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2 years ago

This system has one solution.

Mathematics

2 answers:

erica [24]2 years ago

7 0

Answer:

The y-coordinate of the solution is, 10

Step-by-step explanation:

Given the system of equation:

$y = -2x+4$ ....[1]

$y=x^2+4x+13$ ....[2]

Equate the equation [1] and [2] we have;

$-2x+4 = x^2+4x+13$

Add 2x to both sides of an equation:

$4 = x^2+6x+13$

Subtract 4 from both sides we have;

$0= x^2+6x+9$

$x^2+6x+9=0$

Using perfect square:

$(x+a)^2 = x^2+2ax+a^2$

⇒We can write the equation as:

$x^2+2 \cdot 3x+3^2=0$

then;

$(x+3)^2 = 0$

⇒ $x+3 = 0$

Subtract 3 from both sides we have;

x = -3

Substitute value of x in [1] we have;

$y = -2(-3)+4$

⇒ $y =6+4=10$

Solution for the given system of equation = (-3, 10)

Therefore, the y-coordinate of the solution is, 10

matrenka [14]2 years ago

4 0

Hello there!
I have just taken the test on this answer and I got 10...
I hope this helps!!

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svetlana [45]

Factor the following:
4 p (4 p - 1) - 3 (4 p - 1)^2

Factor 4 p - 1 from 4 p (4 p - 1) - 3 (4 p - 1)^2:
(4 p - 1) (4 p - 3 (4 p - 1))

-3 (4 p - 1) = 3 - 12 p:
(4 p - 1) (4 p + 3 - 12 p)

Grouping like terms, 4 p - 12 p + 3 = 3 + (4 p - 12 p):
(4 p - 1) (3 + (4 p - 12 p))
4 p - 12 p = -8 p:

Answer: (4 p - 1) (-8 p + 3)

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Factor the following:
m (m + n) - 3 m (m + n)^2

Factor m + n out of m (m + n) - 3 m (m + n)^2, resulting in (m + n) (m - 3 m (m + n)^(2 - 1)):
(m + n) (m - 3 m (m + n)^(2 - 1))

2 - 1 = 1:
(m + n) (m - 3 m (m + n))

Factor m out of m - 3 m (m + n), resulting in m (1 - 3 (m + n)):
m (1 - 3 (m + n)) (m + n)

-3 (m + n) = -3 m - 3 n:
Answer: m (m + n) (-3 m - 3 n + 1)

___________________________________________________________Answer : -(-6 + p^2) (-1 - 6 q + p^2 q)

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Factor the following:
6 u^2 (2 u - 5)^2 - 12 u^2 (2 u - 5) (u + 5)

Factor u^2 out of 6 u^2 (2 u - 5)^2 - 12 u^2 (2 u - 5) (u + 5), resulting in u^2 (6 (2 u - 5)^2 - 12 (2 u - 5) (u + 5)):
u^2 (6 (2 u - 5)^2 - 12 (2 u - 5) (u + 5))

(2 u - 5) (2 u - 5) = (2 u) (2 u) + (2 u) (-5) + (-5) (2 u) + (-5) (-5) = 4 u^2 - 10 u - 10 u + 25 = 4 u^2 - 20 u + 25:
u^2 (6 4 u^2 - 20 u + 25 - 12 (2 u - 5) (u + 5))

6 (4 u^2 - 20 u + 25) = 24 u^2 - 120 u + 150:
u^2 (24 u^2 - 120 u + 150 - 12 (2 u - 5) (u + 5))

(u + 5) (2 u - 5) = (u) (2 u) + (u) (-5) + (5) (2 u) + (5) (-5) = 2 u^2 - 5 u + 10 u - 25 = 2 u^2 + 5 u - 25:u^2 (150 - 120 u + 24 u^2 - 122 u^2 + 5 u - 25)

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u^2 ((-120 u - 60 u) + (24 u^2 - 24 u^2) + (150 + 300))

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u^2 (-180 u + (24 u^2 - 24 u^2) + (150 + 300))
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u^2 (-180 u + (24 u^2 - 24 u^2) + 450)

24 u^2 - 24 u^2 = 0:
u^2 (450 - 180 u)

Factor 90 out of 450 - 180 u:
Answer: u^2×90 (5 - 2 u)

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