X2 - x - 6 =Simplified. I know the answer is (x+2)(x-3), but I don't understand how the answer was achieved. Can I please get an explanation of this?

Answers

Answer 1

Answer: $x^2-x-6=(x+2)(x-3)\n\n-x=2x-3x\n-6=2*(-3)\n\nor\n\nx^2-x-6=x^2+2x-3x-6=x(x+2)-3(x+2)=(x+2)(x-3)$

Answer 2

Answer: I had a lot of trouble with this when my algebra class started doing it,
a long time ago.

The key is this: Look at the -6 at the end. You have to find two factors
of that number that add up to the -1 in the middle.

Here are the possible factors of -6 :

-1 ... 6
+1 ... -6
-2 ... 3
+2 ... -3

Can you find a pair on the list that adds up to -1 ?
How about +2 and -3 ?
Their product is -6 and their sum is -1. That's what you need.

Now set up a couple of binomial factors like this: (x....) (x....)
and write in the pair of numbers you found: (x + 2) (x - 3)
That's the factored form of the original expression.

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What is the perimeter of a triangle with vertices located at (-1, 4), (2, 7), and (1, 5), rounded to the nearest hundredth? A. 7.63 units B. 7.89 units C. 8.71 units D. 9.24 units

Answers

we are given with the points (-1,4), (2,7) and (1,5) as the sides of the triangle. The area of the triangle can be determined by determining first the length of the sides. Via distance formula, the sides are 3 sqrt 2, sqrt 5 and sqrt 5. The perimeter thus is equal to 8.71 units

The perimeter of a triangle with vertices located at (-1, 4), (2, 7), and (1, 5) is 8.71 units

How to determine the perimeter?

The coordinates are given as:

(-1, 4), (2, 7), and (1, 5)

Calculate the distance between these points using:

$d = √((x_2 -x_1)^2 + (y_2 - y_1)^2)$

So, we have:

$AB = √((-1 -2)^2 + (4 - 7)^2) = 4.24$

$BC = √((2-1)^2 + (7 - 5)^2) = 2.24$

$AC = √((-1-1)^2 + (4 - 5)^2) = 2.24$

The perimeter P is then calculated using:

P = 4.24 + 2.24 + 2.24

Evaluate the sum

P = 8.71

Hence, the perimeter of the triangle is 8.71 units

Answers

Alright...simple...showing all steps.. ;)

You have the equations...

2x+y=7
and
3x+5y=14

To be able to even solve for any of the variables...multiply the equations by...2...and..3...

2x+y=7----*3--> 6x+3y=21
and
3x+5y=14-----*2--->6x+10y=28

Thus,

6x+3y=21
-
6x+10y=28

=========

-7y=-7

y=1

Now, plug y back into any of the original equations....we'll use 2x+y=7 in this case....

2x+(1)=7

2x+1=7
-1 -1

2x=6

x=3

Thus, the point of intersection for these two equations is (3,1)

Help? I'll mark brainliest

Answers

Answer:

x=6 y=3

Step-by-step explanation:

x=y+3 replace that in the other problem x+3=3y becomes y+3+3= 3y. solve and get y=3. replace in x=y+3 to get x=6

Help me please ..........................

Answers

G(x)= (x-4)^2+1......

Answer: G(x)=(x-2)^2+1

Apex certified

what is the range of the function g(x) = |x – 12| – 2? {y | y > –2} {y | y > –2} {y | y > 12} {y | y > 12}

Answers

Range = {y | y ≥ –2}

Answer:

The range of function is $R= \left \{ y|y\geq -2 \right \}$

Step-by-step explanation:

Given : Function $g(x) = |x -12| -2$

To find : What is the range of the function?

Solution :

The range is defined as the set of y values for which function is defined.

We have given function $g(x) = |x -12| -2$ in the vertex form.

The general vertex form is $y=a|x-h|+k$ where (h,k) are the vertex of the equation.

On comparing the vertex of the given function is (h,k)=(12,-2)

i.e. The y-values taken is less than -2.

So, the range would be the all y values greater than or equal to -2.

Therefore, The range of function is $R= \left \{ y|y\geq -2 \right \}$

Refer the attached figure below of the function.

You have six trophies to arrange on the top shelf of the bookcase how many ways are there to arrange the trophies

Answers

Answer:

So, we can do it in 720 ways.

Step-by-step explanation:

We have been given total of six trophies to arrange in the top shelf of the bookcase

If we need to arrange n things in different ways we can do it in n! ways

Similarly, Here we will do it in 6! ways

n!=n(n-1)(n-2).....1

So, 6!=6 x 5 x 4 x 3 x 2 x 1=720

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