Recall that the diagonals of a rectangle bisect each other and are congruent, therefore:
Substituting the given expression for each segment in the first equation, we get:
Solving the above equation for x, we get:
Substituting x=10 in the equation for segment EI, we get:
Therefore:
Now, to determine the measure of angle IEH, we notice that:
therefore,
Using the facts that the triangles are right triangles and that the interior angles of a triangle add up to 180° we get:
Okay, let's see...
The problem is asking for a linear equation most likely in the form of y=mx+b
y is another way to say f(x)
<em>m = slope </em>
<em>b = y intercept </em>
Let's start with the y intercept first.
Y intercept means ' When does the line touch (intercept) the y axis.
In this case, if you look at the graph, the line <em>touches </em>the y axis at -1.
-1 will replaces b
To find the slope we are going to take 2 precise points from the graph.
Lets use <em>(0,-1)</em> and <em>(-6,4) </em>
To find the slope, we're going to use
4 - (-1) / -6 - 0
Solve, our slope is 5/-6
That is our m
Our final equation is
Answer:
Step-by-step explanation:
Given that the current average property value is two-sevenths more than last year’s average value.
Let x be the last year's average property
Then we have as per the given information this year property value
=
Equate this to
Answer:
Step-by-step explanation:
In rectangle ABCD, AB = 6, BC = 8, and DE = DF.
ΔDEF is one-fourth the area of rectangle ABCD.
We want to determine the length of EF.
First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:
The area of the triangle is 1/4 of this. Therefore:
The area of a triangle is half of its base times its height. The base and height of the triangle is DE and DF. Therefore:
Since DE = DF:
Thus:
Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:
Therefore:
Square:
Add:
And finally, we can take the square root of both sides: