Answer:
2: 67
3:67
4: 113
Step-by-step explanation:
Answer:
y = 5x-11
Step-by-step explanation:
The slope intercept form of a line is y =mx+b where m is the slope
y = -1/5 x-3
The slope is -1/5
Lines that are perpendicular have negative reciprocal slopes
-1 /(-1/5)
-1 * -5/1
5
The slope of the line that is perpendicular is 5
y=5x+b
Using the point (4,9)
9 = 5(4)+b
9 = 20+b
9-20 =b
-11
y = 5x-11
The measure of Arc Q P is 96°. We also know that ∠QTP is central angle, then the measure of arc QP is 96°.
Step-by-step explanation:
<u>Step 1</u>
If QS is a circle diameter,
then m∠QTS=180°.
Let x be the measure of angle RTQ: ∠RTQ =x.
so, let ∠RTQ = x
<u />
<u>Step 2</u>
According to the question,
∠RTQ = ∠RTS - 12°
⇒ ∠RTS = x + 12°
∴ ∠QTS = ∠RTQ + ∠RTS
= x + x + 12° = 2x + 12° = 180°
⇒ 2x = 168°
⇒ x = 84°
⇒ ∠RTQ = 84°
<u></u>
<u>Step 3</u>
Now,
∵∠QTP and ∠RTS are vertical angles
∴ ∠QTP = 84° + 12° = 96°
As ∠QTP is the central angle, hence the measure of arc QP is 96°
<u></u>
<u>Step 4</u>
The Measure of arc QP = 96°
Answer:
Step-by-step explanation:
Begin by squaring both sides to get rid of the radical. Doing that gives you:
Now use the Pythagorean identity that says
and make the replacement:
. Now move everything over to one side of the equals sign and set it equal to 0 so you can factor:
and then simplify to
Factor out the common cos(x) to get
and there you have your 2 trig equations:
cos(x) = 0 and 1 - cos(x) = 0
The first one is easy enough to solve. Look on the unit circle and see where, one time around, where the cos of an angle is equal to 0. That occurs at
The second equation simplifies to
cos(x) = 1
Again, look to the unit circle and find where the cos of an angle is equal to 1. That occurs at π only.
So, in the end, your 3 solutions are
