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3 years ago

1) Find the 128th term for the sequence 9, 4, -1, -6, 11,...

1 answer:

5 0

To determine an nth term of an arithmetic sequence, we use the expression an = a1 + (n-1)d where a1 is the first term in the sequence, n is the number of the term in the sequence and d is the common difference. For a geometric sequence, it is expressed an = a1r^(n-1). We calculate as follows:

1. a128 = 9 + (128-1)(-5)
a128 = -626

2. a97 = (-3)(-2)^(97-1)
a97 = -2.377x10^29

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What is the perimeter of CDE?

LuckyWell [14K]

<h3>Answer: 32.5 units (choice C)</h3>

This value is approximate.

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Explanation:

To find the perimeter, we simply add up the lengths of the three external sides.

The horizontal side from D to E is 16 units long since |-10-6| = 16. I subtracted the x coordinates of the points and applied absolute value. You could also count out the spaces and you should count 16 spaces from D to E.

Unfortunately, the diagonal lengths aren't as straight forward. We have two options here: The pythagorean theorem, or the distance formula.

I'll go with the distance formula.

Let's find the distance from C to D, aka the length of side CD

$C = (x1,y1) = (-1,-2)\\\\D = (x2,y2) = (-10,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-1-(-10))^2 + (-2-0)^2}\\\\d = \sqrt{(-1+10)^2 + (-2-0)^2}\\\\d = \sqrt{(9)^2 + (-2)^2}\\\\d = \sqrt{81 + 4}\\\\d = \sqrt{85}\\\\d \approx 9.2195\\\\$

Side CD is roughly 9.2195 units long.

Repeat this idea to find the length of CE

$C = (x1,y1) = (-1,-2)\\\\E = (x2,y2) = (6,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-1-6)^2 + (-2-0)^2}\\\\d = \sqrt{(-7)^2 + (-2)^2}\\\\d = \sqrt{49 + 4}\\\\d = \sqrt{53}\\\\d \approx 7.2801\\\\$

Side CE is roughly 7.2801 units long

The perimeter of triangle CDE is approximately...

P = DE+CD+CE

P = 16 + 9.2195 + 7.2801

P = 32.4996

This then rounds to 32.5 units. The answer is choice C.

7 0

3 years ago

Graph any third-degree polynomial (a cubic graph) that has exactly one x-intercept, a relative/global minimum at (-2.1), and a r

rewona [7]

Step-by-step explanation:

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2 years ago

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Aleks [24]

2a + 8a simplified is 10a

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4 years ago

Melinda’s heart beats 15 times during 1/6 of a minute at that rate how many times does a heartbeat each minute

Elena L [17]

Ok so obvi you can’t multiply 1/6 so u have to divide top on bottom out so 1 divided by 6 so your awnser would be 2.5

7 0

3 years ago

Cos10+cos80/sin10+sin80=1

eduard

Evaluate cos(10)cos10 to get 0.984807750.98480775.0.98480775cos(80)−sin(10)sin(80)0.98480775⁢cos80-⁢sin10⁢sin80Evaluate cos(80)cos80 to get 0.173648170.17364817.0.98480775⋅0.17364817−sin(10)sin(80)0.98480775⋅0.17364817-⁢sin10⁢sin80Multiply 0.984807750.98480775 by 0.173648170.17364817 to get 0.171010070.17101007.0.17101007−sin(10)sin(80)0.17101007-⁢sin10⁢sin80Evaluate sin(10)sin10 to get 0.173648170.17364817.0.17101007−1⋅0.17364817sin(80)0.17101007-1⋅0.17364817⁢sin80Multiply −1-1 by 0.173648170.17364817 to get −0.17364817-0.17364817.0.17101007−0.17364817sin(80)0.17101007-0.17364817⁢sin80Evaluate sin(80)sin80 to get 0.984807750.98480775.0.17101007−0.17364817⋅0.984807750.17101007-0.17364817⋅0.98480775Multiply −0.17364817-0.17364817 by 0.984807750.98480775 to get −0.17101007-0.17101007.0.17101007−0.171010070.17101007-0.17101007Subtract 0.171010070.17101007 from 0.171010070.17101007 to get 0.0

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3 years ago