You can use the fact that when mode is used, negative and positive all values become non-negative.
The equation that represents the function graphed on the given coordinate plane is given by
Option B: g(x) = |x+4| -10 is the equation which represents the function graphed on the coordinate plane.
<h3>How to know what function is graphed on the coordinate plane?</h3>We see what points it goes through, what type of nature it is showing where (like for example, the given function firstly goes down straightly, then rise up straightly after x = -4 ). We can see on what value of x, does the function become 0.
Many such graphical analysis help us to analyze which function can represent the given graph.
<h3>How to analyze given graph?</h3>The graph contains straight lines, so it must be linear.
The graph contains a twist in the direction where it was going initially and changes the direction. This shows that the graph is using something else than just a regular linear equation.
The graph turns up after it goes through x = -4.
Let we try to make equation of straight lines before and after x = -4 which the graph follows.
The first line goes 1 block down (1 block is of 2 units) on y axis as we go 1 block left on x axis. Thus the slope will be -2/2 = -1 (we take slope as rise/run and since rise was down thus it is taken as -ve rise).
The slope intercept form of this line would be
Since the line passes through point x = -4, y = -10, thus this point must satisfy the equation of that line since an equation represents the family of points which make up the given line.
Thus,
Thus, the equation of first line would be y = -x -14
The equation of second line, let be y = mx + c.
Since the second line intersects the y axis at y = -6, thus the y intercept of this line is -6 or c = -6.
Since the line rises 1 block( = 2 units) as one block of run happens on x axis in left direction (we take left as positive and right direction run as negative. This is standard sign convention used by most of the mathematical community. Conventions are just to remove ambiguity on international level). Thus, the slope of this line is 2/2 = 1
Thus, m = 1 or the equation of this line would be:
We can rewrite both the lines as:
But the graph has first line till x <= -4 and second line from x >= -4
Thinking carefully on this fact, we can see that when x <= -4 in first line, the -(x+4) is positive or 0
Similarly, for second line, when x >= -4,
the (x+4) is positive or 0
Thus, we can merge both equations using mode:
y = -10 + |x+4|
which will make x+4 to stay positive all the way. Thus, when x <= -4, this will simulate the first line, and when x >= -4, this will simulate the second line.
Note that at x = -4, both the lines have y = -10.
Thus, Option B: g(x) = |x+4| -10 is the equation which represents the function graphed on the coordinate plane.
Learn more about straight line here:
The correct order of the radius .
What is decreasing and increasing order?
A set of data is said to be in descending order, often referred to as decreasing order, when it is arranged from highest to lowest or largest to smallest.
The same concepts apply regardless of the type of information you're working with, whether it's letters, dates, sizes of things or any other group of information like numbers or dates.
For instance, arranging a group of numbers in descending order means doing so from biggest to smallest value.
Ascending order, often known as ascending order of importance, is the exact opposite of declining order.
The order of the items is lowest to highest value. The lowest value is placed first in the order, while the highest value is placed last.
The value of = 1.732
so / 11 = 1.732/11
=1732/11000
The value of = 3.14
so / 24 = 3.14/24
= 314/2400
To know more about ascending descending order, visit:
#SPJ4
9514 1404 393
Answer:
6. (A, B, C) ≈ (112.4°, 29.5°, 38.0°)
7. (a, b, C) ≈ (180.5, 238.5, 145°)
Step-by-step explanation:
My "work" is to make use of a triangle solver calculator. The results are attached. Triangle solvers are available for phone or tablet and on web sites. Many graphing calculators have triangle solvers built in.
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We suppose you're to make use of the Law of Sines and the Law of Cosines, as applicable.
6. When 3 sides are given, the Law of Cosines can be used to find the angles. For example, angle A can be found from ...
A = arccos((b² +c² -a²)/(2bc))
A = arccos((8² +10² -15²)/(2·8·10)) = arccos(-61/160) = 112.4°
The other angles can be found by permuting the variables appropriately.
B = arccos((225 +100 -64)/(2·15·10) = arccos(261/300) ≈ 29.5°
The third angle can be found as the supplement to the other two.
C = 180° -112.411° -29.541° = 38.048° ≈ 38.0°
The angles (A, B, C) are about (112.4°, 29.5°, 38.0°).
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7. When insufficient information is given for the Law of Cosines, the Law of Sines can be useful. It tells us side lengths are proportional to the sine of the opposite angle. With two angles, we can find the third, and with any side length, we can then find the other side lengths.
C = 180° -A -B = 145°
a = c(sin(A)/sin(C)) = 400·sin(15°)/sin(145°) ≈ 180.49
b = c(sin(B)/sin(C)) = 400·sin(20°)/sin(145°) ≈ 238.52
The measures (a, b, C) are about (180.5, 238.5, 145°).
