The quadratic equation 3x2 + 45x + 24 = 0 was solved using the Quadratic Formula, x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a.

One solution is −14.45. What is the other solution? Round to the hundredths place.

−1.11
−0.55
0.52
14.45

-0.55

Step-by-step explanation:

Quadratic Formula:

Case 1:

Substitute values:

= -0.55 (2dp) (Answer)

Case 2:

Substitute values:

= -14.45 (2dp)

Since x = -14.45 is known, the other solution  is x = -0.55

-0.55

Step-by-step explanation:

3x² + 45x + 24 = 0

x² + 15x + 8 = 0

General form:

x² - (sum of roots)x + product = 0

Product = 8

(-14.45)(X) = 8

X = 8/-14.45

X = -0.553633218 = -0.55

theres no picture: /

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240