Allen's Roofing posts $5,000 in net income and $200 in dividends for the year. How does this affect the retained earnings on the
2 answers:
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Answer:
The time it took until 2 inches of rain fell is 8 hours
Step-by-step explanation:
You know that the proportional relationship between the amount of time (in hours) it had been raining, x, and the amount of rain (in inches) it had fallen, y, is y = 0.25*x
To find the time that passed until 2 inches of rain fell, you must replace the amount of rain (in inches) that had fallen "and" by that value. In this way the following expression is obtained:
2= 0.25*x
Solving:
8 = x
So, remembering that the amount of time it had been raining, x, is expressed in hours, <u><em>the time it took until 2 inches of rain fell is 8 hours</em></u>.
Answer:
Step-by-step explanation:
We want to find the equation of a straight line that cuts off an intercept of 2 from the y-axis, and whose perpendicular distance from the origin is 1.
We will let Point M be (x, y). As we know, Point R will be (0, 2) and Point O (the origin) will be (0, 0).
First, we can use the distance formula to determine values for M. The distance formula is given by:
Since we know that the distance between O and M is 1, d=1.
And we will let M(x, y) be (x₂, y₂) and O(0, 0) be (x₁, y₁). So:
Simplify:
We can solve for y. Square both sides:
Rearranging gives:
Take the square root of both sides. Since M is in the first quadrant, we only need to worry about the positive case. Therefore:
So, Point M is now given by (we substitute the above equation for y):
We know that Segment OM is perpendicular to Line RM.
Therefore, their <em>slopes will be negative reciprocals</em> of each other.
So, let’s find the slope of each segment/line. We will use the slope formula given by:
Segment OM:
For OM, we have two points: O(0, 0) and M(x, √(1-x²)). So, the slope will be:
Line RM:
For RM, we have the two points R(0, 2) and M(x, √(1-x²)). So, the slope will be:
Since their slopes are negative reciprocals of each other, this means that:
Substitute:
Now, we can solve for x. Simplify:
Cross-multiply:
Distribute:
Simplify:
Distribute:
So:
Adding 1 and then dividing by 2 yields:
Then:
Therefore, the value of x is:
Then, Point M will be:
Therefore, the slope of Line RM will be:
And since we know that R is (0, 2), R is the y-intercept of RM. Then, using the slope-intercept form:
We can see that the equation of Line RM is: