You fill the entire fish tank with water. Then you dump out some of the water. The volume of the water in the tank decreases by 96 cubic inches. How deep is the water now? (The height is 12 inches, the base is 48)

Answer:

9(x-1)(x-1) or 9(x-1)²

Step-by-step explanation:

9x² - 18x + 9

factor out a 9

9(x² - 2x + 1)

use middle term factorization to factor x² - 2x + 1

9(x-1)(x-1) or 9(x-1)²

Middle term factorization explained:

For x² - 2x + 1, you want to find 2 numbers that multiply to +1 and add to -2. You then split x² to x and x and add the 2 numbers individually to x.

It should look something like (x+1st number)(x+2nd number)

the two numbers that multiply to get to 1 and add to get to -2 are -1 and -1

( -1 × -1 = 1 and -1 + -1 = 2 )

so we then add the number to the split x² to get (x-1)(x-1) which is the same as (x-1)², the 9 is then added to the factored form to get 9(x-1)(x-1) or 9(x-1)²

Answer:

  -56

Step-by-step explanation:

It is often easiest to find terms of a sequence by simply writing each one based on the previous one. Here, the common ratio of -2 tells you that each term is -2 times the previous term.

The first four terms are ...

  7, -14, 28, -56

The fourth term is -56.

Answer:

n is 68 and m is 44

Step-by-step explanation:

Answer:

I think 4 years

(not sure)

Answer: 7.1 years

Step-by-step explanation:

Lets write a simple interest expression for this:

SI = P(1 + rt)

10,000 = 1,000(1 + 0.065[t])

This model is not quite complete yet, since he is adding 1200 every year. To fix this, we simply add a constant term, 1200t, where t is the number of years that have passed.

10,000 = 1,000(1 + 0.065[t]) + 1200t

Now we just need to evaluate this:

10,000 = 1,000 + 65t + 1200t

9,000 = 1265t

.: t ≅ 7.115

It will take about 7.1 years

Answer:

I can't see the full question but as far as I can tell

by the picture

x=100

Answer:

9x²

Step-by-step explanation:

(- 3x)²

= - 3x × - 3x

= - 3 × - 3 × x × x

= 9 × x²

= 9x²

Answer:

The correct option is C because it shows the accurate cosine rule

Equation to get the third side :  [tex]c = \sqrt{(42^2 +35^2 -2\times 42\times35\times cos(120\degrees ))}[/tex]

The correct option is C.

Given, that sides of triangle are 42 cm and 35 cm .

The third side can be found using the Law of Cosines,

[tex]c^2 = a^2 +b^2 - 2ab\times cos(C)[/tex]

where C is the angle opposite the third side (c) .

For the given side lengths, then the third side can be found .

Here,

a = 42

b = 35

∠C = 120°

Substitute the values,

[tex]c = \sqrt{(42^2 +35^2 -2\times 42\times35\times cos(120\degrees ))}[/tex]

[tex]c = \sqrt{1764 + 1225 + 1470} \\c = \sqrt{4456}\\c = 66.75[/tex]

Hence the third side is of 66.75 units.

The correct option is C .

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Answer:

Length = 8+7 = 15

Width = 8

Step-by-step explanation:

                       New

Length = x+7 , x+4

Width = x ,x+2

(x+7) x = (x+4)( x+2)

expand and simplify x =8

The length of the shorter side length of original rectangle is 8 inches and of original rectangle longer side length is 15 inches.

Let l is the length and b is the breadth of the rectangle.

then the area of the rectangle is ab.

Given One side of a rectangle is 7 inches longer than another side.

then shorter side length is x and the large side length is 7+x.

then the area of the original rectangle is x(x+7)

Now calculate the sides of the new rectangle.

longer side of this rectangle decreases by 3 then new side is 7+x -3= 4+x

The shorter side increases by 2 inches then x+2.

So new rectangle area is (x+4)(x+2)

Both rectangle area is equal then

(x+4)(x+2) = x(x+7)

x² +2x+4x+8 = x²+7x

x²+6x+8 = x²+7x

x²-x²+7x-6x = 8

x = 8

Since a shorter side length is 8 inches and a longer side length is 8+7 =15 inches.

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Answer:

12

Step-by-step explanation:

collect the like terms and divide

1) Water in a plastic container, p'= 10 - 3 p

2) Water in a glass container = 27 quarts

Water in a plastic container = 1 quarts

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A glass jug can hold (p + 6) quarts less water than a plastic container, 2 glass jugs and 2 plastic containers contain 6p quarts of water in all.

Now,

Let j represents water in one glass jag while p' represents the water in one plastic container,

Hence, According to the question,

⇒ j - p' = 6p+8 --------(1)

And, 2j+2p'=56p --------(2)

2 × equation (1)

⇒ 2 j - 2 p' = 12p + 16 ---------(3)

Equation (2) + equation (3)

We get, 4 j = 12 p + 72

⇒ j = 3 p + 18

Putting this value in equation (1),

We get, 3p+18-p'=6p+8

p' = -3p + 10 = 10 - 3p

Thus, water in a plastic container, p'= 10 - 3 p

b) If p=3

Water in a glass container = 3 × 3 + 18 = 27 quarts

Water in a plastic container = 10 - 3 × 3 = 1 quarts

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Using the equivalence concept, it is found that the correct option is given by:

a the expressions have the same value for any value of y.

Two expressions are said to be equivalent if for the same input, they have the same value.

In the expressions given in this problem, the input is y, hence they have the same value for any value of y, which means that option A is correct.

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Answer:

68.7

Step-by-step explanation:

Lets say this triangle is represented as ABC.

AB = BC

So:

23+23+22.7 = p

p = 68.7

Answer: y = [tex]\frac{1}{6}[/tex]x + 2

Step-by-step explanation:

    [1] First, we will graph the points given. See the attachment with [1] in the corner.

    [2] Next, we will find the slope.

    (2a) Using rise over run. See the attachment with [2] in the corner.

    (2b) Use the slope equation:

[tex]\displaystyle \frac{1-3}{-6-6}= \frac{-2}{-12} =\frac{1}{6}[/tex]

    [3] Find the y-intercept. Look to the graph. See the attachment with [3] in the corner.

         This gives us a final answer of y = [tex]\frac{1}{6}[/tex]x + 2

Answer:

m∠5 = 75°

Step-by-step explanation:

Angle 2 and Angle 4 are the same as they are alternate interior angles.

Since m∠2 = 45°

We then have m∠4 = 45°

We are given m∠3 = 60°

Now, we just have to find 7∠5.

The sum of the angle of a triangle adds up to 180°.

So, m∠3 + m∠4 + m∠5 = 180°.

60° + 45° + m∠5 = 180°.

Solving for ∠5

m∠5  = 180° - (60° + 45°)

m∠5 = 180° - (105°)

m∠5 = 75°

Answer:

[tex]\frac{2}{9}[/tex]

Step-by-step explanation:

1. [tex]\frac{2}{3} -\frac{4}{9}[/tex]

2. Multiply [tex]\frac{2}{3}[/tex] by [tex]\frac{3}{3}[/tex] to get a denominator equal to [tex]\frac{4}{9}[/tex]

3. [tex]\frac{2}{3} *\frac{3}{3} =\frac{6}{9}[/tex]

4. [tex]\frac{6}{9}-\frac{4}{9} =\frac{2}{9}[/tex]

The expression is:  [tex]\frac{2}{3}*\frac{3}{3} -\frac{4}{9}[/tex]

Answer:

6/9-4/9

Step-by-step explanation:

ez pls mark branliest

Answer:

1

Step-by-step explanation:

The only number 24 and 25 can both have is 1

Answer:

h = 19 mm

Step-by-step explanation:

the volume (V) of the prism is calculated as

V = Ah ( A is the area of the base and h the height )

the base is a regular pentagon whose area (A) is calculated as

A = [tex]\frac{1}{2}[/tex] pa ( p is the perimeter and a the apothem )

p = 5 × 12 = 60 mm and a = 5 mm , then

A = [tex]\frac{1}{2}[/tex] × 60 × 5 = 30 × 5 = 150 mm²

given V = 2850 , then

150h = 2850 ( divide both sides by 150 )

h = 19 mm

Step 1. Isolate the variable x:

[tex]3x-11 > 7x+9[/tex]

[tex]-4x > 20[/tex]

[tex]x > -5[/tex]

Step 2. Use the simplified inequality to graph:

I hope this helps!

Answer:

6.2

Step-by-step explanation:

I don't think you need my explanation anymore.

Answer:

6ft, the missing side is the base(b), 10ft is the hypotenuse(h) and 8ft is the perpendicular(p). The formula for base is root over h²-p² and root over 10²-8² equals 6.

one less than the 18 and a number

18 × n = (product) - 1

Answer:

Pi is the number you get from dividing the circumfrence by the diameter of a perfect circle. It is important because without this, we wouldnt have perfect circles and even wheels could be disformed and cause crashes.

Answer:

Pi is an infinite number. We need it to find the area and circumference of a circle.

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

.2 of an hour   is     .2 * 60 min = 12 min

120 min / 10 times = 12 min per trip

The train takes 12 minutes to go around the museum once.

A mathematical arithmetic operation is multiplication. Moreover, it is the practice of repeatedly adding the same expression kinds.

Example: 2 x 3 means that 2 is multiplied by 3 or that 3 is multiplied by 2 times.

A toy train that travels the length of a train museum is present. In two hours, the train travels roughly ten times.

The error in the student's work is converting 0.2 hours to 20 minutes. 0.2 hours is equal to 12 minutes, not 20 minutes.

To correct the student's work, we can multiply 0.2 by 60 to convert it to minutes:

0.2 hours × 60 minutes/hour = 12 minutes

Therefore, it takes 12 minutes for the train to go around the museum 1 time.

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Answer: y = [tex]\frac{1}{5}[/tex]x + 8

Step-by-step explanation:

       This is asking us to remove the parameter. In other words, we want an equation with only the relation between x and y, so we need to remove the t. There are a few ways to do this, but I am going to set one equation equal to t and then plug it into the next one.

     Given:

x = 5t

    Divide both sides of the equation by 5:

t = [tex]\frac{1}{5}[/tex]x

     -

    Given:

y = t + 8

    Plug in:

y = ([tex]\frac{1}{5}[/tex]x) + 8

    Answer:

y = [tex]\frac{1}{5}[/tex]x + 8

Answer:

153.86

Step-by-step explanation:

The area of a circle is π[tex]r^2[/tex].

Since the radius of that circle, and we are using 3.14 for π, we get:

[tex]3.14 * 7^2 = 153.86[/tex]

Answer:

Technically you should get :153.94

But for your answer choice its the 2nd one.

Step-by-step explanation:

area=πr^2

Which means that you would plug in 7 for r.

Which means it would look like this: area=π7^2

Next you would square 7 which comes out to 49

Lastly multiply 49 time π (3.14)

Answer:

6. 30% 7. -30%

Step-by-step explanation:

6. The total comment after the song released =5000

Then, the next day comment add up by 1500

Thus, (1500/5000) × 100

=30% of increase

7. 15.5-10.75 =4.75

(4.75/15.5 )×100= 30%

So, the decrease is -30%( If its about increase then its a positive number, but if its decrease just add a '-')

Answer:

See below ↓↓

Step-by-step explanation:

6.

8.

Answer:

5x+3=8

Step-by-step explanation:

this is the answer

Answer:

  9

Step-by-step explanation:

The scale factor is the ratio of a Figure B dimension to the corresponding Figure A dimension.

__

The ratio of left-side dimensions is ...

  scale factor = fig B/fig A = 81/9 = 9

The scale factor is 9.

Answer:9

Step-by-step explanation:

Step-by-step explanation:

I hope this helps, you can ask any questions for clarification