The line y - 3 = 2x intersects the curve 20 + xy = 5y at P and Q. Calculate the coordinates of P and Q.
1 answer:
Answer:
see explanation
Step-by-step explanation:
Given the 2 equations
y - 3 = 2x → (1)
20 + xy = 5y → (2)
Rearrange (1) expressing y in terms of x by adding 3 to both sides
y = 2x + 3 → (3)
Substitute y = 2x + 3 into (2)
20 + x(2x + 3) = 5(2x + 3) ← distribute parenthesis
20 + 2x² + 3x = 10x + 15 ← subtract 10x + 15 from both sides
2x² - 7x + 5 = 0 ← in standard form
(x - 1)(2x - 5) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
2x - 5 = 0 ⇒ 2x = 5 ⇒ x =
Substitute each of these values into (3) for corresponding values of y
x = 1 : y = 2 + 3 = 5 ⇒ P(1, 5 )
x = : y = 5 + 3 = 8 ⇒ Q(
, 8 )
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Answer:
C. The graph of the function starts high and ends low
Step-by-step explanation:
For , as
approaches negative infinity,
approaches infinity, and as
approaches infinity,
approaches negative infinity.
Thus, we have:
This corresponds with answer choice C. The graph of the function starts high and ends low.
Linear pair angles, which are angles that together form a straight line are
supplementary angles.
The one that completed the proof incorrectly is <u>Becky</u>.
Reasons:
The two column proof is presented as follows;
Statement Reason
1. Segment GH intersects segment AB at K 1. Given
2. m∠AKG + m∠HKB = 180° 2.Definition of Supplementary Angles
m∠GKB + m∠HKB = 180°
3. m∠AKG + m∠HKB = m∠GKB + m∠HKB 3. Substitution property
4. m∠AKG = m∠HKB 4. Subtraction Property
The difference between Angie's Proof and Becky's Proof is in Statement 2.
- Angie states that; m∠AKG + m∠HKB = 180° and m∠GKB + m∠HKB = 180° by definition of Supplementary Angles
- Becky states that; m∠AKG + m∠HKB = 180° and m∠GKB + m∠HKB = 180° by Angle Addition Postulate
Becky's proof is incorrect because the measure of angles m∠AKG and
m∠HKB and m∠GKB and m∠HKB are not given, therefore, the use of the
reason of Angle Addition Postulate in statement 2. is incorrect.
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