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
Answer:
Let total students who prefer lemonade is 2a and who prefer ice tea is a.
Students in 6th grade=39
2a+a=39
3a=39
a=39/3
a=13
students who prefer lemonate is 13
and those who prefer ice tea is 2a=26
226,000
Step-by-step explanation:
250,000-24,000=226,000
There is one solution. The solution of the system is (9,-5)
Option A is correct.
Step-by-step explanation:
We need to solve the system of equations by elimination method
Rearranging the equations:
Eliminating y to find value of x:
Multiply eq(1) by 5 and eq(2) by 2 and add both equations:
So, value of x= 9
Eliminating x to find value of y:
Multiply eq(1) by 2 and eq(2) by 6 and subtract both equations:
So, value of y = -5
There is one solution. The solution of the system is (9,-5)
Option A is correct.
Keywords: Solving system of equations
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C doesn’t belong because it has rounded edges. all the other options have vertices
