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iris [78.8K]
4 years ago
14

The Jurassic Zoo charges $13 for each adult admission and $4 for each child . The total bill for the 238 people from a school tr

ip was $1330. How many adults and how many children went to the zoo ?

Mathematics
1 answer:
slava [35]4 years ago
6 0

Answer:

42 adults and 196 children went to the zoo

Step-by-step explanation:

Let

x ----> the number of adults

y ----> the number of children

we know that

The total bill for the 238 people from a school trip was $1330

so

x+y=238 ----> equation A

13x+4y=1,330 ----> equation B

Solve the system of equations by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

the solution is the point (42,196)

see the attached figure

therefore

42 adults and 196 children went to the zoo

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Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3
nlexa [21]

Answer:

(x,y) = (5,-6)

Step-by-step explanation:

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                     ~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)

\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\

\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5

y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6

\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)

7 0
2 years ago
What is m∠AEB? <br> (See attachment)
aleksley [76]
Hey there,
Angle AEB + Angle CED = 180 degrees (vertically opposite angles)
(5x-10) degrees + (3x + 40) degrees = 180 degrees
5x -10 + 3x + 40 = 180 degrees
5x + 3x= 180 + 10 - 40
8x = 150
x = 150 / 8
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Angle AEB = (18.75 x 5) - 10 
                  =83.75 degrees.

Hope this helps ^_^

~Top
3 0
3 years ago
YO please help actually been waiting for an hour and a half cuz so many trolls lol. &lt;3 giivng brainliest, and ty in advance g
kati45 [8]

Hello!

For this problem we are given that quadrilateral ABCD is congruent to quadrilateral GJIH, meaning that all sides and angle measures will be equivalent to its corresponding side.

This means that to find x, we can look at quadrilateral GJIH's corresponding side to quadrilateral ABCD's side AD, which is side GH, which has a value of 9.

This means that 9 should also be the side length of side AD, which we're given a value of x/3.

x/3=9

Solve.

x=27

Hope this helps!

8 0
3 years ago
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mrs_skeptik [129]
M<2 = 90 - 50 = 40
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Alex73 [517]

Answer:

yes

Step-by-step explanation:

come with your money

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3 years ago
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