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Alekssandra [29.7K]
3 years ago
13

Simplify:

D%20" id="TexFormula1" title=" \sqrt[5]{3} + \sqrt{12} + \sqrt{32} " alt=" \sqrt[5]{3} + \sqrt{12} + \sqrt{32} " align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Juliette [100K]3 years ago
7 0

\sqrt[5]3+\sqrt{12}+\sqrt{32}=\sqrt[5]3+\sqrt{4\cdot3}+\sqrt{16\cdot2}=\sqrt[5]3+\sqrt4\cdot\sqrt3+\sqrt{16}\cdot\sqrt2\\\\=\boxed{\sqrt[5]3+2\sqrt3+4\sqrt2}

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Solve the system of equations.
Orlov [11]

Answer:

x=-1, y = 2, z = 1

Step-by-step explanation:

We are given with three equations and we are asked to find the solution to them.

2x + 2y + 3z = 5  ------------- (A)

6x + 3y + 6z = 6  --------------(B)

3x + 4y + 4z = 9 ---------------(C)

Step 1 .

multiplying equation (A) by 3 and subtracting B from the result

6x + 6y + 9z = 15

6x + 3y + 6z = 6

-     -       -       = -

_______________

3y+3z=9

y+z=3

y=3-z  ----------------- (C)

Step 2.

Substituting this value of y in equation B and C

6x + 3(3-z) + 6z = 6  

6x+9-3z+6z=6

6x+3z=-3

2x+z=-1 ----------------(D)

3x + 4(3-z) + 4z = 9

3x+12-4z+4z=9

3x=-3  

x=-1 ------------ (E)

Putting this value f x in (D)

2(-1)+z=-1

-2+z=-1

z=1

Now we put this value of z in equation (C)

y=3-z

y=3-1

y=2

Hence we have

x=-1, y=2 and z=1

6 0
4 years ago
A 12-inch candle is lit and steadily burns until it is burned out. As the burned length of the candle increases from 4 to 7.5 in
MatroZZZ [7]

Answer:

The remaining length of the candle varies from 8 inches to 4.5 inches.

The required expression is: r=12-b

Where, b represents the burned length and r represents the remaining length.

Step-by-step explanation:

Consider the provided information.  

A 12-inch candle is lit and steadily burns until it is burned out.

The length of the candle is 12 in.

The burned length of the candle is 4 in.

That means the remaining length is 12 - 4 = 8 in

The burned length of the candle is 7.5 in.

That means the remaining length is 12 - 7.5 = 4.5 in

Hence, the remaining length of the candle varies from 8 inches to 4.5 inches.

Suppose b represents the burned length of the candle in inches (or the number of inches that have burned from the candle since it was lit) and r represents the the remaining length of the candle (in inches).

The required expression is: r=12-b

8 0
4 years ago
Given: g ∥ h and ∠2 ≅ ∠3
Yuliya22 [10]

Answer: What's up?

LOL

7 0
3 years ago
Read 2 more answers
The symphonic choir and the jazz choir are recording songs for an album. The album can be no more than 72 minutes long. The jazz
zimovet [89]

Answer:

The symphonic choir can record a maximum of 14 songs.

Step-by-step explanation:

We know that the album cannot be more than 72 minutes long, and the jazz choir records a total of 7 (3min) = 21  song minutes.

If we call c the number of songs the symphonic choir records , and each song is 3.5 minute long, then the song minutes for the symphonic choir are 3.5c; therefore, we have the inequality

3.5c+21\leq 72<em> (this says the song minutes for jazz choir plus song minutes for symphonic choice cannot exceed 72 minutes )</em>

We solve this inequality by subtracting 21 from both sides and then dividing by 3.5:

3.5c\leq 51

$c\leq \frac{51}{3.5} $

c\leq 14.47

The maximum integer value c can take is 14; therefore, the maximum number of songs the symphonic choir can record is 14 songs.

3 0
3 years ago
I need help asap <br> Pleasssee
Svetllana [295]
-2+4-3+8-2-0.5 = -7.5+12
-7.5+12 = 4.5
4.5/6 (number of months) = 0.75
0.75 = -3/4
-3/4 is your answer. :)

6 0
4 years ago
Read 2 more answers
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