What is the distance between points M(-3, 1)and N(7, -3)​

d = 2√29 units

Step-by-step explanation:

M(-3, 1)and N(7, -3)​

To find the distance between these two points, we want to use the distance formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Plug in the values.

d = √[(7 - (-3))² + (-3 - 1)²]

Simplify the parentheses.

d = √[(7 + 3)² + (-4)²]

d = √[(10)² + (-4)²]

Simplify the exponents

d = √[(100 + 16)]

Simplify the parentheses by adding.

d = √[116]

Simplify the brackets with the square root.

Since 116 is not a perfect square, we need to find two numbers that multiply to 116. One number must be a perfect square. The other must be a prime number.4 • 29 = 116. Therefore √4 • √29 = √116√4 = 2. Therefore 2√29 = √116

d = 2√29 units

Hope this helps!

x(t) = 20t

y(t) = 40t - 5t^2

Since we are only interested in comparing the two at time t = 5 seconds, we plug in 5 everywhere we see the variable t and then compare x and y

x(5) = 20(5) becomes x(5) = 100

y(5) = 40(5) - 5(5)^2 becomes y(5) = 200 - 125 and then y(5) = 75

The ratio of y to x can be expressed as: y/x, so we can say the ratio is equal to 75/100 or 0.75

0.75