When you replace the comparison symbol (<) with an equal sign (=), you get the equation of a line in slope-intercept form:
... y = mx + b
where <em>m</em> is the slope, and <em>b</em> is the y-intercept.
Your equation has m = -1/4 and b = -1. To graph this line, find the point (0, -1) on the y-axis. To find another point on the line, you can use the slope value (rise/run = -1/4), which tells you the line "rises" -1 for each "run" of +4. That is, another point on the line will be 4 units to the right and 1 unit down, at (4, -2). Working in the other direction (to the left, instead of to the right), the -1/4 slope tells you the point 4 units left and 1 unit up (-4, 0) will also be on the line. <em>Draw a dashed line through these points,</em>
The dashed line you just drew is the boundary of the solution region. It is dashed because the line itself is not part of the solution. (Those points do not meet the requirement for "less than.")
Appropriate values of y are ones that are <em>less than</em> those on the line, so the solution region is indicated as being the half-plane <em>below</em> the line. You indicate this by shading the solution region. (See the attachment for an example of the way this can be graphed.)
_____
If the comparison is ≤ instead of <, then the line is solid (not dashed), indicating it is part of the solution region. If the comparison is > or ≥, then the shaded region is <em>above</em> the line, where y-values are greater than those on the line.
Answer:
(x - 10)(x - 8)(x + 3) = x³ - 15x² + 34x + 240
Step-by-step explanation:
To find the common denominator of the two fractions, you need to first factor the polynomials:
x² - 7x - 30 = (x - 10)(x + 3)
x² - 5x - 24 = (x - 8)(x + 3)
Since the common binomial is (x + 3), both denominators would need to also include (x - 10) and (x - 8). So, the full common denominator is:
(x + 3)(x - 10)(x - 8)
When you multiply these polynomials out using distribution and FOIL:
x³ - 15x² + 34x + 240
9514 1404 393
Answer:
0
Step-by-step explanation:
The slope can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (4 -4)/(-9-3) = 0/-12 = 0
The slope of the line is zero. It is a horizontal line (y=4).
Answer:
<u>The correct answer is C. 4.7%</u>
Correct statement and question:
A marine biologist is setting up a net 6 feet below the surface of the water. Each foot of the water screens out 40% of the light coming from the surface. Which of the following is the approximate percentage of light remaining after passing through 6 feet of water, to the nearest tenth of a percent?
0.4%
1.0%
4.7%
7.8%
Source: brainly.com/question/4136163
Step-by-step explanation:
1. Let's review all the information given to us to answer the question correctly:
Depth of the net = 6 feet below the surface of the water
Each foot of the water screens out 40% of the light coming from the surface.
2. Which is the approximate percentage of light remaining after passing through 6 feet of water, to the nearest tenth of a percent?
After one feet: 100 - 40 = 60%
After two feet = 60 - 0.4 * 60 = 60 - 24 = 36
After three feet = 36 - 0.4 * 36 = 36 - 14.4 = 21.6
After four feet = 21.6 - 0.4 * 21.6 = 21.6 - 8.64 = 12.96
After five feet = 12.96 - 0.4 * 12.96 = 12.96 - 5.18 = 7.78
<u>After six feet = 7.78 - 0.4 * 7.78 = 7.78 - 3.11 = 4.67 = 4.7 (Rounding to the nearest tenth)</u>
<u>The correct answer is C. 4.7%</u>