The vertex is when x=-b/2a, which is also the line of symmetry.
in this case, b=6, a=3, so x=-6/6=-1
when x=-1. y=3-6-1=-4
another way to do it is to write the equation into vertex form by making a square:
3x²+6x-1
3(x²+2x-1/3)
3(x²+2x+1-1-1/3))
3(x²+2x+1-4/3))
notice the bold part makes a square:
3(x+1)²-4
Either way,
the vertex is (-1, -4)
the axis of symmetry is x=-1
the coefficient of x² is 3, a positive number, so this parabola opens upward. the function has a minimum value of y=-4
the range is all real number larger than -4
Answer:
x = 17
y = 8
QPR = 35º
QRP = 60º
Step-by-step explanation:
2x + 1 = x + 18
Subtract x from both sides
x + 1 = 18
Subtract 1 from both sides
x = 17
QPR = 2x + 1
QPR = 2(17) + 1
QPR = 35º
-------------------------------
8y - 4 = 4y + 28
Subtract 4y from both sides
4y - 4 = 28
Add 4 to both sides
4y = 32
Divide both sides by 4
y = 8
QPR = 8y - 4
QRP = 8(8) - 4
QRP = 60º
Answer:
about 31 percent
Step-by-step explanation:
Answer:
Kayla bought 7 tacos and 10 hotdogs
Step-by-step explanation:
Let the number of hotdogs be x.
Let the number of tacos be y.
i) It is given that x = y + 3
ii) It is also given that 3.5x + 4y = 63, therefore 7x + 8y = 126
iii) substituting the value of x from i) in ii) we get 7(y + 3) + 8y = 126
therefore 15y + 21 = 126
therefore 15y = 105
therefore y = 7
Therfore Kayla bought 7 tacos
iv) Using the value of y from iii) in i) we x = 7 + 3 = 10
Therefore Kayla bought 10 hotdogs
Answer:
It is a 50% increase
Step-by-step explanation:
2.4 million /2 = 1.2 million
2.4m + 1.2m = 3.6m
50% of 2.4 is 1.2
it is a +50% increase to get from 2.4 to 3.6
