<u>Given</u>:
Given that the graph of the quadratic function.
We need to determine the value of a in the function's equation.
<u>Value of a:</u>
The value of a can be determined using the formula,
where (h,k) is the vertex and a is a constant.
From the graph, it is obvious, that the vertex of the parabola is (0,9).
Thus, substituting the vertex (h,k) = (0,9) in the above formula, we get;
-------- (1)
Let us substitute any one of the coordinate that the graph passes through to determine the value of a.
Let us substitute the point (3,0) in the equation (1), we have;
Thus, the value of a is -1.
Hence, Option B is the correct answer.
Answer:
The number of liters of the 45% acid solution = 10 liters
The number of liters of the 70% acid solution is = 40 liters
Step-by-step explanation:
How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution? (Round to two decimal places if necessary.)
Let x be the number of liters of the 45% acid solution
The number of liters of the 70% acid solution is y
x + y = 50
x = 50 - y
Also
How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution?
We have:
45% × x + 70% × y = 65% × 50
0.45x + 0.70y = 0.65 × 50
0.45x + 0.70y = 32.5
We substitute x = 50 - y in the equation
0.45(50 - y) + 0.70y = 32.5
= 22.5 - 0.45y + 0.70y = 32.5
= - 0.45y + 0.70y = 32.5 - 22.5
= 0.25y = 10
Divide both sides by 0.25
= y = 10/0.25
y = 40 liters
x = 50 - y
x = 50 - 40
x = 10 liters
Hence,
The number of liters of the 45% acid solution = 10 liters
The number of liters of the 70% acid solution is = 40 liters
y=13x+5 ===(0,5) , (-2, -21)
y=-3x ===(0,0) , (-3,9)
y=x-10 ===(8,-2) , (-5, -15)
