Two geometry theorems get a workout here:
1) The sum of the angles of any triangle is 180 degrees,
2) If two angles are supplementary, their sum is 180 degrees.
From this we know that ∠RST + ∠STR + ∠TRS = 180. in ΔRST.
Next, look at line QS with points Q, R, and S. A straight line measures 180 degrees. and any two angles created by the line are supplements.
So, ∠QRT + ∠TRS = 180
Since we have two things equal to 180, we can set them equal to one another through transitivity (if a = b and b = c, then a = c).
∠RST + ∠STR + ∠TRS = ∠QRT + ∠TRS
Now we put in values we know for x.
(9 + x) + 5x + ∠TRS = 9x + ∠TRS
∠TRS was not filled in, but that's okay. If we subtract it from both sides, it won't be there regardless of its measure. The rest of this problem plays out like algebra class.
9 + x + 5x = 9x
9 + 6x = 9x
9 = 3x
x = 3
So x = 3, and we can find our angle measures for all angles in the problem.
<span>2 inches = 25 miles
?,,,,,,,,,,,,,,,</span><span>60 miles
</span>
60 x 2 / 25 = 4.8 inches
<span>1/4 = 0.25 inches
0.25 x 25 / 2 = 3.125 miles
answer
</span><span>How many inches on the map represent 60 miles?
Enter your answer in the box.
answer: </span>4.8 inches
<span>
Part B
How many miles are represented by 1/4inch on the map?
Enter your answer in the box.
</span>answer: 3.125 miles
Let's break down the problem step by step.
The sum of 4 times a larger integer can be summarized as:
4x
9 times a smaller integer can be summarized as:
9y
We know that we're adding the two expressions because the beginning of the problem has sum. We also know the sum is 3.
So, we get:
4x + 9y = 3
Continuing with the problem, we have the difference between 8 times the larger
8x
We also have 3 times the smaller
3y
This part of the problem mentions the difference between these expressions so we subtract and we know the difference is 27.
8x - 3y = 27
Now, we have both equations so we can solve for either x or y.
4x + 9y = 3
8x - 3y = 27
It's easier to multiply the 4x equation by 2 to have both equations resulting in 8x
(4x + 9y = 3) * 2
We get:
8x +18y = 6
So, we now have:
8x + 18y = 6
8x - 3y = 27
We can subtract the x to get y by itself. We get:
21y = -21
Solve for y and we get:
y = -1
Since we know what y is, we can plug that in and solve for x. It doesn't matter which equation you plug y back in. I'm gonna use the second equation.
8x - 3y = 27
8x - 3 (-1) = 27
8x + 3 = 27
8x = 24
x = 3
So, we now know that
y = -1
x = 3
Hope this helped! If you have any questions then please leave a comment!
A circle is one shape that can be reflected
Hope this helps :)
850 - 400 = 450
450;400
/ 5
9;8
9 girls for every 8 boys