a+bi=0\end{cases}\\\\\text{(1,-i) is a base of this space, as i-i=0 and -1-}i^2\text{=-1+1=0.}$

$A\lambda_2-\lambda_2 I=\left[\begin{array}{cc}-3i&3\\-3&-3i\end{array}\right] \\\\=3\left[\begin{array}{cc}-i&1\\-1&-i\end{array}\right]\\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}-ai+b=0\\-a-bi=0\end{cases}\\\\\text{(1,i) is a base of this space as -i+i=0 and -1-i*i=0.}$

Thank you

4 0

3 years ago

21 students went on an exchange program to hong kong. There were 11 more women than men. How many woman are there?

daser333 [38]

Answer:

Step-by-step explanation:

11 + 10 = 21

8 0

3 years ago

Evaluate -2x^2-4x+3 when x=-2

Misha Larkins [42]

Answer:

Step-by-step explanation:

A polynomial is sometimes easier to evaluate if it is first written in Horner form:

-2x^2 -4x +3 = (-2x -4)x +3

For x = -2, this is ...

(-2(-2) -4)(-2) +3 = 0(-2) +3 = 3

The value is 3 when x = -2.

8 0

2 years ago

A cylinder has a diameter of 10 decimeters. What is the length of the curved surface?

shepuryov [24]

The length of the curved surface is the circumfrence of a circle with radius r = 10/2 = 5 decimeters.

Length of curved surface = 2π x 5 = 10π ≈ 31.4 decimeters.

6 0

3 years ago