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Ivan
3 years ago
9

Circle T is shown. Line segments P R and Q S are diameters. Lines are drawn to connect point P and point Q and point S and point

R to form 2 triangles. Angle P Q T is 40 degrees. Line P R and Line Q S are diameters of circle T. What is the measure of Arc S R? 50° 80° 100° 120°

Mathematics
1 answer:
mamaluj [8]3 years ago
5 0

Answer:

(C)100°

Step-by-step explanation:

See attached diagram to understand the problem better.

|QT|=|PT|$ (radii of circle T)\\Therefore \triangle QPT $ is an isosceles triangle\\\angle PQT=\angle QPT=40^\circ$ (base angles of an isosceles triangle)

\angle PQT+\angle QPT+\angle PTQ=180^\circ$ (sum of angles in a \triangle )\\40^\circ+40^\circ+ \angle PTQ=180^\circ\\\angle PTQ=180^\circ-80^\circ\\\angle PTQ=100^\circ

The measure of arc SR=Central Angle STR

\angle PTQ=\angle STR $ (Vertically opposite angles)\\\angle STR=100^\circ\\mSR=100^\circ

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You will need to sell $50 worth of stuff 9 times

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7 0
3 years ago
Simplify the following expression. a^-3/a^-3
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3 years ago
Consider the following argument. If I get a Christmas bonus, I'll buy a stereo. If I sell my motorcycle, I'll buy a stereo. ∴ If
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Answer:

p → r valid, proof by division into cases

q → r

∴ p ∨ q → r

Step-by-step explanation:

Let

p = "if I get a Christmas bonus,"

q = "if I sell my motorcycle,"

and

r = "I'll buy a stereo."

This can be written as:

If I get a Christmas bonus, I'll buy a stereo

p → r

If I sell my motorcycle, I'll buy a stereo

q → r

∴ If I get a Christmas bonus or I sell my motorcycle, then I'll buy a stereo.

∴ p ∨ q → r

To prove this argument we partition the argument into a group of smaller statements that together cover all of the original argument and then we prove each of the smaller statements. If you see the conclusion ∴ p ∨ q -> r so if the conclusion contains a conditional argument of form "If A1  or A2 or... or An then C ”, then we prove "If A1 then C", "If A2 then C" and so on upto "If An then C" . This depicts that the conclusion  C is true no matter which if the Ai holds true. This method is called proof by division into cases. In the given example, this takes the form:

p → r

q → r

p ∨ q

∴ r

Since proof by division into cases is an inference rule thus given argument is valid. Lets make a truth table to show if this argument is valid

p   q   r   p ∨ q   p → r    q → r    p ∨ q → r

0   0   0     0        1           1             1

0   0   1      0        0          0            0

0   1    0     1         1           0            0

0   1    1      1         0          1               1

1    0   0     1         0          1             0    

1    0   1      1         1           0            1    

1    1    0     1         0          0            0    

1    1    1      1         1           1              1    

An argument is valid if all of the premises are true, then the conclusion is true. So the truth table shows that the conclusion is true i.e. 1 where all premises are true i.e. 1. So the argument is valid.

Hence

p → r valid, proof by division into cases

q → r

∴ p ∨ q → r

4 0
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Answer:

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ioda

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