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GenaCL600 [577]
3 years ago
6

Anna is really involved in after school activities and is a part of the Drama club, as well as the Junior Optimist club. Every t

hree days, there is a Drama club meeting, and every 8th day, she has Junior Optimist club meeting. Today she is scheduled to attend both meetings. How many days will it be until she will have both meetings on the same day again?
Mathematics
1 answer:
lisabon 2012 [21]3 years ago
5 0

Answer:

The next time she will have both meetings on the same day again is 24 days time

Step-by-step explanation:

The given information are;

The frequency of the Junior Optimist club meeting = Every 3 days

The frequency of the Drama club meeting = Every 8th day

The club meeting Anna will attend today = Both meetings

The next time she will have both meetings on the same day again is given as follows;

The next time she will have both meetings on the same day again = The number of days the complete cycles of both meetings will coincide = The product of the cycles of both meetings

The next time she will have both meetings on the same day again = 8 × 3 = 24 days

The next time she will have both meetings on the same day again = 24 days time.

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A company has two large computers. The slower computer can send all the company's email in minutes. The faster computer can comp
postnew [5]

Both the computers will take 18 minutes to do the job together.

The slower computer sends all the company's email in 45 minutes.

The faster computer completes the same job in 30 minutes.

Let's take minutes t  to complete the task together.

As they complete one job, we get the following equation:

\frac{t}{45}+\frac{t}{30}=1

LCM of 45 and 30 is:

45 = 3 x 3 x 5

30 = 2 x 3 x 5

LCM = 2 x 3 x 3 x 5 = 90

Now, solving for t;

⇒\frac{2t+3t}{90} = 1\\\frac{5t}{90} =1\\5t=90\\

Dividing both sides by 5;

\frac{5t}{5}=\frac{90}{5}

We get t = 18

Hence, it will take both the computers 18 minutes to do the job together.

A company has two large computers. The slower computer can send all the company's emails in 45 minutes. The faster computer can complete the same job in 30 minutes. If both computers are working together, how long will it take them to do the job?

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6 0
2 years ago
How can you determine the number of solutions of a system of linear equations by inspecting its equations?
bearhunter [10]

Step-by-step explanation:

To find - How can you determine the number of solutions of a system

              of linear equations by inspecting its equations?

Proof -

There exists three types of solution for a system of linear equations.

1. No solution.

2. Unique solution.

3. Infinite many solutions.

Now,

Let the 2 linear equations are as follows :

y = ax + b

y = cx + d

1. For no solution -

a = c and b ≠d

For example-

y = -2x + 5

y = -2x  - 1

Subtract first equation from second , we get

y - y = -2x - 1 - ( -2x + 5)

⇒0 = -2x - 1 + 2x - 5

⇒0 = -6

Not possible

So, There exist no solution.

2. For unique solution -

a ≠ c and b , d can be any value

For example -

If b and d are same ,

y = 2x - 4

y = -3x - 4

Subtract equation 1st from 2nd , we get

y - y = -3x - 4 - ( 2x - 4)

⇒0 = -3x - 4 - 2x + 4

⇒0 = -5x

⇒x = 0

⇒y = 2(0) - 4 = -4

∴ we get

x = 0, y = -4

If b and d are different

y = 2x - 4

y = -3x + 5

Subtract equation 1st from second

y - y = -3x + 5 - 2x + 4

⇒0 = -5x + 9

⇒-5x = -9

⇒x = \frac{9}{5}

⇒y =2(\frac{9}{5}) - 4 = \frac{18}{5} - 4 = \frac{18 - 20}{5} = -\frac{2}{5}

∴ we get

x = \frac{9}{5} , y = -\frac{2}{5}

3. Infinitely many solution -

a = c and b = d

For example -

y = -4x + 1

y = -4x + 1

Subtract equation first from equation second

y - y = -4x + 1 - ( -4x + 1)

⇒0 = -4x + 1 + 4x - 1

⇒0 = 0

Satisfied

So, Infinite many solution possible.

6 0
3 years ago
(4,5,6) is a subset of (4,5,6) True or False​
Nimfa-mama [501]

Answer:

true~ bc the amount basically

4 0
3 years ago
A tree is supported by HELP! a wire anchored in the ground 9 feet from its base. the wire is 1 foot longer than the height that
olga55 [171]
For a right triangle with legs legnth a and b and hyptonuse c
a^2+b^2=c^2
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wire is hypotnuse, it's 1 more than height on tree
c=b+1

so
9^2+b^2=(b+1)^2
81+b^2=b^2+2b+1
minus b^2+1 from both sides
80=2b
divide both sides by 2
40=b
c=b+1
c=40+1
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7 0
3 years ago
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12. Classify the triangle by side length and angle measurement. (1 point) A. equilateral, acute B.isosceles,obtuse C. isosceles,
ella [17]

Answer:

B. isosceles, obtuse

Step-by-step explanation:

An isosceles triangle has 2 congruent sides and the is an obtuse angle.

7 0
3 years ago
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