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Nataly [62]
3 years ago
8

For what values of x is each function increasing? For what values of x is it decreasing? a. f(x) = x2 - 4x​

Mathematics
1 answer:
Harrizon [31]3 years ago
6 0

Answer:

to the right of x = 2 the function is increasing

{ x | x > 2}

Step-by-step explanation:

Recall that this is a quadratic function, and therefore responds to the shape of a parabola. In this case is also a parabola with branches opening up since the coefficient of the square term is positive. So, we just need to find where the vertex is located, and we know that to the left of the x-value of the vertex the function is decreasing, and to the right of it the function is increasing.

The formula for the x of the vertex of a parabola of the form:

y=ax^2+bx+c

is  x_{vertex}=\frac{-b}{2\,a}

which in our case gives:

x_{vertex}=\frac{-b}{2\,a} =\frac{4}{2} =2

Therefore, to the left of x = 2 the function decreases , and to the right of x = 2 the function is increasing.

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Im 4 and i need help with my math the question is 11+10
Arada [10]

Answer:

21

Step-by-step explanation:

5 0
3 years ago
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You purchased concentrated cleaner that must be diluted (watered down)
abruzzese [7]

Answer:

The volume of the concentrated 80 gallons mixture is 20 gallons

The volume of water in the 80 gallons mixture is 60 gallons

Step-by-step explanation:

The given parameters are;

The content of Container A = The cleaner

The concentration of the cleaner = 20% solution

The content of Container B = Pure water

The concentration of the desired solution = 5%

The volume of the required solution = 80 gallons

Let x represent the volume of the concentrated solution and y represent the volume of water in the 80 gallons mixture

Therefore, we have;

20/100 × x + y×0 = 5/100×80

x + y = 80

y = 80 - x

20/100 × x + (80 - x)×0 = 5/100×80

0.2·x = 4

x = 4/0.2 = 20

x = 20 gallons

y = 80 - x = 80 - 20 = 60

y = 60 gallons

The volume of the concentrated solution (80 gallons mixture) = x = 20 gallons

The volume of water in the 80 gallons mixture = y = 60 gallons.

8 0
3 years ago
Today, 6 friends went out for lunch. Their total bill was $27.60, including tax and gratuity. They decided to split the bill equ
Paladinen [302]

Step-by-step explanation:

Right, okay, so this is a bit of a weird one. Let's go step by step.

"Today, 6 friends went out for lunch." = The number 6 is gonna be in our equation somewhere.

"Their total bill was $27.60" = so is the number 27.6

"They decided to split the bill equally" = 27.6 "split equally" (aka divided by) 6 friends is 4.6

"each paid with a $10 bill" = This is where it gets a lil weird. So, if they divided the bill among them, none of their amounts are gonna be anywhere near ten dollars. This is one of those questions that wouldn't really happen in real life. People would probably use fives instead, but whatever. So a number we'll be using for something is 10.

"How much money will each person get back?" = So we have to find the amount they all paid (10) minus the amount each one had to pay (4.6).

To put it all into a full equation...

10 - ( 27.6 / 6 )

Divide.

10 - 4.6

Subtract.

5.4

Put back into money form.

$5.40

Answer:

Each person will get back $5.40.

7 0
3 years ago
Read 2 more answers
Solve for the missing side in the following right triangle: hypotenuse = 17, leg = 8, leg = ?.
krek1111 [17]
Hyp^2 = leg1^2 + leg2^2
hyp^2  -leg1^2 = leg2^2
17^2 - 8^2 = leg2^2
leg2^2 = 289 -64
leg2^2 = 225
leg2 = 15



7 0
3 years ago
Look at the graph below. Which of the following best represents the slope of the line? A. -3 B. - 1 3 C. 1 3 D. 3
Salsk061 [2.6K]

Answer and Explanation:

The line seems to pass trough the points (0,6) and (-3,4).

Slope is: m=\frac{y_2-y_1}{x_2-x_1}

m=\frac{4-6}{-3-0} =\frac{-2}{-3} =\boxed{\frac{2}{3}}

The slope of the line should be \frac{2}{3}.

3 0
3 years ago
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