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3 years ago

3 folders cost $2.91 which equation would help determine the cost of 2 folders

Mathematics

2 answers:

eimsori [14]3 years ago

5 0

Answer:

The equation that will determine the cost of two folders is; 3x = 2× $2.91

and the cost of the 2 folders is $1.94

Step-by-step explanation:

To solve this problem, we will follow the steps below;

Using proportion;

Let x be the cost of 2 folders

3 folders = $2.91

2 folders = x

Cross-multiply

3x = 2× $2.91

The equation that will determine the cost of two folders is

3x = 2× $2.91

We can go ahead and solve

3x = $5.82

Divide both-side of the equation by 3

$\frac{3x}{3}$ = $\frac{5.82}{3}$

x = $ 1.94

The cost of 2 folders is $1.94

nadezda [96]3 years ago

3 0

Answer:

2/x = 3/$2.91

Step-by-step explanation:

Let x represent the unknown cost of 2 folders. Since 2 folders cost x, we have the following proportion:

2/x

We can write the fact that 3 folders cost $2.91 as a proportion:

3/$2.91

The cost changes along with the number of folders purchased, and so the two proportions are equivalent.

2/x = 3/2.91

hope this helps! Please make me brainliest

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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,

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

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,

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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,

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

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,

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

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