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natulia [17]
3 years ago
11

22 – 25x + 5 = -63 + 5x​

Mathematics
1 answer:
ra1l [238]3 years ago
4 0

Answer: x = 3

Step-by-step explanation:

<em>first, we calculate.</em>

27 - 25x = -63 + 5x

<em>then, we move the terms around.</em>

-25x - 5x = -63 - 27

<em>next, we collect the like terms.</em>

-30x = -90

<em>finally, we divide both sides.</em>

x = 3

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What ratio of height to width is considered most appropriate in graphing a frequency distribution?
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3 0
3 years ago
Please answer quickly!
Zanzabum

19) The sum of the <em>arithmetic</em> series is - 397. (Correct choice: E)

33) The sum of the <em>geometric</em> series is 1700. (Correct choice: E)

<h3>How to determine the sum of a given series</h3>

19) <em>Arithmetic</em> series are sets of elements generated by a <em>linear</em> expression of the form:

aₙ = a₁ + (n - 1) · d      (1)

Where:

  • aₙ - n-th term of the series
  • a₁ - First term of the series
  • n - Index of the n-th term of the series.
  • d - Change between two consecutive elements of the series.

If we know that a₁ = 27, n = 20 and d = - 5, then sum of the first 20 terms of the series is:

x = 27 + 22 + 17 + 12 + 7 + 2 + (- 3) + (- 8) + (- 13) + (- 18) + (- 23) + (- 28) + (- 33) + (- 38) + (- 43) + (- 48) + (- 53) + (- 58) + (- 63) + (- 68)

x = - 397

The sum of the <em>arithmetic</em> series is - 397. (Correct choice: E)

33) <em>Geometric</em> series are sets of elements generated by a <em>exponential</em> expression of the form:

aₙ = a₁ · rⁿ     (2)

Where:

  • aₙ - n-th term of the series
  • a₁ - First term of the series
  • r - Ratio between two consecutive elements of the series.

If we know that a₁ = 1458 and r = 1 / 3, then the sum of the first 6 terms of the geometric series is:

x = 1458 + 162 + 54 + 18 + 6 + 2

x = 1700

The sum of the <em>geometric</em> series is 1700. (Correct choice: E)

To learn more on geometric series: brainly.com/question/4617980

#SPJ1

6 0
2 years ago
1. Write an equation in point slope form for the line that has a slope of 6 and contains the point (-8,-7).
antiseptic1488 [7]
1.    y - y₁ = m(x - x₁)
     y - (-7) = 6(x - (-8))
       y + 7 = 6(x + 8)
       y + 7 = 6(x) + 6(8)
       y + 7 = 6x + 48
       <u>   - 7          -   7</u>
             y = 6x + 41

2. <u>y₂ - y₁</u> = <u>-8 - (-3)</u> = <u>-8</u><u> + 3</u> = <u>-5</u> = -1²/₃
    x₂ - x₁    -1 - (-4)    -1 + 4      3

3. 2x -  3y = 11
    <u>3x + 3y =   9</u>
            <u>5x</u> = <u>20</u>
             5      5
              x = 4
     2x - 3y = 11
   2(4) - 3y = 11
       8 - 3y = 11
     <u>- 8          - 8</u>
           <u>-3y</u> = <u>3</u>
            -3    -3
              y = -1
        (x, y) = (4, -1)

4. 2x - 5y = -7  ⇒   -6x + 15y =  21
    5x - 3y = 11 ⇒ <u>-25x + 15y = -55</u>
                                        <u>19x</u> = <u>76</u>
                                         19     19
                                            x = 4
                                   2x - 5y = -7
                                 2(4) - 5y = -7
                                     8 - 5y = -7
                                   <u>- 8          - 8</u>
                                         <u>-5y</u> = <u>-15</u>
                                          -5      -5
                                            y = 3
                                      (x, y) = (4, 3)

5. 4.9 × 10¹¹, 8.9 × 10¹⁸, 1.3 × 10⁸, 6.7 × 10⁸, 2.7 × 10⁸
    <u>1.3 × 10³</u>, 2.7 × 10⁸, 6.7 × 10⁸, 4.9 × 10¹¹, <u>8.9 × 10¹⁸</u>
      Least                                                         Greatest
4 0
3 years ago
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