Benchmark estimate of 8.01

Use the method of completing the square to transform the quadratic equation into the equation form (x – p)2 = q. x2 - 12x - 9 =

marissa [1.9K]

Hence, the correct answer is: C) (x - 6)^2 = 45

Further explanation:

Given equation is:

$x^2-12x-9=0$

We will move the constant term on other side of the equation

$x^2-12x=9$

To complete the square, we will take the coefficient of x and divide it by 2, as we already know that one term is x.

$\frac{12}{2}=6$

So, adding (6)^2 on both sides

$(x)^2-2.x.6+(6)^2=9+(6)^2\\(x-6)^2=9+36\\(x-6)^2=45$

Hence, the correct answer is: C) (x - 6)^2 = 45

Keywords: Quadratic Equation, Solution of equation

Learn more about quadratic equation at:

#LearnwithBrainly

7 0

3 years ago

Please help me, I'm suffering from all of these parallel lines ;9

Anarel [89]

Answer:

1. y = 4x - 27

2. y = -4x - 15

Step-by-step explanation:

If two lines are parallel, then they have the same slope. So, the slope of the line we are looking for needs to be 4. We can start by writing a point-slope equation:

y - y1 = m(x - x1)

We can substitute the values we have, the point we are using is (8, 5) because it needs to be on the line:

y - 5 = 4(x - 8)

We can distribute:

y - 5 = 4x - 32

y = 4x - 27

We are not given the slope-intercept form, so we must divide both sides by two to get it:

y = 1/4 x + 8

A perpendicular line has the slope that is the negative reciprocal of the one that is given. So, the slope of the line would be - 4. We can start by writing a point-slope equation:

y - y1 = m(x - x1)

We can substitute the values we have, the point we are using is (-5, 5) because it needs to be on the line:

y - 5 = -4(x + 5)

We can distribute:

y - 5 = -4x - 20

y = -4x - 15

6 0

2 years ago

Help I dont get what to do

Mars2501 [29]

Answer:

a/(bxy) if b≠0, x≠0, y≠0, x≠y

Step-by-step explanation:

You have correctly simplified the expression. The conditions placed on both the original and simplified forms are that none of the denominator factors may be zero. The denominator factors are b, x, y, and (x-y).

$\dfrac{a}{bxy}\text{ if $b\ne0;$ $x\ne0;$ $y\ne0;$ $x\ne y$}$

6 0

1 year ago

I’m confused :( I will mark as Brainliest and give you points

Ludmilka [50]

Answer:

123.5 square inches

Step-by-step explanation:

Given: To find the area of a rectangle, you have to multiply base times height.

To find the area of a triangle, you have to do base times height devided by 2.

Finding the area: Let's break up this shape into polygons. At the bottom there is a rectangle. We know that to find the area of the rectangle you have to do base times height. 13in•7in will give you 91in square for the rectangle.

Now for the triangle. If you can see, if you break the triangle in half, there are 2 right triangles. Let's look at the right one for now. Since we know that to find the area of a triangle you have to do base times height divided by 2, you do 5in•6.5in=32.5in. 32.5in divided by 2 is 16.25in square which is the area of one triangle. You might be wondering why i did 5•6.5, and that's because at the bottom of the rectangle you can see it's 13in, and 13in÷2=6.5in.

We already found the area of the rectangle and one triangle. The other triangle is equal to it so we can just do 16.25+16.25=32.5in square for both of the triangles.

Now we add it all up: 32.5+91=123.5 square inches

8 0

2 years ago

At the local market, Bill buys 3 juice boxes and 2 hot dogs at a cost of $8, while Sarah buys 2 juice boxes and 1 hot dog at a c

baherus [9]

Answer:

The cost of each juice boxes is $ 2

The cost of each hot dogs is $ 1 .

Step-by-step explanation:

Given as :

The amount which Bill pays for 3 juice boxes and 2 hot dogs = $ 8

The amount which Sarah pays for 2 juice boxes and 1 hot dogs = $ 5

Let The cost of each juice boxes = $ j

And The cost of each hot dogs = $ h

Now, According to question

3 j + 2 h = 8 .........A

2 j + 1 h = 5 ..........B

Now, solving the equations

2 × ( 2 j + 1 h ) = 2 × 5

or, 4 j + 2 h = 10

I.e ( 4 j + 2 h ) - ( 3 j + 2 h ) = 10 - 8

Or, ( 4 j - 3 j ) + ( 2 j - 2 h ) = 2

Or, j + 0 = 2

∴ j = 2

So , The cost of each juice boxes = j = $ 2

Now, Put the value of j in Eq A

I.e 3 × 2 + 2 h = 8

Or, 6 + 2 h = 8

Or. 2 h = 8 - 6

or, 2 h = 2

∴ h = $\frac{2}{2}$ = 1

So, The cost of each hot dogs = h = $ 1

Hence The cost of each juice boxes is $ 2

And The cost of each hot dogs is $ 1 . Answer

4 0

3 years ago