Answer: 180 degrees
Step-by-step explanation:
A rotation of 180 degrees about the origin maps .
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2 answers:
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<em><u>Note: The complete question, along with the graph, is attached below.</u></em>
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Answer:
The value of a = 3
Step-by-step explanation:
Given the function
From the attached graph, it is clear that
at x = 0,
∵
Thus
When x = 0, the y-intercept will be:
From the attached figure, it is clear that
at x = 0, the value of y = 3
so
putting y = 3 in the equation
3 = a ∵
Therefore, the value of a = 3
Answer:
This system of equations has one real solution, (2, 8).
Step-by-step explanation:
Given:
y = x² + 4
y = 4x
1. Substitute the given value of y into y = x² + 4:
⇒ 4x = x² + 4
2. Solve for x (by factoring):
⇒ 4x = x² + 4
⇒ 0 = x² - 4x + 4
⇒ 0 = (x - 2)² [perfect square rule: a² -2ab + b² = (a - b)²]
⇒ 0 = (x - 2)² [take the square root of both sides]
⇒
⇒ 0 = x - 2 [add 2 to both sides]
⇒ 0 + 2 = x - 2 + 2
⇒ 2 = x
3. Find the value of y by substituting the given value of x into y = 4x:
⇒ y = 4(2)
⇒ y = 8
4. Check your work:
⇒ y = x² + 4 and ⇒ y = 4x
⇒ 8 = 2² + 4 and ⇒ 8 = 4(2)
⇒ 8 = 4 + 4 and ⇒ 8 = 8 ✔
⇒ 8 = 8 ✔
Solution: (x, y) ⇒ (2, 8)
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