Simplify each expression by combing like terms -12+3y-9
1 answer:
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Answer:
Roots: 3.746 and -13.746
Vertex: (-5, 153)
Step-by-step explanation:
- The roots of the quadratic equation y = ax² + bx + c, are the values of x at y = 0
- Its vertex is (h, k), where, h =
, and k is the value of y at x = h
Let us use these facts to solve the question
∵ y = -2x² - 20x + 103
→ Compare it by the form of the equation above
∴ a = -2, b = -20, and c = 103
→ To find its roots equate y by 0
∵ 0 = -2x² - 20x + 103
→ Use your calculator to find the values of x
∴ x = 3.746427842 and x = -13.74642784
→ Round them to 3 decimal places
∴ x = 3.746 and x = -13.746
∴ Roots: 3.746 and -13.746
→ To find its vertex use the rule of h above
∵ a = -2 and b = -20
∵ h = =
∴ h = -5
→ To find k substitute y by k and x by -10 in the equation
∵ k = -2(-5)² - 20(-5) + 103
∴ k = -2(25) + 100 + 103
∴ k = -50 + 100 + 103
∴ k = 153
∴ The vertex of the quadratic is (-5, 153)
∴ Vertex: (-5, 153)
A reflex angle is equal to the sum of 180 degreesand any of the primaryangles (acute, right andobtuse angles). Therefore, Reflex angle = 180° + Acute angle.
First, make sure that it is the reflex angle you’re being asked to measure! Lots of children mistakenly, but very carefully measure the wrong angle. Usually, the angle you’re being asked to measure will have a little circle drawn around the point to show you which side needs measuring
2. Make a small mark on your paper to show where 180° is. If you want to, you could even draw a faint line to show the 180° line.
3.You now need to measure the remainder. Using the outside scale on your protractor, measure the angle from the 180° line you have drawn to the second line you have been given (in this case y to x).
4. Add together 180° to the second measurement and this will be your reflex angle.
5. If you want to check your answer, measure the inside angle and check that the two measurements added together equal 360°.
