- Given ⇔ 1. ∠PRS and ∠VUW are supplementary
- Angles forming a linear pair sum of 180° ⇔ 3. ∠PRS + ∠SRU = 180°
- Definition of Supplementary angle ⇔ 2. ∠PRS + ∠VUW = 180°
- Transitive property of equality ⇔ 4 . ∠PRS + ∠VUW = ∠PRS + ∠SRU
- Algebra ⇔ 5. ∠VUW = ∠SRU
- Converse of Corresponding angle Postulate ⇔ Line TV || Line QS
<u>Step-by-step explanation:</u>
Here we have , ∠PRS and ∠VUW are supplementary . We need to complete the proof of TV || QS , with matching the reasons with statements .Let's do this :
- Given ⇔ 1. ∠PRS and ∠VUW are supplementary
- Angles forming a linear pair sum of 180° ⇔ 3. ∠PRS + ∠SRU = 180°
- Definition of Supplementary angle ⇔ 2. ∠PRS + ∠VUW = 180°
- Transitive property of equality ⇔ 4 . ∠PRS + ∠VUW = ∠PRS + ∠SRU
- Algebra ⇔ 5. ∠VUW = ∠SRU
- Converse of Corresponding angle Postulate ⇔ Line TV || Line QS
Above mentioned are , are the statements matched with expressions on right hand side (RHS) .
- The Corresponding Angles Postulate states that, when two parallel lines are cut by a transversal , the resulting corresponding angles are congruent .
- The converse states: If corresponding angles are congruent, then the lines cut by the transversal are parallel.
<h2>
Answer:</h2><h2><em><u>
8x^3 + 3x^2 - 5x + 4 is the answer.</u></em></h2>
Step-by-step explanation:
(6x^3 + 3x² + 3) + (2x^3 - 5x + 1)
6x^3 + 2x^3 = 8x^3
3x^2 + 0 = 3x^2
-5x + 0 = -5x
3 + 1 = 4
8x^3 + 3x^2 - 5x + 4 is the answer because you have to put all the terms that were solved together. This will lead to 8x^3 + 3x^2 - 5x + 4. And, standard form is ax^2 + bx + c. So, 8x^3 + 3x^2 - 5x + 4 is the answer.
<em><u>8x^3 + 3x^2 - 5x + 4</u></em>
<em><u></u></em>
Hope this helped,
Kavitha
Answer:
A
Step-by-step explanation:
Process of elimination
Answer:
.
Step-by-step explanation:
Let x represent height of the cone.
We have been given that Sand pouring from a chute forms a conical pile whose height is always equal to the diameter.
We know that radius is half the diameter, so radius of cone would be
.
We will use volume of cone formula to solve our given problem.

Upon substituting the value of height and radius in terms of x, we will get:



Now, we will take the derivative of volume with respect to time as:


Upon substituting
and
, we will get:




Therefore, the sand is pouring from the chute at a rate of
.