The Smith'd CD’s sell for $10 and Arctic Monkeys CD’s sell for $15. If a music store sold 18 CD’s and worth $240, how many of each CD did they sell?​

The quadraticequation is 4x² - 20x - 24 = 0 whose roots are-1 and 6.

What is a quadratic equation?

The quadratic equation is defined as a function containing the highest power of a variable is two.

The roots are given in the question, as follows:

-1 and 6

As we know that the standard quadratic equation ax² + b x + c = 0.

Since the leading coefficient of the quadratic equation is 4

So, a = 4

The sum of roots = -b/a

-1 + 6 = -b/4

5 = -b/4

b = -20

The multiplication of roots = c/a

-1 × 6 = c/4

c = -24

So, the quadratic equation is 4x² - 20x - 24 = 0.

Learn more about quadratic function here:

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You've got a=4

-b/a=sum=-1+6=5 so b=-20

c/a=product=-1*6=-6 so c=-6

Final equation:

Answer:

a = 25m^2

b = 5m

d = 35.73 m^2

c = 7.94m

Step-by-step explanation:

First, remember that the area of a square of side length L is:

A = L^2

And for a triangle rectangle with catheti a and b, and hypotenuse H, we have the relation:

H^2 = a^2 + b^2  (Phytagorean's theorem)

Ok, let's look at the left image, we have a green triangle rectangle.

The bottom cathetus has a length equal to the side length of a square with area of 16m^2

Then the side length of that square (and the cathetus) is:

L^2 = 16m^2

L = √(16m^2) = 4m

The left cathetus has a length equal to the side length of a square of area = 9m^2

Then the side length of that cathetus is:

K^2 = 9m^2

K = √(9m^) = 3m

Then the catheti of the green triangle rectangle are:

4m and 3m

Then the hypotenuse of this triangle (b) is:

b^2 = (4m)^2 + (3m)^2

b^2 = 16m^2 + 9m^2 = 25m^2

b = √(25m^2) = 5m

And b is the side length of the red square, then the area of that square is:

a = b^2 = 25m^2

Now let's go to the other image.

Here we have an hypotenuse of side length H, such that:

H^2 = 144m^2

And we have a cathetus (the one adjacent to the green triangle) of side length L such that:

L^2 = 81m^2

The other cathetus will have a sidelength c, such that:

c^2 = area of the purple square

By the Pythagorean's theorem we have:

144m^2 = 81m^2 + c^2

144m^2 = 81m^2 + c^2

144m^2 - 81m^2 = c^2

63m^2 = c^2

(√63m^2) = c = 7.94m

And the area of a triangle rectangle is equal to the product between the catheti divided by two.

We know that one cathetus is equal to c = 7.94m

And the other on is equal to the square root of 81m^2

√(81m^2) = 9m

then the area of the triangle is:

d = (7.94m)*(9m)/2 = 35.73 m^2