MATHEMATICS HIGH SCHOOL

Find the nth term in the sequence
-6,-3,0,3,6

Answers

Answer 1
Answer:

Answer:

3n-9

Step-by-step explanation:

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Answer 2
Answer: First, determine what type of sequence the set of numbers make up. Through simple logic, it is an arithmetic sequence, because one can see by inspection that there is a common difference of 3 (positive 3, just to be a bit more pedantic).

We then use the formula, t_(n) = a + (n - 1)d
where t_(n) represents the n^(th) term; a represents the starting term (so the first number in the set of numbers, which in this case is -6); n is the term number (1st, 2nd, 3rd term, etc.); d is the common difference, that is, when you subtract the next term to the previous term – what is that numerical value.

To elaborate a bit more, your  1 st term is -6,  2 nd   is -3,  3 rd is 0, etc.

Also, the formula above is something you just learn, unless you learn to proof this formula, which is something different.

So, here, t_(n) = -6 + (n-1)3, which can be expanded to:
t_(n) = -6 + 3n-3
Therefore, t_(n) = 3n - 9

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(1 pt) A delivery truck made 8 stops in one neighborhood. By stop 5, there were 11 packages delivered. How many stops did it take to have 5 packages delivered? A. 12 B. 8 C. 3 D. 2

Answers

First, divide 11/5 because to deliver 11 packages, you go 5 stops. To deliver 5 packages, you go x number of stops. So, 11/5=5/x. Then find a common denominator. So, 11x/5x=25/5x. Then solve the numerators of 11x=25. So, divide 25/11 to isolate x. This gives you 2.27. This means the answer is C) 3 because, although the answer is closer to 2, and by stop 3, there will be more than 5, but at stop 2, it will be less than 5. Hope this helps! :D

A circle is centered at K(0,0)K(0,0)K, left parenthesis, 0, comma, 0, right parenthesis. The point U(6,-4)U(6,−4)U, left parenthesis, 6, comma, minus, 4, right parenthesis is on the circle.Where does the point V(\sqrt{2},-7)V(
2
​
,−7)V, left parenthesis, square root of, 2, end square root, comma, minus, 7, right parenthesis lie?

Answers

Answer:

inside the circle

Step-by-step explanation:

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Final answer:

The point V(√2, -7) lies inside the circle centered at K(0,0) with point U(6, -4) on it. This is determined by comparing the distances (or radii) from the circle center to the points.

Explanation:

To determine where the point V(√2, -7) lies in relation to the circle centered at K(0,0) with point U(6, -4) on the circle, we first need to identify the radius of the circle. The radius can be found using the distance formula for points in the Cartesian plane,

Distance = √[(x2-x1)^2 + (y2-y1)^2]

So the distance between points K(0,0) and U(6, -4) (which is the radius of our circle) is √[(6-0)^2 + (-4 - 0)^2] = √[36 + 16] = √52

Now we calculate the distance between the circle center K(0,0) and point V(√2, -7) using the same formula. This results in a distance of √[(√2 - 0)^2 + (-7 - 0)^2] = √[2 + 49] = √51.

Since √51 is less than √52, the point V(√2, -7) lies inside the circle.

Learn more about Circle Geometry here:

brainly.com/question/35055577

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Simplify the expression: -8(-8a - 9)

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