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Taya2010 [7]
3 years ago
12

A new video game is expected to sell 130 copies the first hour at a local game store. After that, the sales will follow the func

tion s(x) = 9(x − 1) where x is the number of hours. What is the function that shows total sales, including the first hour?
A) s(x) = 130 + 9(x − 1)
B) s(x) = 9(x − 1) − 130
C) s(x) = 130x − 9
D) s(x) = 130 − 9(x − 1)
Mathematics
2 answers:
lapo4ka [179]3 years ago
8 0

Answer:

s(x) = 130 + 9(x-1)

Step-by-step explanation:

Video games sold in first hour = 130

After the first hour the sales will follow the function:

s(x) = 9(x-1)

Where x is the number of hours.

So, in x hours hours video games sold = 9(x-1)

So, total video games sold (including first hour) = 130+9(x-1)

Thus the function that shows total sales, including the first hour:

s(x) = 130 + 9(x-1)

Hence Option A is correct : s(x) = 130 + 9(x-1)

suter [353]3 years ago
4 0
The answer is A I believe. 

At hour 1, the equation must equal 130,

therefore s(1) = 9(1-1) + 130
                s(1) = 9(0) + 130
                s(1) = 130

then so on when 
s(2) = 9(2-1) + 130
s(2) = 139

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Calculate the discriminant to determine the number solutions. y = x ^2 + 3x - 10
Nataly_w [17]

1. The first step is to find the discriminant itself. Now, the discriminant of a quadratic equation in the form y = ax^2 + bx + c is given by:

Δ = b^2 - 4ac

Our equation is y = x^2 + 3x - 10. Thus, if we compare this with the general quadratic equation I outlined in the first line, we would find that a = 1, b = 3 and c = -10. It is easy to see this if we put the two equations right on top of one another:

y = ax^2 + bx + c

y = (1)x^2 + 3x - 10

Now that we know that a = 1, b = 3 and c = -10, we can substitute this into the formula for the discriminant we defined before:

Δ = b^2 - 4ac

Δ = (3)^2 - 4(1)(-10) (Substitute a = 1, b = 3 and c = -10)

Δ = 9 + 40 (-4*(-10) = 40)

Δ = 49 (Evaluate 9 + 40 = 49)

Thus, the discriminant is 49.

2. The question itself asks for the number and nature of the solutions so I will break down each of these in relation to the discriminant below, starting with how to figure out the number of solutions:

• There are no solutions if the discriminant is less than 0 (ie. it is negative).

If you are aware of the quadratic formula (x = (-b ± √(b^2 - 4ac) ) / 2a), then this will make sense since we are unable to evaluate √(b^2 - 4ac) if the discriminant is negative (since we cannot take the square root of a negative number) - this would mean that the quadratic equation has no solutions.

• There is one solution if the discriminant equals 0.

If you are again aware of the quadratic formula then this also makes sense since if √(b^2 - 4ac) = 0, then x = -b ± 0 / 2a = -b / 2a, which would result in only one solution for x.

• There are two solutions if the discriminant is more than 0 (ie. it is positive).

Again, you may apply this to the quadratic formula where if b^2 - 4ac is positive, there will be two distinct solutions for x:

-b + √(b^2 - 4ac) / 2a

-b - √(b^2 - 4ac) / 2a

Our discriminant is equal to 49; since this is more than 0, we know that we will have two solutions.

Now, given that a, b and c in y = ax^2 + bx + c are rational numbers, let us look at how to figure out the number and nature of the solutions:

• There are two rational solutions if the discriminant is more than 0 and is a perfect square (a perfect square is given by an integer squared, eg. 4, 9, 16, 25 are perfect squares given by 2^2, 3^2, 4^2, 5^2).

• There are two irrational solutions if the discriminant is more than 0 but is not a perfect square.

49 = 7^2, and is therefor a perfect square. Thus, the quadratic equation has two rational solutions (third answer).

~ To recap:

1. Finding the number of solutions.

If:

• Δ < 0: no solutions

• Δ = 0: one solution

• Δ > 0 = two solutions

2. Finding the number and nature of solutions.

Given that a, b and c are rational numbers for y = ax^2 + bx + c, then if:

• Δ < 0: no solutions

• Δ = 0: one rational solution

• Δ > 0 and is a perfect square: two rational solutions

• Δ > 0 and is not a perfect square: two irrational solutions

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alexira [117]
<h3>Answer:   83.85%</h3>

This value is approximate.

==========================================================

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z = (x-mu)/sigma

z = (40-47)/7

z = -1

We're exactly one standard deviation below the mean.

Repeat these steps for x = 68

z = (x-mu)/sigma

z = (68-47)/7

z = 3

This score is exactly three standard deviations above the mean.

Now refer to the Empirical Rule chart below. We'll add up the percentages that are between z = -1 and z = 3. This consists of the two pink regions (each 34%), the right blue region (13.5%) and the right green region (2.35%). These percentages are approximate.

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OLga [1]

Answer:

The longer length is either 99, 33 or 11 inches

Step-by-step explanation:

Given

Area = 99

Required

The length of the longer side

Area of a rectangle is:

Area = Length * Width

List out all possible products that give 99 [Assume the dimension are whole numbers]

Length * Width = 99 * 1 = 99

Length * Width = 33 * 3 = 99

Length * Width = 11 * 9 = 99

List out the longer factors

L = \{99, 33, 11\}

<em>Hence, the longer length is either 99, 33 or 11 inches</em>

8 0
3 years ago
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