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Vitek1552 [10]
3 years ago
14

5. Ms. Lee bought 8 tickets to the basketball game and spent a total of $30. She bought a combination of adult tickets for $5 an

d child tickets $3 each. Which system of equations below will determine the number of child tickets, c, and the number of adult tickets, a, she bought?​
Mathematics
1 answer:
Strike441 [17]3 years ago
7 0

Answer:

she bought five children tickets and 3 adult tickets

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Write the given expression as an algebraic expression in x. tan(2 cos^-1(x))
miv72 [106K]
\bf tan\left[ 2cos^{-1}(x) \right]\implies tan\left[ 2cos^{-1}\left( \frac{x}{1} \right) \right]
\\\\\\
\textit{if we say }cos^{-1}\left( \frac{x}{1} \right)=\theta\textit{  that means }tan\left[ 2cos^{-1}\left( \frac{x}{1} \right) \right]\iff tan(2\theta)\\\\
-----------------------------\\\\
cos^{-1}\left( \frac{x}{1} \right)=\theta\implies cos(\theta)=\cfrac{x}{1}\cfrac{\leftarrow adjacent=a}{\leftarrow hypotenuse=c}\\\\
-----------------------------\\\\


\bf \textit{again, using the pythagorean theorem to get the opposite side}
\\\\\\
c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b\implies \pm\sqrt{1^2-x^2}=b
\\\\\\
\pm\sqrt{1-x^2}=b\\\\
-----------------------------\\\\
tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\implies tan(2\theta)=\cfrac{2\cdot \frac{\pm\sqrt{1-x^2}}{x}}{1-\left( \frac{\pm\sqrt{1-x^2}}{x} \right)^2}
\\\\\\

\bf tan(2\theta)=\cfrac{\frac{\pm2\sqrt{1-x^2}}{x}}{1-\frac{1-x}{x}}\implies 
tan(2\theta)=\cfrac{\frac{\pm2\sqrt{1-x^2}}{x}}{\frac{x-1+x}{x}}
\\\\\\
tan(2\theta)=\cfrac{\pm2\sqrt{1-x^2}}{x}\cdot \cfrac{x}{2x-1}
\implies 
tan(2\theta)=\cfrac{\pm 2\sqrt{1-x^2}}{2x-1}


6 0
3 years ago
lexi bought 1 2\5 pounds of green grapes and 2 3\10 pounds of red grapes. Grapes are 2.99 a pound. Did lexi spend more or less t
prisoha [69]

Answer:

Less than $12

Step-by-step explanation:

I changed everything into decimals to make it easier to solve:

1 2/5= 1.4

2 3/10= 2.3

1.4+2.3=3.7

2.99·3.7=11.063 (Round it to the nearest hundredth and you get 11.06)

7 0
3 years ago
Read 2 more answers
Help me please...............
Alina [70]

Answer:

answer choice a and e

Step-by-step explanation:

i hope this helps :) please let me know if this answer is incorrect

have a nice day !!

4 0
3 years ago
A store asked 250 of its customers whether or not they were satisfied with the service. The responses were also classified accor
anyanavicka [17]

Answer:

Correct option: e) a two-way table.

Step-by-step explanation:

In this case the store wants to see whether there is a relationship between the satisfaction level of the customer and their gender.

In statistics when there is a need to analyze or derive a relation between two categorical variables one should use a two-way table.

Categorical variables are qualitative variables that take on specific values that are usually labels. For example, grades obtained in an exam, gender, etc.

In this case the two categorical variables are: Gender and Satisfaction level.

To study the relation between the gender of a customer and their satisfaction level use a two-way table.

 

3 0
3 years ago
Find the equation of a line that passes through (1,5) and is parallel to the graph of y=3x+3
slavikrds [6]
Parallel = same slope
y = 3x + b
5 = 3(1) + b, b = 2
Solution: y = 3x + 2
4 0
3 years ago
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