It sounds like everything is being described in reference to angle A, so a good starting point is to pick a variable to represent the measure of angle A. I'm going to use "a" for that.
Next, I'm going to take the verbal descriptions in the problem and "translate" them into "math language". They say angle B is 5 times angle A, so that means the measure of angle B is actually 5a. The size of angle C is 5 degrees less than 4 times the size of A, so that translates to 4a-5.
We now know the following:
Angle A: a
Angle B: 5a
Angle C: 4a-5
Now, to find the value of a, we need to remember that all the angles in a triangle add up to 180 degrees.
So we have: a+5a+4a-5 = 180
We can solve that equation by combining like terms to get: 10a-5=180
We can add 5 to both sides: 10a =185
And divide by 10: a = 18.5
That tells us the measure of angle A! (It's 18.5 degrees). Now we can go back and find B by multiplying A by 5. We get 92.5 degrees for that.
Finally, we can find C by taking 4*18.5-5. We get 69 degrees for that.
One last thing-- let's check that they really do add up to 180! 69+92.5+18.5 = 180. Yep!
Hope that helps you!!
Answer:
1. 60 degrees
2. 50 degrees
4. 49 degrees
5. 26 degrees
Step-by-step explanation:
The sum of the measures of the angles of a triangle is 180 degrees.
1.
x + 80 + 40 = 180
x + 120 = 180
x = 60
2.
x + 75 + 55 = 180
x + 130 = 180
x = 50
4.
x + 90 + 41 = 180
x + 131 = 180
x = 49
5.
x + 81 + 73 = 180
x + 154 = 180
x = 26
Answer:
2.6
Step-by-step explanation:
The Mean Absolute Deviation (MAD) is the average amount that each point is from the overall average of the data set.
So, first find the overall average (also called the mean):
avg = (1 + 1 + 2 + 3 + 5 + 7 + 9) / 7
= 28 / 7
= 4
The average (mean) is 4, so now you calculate how far each point is from 4 and average those numbers:
Note: Remember to use absolute values, since distance can't be negative.
4 - 1 = 3
4 - 1 = 3
4 - 2 = 2
4 - 3 = 1
4 - 5 = |-1| = 1
4 - 7 = |-3| = 3
4 - 9 = |-5| = 5
And finally, average (or find the mean) the new data set:
avg = (1 + 1 + 2 + 3 + 3 + 3 + 5) / 7
so 18 / 7 is the MAD of the data set.
Finally, round it to the nearest tenth:
18 ÷ 7 = 2.57142857143 ≈ 2.6
Answer:
2.4 ft
Step-by-step explanation:
h = v/ pie r^2
A function cannot have the same number of ‘x’ repeated in ordered pairs, so therefore the answer would be D, (2,2) because the x wouldn’t repeat.
