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avanturin [10]
2 years ago
11

2x² – xy - 15y2 How to factor by grouping

Mathematics
1 answer:
dsp732 years ago
6 0

Answer:

(2x + 5y) (x - 3y)

Step-by-step explanation:

Hope this helps!

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Which statements are true about the graph of the function f(x) = x2 – 8x + 5? Check all that apply.
statuscvo [17]

Answer:

A, D, E are true

Step-by-step explanation:

You have to complete the square to prove A.  Do this by first setting the function equal to 0, then moving the 5 to the other side.

x^2-8x=-5

Now we can complete the square.  Take half the linear term, square it, and add it to both sides.  Our linear term is 8 (from the -8x).  Half of 8 is 4, and 4 squared is 16.  So we add 16 to both sides.

(x^2-8x+16)=-5+16

We will do the addition on the right, no big deal.  On the left, however, what we have done in the process of completing the square is to create a perfect square binomial, which gives us the h coordinate of the vertex.  We will rewrite with that perfect square on the left and the addition done on the right,

(x-4)^2=11

Now we will move the 11 back over, which gives us the k coordinate of the vertex.

(x-4)^2-11=y

From this you can see that A is correct.

Also we can see that the vertex of this parabola is (4, -11), which is why B is NOT correct.

The axis of symmetry is also found in the h value.  This is, by definition, a positive x-squared parabola (opens upwards), so its axis of symmetry will be an "x = " equation.  In the case of this type of parabola, that "x = " will always be equal to the h value.  So the axis of symmetry is

x = 4, which is why C is NOT correct, either.

We can find the y-intercept of the function by going back to the standard form of the parabola (NOT the vertex form we found by completing the square) and sub in a 0 for x.  When we do that, and then solve for y, we find that when x = 0, y = 5.  So the y-intercept is (0, 5).

From this you can see that D is also correct.

To determine if the parabola has real solutions (meaning it will go through the x-axis twice), you can plug it into the quadratic formula to find these values of x.  I just plugged the formula into my graphing calculator and graphed it to see that it did, indeed, go through the x-axis twice.  Just so you know, the values of x where the function go through are (.6833752, 0) and (7.3166248, 0).  That's why you need the quadratic formula to find these values.

7 0
3 years ago
What is the sum of the interior
frutty [35]
N is the amount of sides
sum=13 times 180 =2340
7 0
2 years ago
Please helpppp its due nowwwww
IceJOKER [234]

Answer:

Step-by-step explanation:

instead of (2x - 60 ) there should be (60 - 2x) because since they are parallel lines corresponding sides must be equal . It is contradictory because the size of the corresponding angles is different.

Note : Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).

4 0
2 years ago
Find g(x) where g(x) is the translation 3 units right of f(x)=x^2
Fed [463]

Answer:

  g(x) = x^2 -6x +9

Step-by-step explanation:

A function f(x) translated right h units and up k units will become ...

  g(x) = f(x -h) +k

You want the function f(x) = x^2 to be translated right h=3 units, so it will become ...

  g(x) = f(x -3) = (x -3)^2

  g(x) = x^2 -6x +9

6 0
2 years ago
Number 23 please answer
vfiekz [6]
I dont see a picture... :(

5 0
3 years ago
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