Answer:
y = 18 and x = -2
Step-by-step explanation:
y = x^2+bx+c To find the turning point, or vertex, of this parabola, we need to work out the values of the coefficients b and c. We are given two different solutions of the equation. First, (2, 0). Second, (0, -14). So we have a value (-14) for c. We can substitute that into our first equation to find b. We can now plug in our values for b and c into the equation to get its standard form. To find the vertex, we can convert this equation to vertex form by completing the square. Thus, the vertex is (4.5, –6.25). We can confirm the solution graphically Plugging in (2,0) :
y=x2+bx+c
0=(2)^2+b(2)+c
y=4+2b+c
-2b=4+c
b=-2+2c
Plugging in (0,−14) :
y=x2+bx+c
−14=(0)2+b(0)+c
−16=0+b+c
b=16−c
Now that we have two equations isolated for b , we can simply use substitution and solve for c . y=x2+bx+c 16 + 2 = y y = 18 and x = -2
This is a 2 part question, so we will go step by step
Since Angel makes 13.50 an hour, and she works 40 hours a week, we have to make an equation and solve it.
First, let's make the equation, and we should multiply. Why?
Because finding out how much she made in a week would make it easier to find out how much she makes in a year. To find out how much she makes in a week, we need to add 13.50 40 times, and multiplication is an easier way of doing that.
Now to set it up, 40 is the number we are multiplying by (Because 40 is how many hours she works, and 13.50 is how much she makes in that hour)
and 13.50 is the number getting multiplied
Now we insert numbers into typical multiplication format
13.50 x 40 = ?
Now we solve
13.50 x 40 = 540
So she makes 540 dollars in a week, now we need to multiply that by the number of weeks they are in a year and we are done.
With a little help from Google, we can learn that there are in 52.1 weeks<span> in a common year.
Now we do the same thing we did the last time and insert our numbers into the equation.
(52.1 is what we are multiplying by, and 540 is the number that is getting multiplied.)
540 x 52.1 = ?
Solve
</span>540 x 52.1 = 28,134
She makes <span>28,134 in a year
</span>
Hope this helped!
First we clear y from the given equation
x + 10y = 260
10y = 260-x
y = (260-x) / (10)
Then, we evaluate the function within the domain of it
x = 0
y = (260- (0)) / (10)
y = (260) / (10)
y = 26
x = 10
y = (260- (10)) / (10)
y = (250) / (10)
y = 25
That is, you travel 1 mile in 10 minutes.
Therefore, traveling 26 miles will take:
(26) * (10) = 260 min
answer
it takes for the runner to reach the school 260min.
A: 2,5
B: 3,1
C: -2,4
Explanation:
When you’re moving right and up you would add however many numbers you moved up to the original points because going right on a graph makes the X a larger number, and going up makes it larger.
To justify the yearly membership, you want to pay at least the same amount as a no-membership purchase, otherwise you would be losing money by purchasing a yearly membership. So set the no-membership cost equal to the yearly membership cost and solve.
no-membership costs $2 per day for swimming and $5 per day for aerobic, in other words, $7 per day. So if we let d = number of days, our cost can be calculated by "7d"
a yearly membership costs $200 plus $3 per day, or in other words, "200 + 3d"
Set them equal to each other and solve:
7d = 200 + 3d
4d = 200
d = 50
So you would need to attend the classes for at least 50 days to justify a yearly membership. I hope that helps!
