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tangare [24]
2 years ago
10

Q, Fixed a system of coordinates in the plane, conficer the curve C having equation y = (x-2)^2. The line x + y - 2 = 0 intersec

ts C in:
(A)1 poin

(B) no point

(C) 2 points

(D) infinitely many points

3 points
Mathematics
2 answers:
Liula [17]2 years ago
5 0

Answer:

C

Step-by-step explanation:

y = (x - 2)² = x² - 4x + 4 → (1)

x + y - 2 = 0 → (2)

substitute y = x² - 4x + 4 into (2)

x + x² - 4x + 4 - 2 = 0

x² - 3x + 2 = 0

(x - 1)(x - 2) = 0

equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 2 = 0 ⇒ x = 2

substitute these values into (2) and solve for y

x = 1 : 1 + y - 2 = 0 ⇒ y - 1 = 0 ⇒ y = 1 ⇒ (1, 1 )

x = 2 : 2 + y - 2 = 0 ⇒ y + 0 = 0 ⇒ y = 0 ⇒ (2, 0 )

the line intersects curve C at 2 points (1, 1 ) and (2, 0 )

Ludmilka [50]2 years ago
3 0

Answer:

Step-by-step explanation:

ok

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1. Ans: Option (B) -6x^4

Explanation:
Given: 2x^4 - 8x^4
Take the common out:
=> x^4(2 - 8)

Hence: => [tex]-6x^4[/tex] (Option B)

2. Ans: Option (D) -3y^5

Explanation:
Given: 6y^5 - 9y^5
Take the common term(s) out:
=> y^5(6-9)

Hence: => -3y^5 (Option D)

3. Ans: Option (B) 9x^2 - 12x + 6<span> quadratic trinomial 

Explanation:
</span>Given: 6 - 12x + 13x^2 - 4x^2

The standard form of polynomial function must have the highest powered value at the start, then the second highest and so on.

=> 
13x^2 - 4x^2 - 12x + 6
=> 9x^2 - 12x + 6 (Option B)

4. Ans: Option (C) 7.3x^2 + 0.8x + 1.3

Explanation:
In order to find the total number of C<span>ommon and Endler's guppies, you need to add both Common and Endler's guppies' polynomials, as follows:

</span>Common guppies: 3.1x^2 +6.0x + 0.3<span>
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Total number:          7.3x^2 +0.8x + 1.3
-----------------------------------------------------------------
Hence the ans is Option(C) 7.3x^2 + 0.8x + 1.3

5. Ans: Option (D) 2x^2(133 - 18 \pi )

Explanation:
First let's find the total area of the yard:
Total Area of the Yard = 14x * 19x = 266x^2

Now the area of the circular fountain:
Area of the Circular Fountain = \pi r^2
Since, r=6x
Therefore,
Area of the Circular Fountain = \pi (6x)^2 = 36 \pi x^2

Now the final Area of the yard would be:
Final area of the Yard = Total Area of the Yard - Area of the Circular Fountain
Final area of the Yard = 266x^2 - 36 \pi x^2
=> Final area of the Yard = 2x^2(133 - 18 \pi) (Option D)

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Explanation:
First let's find the total area of the lot:
Total Area of the lot= 6x * 10x = 60x^2

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Area of the stadium = 1x * 4x = 4x^2

Now the final Area of the lot would be:
Final area of the lot= Total Area of the lot - Area of the stadium
Final area of the lot= 60x^2 - 4x^2
=> Final area of the lot = 56x^2 (Option A)

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