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3 years ago

Use tables to show which of these ratios are equivalent: 4/6, 10/25, and 6/15

Mathematics

1 answer:

hoa [83]3 years ago

8 0

Answer:

4/6 and 6/15

Step-by-step explanation:

simplify all fractions to lowest possible.

4/6 = 2/3

10/25 = 2/5

6/15 = 2/3

4/6 and 6/15 are equivalent

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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

The final value of a painting after its initial value, m, increases by 2/5

Dennis_Churaev [7]

Your answer is D. 2/5m

This expression means 2/5 times the initial value (m).

3 0

4 years ago

Jason is traveling by car from his home to his office. He has gone 3.5 miles so far. From this point on, he can cover 100 miles

natka813 [3]

Answer:

y = 50x + 3.5

Step-by-step explanation:

Given:

Distance already covered = 3.5 miles

100 miles covered in 2 hour

FInd;

Equation of given scenario

Computation:

Assume;

Total miles covered = y

Total number of hours = x

Speed of car = 100 / 2

Speed of car = 50 miles per hour

Total miles covered = Distance already covered + [Speed of car][Total number of hours]

y = 3.5 + [50][x]

y = 50x + 3.5

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3 years ago

Thesaurus entries:

Artyom0805 [142]

The answer is A endurance

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A parking lot has two entrances. Cars arrive at Entrance 1 according to a Poisson Probability Distribution at an average of thre

dusya [7]

Answer:

note:

please find the attached solution

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3 years ago