It would be b or d i hope that help
9514 1404 393
Explanation:
<h3>8.</h3>
An exterior angle is equal to the sum of the remote interior angles. Define ∠PQR = 2q, and ∠QPR = 2p. The purpose of this is to let us use a single character to represent the angle, instead of 4 characters.
The above relation tells us ...
∠PRS = ∠PQR +∠QPR = 2q +2p
Then ...
∠TRS = (1/2)∠PRS = (1/2)(2q +2p) = q +p
and
∠TRS = ∠TQR +∠QTR . . . . . exterior is sum of remote interior
q +p = (1/2)(2q) +∠QTR . . . . substitute for ∠TRS and ∠TQR
p = ∠QTR = 1/2(∠QPR) . . . . . subtract q
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<h3>9.</h3>
For triangle ABC, draw line DE parallel to BC through point A. Put point D on the same side of point A that point B is on the side of the median from vertex A. Then we have congruent alternate interior angles DAB and ABC, as well as EAC and ACB. The angle sum theorem tells you that ...
∠DAB +∠BAC +∠CAE = ∠DAE . . . . a straight angle = 180°
Substituting the congruent angles, this gives ...
∠ABC +∠BAC +∠ACB = 180° . . . . . the desired relation
To answer this, set up a system of equations. What we know is that
5x + 2y = 100
And...
x+y=38
x represents the unknown number of 5 points questions
y represents the unknown number of 2 point questions
In my opinion the easiest way to solve this is to use substitution (that is when you find out the value of one variable, either x or y, and substitute that value as the variable).
So,
x+y=38
Subtract x from both sides
y=38-x
Now, plug (38-x) in as y in the other equation.
5x + 2(38-x) = 100
5x + 76-2x= 100
3x+76=100
3x=24
x=8
Now that you know that x=8, you can solve for y.
5x+2y=100
5(8)+2y=100
40+2y=100
2y=60
---- ------
2 2
y=30
X=8
Y=30
There are 8 five point questions on the test and 30 two point questions on the test
Answer: C.The equation has infinite
solutions.
