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)
Answer combine 1/2 and x.
X/2+2/3=1/6
Subtract 2/3 from both sides of the equation
X/2=1/6-2/3
Simplify the right side of the equation
-2/3 as a fraction with a common denominator, multiply by 2/2
X/2=1/6-2/3 x 2/2
Multiply 3 by 2
X/2 = 1/6 - 2/6 x 2
Combine the numerators over the common denominator
X/2 = 1-2 x2/ 6
Simplify the numerator
Multiply by -2 by 2
X/2 =1-4/6
Subtract 4 from 1
X/2= -3/6
Cancel the common factor of -3 and 6
Factor 3 out of -3
X/2 = 3(-1)/6
Cancel the common factor of 6
X/2 = 3 .-1/3.2
Rewrite the expression
X/2 = -1/2
Move the negative in front of the fraction
X/2= -1/2
Since both sides have the same Denominator the numerators must be equal.
X=-1
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Answer: 2/12 2.12
Step-by-step explanation: You did not put the answers in so
Answer:
B
Step-by-step explanation:
6n - 2(4n + 7) + 4= -2 firstly you open the bracket
6n - 8n - 14 + 2 = -2 then you collect the like terms
6n - 8n= -2 + 14 - 4 then add and subtract and divide by the coefficient
-2n= 12 - 4
-2n = 8
= n = 8 ÷ -2
n = -4
