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3 years ago

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

Mathematics

2 answers:

Vsevolod [243]3 years ago

8 0

Answer:

after 1 minute they will both have 9

Step-by-step explanation

1 minute

5 9

_________________

9 9

9 flashcards is how many each student will have to make.

It will take 1 minute

Korolek [52]3 years ago

3 0

Chloe and Fiane will each have 9 flash cards in 1 minute.

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Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank i

jeka94

Let $a,b,c$ be the time it takes for pumps A, B, and C (respectively) to fill 1 tank. Then

$\begin{cases}\dfrac1a+\dfrac1b=\dfrac1{\frac65}=\dfrac56\\\\\dfrac1a+\dfrac1c=\dfrac1{\frac32}=\dfrac23\\\\\dfrac1b+\dfrac1c=\dfrac12\end{cases}$

Now,

$\left(\dfrac1a+\dfrac1b\right)-\left(\dfrac1a+\dfrac1c\right)=\dfrac56-\dfrac23\implies\dfrac1b-\dfrac1c=\dfrac16$

Then

$\left(\dfrac1b+\dfrac1c\right)+\left(\dfrac1b-\dfrac1c\right)=\dfrac12+\dfrac16\implies\dfrac2b=\dfrac23\implies b=3$

This means

$\dfrac1a+\dfrac13=\dfrac56\implies\dfrac1a=\dfrac12\implies a=2$

and

$\dfrac13+\dfrac1c=\dfrac12\implies\dfrac1c=\dfrac16\implies c=6$

Working together, all 3 pumps would operate at a rate of

$\dfrac1a+\dfrac1b+\dfrac1c=1$

or 1 tank in 1 hour, so the answer is D.

8 0

3 years ago

Five friends are leaving a bar for home. Aside from the owner of the car, one other person is deemed able to operate the vehicle

erastova [34]

Answer:

Step-by-step explanation:

one person is deemed to drive and that person is fixed on the driver's seat no mater which arrangement.

we have now 2 more seats one adjacent to the driver and one rear (two combined).

so the total ways in which all five can be arranged is as follows.

driver, adjacent to him(1) and three back.

driver adjacent to him (different person) and three back.

see the driver is always fixed so we can ignore him.

thus we when driver set fixed , on two remaining seats (adjacent to driver and the back )there can be 4 different combinations.

3 0

3 years ago

Hannah has to make 180 gallons of punch for a big party. The punch is made of soda and fruit drink. The cost of the soda is $2.4

vesna_86 [32]

Answer: 90 per each is you want how much money is needed in total that is 47.20 dollars

Step-by-step explanation:

8 0

3 years ago

What is the difference of 938.65-46.17

mestny [16]

892.48 You have to subtract he given numbers.

7 0

3 years ago

Andrew has a round trampoline with a diameter of 4 yards. What is the circumference of the trampoline?

OLga [1]

You would use this formula for the problem...

(C=2πr) The circumference equals 2 multiplied by pi and radius.

In this problem it says diameter, but the diameter is just twice the length of the radius, so just multiply the radius by 2. Plugin your number.

C=2π(2) since 2 is half of 4, that's your radius.

Your answer is roughly C= 12.57.

You're welcome.

8 0

3 years ago