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Masja [62]
3 years ago
11

A group of students is arranging squares into layers to create a project. The first layer has 5 squares. The second layer has 10

squares. Which formula represents arithmetic explicit formula to determine the number of squares in each layer?
A.a1 = 5; an = 5 ⋅ an − 1, n > 0
B.a1 = 5; an = 5 ⋅ an + 1, n > 0
C.a1 = 5; an = 5 + an − 1, n > 0
D.a1 = 5; an = 5 + an + 1, n > 0
Mathematics
1 answer:
True [87]3 years ago
8 0

Answer:

  • Recursive formula:

                                         a_1=5;a_n=5+a_{n-1},n>0

Explanation:

All the shown formulae in the choice list are recursive formulae instead of explicit formulae.

Explicit formulae that represent arithmetic sequences are of the form:

  • a_n=a_1+(d-1)n

That kind of formula permits to determine any term knowing the first term, the number of the term searched, and the common difference (d).

On the other hand, the recursive formulae let you to calculate one term knowing the previous term and the difference.

In this case, the difference in the number of squares of two consecutive terms is:

  • differece = number of squares in the second layer - number of squares in the first layer.

  • d = 10 - 5 = 5

Then, the recursive formula is:

  • a_1=5;a_n=5+a_{n-1},n>0

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Answer:

2

Step-by-step explanation:

1. 20/10

2. divide numerator and denominator by 10

2. 2/1 = 2

4 0
3 years ago
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What does it mean for a scatter plot to have a negative trend? A. Higher x-values tend to go with higher y-values. B. Higher x-v
BARSIC [14]

Answer:

Option D = None of these are related

Step-by-step explanation:

A scatter plot is said to have a negative trend if both x & y values are negative from the origin (0,0)

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3 years ago
Write the Slope-Intercept and Point-Slope forms of the line passing through the point (-3, 2) and having a slope of -4/5
weeeeeb [17]

Answer:

slope-intercept: y=\frac{-4}{5} x-\frac{2}{5}

point-slope: y-2=\frac{-4}{5} (x+3)

Step-by-step explanation:

The slope-intercept form of a line is written as y = mx + b, where m is the slope and b is the y-intercept.

The point-slope form of a line is written as y - y1 = m(x - x1), where (x1, y1) is a given point and m is the slope.

Here, we see that the slope is -4/5, which means that m = -4/5. Since we're given a point (-3, 2), let's go ahead and just write the point-slope form already. (x1, y1) = (-3, 2) so x1 = -3 and y1 = 2. Then:

y - y1 = m(x - x1)

y - 2 = (-4/5) * (x + 3)

y-2=\frac{-4}{5} (x+3)

Now, we want to find the slope-intercept form, so we need to figure out the y-intercept. Well, first, let's plug in what we know:

y = mx + b

y = (-4/5)x + b

Any point on this line will satisfy the above equation. Since (-3, 2) is on this line, if we plug -3 in for x and 2 in for y, the equation should hold true, so we can solve for b:

y = (-4/5)x + b

2 = (-4/5) * (-3) + b

2 = 12/5 + b

b = -2/5

So, the y-intercept is -2/5. Then the slope-intercept form is:

y=\frac{-4}{5} x-\frac{2}{5}

Thus, our two equations are:

slope-intercept: y=\frac{-4}{5} x-\frac{2}{5}

point-slope: y-2=\frac{-4}{5} (x+3)

8 0
2 years ago
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yKpoI14uk [10]

Answer: Lol ten points for your whole assignment

Step-by-step explanation:

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Subtract the 12x^2 first.
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Then divide the 5 from both sides
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