- A fish tank filter cleans 3 gallons of water every 1/4 hour. Set up and solve a proportion to determine how many gallons of water are cleaned in 4 hours.​

Question:

A fastball is hit straight up over home plate. The ball's height, h (in feet), from the ground is modeled by h(t)=-16t^2+80t+5, where t is measured in seconds.  Write an equation to determine how long it will take for the ball to reach the ground.

Answer:

[tex]t = 5.0625[/tex]

Step-by-step explanation:

Given

[tex]h(t)=-16t^2+80t+5[/tex]

Required

Find t when the ball hits the ground

This implies that h(t) = 0

So, we have:

[tex]0=-16t^2+80t+5[/tex]

Reorder

[tex]-16t^2+80t+5 = 0[/tex]

Using quadratic formula, we have:

[tex]t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]

Where

[tex]a = -16[/tex]      [tex]b =80[/tex]      [tex]c = 5[/tex]

So, we have:

[tex]t = \frac{-80\±\sqrt{80^2 - 4*-16*5}}{2*-16}[/tex]

[tex]t = \frac{-80\±\sqrt{6400 +320}}{-32}[/tex]

[tex]t = \frac{-80\±\sqrt{6720}}{-32}[/tex]

[tex]t = \frac{-80\±82.0}{-32}[/tex]

This gives:

[tex]t = \frac{-80+82.0}{-32}[/tex] or [tex]t = \frac{-80-82.0}{-32}[/tex]

[tex]t = \frac{2}{-32}[/tex] or [tex]t = \frac{-162}{-32}[/tex]

[tex]t = -\frac{2}{32}[/tex] or [tex]t = \frac{162}{32}[/tex]

But time can not be negative.

So, we have:

[tex]t = \frac{162}{32}[/tex]

[tex]t = 5.0625[/tex]

Hence, time to hit the ground is 5.0625 seconds

Answer:

6? cause it is six times bigger so six

Answer:

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Answer:

The first and second one are functions, the rest are not

Step-by-step explanation:

Answer:

They actually can all be functions

Answer:

the answer is c

Step-by-step explanation:

if it is a right triangle most of the time the 2 acute angles will most likely be 45 degrees

Answer:C.45 degrees

Step-by-step explanation:

135º+yº=180º

y=180º-135º

y=45º

Answer:

4%

Step-by-step explanation:

dude if you got a whole number and a decimal, the whole number is going to be greater (as long as it isn't negative)

Answer:

Number line C

Step-by-step explanation:

First, you isolate x. This gives you x>=3+4 or x>= 7. Next, you find a number line greater than or equal to which cancels out A and D. Now whichever line starts on 7, is the answer which is C

Answer:

C

Step-by-step explanation:

If you solve the equation your answer will be x≥7

This is a less than or equal to 7 so the point on the graph will be closed (or filled in) which means your closed point goes on 7 and goes down the line to the left because of the direction of the sign. (less than)

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

D. 48

Step-by-step explanation:

4pi r^2

4 × 3 × 2^2 = 48

Answer:

The answer is D.

Step-by-step explanation:

You only have to substitute π value and r value into the formula :

[tex]s.a = 4\pi {r}^{2} [/tex]

[tex]let \: \pi = 3,r = 2[/tex]

[tex]s.a = 4 \times 3 \times {2}^{2} [/tex]

[tex]s.a = 12 \times 4[/tex]

[tex]s.a = 48 \: {m}^{2} [/tex]

9514 1404 393

Answer:

  f(x) = 6x +1

Step-by-step explanation:

Differences in x-values (first row) are 1, 1, 1.

Differences in y-values (second row) are 6, 6, 6.

The constant ratio of differences (6/1) tells you the function is linear, and has a slope of m = 6/1 = 6.

Using the first point in the form ...

  y = mx + b

we have ...

  y = 6x + b

  7 = 6·1 + b . . . . (x, y) = (1, 7)

  1 = b . . . . . . subtract 6

Then the equation can be written ...

  y = 6x +1

In functional form, this is ...

  f(x) = 6x +1

Answer:

See explanation

Step-by-step explanation:

for -2x+4=4 the slope is y=2x-4

for -3x+2y=6 the slope is y=3/2x+3

for -3x+2y=6 the y-intercept is y=3 or (0,3)

(you can plug into desmos to check :) )

Answer:

Yes.

Step-by-step explanation:

When you plug in 6 for x and solve for y, you get 5.

y=5(6)-25

y=30-25

y=5

When X is 6, Y is 5.

Answer:

w=8 inches

Step-by-step explanation:

w( 2w - 4) = 96

Answer:

thx

Step-by-step explanation:

Answer:

105.3

Step-by-step explanation:

deltamath

Answer:

13/12 = x/9

Cross mulitply.

X=9.75

Step-by-step explanation:

Answer:

y=10

Step-by-step explanation:

Answer:

The answer is -300

Step-by-step explanation:

The answer is -300 because -2 multiplied by 6 is -12 and -12 times 25 is -300

Answer

d

Step-by-step explanation:

The polynomial function which represents the number of vehicles ( x ) that go through the drive-thru each hour f ( x ) is given by the function f ( x ) , where f ( x ) = 0.4048x² + 16.9762x + 2.1429

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Daniel keeps track of the number of vehicles that go through the drive-thru each hour

Let the number of hours be x

Let the total number of vehicles that passes be y

Now , the values of x = { 1 , 2 , 3 , 4 , 5 , 6 , 7 }

The values of y = f ( x ) = { 18 , 38 , 60 , 78 , 93 , 117 , 143 }

Let the polynomial equation be represented as f ( x )

Now , the value of f ( x ) is calculated from the curve fitting model of hyperbola , where

f ( x ) = 0.4048x² + 16.9762x + 2.1429

when x = 3

f ( 1 ) = 0.4048 ( 3 )² + 16.9762 ( 3 ) + 2.1429

On simplifying , we get

f ( 1 ) = 3.6432 + 50.9286  + 2.1429

f ( 1 ) ≈ 60

Hence , the polynomial equation is f ( x ) = 0.4048x² + 16.9762x + 2.1429

To learn more about polynomials click :

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Answer:

5

Explanation: y-intercepts are just numbers that don't have any variables and they can be found on the y axis.

Answer:

5

Step-by-step explanation:

Rewrite the equation as y=-7x+5.

y=mx+b is slope-intercept form with mx representing slope and b representing the y-intercept.

Answer:

(x-4)(x-5)

Step-by-step explanation:

x² - 9x + 20

x²-4x-5x+20

x(x-4)-5(x-4)

(x-4)(x-5)

Answer:

Hope it can help you and please mark me as a brainlist..

Answer:

It is the 4th option. Domain -3 ≤ x ≤ 3.   Range -2 ≤ y ≤ 2. This is not a function since it does not pass the vertical line test.

Answer:

28

Step-by-step explanation:

You can split the figure up

3*4/2 = 6

3*4/2 = 6

8*2 = 16

6+6+16 = 28

Answer: 4.189 units

Step-by-step explanation:

AP EX

As per linear equation, the required approximate arc length is 4.19 units.

"An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line.

The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant."

Given,  length of the radius (r) = 1 units

The value of the given angle(θ) = 4π/3 radian.

Therefore, the approximate arc length is

= length of the radius × value of the given angle

= r × θ

= 1 × 4π/3 units

= 4π/3 units

= 4.19 units

The required approximate arc length is 4.19 units.

Learn more about linear equation here: https://brainly.com/question/11897796

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Answer:

The first step you would have to do would be get 4x by itself

Step-by-step explanation:

So it would be 4x +5 = 21

-5 and -5

So it would be 4x = 16