The college that Dora attends is selling tickets to the annual
1 answer:
Answer:
The solution of the system of equations is (11, 12)
Step-by-step explanation:
∵ The price of each student ticket is $x
∵ The price of each adult ticket is $y
∵ They sold 3 student tickets and 3 adult tickets for a total of $69
∴ 3x + 3y = 69 ⇒ (1)
∵ they sold 5 student tickets and 3 adults tickets for a total of $91
∴ 5x + 3y = 91 ⇒ (2)
Let us solve the system of equations using the elimination method
→ Subtract equation (1) from equation (2)
∵ (5x - 3x) + (3y - 3y) = (91 - 69)
∴ 2x + 0 = 22
∴ 2x = 22
→ Divide both sides by 2 to find x
∵
∴ x = 11
→ Substitute the value of x in equation (1) or (2) to find y
∵ 3(11) + 3y = 69
∴ 33 + 3y = 69
→ Subtract 33 from both sides
∵ 33 - 33 + 3y = 69 - 33
∴ 3y = 36
→ Divide both sides by 3
∵
∴ y = 12
∴ The solution of the system of equations is (11, 12)
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Answer:
option D is true.
Step-by-step explanation:
The right-angled triangle is shown.
From the right-angled triangle,
The angle Ф = 60°
We know that the trigonometric ratio
tan Ф = opposite / adjacent
- opposite = 4
- adjacent = n
Thus,
tan 60 = 4 / n
√3 = 4/n
n = 4/√3
Thus,
n = 4/√3
= (4 × √3) / (√3 × √3)
= 4√3 / 3
Thus,
n = 4√3 / 3
Using Pythagorean theorem
m = √n²+4²
Thus,
- n = 4√3 / 3
Therefore, option D is true.