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Leto [7]
3 years ago
6

What is the minimum value of the function g(x) = x2 - 6x – 12? -21 3-21 3 3+21

Mathematics
1 answer:
balandron [24]3 years ago
4 0

Answer:

- 21

Step-by-step explanation:

The minimum value occurs at the vertex of the function

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

Given

f(x) = x² - 6x - 12

add/ subtract ( half the coefficient of the x- term)² to x² - 6x

f(x) = x² + 2(- 3)x + 9 - 9 - 12

     = (x - 3)² - 21

with vertex = (3, - 21 )

The minimum is the value of k, that is minimum value = - 21

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Solve -14-5y &gt;-64<br> A. Y&lt;10<br> B.y&gt;-10<br> C. Y&gt;10<br> D.y&lt;-10
amm1812

Hello :D

Answer:

A. Y

Step-by-step explanation:

First, you add by 14 both sides of an equation.

-14-5y+14>-64+14

Then, simplify by equation.

-64+14=-50

-5y>-50

Multiply -1 both sides.

(-5y)(-1)<(-50)(-1)

5y<50

Divide by 5 both sides of an equation.

5y/5<50/5

Divide numbers from left to right.

50/5=10

y<10 is the correct answer.

Hope this helps you! :D

6 0
3 years ago
What is an equation of the line that passes through the point (-7,-6)(−7,−6) and is parallel to the line x-y=7x−y=7?
kotykmax [81]

Answer:

y = x + 1

Step-by-step explanation:

The gradient of a line can be defined by the equation:

m (gradient) = (y1 – y2 ) ÷ (x1 – x2) ----> "1" and "2" should be in subscript

For (-7,-6) we use x2 and y2 (because this point can be anywhere along a line):

x2 = -7, y2 = -6

Plug these values into the formula above:

m = (y-(-6)) ÷ (x-(-7))

m = (y+6) ÷ (x+7)

At this stage, the equation can't be solved as there are two unknowns. Therefore, the gradient must be found another way. Two lines are parallel if they have the same gradient - in their y=mx+c equations, m will be equal.

x - y=7 is the line alluded to in the question. Rearranging this equation into the line equation format gives:

y = x-7 ---> The gradient (coefficient of x) is 1.

Therefore, the gradient of the other parallel line must also be 1.

This can be substituted into the previous equation to give:

1 = (y+6)÷(x+7)

x+7 = y+6

x+1 = y

Therefore, the answer is y=x+1

5 0
2 years ago
What is the slope of the line given by the equation -3x = 30 - 5y?
zaharov [31]

Answer:

The slope of the line given by the equation -3x=30-5y is \frac{3}{5}.

Step-by-step explanation:

-3x=30-5y

Move the -3x to the right side of the equal sign and the -5y to the left.

5y=30+3x

By switching them to opposite sides, their sign changes from - to +.

Then, divide both sides by 5 in order to isolate the y.

\frac{5y}{5} = \frac{30+3x}{5}

You get:

<em>y= </em>\frac{3}{5} x +6<em />

According to y=mx+b, mx refers to the slope.

In this case, the slope would be \frac{3}{5}.

8 0
3 years ago
Correct answer gets brainliest and 5 stars
Serggg [28]

Answer:

A is false

Step-by-step explanation:

notice how in both diagrams, there are 4 triangles with lengths a, b, c, but in each diagram the triangles are just rotated and positioned differently. if there are the same amount of triangles in both diagrams, and the have equal lengths then the area of the remaining figure, should both match up.

basically the area of the big square in Step 2, is equal to both of the shaded squares, combined area, in Step 1.

3 0
3 years ago
A commuter has $245 in his commuter savings account. This account
tino4ka555 [31]
I’m not 100% sure but probably 16 weeks
8 0
3 years ago
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