Answer:
-56/9
Step-by-step explanation:
By Vieta's formulas,
$r + s = -\frac{4}{3}$ and $rs = \frac{12}{3} = 4.$ Squaring the equation $r + s = -\frac{4}{3},$ we get
$r^2 + 2rs + s^2 = \frac{16}{9}.$ Therefore,
$r^2 + s^2 = \frac{16}{9} - 2rs = \frac{16}{9} - 2 \cdot 4 = -\frac{56}{9}}$
<u>The question does not specify the condition that must satisfy the given angles. We assume they are the internal angles of a triangle.</u>
Answer:
<em>x = 10</em>
Step-by-step explanation:
<u>Internal Angles of a Triangle</u>
The measure of the angles of a triangle are given as 48-x, 9x-38, and 90. Since the sum of the internal angles of a triangle is 180°:
48 - x + 9x - 38 + 90 = 180
Simplifying:
100 + 8x = 180
Subtracting 100:
8x = 180 - 100 = 80
x = 80/8
x = 10
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]
I would use the equation
24 + 8x = 112
let x = the amount of CDs she bought.
Hope this helps!!
Rate = (150 miles)/(3 hrs) = 50 mph
so . . .
(50 mph)*(time) = 400 miles
*divide both sides by 50 mph
time = (400 miles)/(50 mph) = 8 hrs
time = 8 hrs