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2 years ago

In a class of 22 students, 15 play an instrument and 11 play a sport. There are 9

Mathematics

1 answer:

nataly862011 [7]2 years ago

5 0

Answer:

7/22

Step-by-step explanation:

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1/2x + 1/3y = 7

pashok25 [27]

let's multiply both sides in each equation by the LCD of all fractions in it, thus doing away with the denominator.

$\begin{cases} \cfrac{1}{2}x+\cfrac{1}{3}y&=7\\\\ \cfrac{1}{4}x+\cfrac{2}{3}y&=6 \end{cases}\implies \begin{cases} \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( \cfrac{1}{2}x+\cfrac{1}{3}y \right)=6(7)}\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{1}{4}x+\cfrac{2}{3}y\right)=12(6)} \end{cases}\implies \begin{cases} 3x+2y=42\\ 3x+8y=72 \end{cases} \\\\[-0.35em] ~\dotfill$

$\bf \stackrel{\textit{using elimination}}{ \begin{array}{llll} 3x+2y=42&\times -1\implies &\begin{matrix} -3x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-2y=&-42\\ 3x+8y-72 &&~~\begin{matrix} 3x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+8y=&72\\ \cline{3-4}\\ &&~\hfill 6y=&30 \end{array}} \\\\\\ y=\cfrac{30}{6}\implies \blacktriangleright y=5 \blacktriangleleft \\\\[-0.35em] ~\dotfill$

$\bf \stackrel{\textit{substituting \underline{y} on the 1st equation}~\hfill }{3x+2(5)=42\implies 3x+10=42}\implies 3x=32 \\\\\\ x=\cfrac{32}{3}\implies \blacktriangleright x=10\frac{2}{3} \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left(10\frac{2}{3}~~,~~5 \right)~\hfill$

7 0

3 years ago

How to do this question plz answer me step by step plzz plz

faust18 [17]

$\text{Find the perimeter of the track field}\\\\\text{We already have one of our outside value, 50. We can multiply}\\\text{this by 2}\\\\50\cdot2=100\\\\\text{Now we need to find the perimeter, better known as the circumference}\\\text{of the half circle}\\\\\text{Since there is two half circles, we can make one}\\\text{whole circle}\\\text{Use the equation:}\\\\C=\pi \cdot d\\\\\text{Plug in and solve:}\\\\C=\pi \cdot 30\\\\C=94.24778\\\\$

$\text{Add 100 and 94.24778}\\\\100+94.24778= 194.24778\\\\\text{Round to the nearest hundredths place:}\\\\\boxed{\text{194.25 m}}$

6 0

3 years ago

Whats the elasped time between 9:00 and 1:30

Tasya [4]

Answer:

4 hours and 30 minutes

Step-by-step explanation:

I'll assume you have a basic knowledge of time and know the sequence. So all you do is count to 1:00 and see how many steps you took. In this case 4, but then you have 30 minutes left. Add that to the 4 hours, and you have a total of 4 hours and 30 minutes of elapsed time.

Hope this helps :)

7 0

2 years ago

A number added to 12 and then subtracted by 18 equals 26. What is the number

tiny-mole [99]

The answer would be 32. take your 26 and add 18 then subtract 12. then rework it forward if you don't understand.

4 0

3 years ago

Read 2 more answers

Select the graph for the solution of the open sentence. Click until the correct graph appears. |x| > 3/2

Soloha48 [4]

ANSWER

See attachment

EXPLANATION

The given inequality is

$|x| \: > \: \frac{3}{2}$

This implies that,

$x\: > \: \frac{3}{2} \: or \: - x\: > \: \frac{3}{2}$

Multiply both sides of the second inequality by -1 and reverse the inequality sign.

$x\: > \: \frac{3}{2} \: or \: x\: < \: - \frac{3}{2}$

The graphical solution to this inequality is shown in the attachment.

7 0

3 years ago