Two numbers have a product of 20. The second number is three less than twice the first number. What are the two numbers?

Mathematics

1 answer:

yan [13]3 years ago

4 0

Answer:

4 and 5

Step-by-step explanation:

xy = 20

x = 2y - 3

(2y-3)y = 20

2y^2 - 3y = 20

2y^2 - 3y - 20 = 0

Solve the quadratic equation

you get y = 4, -5/2

Use 5 since it is one of the options

xy = 20, y = 4

x = 5

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2 years ago

Suppose h(t)= -0.2 + 2t models the height, in feet, of a ball that is kicked into the air where t is given as time in seconds

ra1l [238]

The maximum height of the ball is found at 64 feet

<h2>Explanation:</h2>

Hello! remember to write complete and clear questions in order to get good and exact answers. I've found a similar question so I have written it in a comment above. We know that h(t) models the height, in feet, of a ball that is kicked into the air where t is given as time in seconds. This equation follows a quadratic function so from math we know that the maximum or minimum of this type of functions is found at the vertex of its graph. So:

$f(x)=ax^2+bx+c \\ \\ \\ Vertex \ (h,k): \\ \\ h=-\frac{b}{2a} \\ \\ k=f(-\frac{b}{2a}) \\ \\ \\ Our \ function \ is: \\ \\ h(t)=-16t^2+64t \\ \\ \\ Comparing: \\ \\ a=-16 \\ \\ b=64 \\ \\ c=0 \\ \\ \\ h=-(\frac{64}{2(-16)})=2 \\ \\ k=-16(2)^2+64(2) \\ \\ k=64$