amanda, lisa, and raquel together sold 54 tickets for the school play. amanda sold 22 tickets and lisa sold 14 tickets. how many
2 answers:
Answer: The number of tickets that Raquel sell is (c) 18.
Step-by-step explanation: Given that Amanda, Lisa, and Raquel together sold 54 tickets for the school play. Amanda sold 22 tickets and Lisa sold 14 tickets.
We are to find the number of tickets that Raquel sell.
Let 'n' represents the number of tickets that Raquel sell.
According to the given condition, we have
Therefore, the number of tickets that Raquel sell is 18.
Thus, (c) 18, is the correct option.
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Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=1(As, a>0 the parabola is open upward), b=10. by putting the values.
-b/2a = -10/2(1) = -5
f(-b/2a)= f(-5)= (-5)²+10(-5)+16= -9
So, Vertex = (-5, -9)
Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+16, we get point (0,16).
Now find x-intercept put y=0 in the above equation. 0= x²+10x+16
x²+10x+16=0 ⇒x²+8x+2x+16=0 ⇒x(x+8)+2(x+8)=0 ⇒(x+8)(x+2)=0 ⇒x=-8 , x=-2
From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.
2. f(x)=−(x−3)(x+1)
By multiplying the factors, the general form is f(x)= -x²+2x+3.
Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(As, a<0 the parabola is open downward), b=2. by putting the values.
-b/2a = -2/2(-1) = 1
f(-b/2a)= f(1)=-(1)²+2(1)+3= 4
So, Vertex = (1, 4)
Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+3, we get point (0, 3).
Now find x-intercept put y=0 in the above equation. 0= -x²+2x+3.
-x²+2x+3=0 the factor form is already given in the question so, ⇒-(x-3)(x+1)=0 ⇒x=3 , x=-1
From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.
3. f(x)= −x²+4
Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(As, a<0 the parabola is open downward), b=0. by putting the values.
-b/2a = -0/2(-1) = 0
f(-b/2a)= f(0)= −(0)²+4 =4
So, Vertex = (0, 4)
Now, find y- intercept put x=0 in the above equation. f(0)= −(0)²+4, we get point (0, 4).
Now find x-intercept put y=0 in the above equation. 0= −x²+4
−x²+4=0 ⇒-(x²-4)=0 ⇒ -(x-2)(x+2)=0 ⇒x=2 , x=-2
From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.
4. f(x)=2x²+16x+30
Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=2(As, a>0 the parabola is open upward), b=16. by putting the values.
-b/2a = -16/2(2) = -4
f(-b/2a)= f(-4)= 2(-4)²+16(-4)+30 = -2
So, Vertex = (-4, -2)
Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+30, we get point (0, 30).
Now find x-intercept put y=0 in the above equation. 0=2x²+16x+30
2x²+16x+30=0 ⇒2(x²+8x+15)=0 ⇒x²+8x+15=0 ⇒x²+5x+3x+15=0 ⇒x(x+5)+3(x+5)=0 ⇒(x+5)(x+3)=0 ⇒x=-5 , x= -3
From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.
5. y=(x+2)²+4
The general form of parabola is y=a(x-h)²+k , where vertex = (h,k)
if a>0 parabola is opened upward.
if a<0 parabola is opened downward.
Compare the given equation with general form of parabola.
-h=2 ⇒h=-2
k=4
so, vertex= (-2, 4)
As, a=1 which is greater than 0 so parabola is opened upward and the graph has minimum.
The graph is attached below.
