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3241004551 [841]
3 years ago
8

Daniella accidentally left the drain partially open as she began filling the bathtub. The amount of water, in gallons, pouring i

nto the tub after x minutes is given by the function f. f( x )=12x The amount of water, in gallons, draining from the tub after x minutes is given by the function g. g( x )=6x What is the equation of a function k that gives the amount of water in the tub in this situation after x minutes?
Mathematics
1 answer:
jok3333 [9.3K]3 years ago
3 0

Answer:

k(x) = 6x

Step-by-step explanation:

A function shows the relationship between two or more variables. It shows the relationship between an independent and a dependent variable.

Given that the amount of water being poured into the tube is given by f(x) = 12x, where x is in minutes and the amount of water draining out of the tub is given by the function g( x )=6x. The amount of water remaining in the tube after x minutes is gotten by finding the difference between the amount of water entering the tube and the amount leaving the tube after x minutes. If k is the function representing the amount of water in the tube after x minutes, it is given by:

k(x) = f(x) - g(x)

k(x) = 12x - 6x

k(x) = 6x

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A bag of marbles contains five red marbles three green marbles and six yellow marbles what is the probability of randomly choosi
maria [59]
That should answer ur question!

5 0
3 years ago
Lance has three times as many pencils as Nick, and they have 84 pencils together. How many pencils does each of them have?
STALIN [3.7K]

Answer:

Let Lance represented by L and Nick represented by N

As per the statement:

Lance has three times as many pencils as Nick

⇒L = 3N         .....[1]

It is also given that:

They have 84 pencils together.

⇒L+N = 84               .....[2]

Substitute the equation [1] into [2] we have;

3N+N = 84

⇒4N = 84

Divide both sides by 4 we have;

N = 21

Substitute this in [1] we have;

L = 3(21) = 63

Therefore, Lance has 63 pencils and Nick has 21 pencils

6 0
4 years ago
Read 2 more answers
The sales tax rate is 15%. How much will Anna expect to pay for a bunch of bananas that cost $5.26?(Bananas $5.26 plus tax) $6.0
MAXImum [283]

Answer:

A is the correct option

Anna will expect to pay $6.05

Explanation:

Given that Anna is expected to pay $5.26 plus additional 15% of $5.26 on tax, the amount she pays in total is:

$5.26 + (15% of $5.26)

= $5.26 + (0.15)($5.26)

= $5.26 + $0.789

= $6.049

This is approximately $6.05

6 0
1 year ago
What are the zeros of the quadratic function f(x) = 6x ^ 2 - 24x + 1 ?
ZanzabumX [31]

Answer:

x = \frac{12+\sqrt{138} }{6} and x = \frac{12-\sqrt{138} }{6}

Step-by-step explanation:

Let's use the quadratic formula, which states that for a quadratic of the form ax² + bc + c, the zeroes are: x=\frac{-b+\sqrt{b^2-4ac} }{2a} or x=\frac{-b-\sqrt{b^2-4ac} }{2a}.

Here, a = 6, b = -24, and c = 1. Plug these in:

x=\frac{-b+\sqrt{b^2-4ac} }{2a}

x=\frac{-(-24)+\sqrt{(-24)^2-4*6*1} }{2*6}=\frac{24+\sqrt{552} }{12}=\frac{24+2\sqrt{138} }{12} =\frac{12+\sqrt{138} }{6}

AND

x=\frac{-b-\sqrt{b^2-4ac} }{2a}

x=\frac{-(-24)-\sqrt{(-24)^2-4*6*1} }{2*6}=\frac{24-\sqrt{552} }{12}=\frac{24-2\sqrt{138} }{12} =\frac{12-\sqrt{138} }{6}

Thus, the zeroes are: x = \frac{12+\sqrt{138} }{6} and x = \frac{12-\sqrt{138} }{6}.

3 0
3 years ago
Read 2 more answers
The length of segment XY is 9 cm. Which statements regarding triangle XYZ are correct? Check all that apply.
Dominik [7]

<u>Answer-</u>

  • YZ = 9 cm
  • XZ=9\sqrt2
  • XZ is the longest segment in triangle XYZ.

<u>Solution-</u>

Triangle XYZ is a right angle triangle with ∠Y=90°

Triangle XYZ is also an isosceles triangle, as

∠X =45°= ∠Z

Therefore, triangle XYZ is a right angle isosceles triangle.

So,

XY = YZ = 9 cm

Applying Pythagoras theorem,

\Rightarrow XZ^2=XY^2+YZ^2\\\\\Rightarrow XZ^2=9^2+9^2\\\\\Rightarrow XZ^2=2\times 9^2\\\\\Rightarrow XZ=\sqrt{2\times 9^2}=9\sqrt2

In a right angle triangle, always the hypotenuse is the largest. So XZ is the longest segment in triangle XYZ.


6 0
3 years ago
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