The graph of y = 1/2 x2 + 2x + 3 is shown. What are the solutions to the equation 1/2 x2 + 2x + 3 = x + 7?
1 answer:
Answer:
Step-by-step explanation:
Let's organise our information :
- the function is (1/2)x²+2x+3
we want to khow the value of x that gives us : (1/2)x²+2x+3=x+7
Now the trick is to write this expression as a quadratic equation with zero at one side :
- (1/2)x²+2x+3=x+7
- (1/2)x²+2x+3-x-7=0
- (1/2)x²+x-4=0
Now let's solve this equation :
- a= 1/2
- b= 1
- c= -4
Δ=1²-4*(1/2)*(-4)
= 9
So we have two solutions :
- y= -4
- x= 2
So the solutions are -4 and 2
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Answer:
x (smallest to largest) = 0,45 ,55
y (smallest to largest) = 0,10,40
Step-by-step explanation:
(hours) Dinghy Rowboat Labor Available
Metal Work 2 3 120
Painting 2 2 110
Let x represent the number of dinghies the company can manufacture and y represent the number of rowboats.
So, total hours for metal work =
So, total hours for Painting =
So, equation becomes:
Plot the inequalities
Refer the attached figure
So, the vertices of the feasible region are (0,40),(45,10) and (55,0)
So, x values are 0 , 45 and 55
x represents the number of dinghies
So, x (smallest to largest) = 0,45 ,55
y values are 40,10,0
y represent the number of rowboats.
So, y (smallest to largest) = 0,10,40
