The measure of angle ABC is 45°
<em><u>Explanation</u></em>
Vertices of the triangle are: A(7, 5), B(4, 2), and C(9, 2)
According to the diagram below....
Length of the side BC (a)
Length of the side AC (b)
Length of the side AB (c)
We need to find ∠ABC or ∠B . So using <u>Cosine rule</u>, we will get...
So, the measure of angle ABC is 45°
Answer:
(4,11/2)
Step-by-step explanation:
5x-2y=9
12x-8y=4
A quick look will tell us that neither the x- nor the y- coefficient is the same in both equations, so combining the two by addition or subtraction. We can see that 2 is a multiple of 8, since 2 x 4 = 8. We should multiply the first equation by 4.
4(5x-2y=9)
Now we need to decide if we should add or subtract the equations.
20x-8y=36
12x-8y=4
Since we need to have a -8 and a +8 to eliminate the variables, we should subtract them. Change all the signs of the second equation and combine.
20x-8y=36
-12x-8y=4
----------------
8x=32
Divide both sides by 8 to get the x-value:
x=4
Now that we have our x-value, we need to plug in the y-value.
5x-2y=9
5(4)-2y=9
20-2y=9
-2y=-11
y=11/2
So our solution is (4,11/2)
Let's check our work.
5x-2y=9
5(4)-2(11/2)=9
20-22/2=9
20-11=9
9=9
12x-8y=4
12(4)-8(11/2)=4
48-88/2=4
48-44=4
4=4
Our solution is correct.