Lilian is building a swimming pool in the shape of a right rectangular prism. The area of the base of the swimming pool is 72 square meters. The depth of the swimming pool is 3 meters. What is the volume of the swimming pool?

Answer:

4

Step-by-step explanation:

We want to find the highest common factor

Breaking them into factors

28 = 4*7 = 2*2*7

40 = 4*10 = 2*2*2*5

12 = 4*3 = 2*2*3

24 = 3*8 = 3*2*2*2

The factor that appears in all is 2*2

2*2 =4

Answer:

4

Step-by-step explanation:

28÷4=7

40÷4=10

12÷4=3

24÷4=6

7, 10, 3 and 6 cannot be divided by any same number.

Answer:

Step-by-step explanation:

When you learn calculus you'll be able to do this by hand (without a calculator) but for now we have to just kind of guess. We know that 8 x 8 = 64 and 9 x 9 = 81, so the number is between 8 and 9. Since 68 is closer to 64 than it is to 81, the number is closer to 8. Like less than 8.5. 8.1 squared is 65.61, (you can do this by hand...without a calculator) and 8.2 squared is 67.24, and 8.3 squared is 68.89. 8.3 squared is too high while 8.1 squared was too low; the estimation to the nearest tenth is 8.2

Answer:

Step-by-step explanation:

x^2 - 6x = -156    Next step is:

x^2 - 6x + (-3)^2 = -156 + (-3)^2

Answer:

I doubt it is not going to be a great

Step-by-step explanation:

the same time as a child support of the year old girl I don't know what you think about it is not going to

Answer:

a^2+2ab = 21

(a+b)^2= 25

Step-by-step explanation:

(a+b)^2 = a^+2ab+b^2

sub a=3 and b=2 and simplify  

Answer I think the answer is 9 if you round off to the nearest ones,in this case you are rounding off to 9 which will still be 9 because 4 is less than 5.

I hope this helps

Answer:

Số tien:S =150000+(x-10)14000

Step-by-step explanation:

Answer:

Below!

Step-by-step explanation:

First you can find the area of the triangular shape using A = bh /2

A = (12)(5.8) / 2

   = 34.8 km^2

Now you can just multiply this area by the length of the prism

V = Area x height

   = (34.8)(10)

   = 348 km^3

Hope this helps! Best of luck <3

Answer:

[tex]x = 5[/tex]

Step-by-step explanation:

Step 1:  Distribute

[tex]4x + 2 = 2(x + 6)[/tex]

[tex]4x + 2 = (2 * x) + (2 * 6)[/tex]

[tex]4x + 2 = 2x + 12[/tex]

Step 2:  Subtract 2 from both sides

[tex]4x + 2 - 2 = 2x + 12 - 2[/tex]

[tex]4x = 2x + 10[/tex]

Step 3:  Subtract 2x from both sides

[tex]4x - 2x = 2x - 2x + 10[/tex]

[tex]2x = 10[/tex]

Step 4:  Divide both sides by 2

[tex]2x / 2 = 10 / 2[/tex]

[tex]x = 5[/tex]

Answer:  [tex]x = 5[/tex]

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]x = 5[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'...}}\\\\4x + 2 =2(x+6)\\------------\\\rightarrow 4x + 2 = 2x + 12\\\\\rightarrow4x - 2x +2 = 2x - 2x + 12\\\\\rightarrow 2x + 2 = 12\\\\\rightarrow2x + 2 - 2 = 12 - 2\\\\\rightarrow 2x = 10\\\\\rightarrow \frac{2x=10}{2}\\\\\rightarrow \boxed{x = 5}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

(2,7/2)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoints and divide by 2

(-4+8) /2 = 4/2 =2

To find the y coordinate of the midpoint, add the y coordinates of the endpoints and divide by 2

(2+5) /2 = 7/2 =

The midpoint is (2,7/2)

Answer:

(2, [tex]\frac{7}{2}[/tex])

Step-by-step explanation:

Hi there!

We want to find the midpoint of (-4,2) and (8,5)

To do that, we'll use the midpoint formula, which will find the midpoint using the formula ( [tex]\frac{x_1+x_2}{2}[/tex],[tex]\frac{y_1+y_1}{2}[/tex]), where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We have everything we need to find the midpoint, but let's label the values of the points to avoid any confusion

[tex]x_1[/tex]=-4

[tex]y_1[/tex]=2

[tex]x_2[/tex]=8

[tex]y_2[/tex]=5

Now substitute those values into the formula and solve

To find the value of the x-coordinate of the midpoint, use [tex]\frac{x_1+x_2}{2}[/tex]

x=[tex]\frac{-4+8}{2}[/tex]

Add the numbers together on the numerator

x=[tex]\frac{4}{2}[/tex]

Divide

x=2

The value of the x-coordinate is 2

Now find the value of the y coordinate by using [tex]\frac{y_1+y_1}{2}[/tex]

y=[tex]\frac{2+5}{2}[/tex]

Add the numbers together on the numerator

y=[tex]\frac{7}{2}[/tex]

So the point is (2, [tex]\frac{7}{2}[/tex])

Hope this helps!

Answer:

yes and?

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

2 units to the right -> -2 in the brackets next to x

4 units down -> -4 as a constant at the end of the equation

Answer: Segment PQ is a median

Step-by-step explanation:

A median is a segment whose endpoints are the vertex of a triangle and the midpoint of the opposite side. This means segment PQ has to be a median for it meets the criteria of a median.

The segment PQ is a median.

A median is a segment whose endpoints are the vertex of a triangle and the midpoint of the opposite side.

The median is the middle number in a sorted, ascending, or descending list of numbers and can be more descriptive of that data set than the average.

This means segment PQ has to be a median for it meets the criteria of a median.

To learn more about line visit:

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Answer:

Step-by-step explanation:

I may get this wrong because I don't think it's clear enough.

3 Letters

The station call letters must start with 1 of 3 letters

3

The next letter must be one of 25 and the last letter is 24

3 * 25 * 24 = 1800

5 letters

3 * 25 * 24 * 23*  22 = 910800

Total 1800 + 910800 = 912600

Answer:  80 cubic meters (choice B)

==============================================================

Explanation:

The floor of the pyramid is a pentagon made of five congruent isosceles triangles as shown in the diagram below. Each triangle has a base of 6 meters and height 2 meters. The base and height are always perpendicular.

Each triangle mentioned therefore has area base*height/2 = 6*2/2 = 12/2 = 6 square meters. Five such triangles results in a total area of 6*5 = 30 square meters. This is the area of the pentagonal floor.

We'll multiply this area by the height of the pyramid (8 meters) and then take 1/3 of this to get the pyramid's volume

volume = (1/3)*(area of floor)*(height of pyramid)

volume = (1/3)*(30)*(8)

volume = 10*8

volume = 80 cubic meters

Answer:

Step-by-step explanation:

If angle 2 is 75, the other angles that are also 75 are angles 4 (it's vertical to angle 2), angle 6 (it's corresponding to angle 2), angle 8 (it's alternate exterior to angle 2). All the other angles measure 180 - 75 which is 105.

Answer:

an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable is called polynomial. A polynomial with real coefficients is a product of irreducible polynomials of first and second degrees.

Answer:

Step-by-step explanation:

a) x=6 (x= 8-2)

b) x=4 ( 4x=21-5=16 -> x=4

c) x=7 (3x=34-13=21 -> x=7)

Answer:

A. Mean

Step-by-step explanation:

Mean, because it's the average of the numbers and if one number's way off, it would throw the average off by a lot! I honestly forgot a bit about interquartile ranges, but it doesn't affect the median at all/have a very little effect so that's why it's not all of these. But mean is for sure!

I hope this helped! :D

Answer:

21a² - 9ab

Step-by-step explanation:

(5a-2a)(7a-3b)

35a² - 15ab - 14a² + 6ab

35a² - 14a² - 15ab + 6ab

21a² - 9ab

Answer:

14

Step-by-step explanation:

[tex]4 \times (4 - .4) -. 4[/tex]

Answer:

I believe the answer would be 48.6 milliliters

Step-by-step explanation:

54 * 0.9 = 48.6

Answer:

56 m³

Step-by-step explanation:

Base area = 8×6/2 = 24 m²

Height = 7 m

Volume = 24×7/3

= 56 m³

Answered by GAUTHMATH

The conclusion is that the expression [tex]\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}[/tex] cannot be solved  without the l'hopital's rule,

The limit expression is given as:

[tex]\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}[/tex]

The limit of the expression cannot be solved without l'hopital's rule, because a direct substitution of ∞ for x would result in the following expression ∞/∞

i.e.

[tex]\lim_{x \to \infty} \frac{6 (2^{\infty}) - 1}{5(\infty)^2+ 10} = \frac{\infty}{\infty}[/tex]

So, the best way is to apply the l'hopital's rule.

This is done as follows:

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \lim_{x \to \infty} \frac{f'(x)}{g'(x)}[/tex]

When the numerator and the denominator are differentiated, we have:

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln(2)\cdot 2^{x + 1}}{10x}[/tex]

Further, differentiate

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln^2(2)\cdot 2^{x + 1}}{10}[/tex]

Now, we can substitute [tex]\infty[/tex] for x

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln^2(2)\cdot 2^{\infty + 1}}{10}[/tex]

Evaluate the numerator

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{\infty}{10}[/tex]

Evaluate the quotient

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \infty[/tex]

Hence, the conclusion is that the expression [tex]\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}[/tex] cannot be solved  without the l'hopital's rule

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Answer:

These are the entervals of the people who are atleast adults and are mature enough to take the surevy seriosly and answer correctly

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

First I found the area of the portion that extends off (if that makes sense??)

It is a triangle, so use A = bh/2

A = (2)(6) / 2

   = 6 cm^2

Next I found the area of the rectangle using A = LW

A = (6)(3)

   = 18 cm^2

Total area = 18 + 6

                 = 24 cm^2

Hope this helps! Best of luck <3

Step-by-step explanation:

First, a half plane can be defined as one side of a line, e.g. x < y-3.

1: True. A solution to two half planes is where the two half planes intersect. If they never intersect, then there literally cannot be a solution.

2: False. Take, for example, y=x and y=x+1. These two lines are parallel because in the equation y=mx+b, m represents the slope, and in these two lines, x is multiplied by 1, so both lines have the same slope and are therefore parallel. Then, take two boundary planes -- y > x and y>x+1. If we graph this out (see picture), the planes clearly intersect when y>x+1. The solution is where the planes intersect, so there is a solution area

9514 1404 393

Answer:

Step-by-step explanation:

Let J and M represent the current ages of Jacob and his Mother.

currently:

  M = 3 +9J

in 11 years:

  M+11 = 5 +3(J+11)

Using the first equation to substitute for M in the second, we have ...

  (3 +9J) +11 = 5 +3(J +11) . . . . . substitute for M

  9J +14 = 3J +38 . . . . . . simplify

  6J + 24 . . . . . . . . . . subtract 3J+14

  J = 4 . . . . . . . . . . divide by 6

  M = 3 +9(4) = 39

Jacob is 4 and his mother is 39.