consider a dianmeter of 8 feet and height of h feet.which equation can be used to find v,the volumeof the cylinder in cubic feet

There are 20 juice cups and each juice cup holds 10 fluid ounces. the juice comes in 1 gallon bottles. how many 1 gallon bottles

Andru [333]

20 times 10=200 fluid ounces

128 fluid ounces per gallon
1 gallon is too little
2 gallons is to much
but you can't buy 1 and 72/100 of a bottle so just buy 2

2 bottles

6 0

2 years ago

Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. I

fredd [130]

Answer:

Observe attached image

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

Axis of symmetry:

 $x =4$ 

Step-by-step explanation:

First factorize the function

$f (x) = -2x ^ 2 + 16x-30$

Take -2 as a common factor.

$-2(x ^ 2 -8x +15)$

Now factor the expression $x ^ 2 -8x +15$

You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.

These numbers are -5 and -3

Then we can factor the expression in the following way:

$f (x) = -2(x-5)(x-3)$

The quadratic function cuts the x-axis at x = 3 and at x = 5.

Now we find the coordinates of the vertex.

For a function of the form $ax ^ 2 + bx + c$ the x coordinate of its vertex is:

$x = \frac{-b}{2a}$

In the function $f (x) = -2x ^ 2 + 16x-30$

$a = -2\\b = 16\\c = 30$

Then the vertice is:

$x = \frac{-16}{2(-2)}\\\\x = 4$

The y coordinate of the symmetry axis is

$y = f (4) = -2 (4) ^ 2 +16 (4) -30\\\\y = 2$

The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.

Then the axis of symmetry is the line

$x = 4$

The solutions and the vertice written as ordered pairs are:

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

6 0

2 years ago

Value of x 9(2x-1)-9x - 18

bixtya [17]

Let's simplify step-by-step.9(2x−1)−9x−18

Distribute:=(9)(2x)+(9)(−1)+−9x+−18=18x+−9+−9x+−18

Combine Like Terms:=18x+−9+−9x+−18=(18x+−9x)+(−9+−18)=9x+−27

Answer:=9x−27

5 0

2 years ago

Read 2 more answers

Matt E. Matic was applying for a job. To determine whether he could handle the job, the personnel manager sent him out to poll 1

Rom4ik [11]

Answer:

No; he did the survey incorrectly.

He surveyed 107 people, not 100.

Step-by-step explanation:

Draw a Venn diagram, when you are presented with information like this;

Presenting it in a Venn diagram would look like what is shown in the pic.

P.S. when drawing a Venn diagram, start with the information regarding individuals who fit in all categories and then work your way to the individuals who fit in just in one category.

8 0

3 years ago

How to solve these question?

mart [117]

3.) An extreme value refers to a point on the graph that is possibly a maximum or minimum. At these points, the instantaneous rate of change (slope) of the graph is 0 because the line tangent to the point is horizontal. We can find the rate of change by taking the derivative of the function.

y' = 2ax + b

Now that we where the derivative, we can set it equal to 0.

2ax + b = 0

We also know that at the extreme value, x = -1/2. We can plug that in as well.

$2a (-\frac{1}{2} ) + b = 0$

The 2 and one-half cancel each other out.

$-a + b = 0$

$a = b$

Now we know that a and b are the same number, and that ax^2 + bx + 10 = 0 at x = -1/2. So let's plug -1/2 in for x in the original function, and solve for a/b.

a(-0.5)^2 + a(-0.5) + 10 = 0

0.25a - 0.5a + 10 = 0

-0.25a = -10

a = 40

b = 40

To determine if the extrema is a minima or maxima, we need to go back to the derivative and plug in a/b.

80x + 40

Our critical number is x = -1/2. We need to plug a number that is less than -1/2 and a number that is greater than -1/2 into the derivative.

LESS THAN:
80(-1) + 40 = -40

GREATER THAN:
80(0) + 40 = 40

The rate of change of the graph changes from negative to positive at x = -1/2, therefore the extreme value is a minimum.

4.) If the quadratic function is symmetrical about x = 3, that means that the minimum or maximum must be at x = 3.

y' = 2ax + 1

2a(3) + 1 = 0

6a = -1

a = -1/6

So now plug the a value and x=3 into the original function to find the extreme value.

(-1/6)(3)^2 + 3 + 3 = 4.5

The extreme value is 4.5

7 0

2 years ago