Please Help!!!

1 answer:

5 0

By synthetic division,

-5 | 1 -6 -42 79
. | -5 55 -65
- - - - - - - - - - - - - - - - -
. | 1 -11 13 14

$\implies\dfrac{x^3-6x^2-42x+79}{x+5}=x^2-11x+13+\dfrac{14}{x+5}$
$\implies x^3-6x^2-42x+79=(x^2-11x+13)(x+5)+14$

When $x=-5$ , you're left with a remainder of 14.

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What type of conic is given by the equation 4x^2+9y^2=36

zvonat [6]

Answer:

This is equation of ellipse

Step-by-step explanation:

we are given

$4x^2+9y^2=36$

We can see that right side is 36

so, we can make right side as 1 by dividing both sides by 36

$\frac{4x^2+9y^2}{36} =\frac{36}{36}$

$\frac{4x^2+9y^2}{36} =1$

$\frac{4x^2}{36}+\frac{9y^2}{36} =1$

we can simplify it

$\frac{x^2}{9}+\frac{y^2}{4} =1$

we can rewrite it as

$\frac{x^2}{3^2}+\frac{y^2}{2^2} =1$

now, we can compare it with standard equation of ellipse

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} =1$

we can see that both equations are similar

so, this is equation of ellipse

8 0

3 years ago

I need help guys! <br> Determine if the following relations represent y as a function of x.

Whitepunk [10]

Functions are relations that only have one output per input (or graphically passes the vertical line test). You can either go on Desmos and graph this or just look at my explanations below.

1) function, pretty much all polynomials will be a normal function

2) function. This is a rational function, meaning you'll have some weird gaps and lines going to infinity but it's still a function. It's formed by a polynomial divided by another polynomial.

3) function, looks like you can simplify this into a standard rational function.

4) relation, y with an even square root are never going to give you a single solution (due to the nature of a + or - answer; $\sqrt{9}$ = +3 and -3)