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3 years ago

Solve the simultaneous equation x^2-4y^2=9 and x+2y=1

Mathematics

2 answers:

Salsk061 [2.6K]3 years ago

8 0

Answer:

x=5,y=-2

Step-by-step explanation:

Anna71 [15]3 years ago

3 0

Solve the simultaneous equation
x^2-4y^2=9 and x+2y=1

X=5, Y= -2

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Suppose f (x) = x^2. Find the graph of f(x+2)

NISA [10]

$\bf ~~~~~~~~~~~~\textit{function transformations}
\\\\\\
% templates
f(x)={{ A}}({{ B}}x+{{ C}})+{{ D}}
\\\\
~~~~y={{ A}}({{ B}}x+{{ C}})+{{ D}}
\\\\
f(x)={{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\\\
f(x)={{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\\\
f(x)={{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\\\\
--------------------$

$\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\
~~~~~~\textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\
~~~~~~\textit{reflection over the y-axis}$

$\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
~~~~~~if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }{{ D}}\\
~~~~~~if\ {{ D}}\textit{ is negative, downwards}\\\\
~~~~~~if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}$

with that template in mind,

$\bf f(x)=x^2\qquad \quad f(x+2)=(x+2)^2\implies f(x+2)=\stackrel{A}{1}(\stackrel{B}{1}x\stackrel{C}{+2})^2\stackrel{D}{+0}$

C = 2 B = 1 C/B = 2/1 or +2, horizontal left shift of 2 units

f(x) shifted left by 2 units is f(x+2).

8 0

3 years ago

11) x – 3y = 3<br> How do you graph it?

kvv77 [185]

Hey!

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x – 3y = 3 is written in standard form. We can write in the slope-intercept form.

x - 3y = 3

x - 3y - x = 3 - x

3y = 3 - x

3y/3 = 3/3 - 3/x

y = 1 - 3/x

y = 1/3x - 1

Now, we know that the y-intercept is -1 and the slope is 1/3

------------------------------------------------

Hence, the answer is $\Large\boxed{\mathsf{In~picture}}$

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Hope This Helped! Good Luck!

8 0

4 years ago

What is the simplified polynomial and the value

Elanso [62]

The simplified polynomial is; xy(x²y - xy² +1) and; the value when x=-3 and y=2 is; -186

From the polynomial given;

x²yxy -xy²xy +xy.

The polynomial can be factorised to yield a simpler form as follows;

xy(x²y - xy² +1).

This is so because, xy is a common factor.

The value is therefore;

(-3×2)((-3)²2 - (-3×2²) +1)

-6(18+12+1)

= -186

Solve the simultaneous equation x^2-4y^2=9 and x+2y=1​

Solve the simultaneous equation x^2-4y^2=9 and x+2y=1