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kkurt [141]
3 years ago
10

Let p: x<-3 let q: x>3 what is the represented by p v q

Mathematics
1 answer:
yaroslaw [1]3 years ago
3 0
Values less than -3 or values greater than 3 make the disjunction true
P V Q means that either p or q  or both must be true to be a true statement so it includes x is less than -3 (p) and x is greater than 3 (q).
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Angelina_Jolie [31]
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5 0
3 years ago
Write 3x^2-18x-6 in vertex form
Vedmedyk [2.9K]
The standard form of a quadratic equation is \displaystyle{ y=ax^2+bx+c, while the vertex form is:

                      y=a(x-h)^2+k, where (h, k) is the vertex of the parabola.

What we want is to write \displaystyle{ y=3x^2-18x-6 as y=a(x-h)^2+k

First, we note that all the three terms have a factor of 3, so we factorize it and write:

\displaystyle{ y=3(x^2-6x-2).


Second, we notice that x^2-6x are the terms produced by (x-3)^2=x^2-6x+9, without the 9. So we can write:

x^2-6x=(x-3)^2-9, and substituting in \displaystyle{ y=3(x^2-6x-2) we have:

\displaystyle{ y=3(x^2-6x-2)=3[(x-3)^2-9-2]=3[(x-3)^2-11].

Finally, distributing 3 over the two terms in the brackets we have:

y=3[x-3]^2-33.


Answer: y=3(x-3)^2-33
6 0
4 years ago
A Square was altered so that one side is increased by 9 inches in the other side is decreased by 2 inches.The area of the result
LekaFEV [45]

Let s represent the length of any one side of the original square.  The longer side of the resulting rectangle is s + 9 and the shorter side s - 2.

The area of this rectangle is (s+9)(s-2) = 60 in^2.

This is a quadratic equation and can be solved using various methods.  Let's rewrite this equation in standard form:  s^2 + 7s - 18 = 60, or:

s^2 + 7s - 78 = 0.  This factors as follows:  (s+13)(s-6)=0, so that s = -13 and s= 6.  Discard s = -13, since the side length cannot be negative.  Then s = 6, and the area of the original square was 36 in^2.

4 0
3 years ago
I REALLY NEED SOME HELP! THANK YOU SO MUCH!
Katyanochek1 [597]
I thinkkk it’s both so C
4 0
3 years ago
Hellllllllllllllllllllllllllp
murzikaleks [220]

Answer:

\begin{cases}y=-5x+1\\y=5x-4 \end{cases}

Step-by-step explanation:

Slope-intercept form of a <u>linear equation</u>:

\boxed{y=mx+b}

where:

  • m is the slope.
  • b is the y-intercept (where the line crosses the y-axis).

<u>Slope formula</u>

\boxed{\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}}

<u>Equation 1</u>

<u />

Define two points on the line:

  • \textsf{Let }(x_1,y_1)=(-1, 6)
  • \textsf{Let }(x_2,y_2)=(0, 1)

<u>Substitute</u> the defined points into the slope formula:

\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-6}{0-(-1)}=-5

From inspection of the graph, the line crosses the y-axis at y = 1 and so the y-intercept is 1.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

y=-5x+1

<u>Equation 2</u>

<u />

Define two points on the line:

  • \textsf{Let }(x_1,y_1)=(1, 1)
  • \textsf{Let }(x_2,y_2)=(0, -4)

<u>Substitute</u> the defined points into the slope formula:

\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-1}{0-1}=5

From inspection of the graph, the line crosses the y-axis at y = -4 and so the y-intercept is -4.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

y=5x-4

<u>Conclusion</u>

Therefore, the system of linear equations shown by the graph is:

\begin{cases}y=-5x+1\\y=5x-4 \end{cases}

Learn more about systems of linear equations here:

brainly.com/question/28164947

brainly.com/question/28093918

5 0
2 years ago
Read 2 more answers
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