Brittany’s Hot Tub. When draining her hot tub, the height of the water in Brittany’s hot tub decreases at a rate of 2 inches per minute. After 9 minutes there are 11 inches of water in the tub. Assume that the height is decreasing at a constant rate.
a. Write an equation for the height of water left in the tub (h) as a function of the number of the minutes (t) that have elapsed.
b. How high is the tub when it is full?
c. After how many minutes will the tub be empty?
d. What values of the domain, t, make sense? Why?
e. What values of the range, h, make sense? Why?

Answer:

-1/5

Step-by-step explanation:

i think thsts correct answer if not the answer is 1/2

Answer:

[tex]\text{A) }68\:\mathrm{cm}[/tex]

Step-by-step explanation:

The perimeter of a polygon is equal to the sum of all the sides of the polygon. Quadrilateral PTOS consists of sides TP, SP, TO, and SO.

Since TO and SO are both radii of the circle, they must be equal. Thus, since TO is given as 10 cm, SO will also be 10 cm.

To find TP and SP, we can use the Pythagorean Theorem. Since they are tangents, they intersect the circle at a [tex]90^{\circ}[/tex], creating right triangles [tex]\triangle TOP[/tex] and [tex]\triangle SOP[/tex].

The Pythagorean Theorem states that the following is true for any right triangle:

[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or the longest side, of the triangle

Thus, we have:

[tex]10^2+TP^2=26^2,\\TP^2=26^2-10^2,\\TP^2=\sqrt{576},\\TP=24[/tex]

Since both TP and SP are tangents of the circle and extend to the same point P, they will be equal.

What we know:

Thus, the perimeter of the quadrilateral PTOS is equal to [tex]24+24+10+10=\boxed{\text{A) }68\:\mathrm{cm}}[/tex]

Answer:

the other one should get a brainliest.

I'm just answering to make it technically possible.

Answer:

$100

$120 in and $20 out

Step-by-step explanation:

Answer:

the answer is $100

because if the bank is loosing 2% they are having to pay $20 bc 0.02 x 1,000= 20, and they are earning 12% they getting 120 bc 0.12 x 1,000 = 120, and 120-20= $100. you have to subtract the $20 because that is what the bank is paying, so it's losing money

Answer:

you didnt provide the other 2 measurements, its length x width x height for volume

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Please find the complete question in the attached file.

Arrange the value into the ascending order:

[tex]62, 88, 89, 90, 92, 95, 96, 98, 100, 100[/tex]

Calculating the Range:

[tex]= Greatest - Lowest\\\\= 100 - 62\\\\ = 38[/tex]

Outlier =  This might be the value "far" from other data values= 62

The range of scores would be, sans outlier,

 [tex]88, 89, 90, 92, 95, 96, 98, 100, 100[/tex]

Calculating the range without outlier [tex]= 100 - 88 = 12[/tex]

Inter Quartile Range [tex]= Q_3 - Q_1[/tex]

[tex]IQR = 98 - 89 = 11[/tex]

Calculating the IQR without outlier [tex]= 99 - 89.5 = 9.5[/tex]

Therefore,

Option a is "True".

Option b is "True".

Option c is "True".

Option d is "False".

Option e is "False".

Option f is "True".

Answer: [tex]7\times 10^{-1}[/tex]

Step-by-step explanation:

Given

[tex](4.0\times 105)\div (5.89\times 102)[/tex]

First solve the brackets part in calculator, we obtain

[tex]\Rightarrow 420\div 600.78\\\\\Rightarrow \dfrac{420}{600.78}=0.69909\approx 0.70\\\\\Rightarrow 7\times 10^{-1}[/tex]

Answer:

-7/3 +\- 1/3i

Step-by-step explanation:

Answer:

Using the property of intersecting secant:-

[tex](DE)(CE)=(FE)(LE)[/tex]

[tex](4)(x-1+14)=(5)(x-4+5)[/tex]

[tex]4(x+3)=(5x+1)[/tex]

[tex]4x+12=5x+5[/tex]

[tex]4x+-5x=5-12[/tex]

[tex]-x=-7[/tex]

[tex]x=7[/tex]

[tex]So, CD=x-1=7-1=6[/tex]

[tex]so,~your ~answer ~is ~B) ~6[/tex]

By intersecting secants theorem, the measure of CD is 6 units.

The theorem states that when two secants intersect at an exterior point, the product of the one whole secant segment and its external segment is equal to the product of the other whole secant segment and its external segment.

For the given situation,

The diagram shows the circle with the two secants intersecting at the exterior point.

By intersecting secants theorem,

[tex](CE)(DE)=(LE)(FE)[/tex] -------- (1)

Here, CE = CD + DE

⇒ [tex]CE = (x-1)+4[/tex]

DE = 4

LE = LF + FE

⇒ [tex]LE = (x-4)+5[/tex]

FE = 5

On substituting the above values in 1,

⇒ [tex](x-1+4)(4)=(x-4+5)(5)[/tex]

⇒ [tex](x+3)(4)=(x+1)(5)[/tex]

⇒ [tex]4x+12=5x+5[/tex]

⇒ [tex]5x-4x=12-5[/tex]

⇒ [tex]x=7[/tex]

Thus CD = [tex]x-1[/tex]

⇒ [tex]7-1=6[/tex]

Hence we can conclude that by intersecting secants theorem, the measure of CD is 6 units.

Learn more about intersecting secants theorem here

https://brainly.com/question/9853828

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Answer:

-3

Step-by-step explanation:

[tex]\sqrt{25}[/tex] is equal to 5, so we can sub it in the equation.

This gives 12-3×5 or 12-15.

This solves to -3.

**This content involves simplifying surds, which you may wish to revise. I'm always happy to help!

Answer:

yes the triangle are similar

Answer:

x = 6

Step-by-step explanation:

Given

4x - 2 = 2x + 10 ( subtract 2x from both sides )

2x - 2 = 10 ( add 2 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6

Answer:

x = -2, y = 5/3

Step-by-step explanation:

we have the value of x already (-2).

x=-2

Plug it into the first equation y = 2/3x+3

y = 2/3(-2)+3

y = -4/3+3

y = -4/3+9/3

y = 5/3

x = -2, y = 5/3

Option C is correct, 6n(n³-4n²+3) is the  factored form of expression 6n⁴ – 24n³ + 18n

An expression is combination of variables, numbers and operators.

The given expression is 6n⁴ – 24n³ + 18n.

Six times of n power four minus twenty four times of n cube plus eighteen times of n.

6n⁴ – 24n³ + 18n.

Now we have to find the factored form of 6n⁴ – 24n³ + 18n.

Take 6n as common

6n(n³-4n²+3)

Hence, Option C is correct, 6n(n³-4n²+3) is the factored form of expression 6n⁴ – 24n³ + 18n

To learn more on Expressions click:

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Answer:

7/12 h

Step-by-step explanation:

1/3 of 1 3/4  =  1/3 of 7/4 = 1/3 x 7/4  =  7/12 h

Answer:

ummmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

Step-by-step explanation:

Answer:

(5x2y3+1)(5x2y3−1)

Step-by-step explanation:

In this case, since this equation has both sides as a perfect square, you can apply the difference of squares formula a^2 - b^2 = (a+b) (a-b)

Applying this formula and factoring it accordingly leaves us off with (5x2y3+1)(5x2y3−1).

Answer:

17pigs and 11 chicken  

Step-by-step explanation:

Answer:

The answer will be 2a×3=6a

Because the number increase by a percentage this is an exponential growth problem.

The equation for exponential growth is :

Total = start value x ( 1 + percent) ^ time

Using the information from the problem:

2011-2005 = 6 years.

Total = 23 x (1 + 0.72)^6

Total = 23x 1.72^6

Total = 595.52 = 596 total people

Answer:

-2

Step-by-step explanation:

If you need the work let me know but that should be correct! Good luck :)

Answer:

6x²+17x-12

Step-by-step explanation:

(2x-3)(4-3x)

8x-6x²-12+9x

Reorder.

6x²+9x+8x-12

Combine like terms.

6x²+17x-12

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hope it helps

Step-by-step explanation:

24$

hope this helps please like and mark as brainliest

Answer:

x = 1

y = 1

Step-by-step explanation:

3x - 2y = 1

2x + 2y = 4

3x - 2y + 2x + 2y = 1 + 4

3x + 2x = 5

5x = 5

5x ÷ 5 = 5 ÷ 5

x = 1

2x + 2y = 4

2(1) + 2y = 4

2 + 2y = 4

2 - 2 + 2y = 4 - 2

2y = 2

2y ÷ 2 = 2 ÷ 2

y = 1

Check:

3x - 2y = 1

3(1) - 2(1) = 1

3 - 2 = 1

x and y being 1 works for the first equation.

2x + 2y = 4

2(1) + 2(1) = 4

2 + 2 = 4

x and y being one works for both equations.

Answer: x = 4.5

Step-by-step explanation: First, do x + x, since they are like terms. That equals 2x. The equation is now 2x = 9. Divide both sides by 2. x = 4.5.

  x + x = 9

  2x = 9

÷2    ÷2

---------------------

 x = 4.5  

x + x = 9

4.5 + 4.5 = 9

Answer:

A

Step-by-step explanation:

Desnity: mass/volume

3/20= .15

Answer:

32

Step-by-step explanation: