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Maksim231197 [3]
3 years ago
6

Sophia’s school took a field trip. A total of 21 vehicles were needed for the trip. Some students took the bus, and some student

s car-pooled. There were 30 people on each bus and 4 people in each car. 318 people altogether attended the trip. How many buses and cars were needed for the trip?
Can someone help me find the x and the y using systems of equations?
Mathematics
1 answer:
Alisiya [41]3 years ago
8 0
We know there were 21 vehicles so one of the equations is:

c+b=21

We can find  the second equation with the other given information:

30b+4c=318

We can use manipulate the first equation then use substitution to solve the system:

c=21-b

We can plug this into the second equation:

30b+4(21-b)=318
30b+84-4b=318
26b+84=318
26b=234
b=9

Now we can plug this into one of the original equations to solve for c (the first equation is easier):

c+9=21
c=12

You can check your work by plugging the answers into the two equations:

12+9=21
21=21

(30)(9)+(4)(12)=318
270+48=318
318=318

There are 9 buses and 12 cars.
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Elodia [21]

Answer:

OD = 9.375"

Step-by-step explanation:

We can draw a line from O to B to create a triangle.

Then, Triangle ODB and Triangle ACB are similar, so their corresponding side's ratio are similar as well.

Triangle ACB, we can use pythagorean theorem to figure out CB:

AC^2 + CB^2 = AB^2

15^2 + CB^2 = 17^2

225 + CB^2 = 289

CB^2 = 64

CB = 8

Now relating the corresponding sides, we can figure out OD:

\frac{OD}{DB}=\frac{AC}{CB}\\\frac{OD}{8-3}=\frac{15}{8}\\\frac{OD}{5}=\frac{15}{8}\\8OD=5*15\\OD=\frac{5*15}{8}\\OD=9.375

8 0
3 years ago
Ax-c=2x+5 solve for x
Dmitriy789 [7]
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ax - c + c = 2x + 5 + c
ax = 2x + 5 + c
ax - 2x = 2x - 2x + 5 + c

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X = c+5/a-2

I believe this would be the solution.
8 0
3 years ago
A sales person is given a choice of two salary plans. Plan 1 is a weekly salary of 700 plus 4% commission of sales. Plan 2 is a
bezimeni [28]

Let 's' represent the amount of sales.

Plan 1:

\text{ \$700 + (4\% of s)}\begin{gathered} \text{ \$700+(}\frac{\text{4}}{100}\times s) \\ \text{ \$700+(0.04}\times s)=\text{ \$700}+0.04s \end{gathered}

Plan 2:

12\text{ \% of s}\begin{gathered} \frac{12}{100}\times s \\ 0.12\times s=0.12s \end{gathered}

Equating the two plans together and solving for the amount of sales,

\begin{gathered} \text{Plan 2=Plan 1} \\ 0.12s=\text{ \$700+0.04s} \\  \end{gathered}

Collecting like terms,

\begin{gathered} 0.12s-0.04s=\text{ \$700} \\ 0.08s=\text{\$700} \end{gathered}

Divide both sides by 0.08,

\begin{gathered} \frac{0.08s}{0.08}=\frac{\text{ \$700}}{0.08} \\ s=\text{ \$8750} \end{gathered}

Hence, the amount of sales is $8,750.

6 0
1 year ago
Laila and Bryson are finding the slope of a line that passes through the two points (3, -5) and (-4, -6). Who is correct and why
snow_tiger [21]
Slope formular = (y2-y1)/(x2 - x1)
so
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answer
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3 0
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P = k/w^2 

<span>first of all you need to find k </span>
<span>But I kind of don't like the units of each value so let say </span>
<span>400KPa = 4 * 10^5 Pa = 4 * 10^5 N/m^2 </span>
<span>2 cm = 2 * 10^-2 m </span>

<span>input values in the equation </span>

<span>4*10^5 = k/(4*10^-4) >>> k = 160 N </span>

<span>P = 160/w^2 </span>
<span>it said if she wears a heel with a width of .5 cm </span>

<span>P = 160(0.5 * 10^-2)^2 >>> P = 6400 KPa</span>
4 0
3 years ago
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