A factory produced a batch of handheld video games, but 4% of the games were found to be defective. If the batch had 250 games in all, how many games in the batch were not defective?

Answer:

  D.  8

Step-by-step explanation:

No formula is given, so we use an on-line calculator for the job. The check digit is 8.

The discriminant is 0. As the discriminant is 0 it will have equal roots.

And the real root is -2/3.

What is a Quadratic Equation?

In algebra, a quadratic equation is any equation that can be rearranged in a standard form where x represents an unknown, and a, b, and c represent known numbers, where a ≠ zero.

Conclusion: If a = zero, then the equation is linear, no longer quadratic, as there's no ax^2 term.

9+12x+4=0

a = 9 ; b = 12; c = 4;

discriminant = Δ = - 4ac

Δ = - (4*9*4) = 144 - 144 = 0

roots of quadratic equations are [ (-b ± √Δ)/ 2a)]

let roots of eqation are x1 & x2

As discriminant is zero so, x1=x2

x1 = x2 = -b/2a = - 12/(2*9) = -2/3

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Answer:

hello :

9x^2+12x+4=0

a = 9   b = 12    c = 4

the discriminant  Δ = b² - 4ac = 12² - 4(9) (4   ) =144 -  144 = 0

x1 = x2 = - b/2a = -12/18 = - 2/3

  the real root is : - 2/3

Answer:

16, 24, 29, 29, 29, 31, 35, 49, 52, 62

Mean: 16 + 24 + 29 + 29 + 29 + 31 + 35 + 49 + 52 + 62 = 356/10 = 35.6

Median: 30

Mode: 29

Answer:

The lesser number is y=4

Step-by-step explanation:

Given : The sum of two numbers is 14. the larger number minus three times the lesser number -2.

To find : What is the lesser number?

Solution :

Let the two numbers be x and y,

The sum of two numbers is 14

i.e.  ....(1)

Let x be the larger number and y be the smaller number.

So, the larger number minus three times the lesser number -2

i.e. ...(2)

Solving equation (1) and (2)

Substitute x from (1) into (2)

Put in equation (1)

Therefore, The lesser number is y=4 and larger number is x=10.

Let x be the shorter side, and y be the longer side

There would be 4 fences along the shorter side, and 2 fences along the longer side

4x + 2y = 800

Rewrite in terms of y:

y = 400 − 2x

The area of the rectangular field is

A = x*y

Replace Y with the equation above:

  A = x(400 − 2x)

  A = − 2x^2 + 400x

The area is a parabola that opens downward, the maximum area would occur at the parabola vertex.

At the vertex

x = −b/2a

  = −400/[2(−2)]

  = 100

y = 400 −2x

y = 400 -2(100)

y = 400-200

y = 200

The dimension of the rectangular field that maximize the enclosed area is 100 ft x 200 ft.

The dimension of the rectangular field that maximize the enclosed area is 100 ft by 200 ft.

Application of the vertex of a quadratic equation

The formula for calculating the vertex of  a quadratic equation is given as:

x = -b/2a

From the given question

Let the shorter side be x

Let the longer side of the field be y

If there are 4 fences along the shorter side, and 2 fences along the longer side, hence;

4x + 2y = 800

Write the resultinq equation in slope-intecept form

2y = -4x + 800

y = -2x + 400

y = 400 − 2x

Determine the area of the field

Area = x*y

Substitute the expression above into the area to have:

A = x(400 − 2x)

A = − 2x^2 + 400x

Since the parabola opens downward, the maximum area would occur at the parabola vertex as shown;

x = −b/2a

x = −400/2(-2)

x = 400/4

x = 100

Determine the value of y

y = 400 −2x

y = 400 -2(100)

y = 400-200

y = 200

Hence the dimension of the rectangular field that maximize the enclosed area is 100 ft by 200 ft.

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