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Sedaia [141]
3 years ago
10

In circle o,SU is a diameter What is MST

Mathematics
2 answers:
Rom4ik [11]3 years ago
7 0

We have been given that SU is diameter of our circle so measure of arc ST will be equal measure of central angle SOT.

Diameter is longest line segment of a circle passing through center of circle. So angles formed by our diameter (straight line) will add up-to 180 degrees.

Let us set sum of measures of our angles equal to 180. We have been given that angle SOR and UOT are congruent angles, so we will set our equation as:

2(9x+5)+13x+15=180

Upon distributing 2 we will get,

18x+10+13x+15=180

31x+25=180

31x=180-25

31x=155

x=\frac{155}{31} =5

We can find measure of angle SOT by sum of measures of angle ROT and UOT.

\angle SOT=(13x+15)+(9x+5)

\angle SOT=13x+15+9x+5

Let us combine like terms.

\angle SOT=22x+20

Let us substitute x=5 in our given equation.

\angle SOT=22\cdot 5+20

\angle SOT=110+20=130

Therefore, measure of arc ST will be 130 degrees.

erik [133]3 years ago
6 0
It's 130 hope the answer helps
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Step-by-step explanation:

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3 years ago
What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?
dybincka [34]

What you should do first is simplify the equation into the y = mx + b format. Move 2x to the other side. Know that in doing this, 2x must become the opposite of what it currently is (-2) in order for the equation to remain true. We also have to take away the '10' because the line is parallel, not exactly the same, which means a different y intercept. This looks like:

5y = -2x + b

Next, simplify y to make things easier. This can be done by dividing both sides by 5, like so:

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What you should also know is that if a line is parallel to another, then this means the slope has to be the same because they both have the same changes in rise and run. With this in mind, simply plug in the x and y values.

(-4) = -\frac{2}{5} * (5) + b

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Add 2 to both sides to isolate b.

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Which means that -2 = b.

Now that we have the y intercept, we can write the equation of the line, which is y = -\frac{2}{5}x - 2.

Hope this was helpful.

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Step-by-step explanation:

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