Here's some guidelines to help you:
For 1, 4, 5, and 6, they are 30-60-90 triangles. What's that you may ask? Well, it means that the sides have a predetermined length when one side is given. In #1 for example, you have a side of 11sqrt3, this means that "n" is 11 because in a 30-60-90 triangle, the longer side is the sqrt3 times the length of the shorter side. So to get the shorter side, we divide by sqrt3 to get 11. "m", or the hypotenuse, can be determined by taking twice the length of the shorter side. Since we figured out earlier that the shorter side is 11, 11 times 2 is 22. So the answer for #1 is n=11, m=22.
For 2 and 3, they are 45-45-90 triangles, triangles where the two lengths are the same and the hypotenuse is either leg length times sqrt2. In problem #2 for example, "y" must be 17 because one leg length is 17. "x", or the hypotenuse, is equal to 17sqrt(2) because 17 times sqrt(2).
You can apply all these rules to the other 4 problems I didn't explain.
Hope this long explanation clears your doubts!
To solve q+(-9)=12 we do the following.
q+(-9)=12
+9 +9
q=21
Giving us are end answer of q=21.
Hope this helps!=)
Answer:
33.65
Step-by-step explanation:
You've got five different problems in this photo ... four on top and the word problem on the bottom ... and they're all exactly the same thing: Taking two points and finding the slope of the line that goes through them.
In every case, the procedure is the same.
If the two points are (x₁ , y₁) and (x₂ , y₂) , then
the slope of the line that goes through them is
Slope = (y₂ - y₁) / (x₂ - x₁) .
This is important, and you should memorize it.
#1). (8, 10) and (-7, 14)
Slope = (14 - 10) / (-7 - 8) = 4 / -15
#2). (-3, 1) and (-17, 2)
Slope = (2 - 1) / (-17 - -3) = (2 - 1) / (-17 + 3) = 1 / -14
#3). (-20, -4) and (-12, -10)
Slope = [ -10 - (-4) ] / [ -12 - (-20) ]
=========================================
The word problem:
This question only gives you one point on the graph,
and then it wants to know what's the slope ?
What are you going to do for another point ?
A "proportional relationship" always passes through the origin,
so another point on the line is (0, 0) .
Now you have two points on THAT line too, and you can easily
find its slope.
