Answer:
(- 1, 2)
Step-by-step explanation:
Given a quadratic in standard form y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
= - 
f(x) = x² + 2x + 3 ← is in standard form
with a = 1 and b = 2, hence
= - 
= - 1
Substitute x = - 1 into f(x) for corresponding value of y
f(- 1) = (- 1)² + 2(- 1) + 3 = 1 - 2 + 3 = 2
vertex = (- 1, 2 )
The angle x has a measure of 110 degrees
<h3>How to determine the value of x?</h3>
From the question, we have the triangle shape that can be used in our computation:
On the triangle, the external angles are
x, 140 and 110
These angles are on the same straight line with their corresponding internal angles
By the angle on a straight line theorem, we have the internal angles to be
180 - x, 180 - 140 and 180 - 110
The sum of these angles is 180
So, we have
180 - x + 180 - 140 + 180 - 110 = 180
Evaluate
x = 110
Hence, the value of x is 110 degrees
Read more about angles at
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Answer:
D
Step-by-step explanation:
To convert from polar to rectangular form
• x = rcosΘ , y = rsinΘ
• r = 
⇒ r² = x² + y²
Given
r = 8cosΘ
r = 8 × 
( multiply both sides by r )
r² = 8x, hence
x² + y² = 8x ⇒ D
The second one is correct
Answer:
-2x² + 90x + 500
Step-by-step explanation:
Use FOIL method
Area of rectangle = length * width
= (50 - x)(2x + 10)
= 50*(2x) + 50*10 + (-x)*2x + (-x)*10
= 100x + 500 - 2x² - 10x
= -2x² + 10<u>0x - 10x </u>+ 500 {Combine like terms}
= -2x² + 90x + 500
