Which angle has a measure equal to the sum of the m∠SQR and the m∠QRS?
2 answers:
Answer: 180° - m∠RSQ
Proof:
Refer to the diagram shown below.
Let
x = m∠SQR
y = m∠QRS
z = m∠RSQ
w = the external angle (supplement) of m∠RSQ
Because the sum of angles in a triangle is 180°, therefore
x + y + z = 180°
x + y = 180° - z
That is,
m∠SQR + m∠QRS = 180° - z (1)
Because the sum of angles on one side of straight line is 180°, therefore
w + z = 180°
or
w = 180° - m∠RSQ (2)
Equate equations (1) and (2) to obtain
m∠SQR + m∠QRS = completes∠RSQ
This completes the proof.
Proof:
Refer to the diagram shown below.
Let
x = m∠SQR
y = m∠QRS
z = m∠RSQ
w = the external angle (supplement) of m∠RSQ
Because the sum of angles in a triangle is 180°, therefore
x + y + z = 180°
x + y = 180° - z
That is,
m∠SQR + m∠QRS = 180° - z (1)
Because the sum of angles on one side of straight line is 180°, therefore
w + z = 180°
or
w = 180° - m∠RSQ (2)
Equate equations (1) and (2) to obtain
m∠SQR + m∠QRS = completes∠RSQ
This completes the proof.
You might be interested in
Answer:
see details in graph and below
Step-by-step explanation:
There are many ways to generate the function.
We'll generate a function whose first derivative f'(x) satisfies the required conditions, say, a quadratic.
1. f(x) has a local minimum at x = -3, and
2. a local maximum at x = 3
Therefore f'(x) has to cross the x-axis at x = -3 and x=+3.
Furthermore, f'(x) must be increasing at x=-3 and decreasing at x=+3.
f'(x) = -x^2+9
will satisfy the above conditions.
Finally f(x) must be decreasing at x= -5, which implies that f'(-5) must be negative.
Check: f'(-5) = -(-5)^2+9 = -25+9 = -16 < 0 so ok.
f(x) can then be obtained by integrating f'(x) :
f(x) = integral of -x^2+9 = -x^3/3 + 9x = 9x - x^3/3
A graph of f(x) is attached, and is found to satisfy all three conditions.
Answer:
49.7%
Step-by-step explanation:
A cdircle is located within a square.
<u>Area of the circle</u>
Area = , where r = 4 units.
Area Circle = 50.3 units^2
<u>Area of the square</u>
Area = l*w or l^2 for a square, since l = w
Area = (10 units)^2
Area = 100 units^2
<u>Area in the square but outside the circle</u>
This is the difference [Square minus Circle Areas]
Square minus Circle Areas = 100 - 50.3 or <u>49.7 units^2</u>
<u>Probability</u>
The probability of picking a point in the square that is not in the circle is the ration of the two areas: <u>[Outside Circle/Square]x100%</u>
<u></u>
<u>(</u>49.7 units^2)/(100 units^2)x100% = 49.7%
<u></u>