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2 years ago

11

A set of barstools were priced $284.80 after a 20% discount was applied. What was the price of the set of barstools before the d

iscount?

1 answer:

Lorico [155]2 years ago

5 0

Answer:

$356.00

Step-by-step explanation:

If d represents the discounted price, and p is the original price, you have ...

d = p - 20% × p = p(1 -20%) = 0.80p

Then the original price is ...

p = d/0.80 . . . . . divide by the coefficient of p

p = $284.80/0.80 = $356.00

The price before the discount was $356.00.

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Inga [223]

Answer:

$y=-\sqrt{3}x+2$

Step-by-step explanation:

We want to find the equation of a straight line that cuts off an intercept of 2 from the y-axis, and whose perpendicular distance from the origin is 1.

We will let Point M be (x, y). As we know, Point R will be (0, 2) and Point O (the origin) will be (0, 0).

First, we can use the distance formula to determine values for M. The distance formula is given by:

$\displaystyle d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Since we know that the distance between O and M is 1, d=1.

And we will let M(x, y) be (x₂, y₂) and O(0, 0) be (x₁, y₁). So:

$\displaystyle 1=\sqrt{(x-0)^2+(y-0)^2}$

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Rearranging gives:

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Take the square root of both sides. Since M is in the first quadrant, we only need to worry about the positive case. Therefore:

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So, Point M is now given by (we substitute the above equation for y):

$M(x,\sqrt{1-x^2})$

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Therefore, their <em>slopes will be negative reciprocals</em> of each other.

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$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

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For OM, we have two points: O(0, 0) and M(x, √(1-x²)). So, the slope will be:

$\displaystyle m_{OM}=\frac{\sqrt{1-x^2}-0}{x-0}=\frac{\sqrt{1-x^2}}{x}$

Line RM:

For RM, we have the two points R(0, 2) and M(x, √(1-x²)). So, the slope will be:

$\displaystyle m_{RM}=\frac{\sqrt{1-x^2}-2}{x-0}=\frac{\sqrt{1-x^2}-2}{x}$

Since their slopes are negative reciprocals of each other, this means that:

$m_{OM}=-(m_{RM})^{-1}$

Substitute:

$\displaystyle \frac{\sqrt{1-x^2}}{x}=-\Big(\frac{\sqrt{1-x^2}-2}{x}\Big)^{-1}$

Now, we can solve for x. Simplify:

$\displaystyle \frac{\sqrt{1-x^2}}{x}=\frac{x}{2-\sqrt{1-x^2}}$

Cross-multiply:

$x(x)=\sqrt{1-x^2}(2-\sqrt{1-x^2})$

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$x^2=2\sqrt{1-x^2}-(\sqrt{1-x^2})^2$

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$x^2=2\sqrt{1-x^2}-(1-x^2)$

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$x^2=2\sqrt{1-x^2}-1+x^2$

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We can see that the equation of Line RM is:

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Answer:

$m(n) = 24 (0.75)^n$

Step-by-step explanation:

1) <u>The two points are</u>:

a) On the first swing she swings forward by 18 degrees: <em>(1, 18)</em>

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