Answer:
O It has the same slope and a different y-intercept.
Step-by-step explanation:
y = mx + b
m = 3/8
b = 12
y = (3/8)x + 12
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Data in the table: slope is the rise (y) over the run (x) between two points (assuming the data represent a linear line).
Change in x and y between two points. I'll choose (-2/3,-3/4) and (1/3,-3/8).
Change in y: (-3/8 - (-3/4)) = (-3/8 - (-6/8)) = 3/8
Change in x: (1/3 - (-2/3)) = (1/3+2/3) = 3/3 = 1
Slope = (Change in y)/(Change in x) = (3/8)/1 = 3/8
The slope of the equation is the same as the data in the table.
Now let's determine if the y-intercept is also the same (12). The equation for the data table is y = (2/3)x + b, and we want to find b. Enter any of the data points for x and y and then solve for b. I'll use (-2/3, -3/4)
y = (3/8)x + b
Use (-2/3, -3/4)
-3/4 =- (3/8)(-2/3) + b
-3/4 = (-6/24) + b
b = -(3/4) + (6/24)
b = -(9/12) + (3/12)
b = -(6/12)
b = -(1/2)
The equation of the line formed by the data table is y = (3/8)x -(1/2)
Therefore, It has the same slope and a different y-intercept.
Treat the matrices on the right side of each equation like you would a constant.
Let 2<em>X</em> + <em>Y</em> = <em>A</em> and 3<em>X</em> - 4<em>Y</em> = <em>B</em>.
Then you can eliminate <em>Y</em> by taking the sum
4<em>A</em> + <em>B</em> = 4 (2<em>X</em> + <em>Y</em>) + (3<em>X</em> - 4<em>Y</em>) = 11<em>X</em>
==> <em>X</em> = (4<em>A</em> + <em>B</em>)/11
Similarly, you can eliminate <em>X</em> by using
-3<em>A</em> + 2<em>B</em> = -3 (2<em>X</em> + <em>Y</em>) + 2 (3<em>X</em> - 4<em>Y</em>) = -11<em>Y</em>
==> <em>Y</em> = (3<em>A</em> - 2<em>B</em>)/11
It follows that
Similarly, you would find
You can solve the second system in the same fashion. You would end up with
Answer: Option B, Option C, Option E
Step-by-step explanation:
The options written correctly, are:
For this exercise you need to use the following Inverse Trigonometric Functions:
When you have a Right triangle (a triangle that has an angle that measures 90 degrees) and you know that lenght of two sides, you can use the Inverse Trigonometric Functions to find the measure of an angle 
:
Therefore, the conclusion is that the angles "x" and "y" can be found with these equations:
With a ratio, you should think of it in terms of a pie of sorts. In this example, the pie has 13 pieces, 9 of which consist of the perimeter of the large parallelogram and 4 of which consist of the perimeter of the smaller parallelogram. If we know that those 4 pieces of pie and equal to 20 units, then we would divide 20 by 4 to find the value of a single piece. 20/4=5 so a single piece of pie has a value of 5 units. We would then multiply 9 by 5 to find the value equivalent of the 9 pieces of pie. 9(5)=45. Therefore, the perimeter of the larger parallelogram is 45.
