What happens when a quadratic function touches the x-axis only once? It means that the quadratic function has only one real zero. So which formula should we use? How about the almighty quadratic formula?
So when does the quadratic formula give you only one real zero? When the discriminant is equal to zero!
The discriminant is: b²-4ac
In our quadratic equation that means:
b = (3+m)
a = 4
c = 1
Thus, we need to solve: (3+m)²- 4*(4)*(1) = 0
m²+ 6m + 9 - 16 = 0
m² + 6m - 7 = 0
(m+7)(m-1) = 0
m = -7, 1
That's it! Plug back in and graph to see that it actually works!
Answer:
2 7/8
Step-by-step explanation:
If I translated correctly into my native language, then you need to write the equation of the straight line.
y=x this is a straight line through the first and third quarters.
1) multiply by 2: y= 2x
2) to raise the function by 3 units, you need to add 3 to it. For example: y=2x to bring it up: y=2x+3
Answer:
- 10 liters of orange juice
- 5 liters of champagne
Step-by-step explanation:
Let c represent the number of liters of champagne Lauren uses. Then (15-c) will be the number of liters of orange juice. The total cost of the mix will be ...
12c +1.50(15-c) = 5.00(15)
10.5c = 52.50 . . . . . subtract 22.50, simplify
52.50/10.5 = c = 5 . . . . divide by the coefficient of c
Then the amount of orange juice is ...
15 -c = 15 -5 = 10 . . . . liters
Lauren should use 5 liters of champagne and 10 liters of orange juice.
Answer:
cannot be determined
Step-by-step explanation:
We do not know if any of the angles are equal and are only given two sides.
We cannot determine if the two triangles are similar
