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tatuchka [14]
1 year ago
11

2. Fran needs a bookcase to hold all of his math books. He decides to try to build the bookcasepictured below. He needs to buy t

hree pieces of wood to make the shelves. Each of thesethree pieces should be 3ş feet long. He needs to buy two pieces for the sides. These twopieces should be 4-— feet each. Finally, he will need to buy one piece for the top. This pieceshould be 4 feet. What is the total length of wood that Fran needs to buy?
Mathematics
1 answer:
astraxan [27]1 year ago
5 0

Let's rewrite the mixed number as a fractions:

\begin{gathered} 3\frac{2}{3}=\frac{11}{3} \\ 4\frac{1}{2}=\frac{9}{2} \end{gathered}

Therefore, the total length will be:

3\cdot(\frac{11}{3})+2(\frac{9}{2})+4=24ft

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If line MO bisects angle PMN, angle PMN =74 and angle OMN =(2x+7)
Valentin [98]

Answer:

<h2>15</h2>

Step-by-step explanation:

We can find the value of x from the question

If If line MO bisects angle PMN at M, then <PMO = < OMN  and

<PMO + < OMN = <PMN

The equation then becomes;

<OMN + < OMN = <PMN

2<OMN = <PMN

Given

angle PMN =74 and

angle OMN =(2x+7)

Substituting the values into the formula to get x

2(2x+7) = 74

open the bracket

4x+14 = 74

Subtract 14 from both sides

4x+14-14 = 74-14

4x = 60

x = 60/4

x = 15

Hence the value of x is 15°

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3 years ago
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tankabanditka [31]

Answer:

Therefore, the solution is:

\boxed{\int \sin 7x\, dx=-\frac{\cos 7x}{7}}

Step-by-step explanation:

We calculate the given integral.  We use the substitution t = 7x.

\int \sin 7x\, dx=\begin{vmatrix} 7x=t\\ 7\, dx=dt\\ dx=\frac{dt}{7} \end{vmatrix}\\\\=\int \sin t \cdot \frac{1}{7}\, dt\\\\=\frac{1}{7}\cdot (-\cos t)\\\\=-\frac{\cos 7x}{7}

Therefore, the solution is:

\boxed{\int \sin 7x\, dx=-\frac{\cos 7x}{7}}

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Answer:

D

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