S=θr
10.91=θ5
10.91/5=θ
therefore
θpie/180= your answer in radians
Answer:
x = 10
Step-by-step explanation:
You can try the answers to see which works. (The first one does.)
Or, you can solve for the variable:
Divide by 75
... (1/5)^(x/5) = 3/75 = 1/25
Recognize that 25 = 5^2, so ...
... (1/5)^(x/5) = (1/5)^2
Equating exponents, you have
... x/5 = 2
... x = 10 . . . . . multiply by 5
_____
You can also start by taking logarithms:
... log(75) +(x/5)log(1/5) = log(3)
... (x/5)log(1/5) = log(3) -log(75) = log(3/75) = log(1/25) . . . . simplify the log
... x/5 = log(1/25)/log(1/5) = 2 . . . . . simplify (or evaluate) the log expression
... x = 10 . . . . . multiply by 5
_____
"Equating exponents" is essentially the same as taking logarithms.
Answer:
18.
∠2 = 40
∠3 = 140
∠4 =140
19.
∠1 = 134
∠2 = 46
∠3 = 134
∠4 = 46
Step-by-step explanation:
18. Using vertical angle theorem, 1 is equal to 2 and 3 is equal to 4. Therefore 2 is equal to 40 degrees. Then since 2 and 3 are supplementary adjacent angles or a linear pair, they equal 180 when combined. 180-40 equals 140. 3 and 4 are also vertical angles so 3 = 4 and they are both 140.
19. Angles 1 & 3 and 2 & 4 are vertical angles because they are directly across from each other and share the same bisectors. You can use what you know about special angle pairs to find the measure of each angle because since 1 & 3 are vertical angles and 2 & 4 are also vertical angles, 1 is equal to 3 and 2 is equal to 4. So, since the angle formed at the right is angle 2, we can confirm that angle 4 is equal to it and therefore angles 2 and 4 are 46 degrees. Then since angles 1 & 2 and 3 & 4 are linear pairs, we can say that angle 1 + angle 2 is equal to 180 and the same for angles 3 & 4. So subtract 180 - 46 and you get 134. Therefore angles 1 and 3 are equal to 134 degrees.
OXY=90degree...and OYZ=90degree because the tangents supported in the circle are always 90
This is an inequality.
-x + 10 < 0
<u> - 10 - 10 </u> deduct 10 from both sides
-x < -10
<u>÷ -1 ÷ -1 </u> divide both sides by negative 1.
x > 10 notice that when you divide x by a negative number, the inequality sign is reversed. from < to >.
The value of x is greater than 10.
Let us assume that x = 11
-x + 10 < 0
-11 + 10 < 0
-1 < 0
