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son4ous [18]
3 years ago
6

Write a system of equations for the following situation:

Mathematics
2 answers:
Assoli18 [71]3 years ago
7 0
<h3><u>Answer:</u></h3>

\boxed{\boxed{\pink{\bf \leadsto Option \ second \ is \ correct .}}}

<h3 /><h3><u>Step-by-step explanation:</u></h3>

Given that , a group of 10 people went to see a movie. The cost to go to the movie is $8 for an adult and $5 for a child. The total cost for thegroup was $59.

<u>Let</u><u> </u><u>:</u><u>-</u>

\implies \bf No. \ of \ adult \ be \ denoted \ by \ a.  \\\\\bf \implies No . \ of \ Children \ be \ denoted \ by \ c .

Since the total number of people in group is 10 . Then ,

\implies \bf n_{adult} + n_{children} = 10 \\\\\bf\implies \boxed{\bf a + c = 10 }

Now , the cost for an adult is $8 and for a child is $5. Hence ,

\bf\implies n_{adult}\times cost_{adult} + n_{child}\times cost_{child} = Total \ cost \\\\\bf \implies a \times \$ 8 + c \times \$ 5 = \$ 59 \\\\\bf\implies \boxed{\bf 8a + 5c =\$ 59 }

Hence our overall answer matches with second option .That is ,

\red{\bf Option \ 2 } \begin{cases} \bf a + c = 10 \\\\\bf 8a + 5c = 59 \end{cases}

<h3><u>Hence</u><u> </u><u>second</u><u> </u><u>option</u><u> </u><u>is</u><u> </u><u>corre</u><u>ct</u><u> </u><u>.</u></h3><h3 />
wariber [46]3 years ago
5 0

Answer: B) a + c = 10

8a + 5c = 59

Step-by-step explanation:

We know that 10 total people went, so the first equation has to be equal to 10. The total was $59, so the second equation should be set equal to $59. Now that the second equation is for cost, we must make it 8a + 5c to represent the cost of the adult and child tickets which are $8 and $5, respectively.

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Determine if line AB and CD are congruent or not congruent given the coordinates A(0, 13), B(7, 11), C(12, 10), and D(10, 3). Ex
drek231 [11]

Answer:

No

Step-by-step explanation:

The lines arent equal

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3 years ago
There are a rack of 14 billiard balls. Balls numbered 1 through 8 are solid-colored. Balls numbered 9 through 14 contain stripes
Jet001 [13]

Answer:

3/7  /    42.8% chance

Step-by-step explanation:

There are 6 striped balls (9, 10, 11, 12, 13, 14) and 8 (1, 2, 3, 4, 5, 6, 7, 8) solid colored balls. So, 6 / 14 balls are striped.

(6 / 14  = 3 / 7)

this means that the probability of a ball being striped has the odds of 3/7

(3/7 = about 42.8% chance)

6 0
1 year ago
Solve the decay equation y' = -ky using the integrating factors method. Show work
Alex777 [14]

Answer:

y=\frac{c}{e^{kx}}

Step-by-step explanation:

\frac{\mathrm{d} y}{\mathrm{d} x} =-ky

\frac{\mathrm{d} y}{\mathrm{d} x} +ky=0

comparing with equation

\frac{\mathrm{d} y}{\mathrm{d} x} + Py=Q(x)

I.F.= e^{\int P dx}

I.F.= e^{\int k dx}

I.F.= e^{kx}

y=\frac{1}{I.F.} ( \int {Q(x)}  dx  +c)

y=\frac{1}{e^{kx}} ( \int {0}  dx  +c)

y=\frac{c}{e^{kx}}

7 0
3 years ago
You opened your first savings account 3 months ago. So far, you have earned $9.90 in simple interest, at an annual interest rate
LekaFEV [45]
I=prt
9.90=p (.06)(3)
9.90=p(.18)
9.90/.18=p.18/.18
55=p

I put in $55 into the account when I opened it.
6 0
3 years ago
Please help.. 10 points
Leokris [45]

Answer:

z = 55.15432893

x = 59.61543424

y = 22.5166605

Step-by-step explanation:

To find length "z" you will have to use SOHCAHTOA.

Labelling the triangle will show us that the side marked "z" is the hyp and the side marked 39 is the opp.

sin 45 = \frac{39}{z}

z sin 45 = 39

         z  = \frac{39}{sin45}

         z = 55.15432893

Using Pythagoras' theorem, you can find that the adj = 39

In the other triangles POV, the adj is actually the opp.

Therefore, use tangent to find y.

tan 60 = \frac{39}{adj}

y tan 60 = 39

           y = \frac{39}{tan60}

           y = 22.5166605

Use Pythagoras's Theorem to find x.

23^{2} + 55^{2} = x^{2}\\\sqrt{23^{2} + 55^{2}}  = x\\59.61543424=x

3 0
2 years ago
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