What is the equation of the line that goes through (2, -1) and is parallel to y= 3x - 3?

Mathematics

1 answer:

larisa86 [58]4 years ago

3 0

Answer:

y + 1 = 3 (x - 2) (the first option - A - in the list of possible answers)

Step-by-step explanation:

Since the new line has to be parallel to y = 3 x - 3, then it has to have the SAME slope (3) and go through (2, -1). Therefore the slope-point general form has to be:

y - (-1) = 3 (x - 2)

y + 1 = 3 (x - 2)

Which is the first option in the list of possible answers

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The base of a solid right pyramid is a regular hexagon with a radius of 2x units and an apothem of units. A solid right pyramid

Xelga [282]

Answer:

$6 x^2*\sqrt{3}$

Step-by-step explanation:

The base of the pyramid we need to study is a hexagon.

Let's look at the attached image of an hexagon to understand how we are going to find the area of this figure.

Notice that an hexagon is the combination of 6 exactly equal equilateral triangles in our case of size "2x" (notice that the "radius" of the hexagon is given as "2x")

Therefore the area of the hexagon is going to be 6 times the area of one of those equilateral triangles.

We know the area of a triangle is the product of its base times its height, divided by 2: $\frac{base*height}{2} = \frac{2x*height}{2}$

We notice that the triangle's height is exactly what is called the "apothem" of the hexagon (depicted in green in our figure) which measures $x\sqrt{3}$ , so replacing this value in the formula above for the area of one of the triangles: