First, we can note that the relation between the independent and the dependent variables is a linear relation.
We will need two points: (1,3) and (2,5)
The general form of the equation of the linear line is:
y = mx + c where m is the slope and c is the y-intercept
To get the slope, we will use the following rule:
m = (y2-y1) / (x2-x1)
m = (5-3) / (2-1) = 2
The equation of the line now becomes:
y = 2x + c
To get the value of the c, use any of the given points and substitute in the equation. I will use (1,3) as follows:
y = 2x + c
3 = 2(1) + c
c = 3-2 = 1
Therefore, the equation of the line is:
y = 2x + 1
Answer:
10. 9
In the first question we can solve using the Pythagorean theorem. It states that the hypotenuse in a right triangle or the longest side of the triangle, squared is equal to the other 2 sides, squared. Its expressed as so: C^2 = A^2 + b^2 where c is the hypotenuse and a and b are the other sides oft eh triangle.
Therefore,
15^2 = 12^2+x^2
225=144+x^2
81=x^2
x=9
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11. x=12
In this figure, there are 2 right triangles on the sides of the square. If we can find the lengths of the base of both triangles then we can find x using the Pythagorean theorem. the total base is 21 and the square is 11. 11+a+b=21. We can assume that both triangles are congruent and therefore we can solve this equation:
11+a+b=21
a+b=10
5+5=10
b=5
a=5
The bases of the two triangles are 5 and the hypotenuse is 13. Now we can solve using the Pythagorean theorem:
c^2 = a^2+b^2
13^2=5^2+x^2
169=25+x^2
144=x^2
144= 12 x 12
x=12
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12.
The diagnol of a triangle is the hypotenuse and since the length is the square root of 3, we have all the information we need.
c^2 = a^2+b^2
2^2 = (square root of 3)^2+b^2
4=3+b^2
1=b^2
b=1
Step-by-step explanation:
We are given a rectangle ABCD
A(-2, 3)
B(4, 6)
We are asked to find the slopes of sides BC, CD, and DA.
Let me first draw a rectangle to better understand the problem
Recall that the slope is given by
So the slope of side AB is
The sides BC and DA are perpenducluar to the side AB.
So their slopes will be
Substituting the value of slope of AB
The side CD is parallel to the side AB.
Parallel sides have equal slopes so
Therefore, the slopes of the rectangle ABCD are
Answer:
look at where the points are placed y is 70 and x is 4 then you get (4, 70)
it was 50 mph hope this helps
