1. Quadratic
2. C. The number of vinyl album sales in the country in the year 2020 will be 20.5 million.
3. A. Yes, Josephine forgot to consider the negative square root of 49, which is -7, which leads to two equations to solve.
4. B. M=-3
5. D. X^2+8x=15 rewritten as X^2+8x +64=15+64
6. D. Both are correct, they both correctly applied mathematical properties and arrived at the same solution.
7. B. (x−5)^2>50
1. A---- equation can be written in the form ax^2+bx+c=0 where a,b and c are real numbers, and ais a nonzero number
Linear
Quadratic
Cubic
Quartic
2. The number of vinyl album sales
y (in millions) in a country x years after 2010 can be modelled for 2010 through 2016 with the function below. y=0.12x^2+0.3x+3.3 Use this model to predict the number of vinyl album sales in the country in the year 2020. (x=10) (x=10)
A. The number of vinyl album sales in the country in the year 2020 will be 18.3 million.
B. The number of vinyl album sales in the country in the year 2020 will be 21.12 million.
C. The number of vinyl album sales in the country in the year 2020 will be 20.5 million.
D. The number of vinyl album sales in the country in the year 2020 will be 7.74 million.
3. Josephine solved a quadratic equation:(x+6)^2=49
Step 1 squared (x+6)^2= squared 49
Step 2 x+6=7
Step 3 7−6x=7−6
Step 4 x=1
Did Josephine make a mistake?
A. Yes, Josephine forgot to consider the negative square root of 49, which is -7, which leads to two equations to solve.
B. No, Josephine made no mistakes in solving this equation.
C. Yes, Josephine should have subtracted 6 from each side to start with to get x^2=43
D. Yes, Josephine should have multiplied out 2(x+6)^2 first
4. What are the solutions to the equation (m+1)^2 +1=5
A. M=-1
B. M=-3
C. m=1
D. m=3
E. m=-5
F. m=5
5. Which of the following rewrites shows the correct process for completing the square?
A. X^2+8x = 15 rewritten as x^2+8+16=15+16
B. 4x^2+10x=−5 rewritten as 4x^2+10x=−5=25
C. 4x^2+10x=−5 rewritten as 4x^2+10x+100=-5+100
D. X^2+8x=15 rewritten as X^2+8x +64=15+64
6. . Jesse and Benjamin are asked to solve 100x^2− 100=0 Here are their solutions. Who is correct? Explain.
Jesse
100x^2−100=0
(10x)^2−10^2=0
(10x−10)(10x+10)=0
10(x−1)⋅10(x+1)=0
(x−1)=0 or (x+1)=0
X=1 or x=-1
Benjamin
100x^2−100
=100(x^2−1)
= 100(x−1)(x+1)
(x−1)=0 or (x−1)=0
X=1or -1
A. Neither of them are correct. They both used a difference of perfect squares pattern which does not apply here.
B. Benjamin is correct they solved it in less steps.
C. Jesse is correct they showed more work.
D. Both are correct, they both correctly applied mathematical properties and arrived at the same solution.
7. Create a quadratic inequality that represents the following phrase: The square of the quantity 5 subtracted from x has a minimum value of 50
A. (x−5)^2≥50
B. (x−5)^2>50
C. (x+5)2>50
D. (x+5)2≥50
3 answers
The profit of a company producing
X thousand units is given by p (x)=2x^2+38x-120 Find the values of x for which the company makes a profit. Explain and justify your answer.
Hint: The company makes a profit when
P(x)>0]
X thousand units is given by p (x)=2x^2+38x-120 Find the values of x for which the company makes a profit. Explain and justify your answer.
Hint: The company makes a profit when
P(x)>0]
To find the values of x for which the company makes a profit, we need to determine when the profit function P(x) is greater than 0.
The profit function is given by P(x) = 2x^2 + 38x - 120.
To determine when P(x) > 0, we need to find the roots of the quadratic equation 2x^2 + 38x - 120 = 0, since the graph of a quadratic function intersects the x-axis at its roots.
To solve the quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula.
The quadratic formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a).
In our case, a = 2, b = 38, and c = -120.
Using the quadratic formula, we have:
x = (-38 ± √(38^2 - 4(2)(-120))) / (2(2))
x = (-38 ± √(1444 + 960)) / 4
x = (-38 ± √(2404)) / 4
x = (-38 ± 49) / 4
Thus, we have two potential values for x:
1) x = (-38 + 49) / 4 = 11 / 4 = 2.75
2) x = (-38 - 49) / 4 = -87 / 4 = -21.75
Since the profit function represents the profit of the company producing x thousand units, the values of x must be positive. Therefore, the company makes a profit when x = 2.75 thousand units.
The profit function is given by P(x) = 2x^2 + 38x - 120.
To determine when P(x) > 0, we need to find the roots of the quadratic equation 2x^2 + 38x - 120 = 0, since the graph of a quadratic function intersects the x-axis at its roots.
To solve the quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula.
The quadratic formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a).
In our case, a = 2, b = 38, and c = -120.
Using the quadratic formula, we have:
x = (-38 ± √(38^2 - 4(2)(-120))) / (2(2))
x = (-38 ± √(1444 + 960)) / 4
x = (-38 ± √(2404)) / 4
x = (-38 ± 49) / 4
Thus, we have two potential values for x:
1) x = (-38 + 49) / 4 = 11 / 4 = 2.75
2) x = (-38 - 49) / 4 = -87 / 4 = -21.75
Since the profit function represents the profit of the company producing x thousand units, the values of x must be positive. Therefore, the company makes a profit when x = 2.75 thousand units.
1 answer