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3 years ago

The table below represents a linear function f(x) and the equation represents a function g(x):

Mathematics

1 answer:

Novosadov [1.4K]3 years ago

7 0

Part A: The slope of f(x) is three times as great as the slope of g(x).

Part B: The y-intercept of g(x) is 12 larger than the y-intercept of f(x).

In order to find these two answers, you need to find a model for f(x). You can do that by first finding the slope. The formula is below.

slope (m) = (y2 - y1)/(x2 - x1)

In this equation (x1, y1) is the first point and (x2, y2) is a second point. For this purpose, we'll pick (1, 0) and (0, -6)

slope (m) = (-6 - 0)/(0 - 1)

m = -6/-1

m = 6

Now we know that the slope is 6, which is 3 times as great as the first slope. Now to find the y-intercept, we can use either point and the slope in slope intercept form.

y = mx + b

0 = 6(1) + b

0 = 6 + b

-6 = b

So we know the y-intercept is -6, which is 12 less than the y-intercept of g(x).

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Choice B is correct; the domain of function A is the set of real numbers greater than 0

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3 years ago

I can't seem to find the answers or understand how this works.

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Answer:

m = 5

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alukav5142 [94]

ind the square root of c2. Use the square root function on your calculator (or your memory of the multiplication table) to find the square root of c2. The answer is the length of your hypotenuse!In our example, c2 = 25. The square root of 25 is 5 (5 x 5 = 25, so Sqrt(25) = 5). That means c = 5, the length of our hypotenuse! The Pythagorean Theorem describes the relationship between the sides of a right triangle. It states that for any right triangle with sides of length a and b, and hypotenuse of length c, a2 + b2 = c2

Make sure that your triangle is a right triangle. The Pythagorean Theorem only works on right triangles, and by definition only right triangles can have a hypotenuse. If your triangle contains one angle that is exactly 90 degrees, it is a right triangle and you can proceed.Right angles are often notated in textbooks and on tests with a small square in the corner of the angle. This special mark means "90 degrees."


Assign variables a, b, and c to the sides of your triangle. The variable "c" will always be assigned to the hypotenuse, or longest side. Choose one of the other sides to be a, and call the other side b (it doesn't matter which is which; the math will turn out the same). Then copy the lengths of a and b into the formula, according to the following example:If your triangle has sides of 3 and 4, and you have assigned letters to those sides such that a = 3 and b = 4, then you should write your equation out as: 32 + 42 = c2.

Find the squares of a and b. To find the square of a number, you simply multiply the number by itself, so a2 = a x a. Find the squares of both a and b, and write them into your formula.If a = 3, a2 = 3 x 3, or 9. If b = 4, then b2 = 4 x 4, or 16.When you plug those values into your equation, it should now look like this: 9 + 16 = c2.


Add together the values of a2 and b2. Enter this into your equation, and this will give you the value for c2. There is only one step left to go, and you will have that hypotenuse solved!In our example, 9 + 16 = 25, so you should write down 25 = c2.

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