Answer:
Part 1) m∠1 =(1/2)[arc SP+arc QR]
Part 2)
Part 3) PQ=PR
Part 4) m∠QPT=(1/2)[arc QT-arc QS]
Step-by-step explanation:
Part 1)
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
we have
m∠1 -----> is the inner angle
The arcs that comprise it and its opposite are arc SP and arc QR
so
m∠1 =(1/2)[arc SP+arc QR]
Part 2)
we know that
The <u>Intersecting Secant-Tangent Theorem,</u> states that the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
so
In this problem we have that
Part 3)
we know that
The <u>Tangent-Tangent Theorem</u> states that if from one external point, two tangents are drawn to a circle then they have equal tangent segments
so
In this problem
PQ=PR
Part 4)
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
In this problem
m∠QPT -----> is the outer angle
The arcs that it encompasses are arc QT and arc QS
therefore
m∠QPT=(1/2)[arc QT-arc QS]
Answer:
y = - 7
Step-by-step explanation:
The equation of a horizontal line is
y = c
where c is the value of the y- coordinates the line passes through.
The line passes through (5, - 7) with y- coordinate - 7, thus
y = - 7 ← equation of horizontal line
In geometry, the definition of a triangle is a two-dimensional closed figure with three sides. Aside from this, it is proven that the sum of the angles of a triangle is 180°. This is a triangle's innate property. Therefore, any closed shape with three sides is a triangle and it follows that the sum of the three angles is equal to 180°.
It is logical therefore, that the first step in proving this is by using the definition of a triangle.
Answer:
Cross Multiply.
Step-by-step explanation:
Multiply the denominator (3) of one side and the numerator (n).
Then, multiply the numerator (2) of on side and the denominator (4) of the other.
3n = 8
You divide both sides by 3 to have n be by itself, equaling ~2.6 or 8/3.
Given:
Tom's earnings: x
Jan's earnings: 2x - 150
Total earnings: 1380
x + 2x - 150 = 1380
3x = 1380 + 150
3x = 1530
3x/3 = 1530/3
x = 510
Tom's earnings: x = 510
Jan's earnings: 2x - 150 = 2(510) - 150 = 1,020 - 150 = 870
total earnings: 1,380
510 + 870 = 1,380
1,380 = 1,380