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3 years ago

The function f(x) = x is translated 6 units right and 8 units up. Which function represents the transformation?

Mathematics

1 answer:

tensa zangetsu [6.8K]3 years ago

6 0

Answer: g(x)=(x-6)+8

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What value of a makes this equation true?

Goshia [24]

9/10=a/30. and value of a is 27

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3 years ago

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Write the equation -4x^2+9y^2+32x+36y-64=0 in standard form. Please show me each step of the process!

IgorC [24]

Hey there, hope I can help!

$-4x^2+9y^2+32x+36y-64=0$

$\mathrm{Add\:}64\mathrm{\:to\:both\:sides} \ \textgreater \ 9y^2+32x+36y-4x^2=64$

$\mathrm{Factor\:out\:coefficient\:of\:square\:terms} \ \textgreater \ -4\left(x^2-8x\right)+9\left(y^2+4y\right)=64$

$\mathrm{Divide\:by\:coefficient\:of\:square\:terms:\:}4$
$-\left(x^2-8x\right)+\frac{9}{4}\left(y^2+4y\right)=16$

$\mathrm{Divide\:by\:coefficient\:of\:square\:terms:\:}9$
$-\frac{1}{9}\left(x^2-8x\right)+\frac{1}{4}\left(y^2+4y\right)=\frac{16}{9}$

$\mathrm{Convert}\:x\:\mathrm{to\:square\:form}$
$-\frac{1}{9}\left(x^2-8x+16\right)+\frac{1}{4}\left(y^2+4y\right)=\frac{16}{9}-\frac{1}{9}\left(16\right)$

$\mathrm{Convert\:to\:square\:form}$
$-\frac{1}{9}\left(x-4\right)^2+\frac{1}{4}\left(y^2+4y\right)=\frac{16}{9}-\frac{1}{9}\left(16\right)$

$\mathrm{Convert}\:y\:\mathrm{to\:square\:form}$
$-\frac{1}{9}\left(x-4\right)^2+\frac{1}{4}\left(y^2+4y+4\right)=\frac{16}{9}-\frac{1}{9}\left(16\right)+\frac{1}{4}\left(4\right)$

$\mathrm{Convert\:to\:square\:form}$
$-\frac{1}{9}\left(x-4\right)^2+\frac{1}{4}\left(y+2\right)^2=\frac{16}{9}-\frac{1}{9}\left(16\right)+\frac{1}{4}\left(4\right)$

$\mathrm{Refine\:}\frac{16}{9}-\frac{1}{9}\left(16\right)+\frac{1}{4}\left(4\right) \ \textgreater \ -\frac{1}{9}\left(x-4\right)^2+\frac{1}{4}\left(y+2\right)^2=1$

$Refine\;once\;more\;-\frac{\left(x-4\right)^2}{9}+\frac{\left(y+2\right)^2}{4}=1$

For me I used
$\frac{\left(y-k\right)^2}{a^2}-\frac{\left(x-h\right)^2}{b^2}= 1$
$As\;\mathrm{it\;\:is\:the\:standard\:equation\:for\:an\:up-down\:facing\:hyperbola}$

I know yours is an equation which is why I did not go any further because this is the standard form you are looking for. I would rewrite mine to get my hyperbola standard form. However the one I have provided is the form you need where mine would be.
$\frac{\left(y-\left(-2\right)\right)^2}{2^2}-\frac{\left(x-4\right)^2}{3^2}=1$

Hope this helps!

4 0

3 years ago

In the expression 3x² + y − 5, which of the following choices is the exponent in the term 3x²?

quester [9]

Answer: the exponent would be the 2

Step-by-step explanation:

7 0

3 years ago

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What is (4c-d+0.2)^2-10c; c=3.1, d=4.6

yuradex [85]

Good evening ,

______

Answer:

(4c-d+0.2)² - 10c = 33

___________________

Step-by-step explanation:

(4c-d+0.2)^2-10c

c=3.1, d=4.6

(4(3.1) - 4.6 + 0.2)² - 10(3.1) = (12.4 - 4.6 + 0.2)² - 31 = (7.8 + 0.2)² -31 = 8² - 31 = 64-31 =33.

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3 years ago

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Segment YZ has endpoints (6, 3) and (3, 9). Find the coordinates of the point that divides the line segment directed from Y to Z

fenix001 [56]

Answer:

(4, 7)

Step-by-step explanation:

The point of interest is ...

P = (2Z +1Y)/(2+1) = ((2·3+6)/3, (2·9+3)/3)

P = (4, 7)

The point that divides the segment into the ratio a:b is the weighted average of the endpoints, with the weights being "b" and "a". The weight of the first end point corresponds to the length of the far end of the segment.

8 0

3 years ago

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