A pool is being drained at a constant rate. The amount of water is a function of the number of minutes the pool has been draining, as shown in the table. Write an equation in slope-intercept form that represents the function. Then find the water in the pool after two and a half hours. Time (mi) 12--------20------50
Volumne (gal) 4962--4754--3974

Answers

Answer 1

Answer:

The equation in the slope-intercept form is $y=-26x+5274$ and there will be $1374$ gallons of water in the pool after $2$ and a half hours.

The equation of a line that passes through two points $(x_1, y_1)$ and $(x_2, y_2)$ is $(y-y_1)=(y_2-y_1)/(x_2-x_1)(x-x_1)$ .

Take points $(12, 4962)$ and $(20, 4754)$ .

Here, $x_1=12, y_1=4962, x_2=20, y_2=4754$ .

The equation is :

$(y-4962)=(4754-4962)/(20-12)(x-12)$

$(y-4962)=(-208)/(8)(x-12)$

$8(y-4962)=-208(x-12)$

$8y-39696=-208x+2496$

$208x+8y-39696-2496=0$

$208x+8y-42192=0$

$8y=-208x+42192$

$y=-(208)/(8)x+(42192)/(8)$

$y=-26x+5274.$

The slope intercept form is $y=mx+c$ , where $m$ is the slope and $c$ is the $y$ -intercept.

After $2$ and a half hours or $150$ minutes.

Put $x=150$ in the equation $y=-26x+5274.$

$y=-26* 150+5274$

$y=-3900+5274$

$y=1374$

So, there will be $1374$ gallons of water in the pool after $2$ and a half hours.

Learn more about slope-intercept form here:

brainly.com/question/21366542?referrer=searchResults

Answer 2

Answer:

Answer:

Using the first two values in the table, we can first find the slope to write an equation of a line, so we have

[4754 - 4962 ] / [20 - 12 ] = -26

So we have

y - 4754 = -26(x - 20)

y - 4754 = -26x + 520

y = -26x + 5274

Let's confirm that the amount after 50 minutes is correct

y = -26(50) + 5274 = 3974

So after 2 + 1/2 hrs (150 min) we have

y = -26(150) + 5274 = 1374 gallons

Step-by-step explanation:

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A pentagon with one interior angle that measures 200 degrees is what type of polygon.

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to multiply a number by 12, Carter likes to multiply the number by 10 and then multiply it by 2 and add the product. Write an expression with parenthesis how carter would solve 12×16

Answers

Since carter multiplies by 10 and then by 2 and adds the two, here we have been given 16 * 12

Step 1: Carter would first multiply the number by 10. This would be = 16*10

Step 2: Carter would multiply the number by 2. This would be = 16*2

Step 3: He would add the two. This would be = (16*10) + (16*2)

Carter's solution would be:

=16*12

=(16*10) + (16*2)

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(x − 2) is a factor of x4 + 2x3 − 7x2 − 8x + 12. The other factors are ___, ___, and ___.

Answers

The all other 3 factors of the equation x⁴ + 2x³ − 7x² − 8x + 12 will b e(x + 2),(x - 1) and (x + 3).

What are the roots of an equation?

Roots of an equation are the solution of that equation since an equation consists of hidden values of the variable to determine them by different processes and then the resultant is called roots.

For example root of x -4 = 0 is x = 4 so 4 will be the only root of this linear equation.

Given the equation,

x⁴ + 2x³ − 7x² − 8x + 12

If (x - 2) is a factor of the equation then it should be divisible by it.

So,

(x⁴ + 2x³ − 7x² − 8x + 12) / (x - 2) = (x³ + 4x² + x - 6)

Now divide by (x - 1) of (x³ + 4x² + x - 6)

(x³ + 4x² + x - 6) / (x - 1) = x² + 5x + 6

So,

⇒ (x - 2)(x - 1)(x² + 5x + 6)

⇒ (x - 2)(x - 1)( x² + 2x + 3x + 6)

⇒ (x - 2)(x - 1)[ x(x + 2) + 3(x + 2) ]

⇒ (x - 2)(x - 1)(x + 2)(x + 3)

Hence "The all other 3 factors of the equation x⁴ + 2x³ − 7x² − 8x + 12 will b e(x + 2),(x - 1) and (x + 3)".

To learn more about the roots of an equation,

brainly.com/question/12029673

#SPJ2

Answer:

Step-by-step explanation:

The given equation is:

$x^4+2x^3-7x^2-8x+12$

Now, (x-2) is a factor of the given equation, therefore

$(x-2)(x^3+4x^2+x-6)$

$(x-2)(x-1)(x^2+5x+6)$

$(x-2)(x-1)(x^2+3x+2x+6)$

$(x-2)(x-1)(x(x+3)+2(x+3))$

$(x-2)(x-1)(x+2)(x+3)$

Therefore, the other factors are (x-1), (x+2) and (x+3).

the sales tax in Illinois is 6.25%. about how much will a pair of jeans that has a ticket price of $48.99 cost, including sales tax?

Answers

Cost of the pair of jeans = $48.99

Sales tax = 6.25%

Total cost = $48.99+6.25%

= $49.05

Therefore, the total cost including sales tax is $49.05

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Answers

Answer:

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Given:

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To find:

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Step-by-step explanation:

$\sf \implies(f - g)x = f(x) - g(x) \n \n \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (3x + 1) - ( {x}^(2) - 6) \n \n \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (3x + 1) + (- {x}^(2) + 6) \n \n \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3x + 1 - {x}^(2) + 6 \n \n \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - {x}^(2) + 3x + 1 + 6 \n \n \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = -{x}^(2) + 3x + 7$

The length of a rectangle is 5 cm more than twice the width the perimeter of the rectangle is 34 cm what are the dimensions

Answers

If the width is 4, we're told that the length is 5 more than twice the width, or (2*4)+5, which is 13.

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