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3 years ago

Simplify completely.

" \sqrt{68} " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Keith_Richards [23]3 years ago

3 0

$\bf \sqrt{68}\qquad 
\begin{cases}
68=2\cdot 2\cdot 17\\
\qquad 2^2\cdot 17
\end{cases}\qquad \sqrt{2^2\cdot 17}\implies 2\sqrt{17}$

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Solve this equation for a. 10a + 3 + 2a = 39

aliina [53]

10a+3+2a=39
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-3 -3
12a=36
/12 /12
a=3

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3 years ago

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The graph below represents data that was collected by students on the number of

Ira Lisetskai [31]

Answer:

Step-by-step explanation:

To calculate the mean or average, add all the data point up and whatever the amount of data point there are is supposed to be divided by the sum of the data points. So in this case, 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. This is the sum of the data points. Now we have to divide by the amount of data points which is 7 (0 obviously has no value whatsoever). 28 divided by 7 is 4. The average/mean of the number of post made is therefore 4.

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2 years ago

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3 years ago

A motorboat travels 244 kilometers in 4 hours going upstream and 749 kilometers in 7 hours going downstream. What is the rate of

Kryger [21]

Answer:

Speed of Motorboat = 84 kmph

Speed of Current = 23 kmph

Step-by-step explanation:

Distance Equation is:

D = RT

Where

D is distance

R is rate

T is time

Downstream rate is rate of boat PLUS current

Upstream rate is rate of boat MINUS current

Let rate of boat be "x" and rate of current be "c".

From first statement, we can write:

244 = (x - c)(4)

From second statement, we can write:

749 = (x + c)(7)

The first equation becomes:

244 = 4x - 4c

The second equation becomes:

749 = 7x + 7c

Multiplying first equation by 7 , we have:

7 * [244 = 4x - 4c] = 1708 = 28x - 28c

Multiplying 2nd equation by 4, we have:

4 * [749 = 7x + 7c] = 2996 = 28x + 28c

Now we add up these equations (in bold):

1708 = 28x - 28c

2996 = 28x + 28c

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4704 = 56x

x = 4704/56

x = 84

Now using this value and plugging in original equation, we can find "c":

244 = 4x - 4c

244 = 4(84) - 4c

244 = 336 - 4c

4c = 92

c = 92/4

c = 23

<u>Speed of Motorboat = 84 kmph</u>

<u>Speed of Current = 23 kmph</u>

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4 years ago

A swim coach has at most $800 to buy equipment for the swim team. Each pull buoys costs $5.50 and each kickboard costs $10. Let

olga2289 [7]

Answer:

A) 5.50x + 10y ≤ 800

B) yes

C) no

D) 80 pull buoys and 35 kick boards

Step-by-step explanation:

A) The sum of costs must not exceed the budget:

5.50x +10.00y ≤ 800

B) 5.50(0) +10.00(50) = 500 ≤ 800 . . . . . yes, the coach could buy these

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D) The point (80, 35) is in the solution space. The coach could buy 80 pull buoys and 35 kick boards.

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3 years ago