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Marysya12 [62]
3 years ago
12

Convert 11.42424242 … to a rational expression in the form of a over b, where b ≠ 0.

Mathematics
1 answer:
babymother [125]3 years ago
3 0

x =  11\frac{42}{99}

Step-by-step explanation:

11.42424242.... = 11. \overline{42} \\ let \: x = 11. \overline{42} .....(1)\\ 100x = 1142.\overline{42}....(2) \\ subtracting \: (1) \: from \:  (2) \: \\  100x - x = 1142.\overline{42} - 11. \overline{42} \\ 99x = 1131 \\ x =  \frac{1131}{99}  \\x =  11\frac{42}{99}  \\

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Find a linear inequality with the following solution set. Each grid line represents one unit.
ikadub [295]

The linear inequality in standard form is: x + y < -2 or x + y + 2 < 0

<h3>How to Write a Linear Inequality?</h3>

To determine what sign to use, follow these rules:

  • Use "<" or ">" when the boundary line is dotted or dashed.
  • Use "<" or "≤" when the shaded area is under the boundary line (dotted or dashed).
  • Use "≤" or "≥" when the boundary line is not  dotted or dashed.
  • Use ">" or "≥" when the shaded area is above the boundary line (dotted or dashed).

The graph given has the following features:

  • It has a boundary line that is dotted/dashed.
  • It has a shaded area that is under the boundary line.
  • Thus, the inequality sign we would use is, "<".

Find the slope:

Slope (m)= rise/run = -(2 units) / (2 units).

Slope (m) = -1.

The y-intercept (b) = -2.

Substitute m = -1 and b = -2 into y < mx + b:

y < (-1)x + (-2)

y < -x - 2

Rewrite

x + y < -2

x + y + 2 < 0

Learn more about inequality on:

brainly.com/question/11234618

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5 0
2 years ago
Consider the infinite geometric series ∑∞n=1−4(13)n−1
vodomira [7]

Answer:

See below

Step-by-step explanation:

-4 (1/3)^(n-1)

Part A

<em><u>For n = 1</u></em>

-4(1/3)^(1 - 1)

-4(1/3)^0    Anything to the 0 power (except 0) is 1

-4 (1)

-4

<em><u>n = 2</u></em>

-4(1/3)^(2 - 1)

-4*(1/3)^1

-4/3

<em><u>n = 3</u></em>

- 4(1/3)^2

-4/9

<em><u>n = 4</u></em>

-4/(1/3)^3

-4 / 27

Part B

The series converges.

1/3 is between -1 <= 1/3 <= 1

Part C

<em><u>Formula</u></em>

Sum = a/(1 - r)

a = - 4

r = 1/3

Sum = -4/(1 - 1/3) = -4//2/3 = - 4/(0.666666666...) = -6

3 0
3 years ago
Read 2 more answers
What is 7 (1+10p) + 8 (1 + 6p)
Komok [63]

Answer:

58p+15

Step-by-step explanation:

First, we want to get rid of the parentheses in the equation. To do that, let's start with 7(1+10p). We multiply 7 by each item in the parenthesis, and get 7+70p. Keep that little thing in mind, we will use it later. Next, same process with the other part, and we get 8+48p. We multiplied both parts out, so now we just add like terms. 7 and 8 don't have letters, so we add them to get 15. 10p and 48p do have letters, so we add those together and get 58p. We can't add that to the other numbers, because 58p is 58 times p, and 15 doesn't have that p so it wouldn't work without knowing p. What we are left with, by simplifying the problem, is 58p+15, or 15+58p. The order doesn't matter, as long as you have that answer.

6 0
4 years ago
Read 2 more answers
Given that a triangle has two sides of lengths 5 inches and 7 inches, which is a possible length of the third side?
victus00 [196]

Answer:

big poop face looking butt with a massive forehead poopy duck dipers

Step-by-step explanation:

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3 0
3 years ago
On a scale drawing, a school is 1.6 feet tall. the scale factor is 1/22. Find the height of the school
Pie

Answer:

35.2 ft

Step-by-step explanation:

Multiply the scale factor and the height.

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