Given equation of the parabola y= -5x^2 -10x -13.
We need to apply formla for x-coordinate of the vertex.
x=-b/2a.
For the given equation we have a=-5 and b=-10.
Plugging values of a and b in formula of x-coordinate of the vertex.
x= -(-10)/2(-5)
x= 10/(-10) = -1.
So, we got x-coordinate of the vertex = -1.
Now, we need to plug x=-1 in given equation to find the y-coordinate of the vertex.
Plugging x=-1 in y= -5x^2 -10x -13, equation we get
y=-5(-1)^2-10(-1)-13.
y= -5(1) +10 -13.
y=-5 +10-13.
y=-18+10.
y=-8.
So, we got y-coordinate of the vertex -8.
Therefore, vertex of the parabola is (-1,-8).
It is not possible for 120 kids and 20 adults to go on the trip, but 120 students can go with a maximum of 12 adults so the expense of the trip can fall in the school's budget.
We know that tickets of the zoo cost $15 for adults and $11 for children.
The equation representing the budget for the trip is 15x + 11y = 1500.
where, x is the no. of adults and y is the number of children that are travelling.
If x = 20 and y = 120 then,
15(20)+11(120)=300+1320=1620 which is out of the budget of the school.
If 120 students want to go to school then, no. of adults that can travel can be determined as
15 x + 11 (120 )<= 1500
15x <=1500-1320
15x<=180
x <=12
Therefore, we can conclude that 120 students and 20 adults cannot travel for the trip but 120 students can travel with a maximum of 12 adults among with them as it will cost school the trip in the budget.
Learn more about Linear Inequality here brainly.com/question/11897796
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Step-by-step explanation:
3x + 12 - 2x + 8 + 5x
Solving like terms
x + 20 + 5x
20 + 6x
20 / 6 = x
Answer: Proportional
Step-by-step explanation: To determine whether x and y have a proportional relationship, see if the line through these points passes through the origin (0, 0). The points are on a line that passes through the origin. So, x and y have a proportional relationship
Answer:
4
Step-by-step explanation:
x = -1
|2x-2| = |2(-1)-2| = |-2-2| = |-4| = 4
