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chubhunter [2.5K]
3 years ago
15

Question 1/14

Mathematics
1 answer:
Lostsunrise [7]3 years ago
8 0

An algebraic expression that represents the weight of this object is W=72+3.9m

  • Let the weight of this object be W.
  • Let the month be m.

<u>Given the following data:</u>

  • Weight of object = 72 pounds.
  • Increment = 3.9 pounds per month.

To write an algebraic expression that represents the weight of this object:

<h3>How to write an algebraic expression.</h3>

In this exercise, you're required to write an algebraic expression that represents the weight of this object. Thus, we would choose some variables to denote the parameters that were given in this word problem.

Therefore, the algebraic expression would be written as follows:

W=72+3.9m

Read more on word problems here: brainly.com/question/13170908

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The area of the circle is 144π m2<br><br> What is the diameter of the circle?
Over [174]

Answer:

Step-by-step explanation:

Remember that

Area of Circle = \pi r^2

\pi  = pi \\r = radius

They told us that for this circle, the area is 144\pi  m^2

If you put it back into the formula for area of a circle we get:

Area of Circle = \pi r^2

144\pi = \pi r^2

Divide both sides by \pi.

144 = r^2

Now we want to solve for r (r = radius).

You need to square root each side

\sqrt{144} = \sqrt{r^2}

12 = r

So now we know the radius, r = 12 metres

Also remember that

Diameter = 2r

So,

Diameter = 2 times 12 = 24 metres

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3 years ago
The football team has 2 large water containers. Each container holds 345π in3 of water. Each player is given a cylindrical water
raketka [301]

Answer:

They'll be able to get 34 bottles from the containers.

Step-by-step explanation:

Since the bottles are cylindrical we can calculate their volume by using the following formula:

V = base_area*h

V = \pi*(r^2)*h

r = d/2 = 4/2 = 2 inches

V = 3.14*(2^2)*5 = 3.14*4*5

V = 3.14*20 = 62.8 inches^3

In order to know how many full bottles the players will get we need to divide the total volume of the containers, which is given by the sum of the volume of each container, and divide it by the volume of each bottle. We have:

bottles = (345*pi + 345*pi)/62.8 = 690*pi/62.8 = 2,166.6/62.8 = 34.5

Since the problem wants the amount of full bottles we only take the integer part, so they will be able to get 34 bottles from the containers.

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3 years ago
Solve the following matrix equations: (matrices)
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Step-by-step explanation:

a)

3X + \begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix} = \begin{pmatrix}  - 1 & 6 \\ 10 & 14 \end{pmatrix} \\  \\  3X  = \begin{pmatrix}  - 1 & 6 \\ 10 & 14 \end{pmatrix} -  \begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix}  \\  \\ 3X  = \begin{pmatrix}  - 1 - 2 & 6 - 3 \\ 10 - 4 & 14 - 5 \end{pmatrix}\\  \\ 3X  = \begin{pmatrix}   - 3 & 3 \\ 6 & 9\end{pmatrix}\\  \\ X  =  \frac{1}{3} \begin{pmatrix}   - 3 & 3 \\ 6 & 9\end{pmatrix}\\  \\ X  =  \begin{pmatrix}  \frac{ - 3}{3}  & \frac{3}{3}  \\  \\ \frac{6}{3}  & \frac{9}{3} \end{pmatrix}\\  \\ \huge \red{ X}  =  \purple{ \begin{pmatrix}  - 1  &1  \\ 2 & 3 \end{pmatrix}}

b)

3X + 2I_3=\begin{pmatrix} 5 & 0 & -3 \\6 & 5 & 0\\ 9 & 6 & 5\end{pmatrix} \\\\3X + 2\begin{pmatrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\end{pmatrix} =\begin{pmatrix} 5 & 0 & - 3\\6 & 5 & 0\\ 9 & 6 & 5 \end{pmatrix} \\\\3X + \begin{pmatrix} 2 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 2\end{pmatrix} =\begin{pmatrix} 5 & 0 & - 3\\ 6 & 5 & 0 \\ 9 & 6 & 5 \end{pmatrix} \\\\3X  =\begin{pmatrix} 5 & 0 & -3 \\ 6 & 5 & 0 \\ 9 & 6 & 5 \end{pmatrix} - \begin{pmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{pmatrix} \\\\3X  =\begin{pmatrix} 5-2 & 0-0 & -3-0 \\ 6-0 & 5-2 & 0-0 \\ 9-0 & 6-0 & 5-2 \end{pmatrix} \\\\3X  =\begin{pmatrix} 3 & 0 & - 3 \\ 6 & 3 & 0 \\ 9 & 6 & 3 \end{pmatrix} \\\\X  =\frac{1}{3} \begin{pmatrix} 3 & 0 & - 3 \\ 6 & 3 & 0 \\ 9 & 6 & 3 \end{pmatrix} \\\\X  =\begin{pmatrix} \frac{3}{3}  & \frac{0}{3}  & \frac{-3}{3} \\\\ \frac{6}{3}  & \frac{3}{3}  & \frac{0}{3} \\\\ \frac{9}{3}  & \frac{6}{3}  & \frac{3}{3} \end{pmatrix} \\\\\huge\purple {X} =\orange{\begin{pmatrix} 1  & 0 & - 1\\ 2  & 1 & 0 \\ 3  & 2  & 1 \end{pmatrix}}\\

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Tom asked his Granny how old she was. Rather than giving him a straight answer, she replied: "I have 6 children, and there are 4
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