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3 years ago

Identify the following equation as that of a line, a circle, an ellipse, a parabola, or a hyperbola. x^2 + 2y^2 = 2

Mathematics

1 answer:

Sergeu [11.5K]3 years ago

7 0

This is an equation representing the ellipse

Explanation:

The general equation for an ellipse is $\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1$ so, when you simplify it according to the characteristics of a and b, you would end up in the similar form of the equation given

where a represents half the length of the major axis and b represents half the length of the minor axis.

The easiest method to identify, look at whether both the variables are squared, and also the coefficient of x and y should be positive but different.

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Alison has three dogs but only two dog biscuits how can she divide them so that each dog get the same amount?

Lera25 [3.4K]

Each dog can get 2/3 of a dog biscuit.

7 0

3 years ago

Read 2 more answers

The first few steps in solving the quadratic equation 5x2 + 27x = 14 − 13x by completing the square are shown.

Katena32 [7]

Answer:

Step-by-step explanation:

Give the equation 5x² + 27x = 14 − 13x, we are to write the steps needed to solve for x using the completing the square method.

Step 1: Rewrite the equation in a quadratic form by first adding 13x to both sides of the equation.

5x² + 27x +13x= 14 − 13x+13x

5x² + 40x = 14

Step 2: factor out the common constant in the left hand side of the equation.

5(x²+8x) = 14

Step3: The next step to take is to divide through by the the value of 5 to have;

5(x²+8x)/5 = 14/5

x²+8x = 14/5

Step 4: complete the square of the equation at the left hand side by adding the square of half of the coefficient of x to both sides i.e {1/2(8)}² which is 4²

x²+8x +4² = 14/5+4²

x²+8x +16 = 14/5+16

(x+4)² = 94/5

Step 5: Taking the square root of both sides

√(x+4)² = ±√94/5

x+4 = ±√94/5

Step 6: subtract 4 from both sides

x+4-4 = ±√94/5 - 4

x = ±√94/5 - 4

Hence the solution to the equation using completing the square method is x = -4±√94/5

8 0

4 years ago

Plźzzz help me ... I'll give brainliest

fgiga [73]

Answer:

$\displaystyle x = \frac{1}{3}$ .

Step-by-step explanation:

Consider the double angle identity for tangents:

$\displaystyle \tan(2\theta) = \frac{2\tan{\theta}}{1 - \tan^{2}{\theta}}$ .

Also, for two complementary angles,

$\displaystyle \tan{\left(\frac{\pi}{2} - \theta \right)} = \frac{1}{\tan{\theta}}$ .

Subtract $\tan^{-1}(x + 1)$ from both sides of this equation:

$\displaystyle 2\tan^{-1}{x} = \frac{\pi}{2} + (-\tan^{-1}(x + 1))$ .

Take the tangent of both sides of this equation:

$\displaystyle \tan(2\tan^{-1}{x}) = \tan\left(\frac{\pi}{2} -\tan^{-1}\left(x + 1\right)\right)$ .

Apply the double-angle identity to the left-hand side of this equation:

$\displaystyle \tan(2\tan^{-1}{x}) \implies \frac{2\tan(\tan^{-1}x)}{1 - \tan^{2}(\tan^{-1}x)}\implies \frac{2x}{1 - x^{2}}$ .

The two angles $\displaystyle \left(\frac{\pi}{2} + (-\tan^{-1}\left(x + 1\right))\right)$ and $(x - 1)$ are complementary. Therefore, for the right-hand side of this equation,

$\displaystyle \tan\left(\frac{\pi}{2} -\tan^{-1}\left(x + 1\right)\right)\implies \frac{1}{\tan(\tan^{-1}(x + 1))} \implies \frac{1}{x + 1}$ .

Equate the two sides of this equation:

$\begin{aligned} & \frac{2x}{1 - x^{2}} = \frac{1}{x + 1}\\ \implies & \frac{2x}{(1 - x)(1 + x)} = \frac{1}{1 + x}\\\implies & 2x = 1 - x,\; x \ne 1,\; x \ne -1\\\implies & x = \frac{1}{3}\end{aligned}$ .

5 0

3 years ago

How many terms are in the algebraic expression 3x - 9xy +10=

Anon25 [30]

The answer would probably 3 because there is 1 x and y plus a 10

7 0

3 years ago

Quadrilateral ABCD is inscribed in a circle. If angle B measures 112°, what is the measure of angle D?

Vitek1552 [10]

Answer:

68°

Step-by-step explanation:

If a quadrilateral is inscribed in a cirle, the sum of its opposite angles is 180°. Angles B and D are opposite => B+D=180° => D=180°-B=180°-112°=68°

4 0

3 years ago