3 years ago

1. Solve the following equation by factoring: 4x2 + 12x + 9 = 0

Mathematics

1 answer:

Luden [163]3 years ago

7 0

Answer:

x = -3/2

Step-by-step explanation:

4x² + 12x + 9 = 0

Use AC method to factor, or recognize the perfect square.

(2x + 3)² = 0

2x + 3 = 0

x = -3/2

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What is the equation of the ellipse with foci at (5, 0), (-5, 0) and vertices (9, 0), (-9, 0)?

forsale [732]

Answer: $\dfrac{x^2}{81}+\dfrac{y^2}{56}=1$

Step-by-step explanation:

General equation of ellipse : $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}$

Given: Vertices of ellipse : (± 9,0)

Since the vertices are of the form (± a, 0).

i.e. a=9

Thus, the major axis is along x-axis.

Also, foci of the ellipse = (±5,0)

Since, foci is of the form (± c,0), i.e. c=5

Since

$c^2=a^2-b^2\\\\\Rightarrow\ 5^2= 9^2-b^2\\\\\Rightarrow\ b^2=81-25\\\\\Rightarrow\ b^2=56$

Equation of ellipse :

$\dfrac{x^2}{9^2}+\dfrac{y^2}{56}=1\\\\\Rightarrow\ \dfrac{x^2}{81}+\dfrac{y^2}{56}=1$

Hence, the required equation : $\dfrac{x^2}{81}+\dfrac{y^2}{56}=1$

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Answer:

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Step-by-step explanation:

1/3(21) - 1 - 1/2(12) = 7 - 1 - 6 = 0

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