Answer: 44 miles
WORKINGS
Given,
The distance between Indianapolis and Lima, IL = 173 miles
The distance between Indianapolis and Dayton, ID = 165 miles
The distance between Dayton and Lima, DL is unknown
Since there are straight roads connecting the three cities, the connection between them form a right angles triangle.
The right angle is at Dayton
The hypotenuse is the distance between Indianapolis and Lima, IL
Therefore IL^2 = ID^2 + DL^2
173^2 = 165^2 + DL^2
DL^2 = 173^2 – 165^2
DL^2 = 29929 – 27225
DL^2 = 2704
DL = 52 miles
Therefore, The distance between Dayton and Lima, DL = 52 miles
The question is asking how many more miles would Meg drive if she stopped in Dayton first than if she drove directly to Lima.
That is, Distance of Indianapolis to Dayton + Distance of Dayton to Lima – Direct distance of Indianapolis to Lima
That is, ID + DL – IL
= 165 miles + 52 miles – 173 miles
= 217 miles – 173 miles
= 44 miles
Therefore, Meg would drive 44 more miles if she stopped in Dayton first than if she drove directly to Lima.
<h3>
Answer: Choice H) 2</h3>
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Explanation:
Recall that the pythagorean trig identity is 
If we were to isolate sine, then,

We don't have to worry about the plus minus because sine is positive when 0 < x < pi/2.
Through similar calculations,
Cosine is also positive in this quadrant.
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So,

Therefore,

is an identity as long as 0 < x < pi/2
Let's solve this system of equations through substitution.
We have these two equations.
-7x-2y=14
6x+6y=18
Now let divide the second equation by 6.
6x+6y=18 ----> x+y=3
Next, let us move y to the right side of the equation.
x+y=3 -------> x=3-y (x equals 3-y)
Because we found out that what x is in terms of y, we can input that in for every instance of x in this equation below.
-7x-2y=14 becomes -7(3-y)-2y=14 (Why? Because x equals 3-y!)
We have a one variable equation now and can solve for y.
-7(3-y)-2y=14
-21+7y-2y=14
5y=35
y=7
Plug in 7 for y in any equation to find x.
x+y=3
x+7=3
x=-4
answer: x=-4, y=7
Answer:
Law of cosines to find missing measures
c^2= a^2+ b^2 - 2ab*cos(C)
Used because it is a SAS triangle
Step-by-step explanation:
This is known as a side, angle, side, or SAS triangle. We can find the missing measures by using the Law of cosines
c^2= a^2+b^2-2ab*cos(C)
Answer:
y - 8 = 3(x - 2)
Step-by-step explanation:
Start with the basic point-slope form of the equation of a straight line:
y - k = m(x - h). Here the given point is (2, 8), so assign the value 2 to h and the value 8 to k, also the value 3 to m. Then:
y - 8 = 3(x - 2)