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IRINA_888 [86]
2 years ago
12

Solve the equation 0.09w+1.8

Mathematics
1 answer:
ella [17]2 years ago
7 0

Step-by-step explanation:

0.09w + 1.8 = 0

0.09w = 0 - 1.8

0.09w = - 1.8

0.09w ÷ 0.09 = - 1.8/ 0.09

w = - 20

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What is the sum of the arithmetic sequence 3, 9, 15..., if there are 24 terms? (5 points)
Vinil7 [7]

There's a fixed difference of 6 between terms (9 - 3 = 6, 15 - 9 = 6, and so on). The first term of the sequence is 3, so the n-th term is

3 + 6(n-1) = 6n - 3

If there are 24 terms in the sum, then the last term is 6×23 - 3 = 135.

Let S be the sum,

S = 3 + 9 + 15 + \cdots + 123 + 129 + 135

Reverse the order of terms:

S = 135 + 129 + 123 + \cdots + 15 + 9 + 3

If we add up the terms in the same positions, we get twice S on the left side, while on the right side we observe that each pair of terms will sum to 138.

S + S = (3 + 135) + (9 + 129) + (15 + 123) + \cdots + (135 + 3)

2S = 138 + 138 + 138 + \cdots + 138

and since there are 24 terms in the sum, the right side is the sum of 24 copies of 138. In other words,

2S = 24 \times 138

and solving for S gives

S = \dfrac{24\times138}2 = \boxed{1656}

3 0
2 years ago
What is the closest circumference of a well
Liula [17]

Answer: the circumference of a well is determined by radius or the diameter

Step-by-step explanation:

The formula is 2πr

5 0
3 years ago
Find x in the triangle below. Round your answer to the nearest tenth.
jonny [76]

Answer:

Step-by-step explanation:

Remark

  • x is opposite the 90 degree angle. It is the hypotenuse.
  • 13 makes up the 57 degree angle. It is the side adjacent.
  • The adjacent side and the hypotenuse define the cos(theta).

Formula

cos(theta) = adjacent side / hypotenuse

Givens

Theta = 57 degrees

Hypotenuse = x

Side adjacent = 13

Solution

  • Cos(57) = 13 / x         Multiply both sides by x
  • x*cos(57) = 13           Divide by cos(theta)
  • x = 13/cos(57)
  • x = 13 / cos(57)
  • cos(57) = 0.5446
  • x = 13/ 0.5446
  • x = 23.87
6 0
3 years ago
The perimeter of a rectangle is 50 ft. the length is 1 ft more than the width. what is the length and width
lesya [120]
X+1+X+1+X+X=50
4x+2=50
4x=48
X=12
Width is 12
Length is 13
6 0
4 years ago
Using mental math, the approximate tip to leave for a bill of $81.79, if you tip 15% would be _____.. a. $8.20 b. $10.30 c. $12.
Anton [14]

Step-by-step explanation:

The approximate tip is - 12.30$

Because bill is 81.79$

and tip - 15%

therefore bill amount divided by 15/100

==> 81.79* 15% is 12.30$

4 0
3 years ago
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