Answer:
The correct options are;
1. Definition of supplementary angles
2. m∠1 + m∠2 = m∠1 + m∠3
3. m∠2 = m∠3
4. Definition of Congruent Angles
Step-by-step explanation:
The two column proof is presented as follows;
Statement 
Reason
1. ∠1 and ∠2 are supplementary Given
∠1 and ∠3 are supplementary
2. m∠1 + m∠2 = 180° Definition of supplementary angles
m∠1 + m∠3 = 180°
3. m∠1 + m∠2 = m∠1 + m∠3 Transitive Property
4. m∠2 = m∠3 Subtraction Property of Equality
5. ∠2 ≅ ∠3 Definition of Congruent Angles
Given that angles ∠1 and ∠2 are supplementary angles and angles ∠1 and ∠3 are are also supplementary angles, then the sums of m∠1 + m∠2 and m∠1 + m∠3 are equal, therefore, ∠2 and ∠3 have equal quantitative value and therefore ∠2 = ∠3 and by definition, ∠2 ≅ ∠3.
Answer:
4 * pi
Step-by-step explanation:
Given r = 10
Formula for the circumference of this full circle is:
2 * r * pi
2 * 10 * pi = 20 * pi
Given one (biggest) part = 16 * pi of this circle.
The other (smaller) part must therefore be:
20 * pi - 16 * pi
4 * pi
Let x = hours worked as a clerk ($12 per hour).Let y = hours worked as a cashier ($8.25 per hour).She worked 55 hours, thereforex + y = 55 (1)She earned $585, therefore12x + 8.25y = 585 (2)From (1), obtainy = 55 - x (3)Substitute (3) into (2).12x + 8.25(55 - x) = 58512x + 453.75 - 8.25x = 5853.75x = 131.25x = 35y = 55 - x = 55 - 35 = 20
Answer: c) Office clerk: 35 hours; cashier: 20 hours.
First, we determine if the parabola is "horizontal" or "vertical", as the directrix is a vertical line, this implies the parabola is "horizontal".
We know that the focus is at the left of the parabola, this tells us that the parabola opens to the left.
We find the distance from the focus to the directrix:
Half of this distance must be the distance from the focus to the vertex, so the vertex of the parabola is the point (3,-7).
This means the vertex form of the equation for the parabola is:
is an arbitrary positive value that determines how "curved" the parabola is, we can only find this value if we know a point of the parabola.
We write the vertex equation in standard form:
Attached is a plot of the parabola if
. It has the directrix, focus, and vertex labeled.
Answer:
A.
Step-by-step explanation:
The negative gives a reflection in the x-axis.
The 2 is a vertical stretch factor 2.
