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3 years ago

What is a expression that is equivalent to 2x^2 + (4x-5x^2) +9-(6x+3)

Mathematics

2 answers:

I am Lyosha [343]3 years ago

8 0

The simplified expression is -3x^2 - 2x + 6. Hope this helps! ;)

agasfer [191]3 years ago

3 0

Simplifying:

2x^2 + (4x - 5x^2) + 9 - (6x + 3)

2x^2 + 4x - 5x^2 + 9 - 6x - 3

End Result: -3x^2-2x+6

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The aquarium has 3 more yellow fish than green fish. 60 percent of the fish are yellow. How many green fish are in the aquarium?

cupoosta [38]

The aquarium has 3 more yellow fish than green fish.

60% of the fish are yellow.

To find:

How many green fish are in the aquarium?

Step-by-step explanation:

Let there be x number of fish in the aquarium.

60% of the fish are yellow.

So there are 60x/100 = 3x/5 yellow fish.

Then (100 - 60)% = 40% fish are green.

So there are 40x/100 = 2x/5 green fish.

Given that, there are 3 more yellow fish than green fish

⇒ 3x/5 = 2x/5 + 3

⇒ 3x/5 = (2x + 15)/5

⇒ 3x = 2x + 15

⇒ 3x - 2x = 15

⇒ x = 15

Now, 2x/5 = 2/5 × 15 = 2 × 4 = 6

Answer:

There are 6 green fish in the aquarium.

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3 years ago

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3 years ago

Complete the square and write in standard form. Show all work.What would be the conic section:CircleEllipseHyperbolaParabola

mote1985 [20]

ANSWER

This is an ellipse. The equation is:

$\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1$

EXPLANATION

We have to complete the square for each variable. To do so, we have to take the first two terms and compare them with the perfect binomial squared formula,

$(a+b)^2=a^2+2ab+b^2$

For x we have to take 16x² and -32x. Since the coefficient of x is not 1, first, we have to factor out the coefficient 16,

$16x^2-32x=16(x^2-2x)$

Now, the first term of the expanded binomial would be x and the second term -2x. Thus, the binomial is,

$(x-1)^2=x^2-2x+1$

To maintain the equation, we have to subtract 1,

$16(x^2-2x+1-1)=16((x-1)^2-1)=16(x-1)^2-16$

Now, we replace (16x² - 32x) from the given equation by this equivalent expression,

$16(x-1)^2-16+9y^2+72y+16=0$

The next step is to do the same for y. We have the terms 9y² + 72y. Again, since the coefficient of y² is not 1, we factor out the coefficient 9,

$9y^2+72y=9(y^2+8y)$

Following the same reasoning as before, we have that the perfect binomial squared is,

$(y+4)^2=y^2+8y+16$

Remember to subtract the independent term to maintain the equation,

$9(y^2+8y)=9(y^2+8y+16-16)=9((y+4)^2-16)=9(y+4)^2-144$

And now, as we did for x, replace the two terms (9y² + 72y) with this equivalent expression in the equation,

$16(x-1)^2-16+9(y+4)^2-144+16=0$

Add like terms,

$\begin{gathered} 16(x-1)^2+9(y+4)^2+(-16-144+16)=0 \\ 16(x-1)^2+9(y+4)^2-144=0 \end{gathered}$

Add 144 to both sides,

$\begin{gathered} 16(x-1)^2+9(y+4)^2-144+144=0+144 \\ 16(x-1)^2+9(y+4)^2=144 \end{gathered}$

As we can see, this is the equation of an ellipse. Its standard form is,

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

So the next step is to divide both sides by 144 and also write the coefficients as fractions in the denominator,

$\begin{gathered} \frac{16(x-1)^2}{144}+\frac{9(y+4)^2}{144}=\frac{144}{144} \\ \\ \frac{(x-1)^2}{\frac{144}{16}}+\frac{(y+4)^2}{\frac{144}{9}}=1 \end{gathered}$

Finally, we have to write the denominators as perfect squares, so we identify the values of a and b. 144 is 12², 16 is 4² and 9 is 3²,

$\frac{(x-1)^2}{(\frac{12}{4})^2}+\frac{(y+4)^2}{(\frac{12}{3})^2}=1$

Note that we can simplify a and b,

$\frac{12}{4}=3\text{ and }\frac{12}{3}=4$

Hence, the equation of the ellipse is,

$\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1$

3 0

1 year ago

Find the exact value of sin 105º.

Jet001 [13]

Answer:

sin 105 = sin (45 + 60) = sin 45 cos 60 + cos 45 sin 60, or

= (1 / √2)(1 / 2) + (1 / √2)(√3 / 2)

1 + √3

= -------------

2√2

Step-by-step explanation:

4 0

3 years ago

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