Answer:
D. 6,358 in³
Step-by-step explanation:
Answer:
f(x) = { x, -5 ≤ x < 0 and 3x - 3, 1 ≤ x < 5
Step-by-step explanation:
The equation of one line is y = x
The equation of the other line is y = 3x - 3
Altogether,
f(x) = { x, -5 ≤ x < 0 and 3x - 3, 1 ≤ x < 5
The slope of the red line that is perpendicular to the green line is: -5/2.
<h3>What are the Slope Values of Perpendicular Lines?</h3>
When one line lies perpendicular to another line, the slope of one must be the negative reciprocal of the other line.
<h3>What is the Negative Reciprocal of a Number?</h3>
If given a number, i.e. a/b, the negative reciprocal of a/b would the opposite value of the reciprocal of a/b.
Reciprocal of a/b is b/a. Negative reciprocal of a/b would therefore be: -b/a.
Given that the slope of the green line is: 2/5. And it is perpendicular to the red line. The slope of the red line would be the negative reciprocal of 2/5.
Negative reciprocal of 2/5 is -5/2.
Therefore, the slope of the red line is: -5/2.
Learn more about slope of perpendicular lines on:
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Okay. So Daniella wants to have a take-home pay of at least $51,000, but she ahs to pay 15% income tax, which means 15% of what she earns will be gone. To find out the least amont of salary she needs to make, we can write and solve a proportion. Set it up like this:
51,000/x = 85/100
This is because we are looking for the amount of money made overall, but the $51,000 is only part of the salary earned, and even though you pay 15% income tax, you still take home 85% of your salary. Cross multiply the valyes in order to get 5,100,000 = 85x. Divide each side by 85 to isolate the variable. 5,100,000/85 is 60,000. Let's check this by multiplying by 85% (0.85). 60,000 * 0.85 is 51,000. There. x = 60,000. Daniella will need to make at least $60,000.
