A student earns $7.50 per hour at her part-time job. She wants to earn at least $200.

To find the hypotenuse of a right triangle with sides measuring 3 and 4, we first need to use the Pythagorean theorem and then add that distance to 3 and 4.

By applying the theorem, the square of the hypotenuse equals the sum of the squares of the sides...

d^2=3^2+4^2

d^2=9+16

d^2=25

d=√25

d=5

Thus, the total distance for her run is 5+4+3=12 km

Average fall rate =

Detailed explanation:

Given that the position of the object is expressed as a function of time, we can compute the average velocity of the object during the first 3 seconds by determining its position at time 0 and at 3 seconds, finding the displacement over that period, and then dividing this distance by the elapsed time (3 seconds). This approach follows the concept that velocity equals distance covered divided by time spent:

Average rate of fall = (h(3) - h(0))/ 3

Average rate of fall =

For this context, we examine the function:

presented as:

The definition of the discriminant in a quadratic equation is provided by:

Sentences correspond to the types of roots: Different real roots, equal real roots, or distinct complex roots

Upon substituting the provided values, we arrive at

This indicates that there are two equal real roots.

To discover the intersections along the x-axis, we apply the quadratic formula:

Plugging in the values yields:

The intersection on the x-axis is