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amid [387]
3 years ago
6

Which choices are in the solution set of inequality below? Check all that apply.

Mathematics
1 answer:
lisabon 2012 [21]3 years ago
8 0
It is D.

hope this helps
You might be interested in
1 The ages of three cats are a, a + 4 and 2a - 3.<br> Their total age is 21. Determine a.<br> ?
Nimfa-mama [501]

Answer:

a = 5

Step-by-step explanation:

a +a+4 + 2a-3 = 21

4a +1 =21

4a = 20

a = 5

8 0
3 years ago
Find the nth term of the sequence 7,25,51,85,127​
olya-2409 [2.1K]

Let <em>a </em>(<em>n</em>) denote the <em>n</em>-th term of the given sequence.

Check the forward differences, and denote the <em>n</em>-th difference by <em>b </em>(<em>n</em>). That is,

<em>b </em>(<em>n</em>) = <em>a </em>(<em>n</em> + 1) - <em>a </em>(<em>n</em>)

These so-called first differences are

<em>b</em> (1) = <em>a</em> (2) - <em>a</em> (1) = 25 - 7 = 18

<em>b</em> (2) = <em>a</em> (3) - <em>a</em> (2) = 51 - 25 = 26

<em>b </em>(3) = <em>a</em> (4) - <em>a</em> (3) = 85 - 51 = 34

<em>b</em> (4) = <em>a </em>(5) - <em>a</em> (4) = 127 - 85 = 42

Now consider this sequence of differences,

18, 26, 34, 42, …

and notice that the difference between consecutive terms in this sequence <em>b</em> is 8:

26 - 18 = 8

34 - 26 = 8

42 - 34 = 8

and so on. This means <em>b</em> is an arithmetic sequence, and in particular follows the rule

<em>b</em> (<em>n</em>) = 18 + 8 (<em>n</em> - 1) = 8<em>n</em> + 10

for <em>n</em> ≥ 1.

So we have

<em>a </em>(<em>n</em> + 1) - <em>a </em>(<em>n</em>) = 8<em>n</em> + 10

or, replacing <em>n</em> + 1 with <em>n</em>,

<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + 8 (<em>n</em> - 1) + 10

<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + 8<em>n</em> + 2

We can solve for <em>a</em> (<em>n</em>) by iteratively substituting:

<em>a</em> (<em>n</em>) = [<em>a</em> (<em>n</em> - 2) + 8 (<em>n</em> - 1) + 2] + 8<em>n</em> + 2

<em>a</em> (<em>n</em>) = <em>a </em>(<em>n</em> - 2) + 8 (<em>n</em> + (<em>n</em> - 1)) + 2×2

<em>a</em> (<em>n</em>) = [<em>a</em> (<em>n</em> - 3) + 8 (<em>n</em> - 2) + 2] + 8 (<em>n</em> + (<em>n</em> - 1)) + 2×2

<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 3) + 8 (<em>n</em> + (<em>n</em> - 1) + (<em>n</em> - 2)) + 3×2

and so on. The pattern should be clear; we end up with

<em>a</em> (<em>n</em>) = <em>a</em> (1) + 8 (<em>n</em> + (<em>n</em> - 1) + … + 3 + 2) + (<em>n</em> - 1)×2

The middle group is the sum,

\displaystyle 8\sum_{k=2}^nk=8\sum_{k=1}^nk-8=\frac{8n(n+1)}2-8=4n^2+4n-8

so that

<em>a</em> (<em>n</em>) = <em>a</em> (1) + (4<em>n</em> ² + 4<em>n</em> - 8) + 2 (<em>n</em> - 1)

<em>a</em> (<em>n</em>) = 4<em>n</em> ² + 6<em>n</em> - 3

4 0
3 years ago
Solve systems of equations for y and x: <br><br> −5y + 8x = −18<br><br> 5y + 2x = 58​
Natali5045456 [20]

Answer:

(4, 10)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

Equality Properties<u> </u>

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

  • Coordinates (x, y)
  • Coefficients
  • Solving systems of equations using substitution/elimination

Step-by-step explanation:

<u>Step 1: Define Systems</u>

-5y + 8x = -18

5y + 2x = 58

<u>Step 2: Solve for </u><em><u>x</u></em>

<em>Elimination</em>

  1. Combine 2 equations:                                                                                      10x = 40
  2. [Division Property of Equality] Divide 10 on both sides:                                x = 4

<u>Step 3: Solve for </u><em><u>y</u></em>

  1. Substitute in <em>x</em> [Original equation]:                                                                  -5y + 8(4) = -18
  2. Multiply:                                                                                                             -5y + 32 = -18
  3. [Subtraction Property of Equality] Subtract 32 on both sides:                      -5y = -50
  4. [Division Property of Equality] Divide -5 on both sides:                                y = 10
7 0
3 years ago
Aidan ran 712 of a mile, then took a break before running another 12 of a mile. How far did Aidan run in all?
sdas [7]

Answer:

Is that supposed to be

7 1/2? If so, answer is 8

Step-by-step explanation:

7 1/2 + 1/2=8

7 0
3 years ago
Given f(x)=x-8 find f(1)+10
Ronch [10]

Answer:

3

Step-by-step explanation:

replace all x variables with 1 and solve that equation ; f(x)=x-8 so.... f(x) = 1-8

there for f(1)=-7

now, add -7 and 10 for your answer:

f(1)+10= 3

6 0
3 years ago
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