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Nikitich [7]
3 years ago
12

The drain in your 45-gallon bathtub is partially clogged, but you need to take a shower. The showerhead had a flow rate of 2.25

gallons per minute, but the bathtub only drains at a rate of -0.5 gallons per minute. What is the longest shower you can take? ​
Mathematics
2 answers:
sleet_krkn [62]3 years ago
4 0

Answer:

25 minutes 42 seconds

Step-by-step explanation:

The tub will fill at the rate of ...

 2.25 gal/min - 0.50 gal/min = 1.75 gal/min

It will take ...

 45 gal/(1.75 gal/min) ≈ 25.714 min

for the tub to fill.

You can shower for about 25 minutes 42 seconds.

Step-by-step explanation:

Vladimir [108]3 years ago
3 0

Answer:

  25 minutes 42 seconds

Step-by-step explanation:

The tub will fill at the rate of ...

  2.25 gal/min - 0.50 gal/min = 1.75 gal/min

It will take ...

  45 gal/(1.75 gal/min) ≈ 25.714 min

for the tub to fill.

You can shower for about 25 minutes 42 seconds.

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Given the polynomial 2x3 18x2 − 18x − 162, what is the value of the constant 'k' in the factored form? 2x3 18x2 − 18x − 162 = 2(
oee [108]

The value of the constant 'k' in the factored form factorization the provided polynomial equation is 3.

<h3>What is polynomial equation?</h3>

Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).

The factor of a polynomial is the terms in linear or equation form, which are when multiplied together, give the original polynomial equation as result.

The given polynomial equation in the problem is,

2x^3 +18x^2 - 18x - 162

The factor of the polynomial equation are given as,

2(x+ k)(x - k)(x +9)

First find out the factors to compare and find the value of k.The above equation has the unknown variable x and the highest power of this unknown variable is 3.

Take out the highest common factor 2, which can divide each term of the above equation (2, 18, -18, -162). Thus,

2(x+ k)(x - k)(x +9)=2(x^3 +9x^2 - 9x - 81)

Take out the highest common factor to make the groups as,

2(x+ k)(x - k)(x +9)=2(x^2( x+9) - 9(x + 9))\\2(x+ k)(x - k)(x +9)=2( x+9) (x^2 - 9)\\2(x+ k)(x - k)(x +9)=2( x+9) (x^2 - 3^2)

Use the property of difference of the square for the (x²-3²) term as,

2(x+ k)(x - k)(x +9)=2( x+9) (x+3)(x-3)\\2(x+ k)(x - k)(x +9)=2 (x+3)(x-3)( x+9)

On comparing the two equation, we get the value of k as 3. Thus, the value of the constant 'k' in the factored form factorization the provided polynomial equation is 3.

Learn more about factor of polynomial here;

brainly.com/question/24380382

7 0
1 year ago
For the equation --4y = 8x, what is the constant of variation?
larisa86 [58]

Answer: 1) B is correct, constant of variation is -2.

Step-by-step explanation:

1)

Direct variation states that a relationship between the two variables. we say y varies directly as x

i.e,  or y =kx.................[1] ;  where k is the constant of variation.

Given the equation:

Divide both sides by -4 we get;

Simplify:

            .......[2]

On comparing equation [2] with [1] we get;

k = -2

6 0
3 years ago
What is the GCF of 35 and 49??
Vlada [557]

Answer: 7

Step-by-step explanation: 7x7=49 and 7x5=35

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3 years ago
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dezoksy [38]

Find the difference in temperature between each 1000 feet:

From 1 to 2: 30 - 23.5 = 6.5

From 2 to 3: 23.5 - 17 = 6.5

From 3 to 4: 17 - 10.5 = 6.5

The temperature change is constant as it drops 6.5 degrees for every 1000 foot gain in elevation.

At 5,000 feet the temperature would be : 10.5 - 6.5 = 4

At 6,000 feet: 4 - 6.5 = -2.5

At 7,000 feet: -2.5 - 6.5 = -9

At 8,000 feet: -9 - 6.5 = -15.5

At 8,000 feet the temperature would be  -15.5 degrees.

5 0
3 years ago
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Help<br> Please I need hekp
AlekseyPX

Answer:

86

Step-by-step explanation:

6 0
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