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Oduvanchick [21]
3 years ago
5

Write each sum using summation notation 12 + 22 + 32 + 42 + ⋯ + 10000^2

Mathematics
1 answer:
Murljashka [212]3 years ago
5 0

Answer:

50,00,70,000

Step-by-step explanation:

The given sequence is Arithmetic Progression.

Arithmetic Progression is a sequence in which every two neighbor digits have equal distances.

Here first we will find the number of terms

For finding the nth term, we use formula

aₙ = a + (n - 1) d

where, aₙ = value of nth term

a = First term

n = number of term

d = difference

Now, In given sequence: 12, 22, 32, 42, ⋯ , 100002

a = 12, d = 10, n = ? and  aₙ= 100002

∴ 100002  = 12 + (n - 1) × (10)

⇒ 99990 = 10(n - 1)

⇒ n = 10000

Now using the formula of Sum of Arithmetic Sequence,

Sₙ = n÷2[2a + (n - 1)d]

⇒ Sₙ = (10000÷2)[2 × 12 + 9999 × 10]

⇒ Sₙ = 5000 [ 24 + 99990]

⇒ Sₙ = 5000 × 100014 = 50,00,70,000

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-10 degrees

Step-by-step explanation:

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3 years ago
There were 935 offenses in 2000 and 2448 offenses in 2019. What is the percentage increase?
Artist 52 [7]

Answer:

Approximately 262%

Step-by-step explanation:

To find the percentage increase divide the new amount of offenses by the old amount of offenses:

2448/935 = 2.618

2.618 rounds to 2.62. Convert 2.62 into a percentage: 262%

The percentage increase between the amount of offenses in 2000 and the amount of offenses in 2019 is approximately 262%.

6 0
3 years ago
The Murphy family bought two rectangular dog beds for their pets fluffys bed was 3 feet by 1 9/12 Pete's bed was 4 feet by 2 4/1
mario62 [17]

Answer:

4 1/12 sq. ft

Step-by-step explanation:

To know the amount of area that Pete’s bed have more than Fluffy’s bed, we simply calculate the area of both beds then subtract the smaller from the larger.

The area of Fluff’s bed would be 3 * 21/12 = 63/12 Sq ft

The area of Pete’s bed would be 4 * 28/12 = 112/12 sq ft

The difference in area is thus: 112/12 - 63/12 = 49/12 = 4 1/12 sq. ft

5 0
3 years ago
the line whose equation is y=1/2x-3 is dilated by a factor of 3 with a center at the point (10,2). Explain why its equation woul
lana [24]
We  have that

<span>y=1/2x-3
1) the slope of this line equation is m=(1/2)
2) the coordinates of the y intercept are
for x=0
y=-3
point (0,-3)
3)</span>the coordinates of the x intercept are
for y=0
0=(1/2)x-3------> (1/2)x=3----> x=6
point (6,0)

<span>if the line is dilated by a factor of 3
then
</span>y=1/2x-3--------> 3y=3*[1/2x-3]-----> 3y=(3/2)x-9
3y=(3x-18)/2-------> y=(3x-18)/6--------> y=(3/6)x-18/6

 y=(3/6)x-18/6
so
1) the slope of this line equation is m=(3/6)-----> 3/6=1/2
2) the coordinates of the y intercept are
for x=0
y=-18/6-------> y=-3
point (0,-3)
3)the coordinates of the x intercept are
for y=0
0=(3/6)x-18/6------> (3/6)x=18/6----> x=18/3------> x=6
point (6,0)

therefore
the equation of the line
y=1/2x-3 is the same that the equation of the line  y=(3/6)x-18/6

<span>the equation does not change because the slope and the x and y intercepts do not change either</span>
6 0
3 years ago
Match the vocabulary terms to the correct definitions. 1. a speed or rate of change where the denominator (or second quantity me
Mrrafil [7]

The vocabulary terms have been matched to the correct definitions as follows;

  • Direct variation: describes variation between proportional relationships
  • Slope: a ratio describing vertical change to horizontal change of a linear relationship on a coordinate grid
  • Rate of change:  a number, k, that represents the unit rate used in a direct variation equation y = kx for comparing proportional relationships between two variables x and y found by using division
  • Unit rate: a speed or rate of change where the denominator (or second quantity measured) in the ratio is 1
  • Constant of proportionality: the ratio of vertical change to horizontal change rate of change

<h3>What are Mathematical Terms?</h3>
  • Mathematical terms refer to phrases and words that define certain arithmetic standards.

  • The above are the definitions of the mathematical terms. Direct variation, for instance, expresses the relationship between two variables, x, and y.

  • The slope is often used after graphing and indicates the relationship of change between the vertical and horizontal axes.

Learn more about slope here:

brainly.com/question/3493733

3 0
2 years ago
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