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Solution to QOTD 5/15/2020

To find the solution to this, we need to use our knowledge of factoring.

First, we need to factor the Greatest Common Factor from all terms, which is 3:

Next, we need to factor the trinomial into a product of two binomials:

So the solution is B.

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Question of the Day 5/14/2020

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Solution to QOTD 5/13/2020

To find the solution to this, we need to use both the Pythagorean Theorem, and trigonometry.

Because we were give that , and knowing that cosine is the ratio of the side adjacent to the hypotenuse, we can draw a triangle and use the information to solve.

First, we need to find the value of the missing side, labeled x in the diagram below:

From the Pythagorean Theorem, we know that , so we can use this to find the missing side:

Now, to find the solution, we use the cosine ratio again, from angle B. We found the measure of the side adjacent to angle B (above) so we can fill in the ratio with the values : . The solution is C.

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Question of the Day 5/13/2020

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Solution to QOTD 5/12/2020

To find the equation of a line perpendicular to the given line, we need to first find the slope of the given line, using the slope formula:

Because we need to find a line perpendicular to the given line, we need to use the opposite reciprocal of this slope, along with the point that is given.

Using the point (0,0) and the slope 5/4, we apply the formula y=mx + b and we get the equation for the new line: .

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Question of the Day 5/12/2020

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Solution to QOTD 5/11/2020

In order to find the location of the new figure, we have to understand how rotations and translations occur.

When a figure is rotated about the origin, the figure remains rigid, it does not change its shape, only its location. Imagine holding your finger on the origin and rotating the paper 90* to the right. This is now where the points of your figure lie. The shortcut for finding the new location is: (x,y) –> (y, -x). In other words, first find the coordinates for each point of your original figure. The coordinates for your rotation 90* clockwise will be switched, and take the opposite sign of whatever your x value was.

For this figure, the original location is: A(-10,0), B(-3,7), C(0,5), D(-2,2)

Rotated 90* clockwise: A(0,-10), B(7,3), C(5,0), D(2,2)

Now, to complete the translation, simply perform the function indicated: here it says to add 1 to the x coordinates, and subtract 2 from the y coordinates. Thus:

A(1,8), B(8,1), C(6,-2), D(3,0)

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Question of the Day 5/11/2020

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Solution to QOTD 5/8/2020

To find the inverse of a function, we swap the x and y values, and solve for y:

Therefore:

So, for part A, the solution is D.

For part B, we need to compose the two functions. When a function and its inverse are composed of each other, the result will always be x. So the solution for part be is x.

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Question of the Day 5/8/2020