Answer:
C. y = 3x - 2
Step-by-step explanation:
Since the y intercept is negative, it is seen in this equation that the b value (the y intercept) is also negative. Since the slope is increasing upward, we know that the slope is greater than 1 and is going upward, and it matches with the equation since it matches with both of the requirements.
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2 and 4 are the answers that apply to this statement
This is geometry through and through. Plus a little trig thrown in for fun. If you inscribe an equilateral triangle inside a circle and the triangle has side lengths of 12, you have part of what you need to use Pythagorean's Theorem to find the hypotenuse of the triangle which is also the radius of the circle. First, use the formula 360/3 to find that the central angle measure of each angle INSIDE a triangle is 120. So you have 3 triangles within the large one, each with a top angle of 120 and a base of 12. If you extract that one triangle and then split it in half, you have a right triangle with a base of 6. This is a 30-60-90 triangle and this is important so you can check your work. Now use the apothem formula for a right triangle as it relates to a side in an equilateral triangle, which is a = sqrt3/6 * s. Our values are a = sqrt3/6(12) which simplifies to 2sqrt3. That's our apothem. If you're familiar with a 30-60-0 triangle, you could check this to see it's correct. Now you have the base leg of 6 and the height of 2sqrt3, now use Pythagorean's Theorem to find the hypotenuse, which is also the radius of the circle. This was really a difficult one to explain.
Answer: sqrt(61)
Step-by-step explanation:
For parts a) and c1), refer to the attached picture.
For part b), the distance formula is:
d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]
Using x1 = -1, y1 = -4, x2 = -6, y2 = 2:
d = sqrt[(-6 + 1)^2 + (2 + 4)^2] = sqrt[25 + 36] = sqrt(61)
Part c2) Another way to find the length of AB without using the distance formula is by drawing the line and measuring it according to the scale.
Part d) This will only work as long as the graph paper is accurately made, and the scale computation is done correctly. However, this will only give approximations, and will not give an exact answer when radicals are involved.
Answer:
2.5cm
Step-by-step explanation:
Radius is half the diameter (length across the circle), which is marked here as 5cm.
