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Gnesinka [82]
3 years ago
10

The image shows three sets of stuffed bears. Each set represents a term of the sequence (1, 4, 7, . . .) What is the next term i

n the sequence?
Describe the domain of the sequence. Describe the range of the sequence btw da numbers represents how many stuffed bears are in each set. (u dont need to see da image)
Mathematics
1 answer:
frosja888 [35]3 years ago
3 0

Next term = 10

You add 3 to each term to get the next

1+3 = 4

4+3 = 7

7+3 = 10

etc etc

The domain of the sequence is 1,2,3,4,... basically the set of positive whole numbers. This is known as the set of natural numbers or counting numbers. We don't include 0. The domain is the set of possible inputs for 'n' in the formula mentioned below.

The range is the sequence of values shown.

The formula to generate the sequence is

an = 3n-2

as shown by these steps below

an = a1 + d(n-1)

an = 1 + 3(n-1)

an = 1+3n-3

an = 3n-2

To get any term you want, plug in a whole number for n. For example, plug in n = 4 to get...

an = 3n-2

a4 = 3*4-2

a4 = 12-2

a4 = 10

Showing that the fourth term is 10 as found earlier above.

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General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

<u>Algebra I</u>

  • Solving systems of equations using substitution/elimination
  • Solving systems of equations by graphing

Step-by-step explanation:

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

y = x + 1

3x + 3y = -9

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

<em>Substitution</em>

  1. Substitute in <em>y</em>:                              3x + 3(x + 1) = -9
  2. Distribute 3:                                   3x + 3x + 3 = -9
  3. Combine like terms:                     6x + 3 = -9
  4. Isolate <em>x</em> term:                               6x = -12
  5. Isolate <em>x</em>:                                        x = -2

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

  1. Define original equation:                    y = x + 1
  2. Substitute in <em>x</em>:                                     y = -2 + 1
  3. Add:                                                      y = -1

<u>Step 4: Graph systems</u>

<em>Check the solution set.</em>

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1. Storing milk at temperatures colder than 35°F can affect its quality of taste. However, storing milk at temperatures warmer t
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Answer:

Part (A): The required inequality is T < 35 or t >40.

Part (B): The correct option is C) Only x=7.

Part (C) |x+1|+5=2 has no solution; |4x+12|=0 has one solution; |3x|=9 has two solution.

Step-by-step explanation:

Consider the provided information.

Part (A)

Storing milk at temperatures colder than 35°F can affect its quality of taste. However, storing milk at temperatures warmer than 40°F is an unsafe food practice.

The union is written as A∪B or “A or B”.

The intersection of two sets is written as A∩B or “A and B”

We need to determine the inequalities represent the union of these improper storage.

That means we will use A∪B or “A or B”.

The improper storage temperatures is when temperature is less than 35°F or greater than 40°F.

Hence, the required inequality is T < 35 or t >40.

Part (B) 15| x-7|+4=10|x-7|+4

Solve the inequality as shown below:

Subtract 4 from both sides.

15| x-7|+4-4=10|x-7|+4-4

Subtract 10|x-7| from both sides

15\left|x-7\right|-10\left|x-7\right|=10\left|x-7\right|-10\left|x-7\right|

5\left|x-7\right|=0\\\left|x-7\right|=0\\x=7

Hence, the correct option is C) Only x=7.

Part (C) Match the solution,

\left|x+1\right|+5=2

Subtract 2 from both sides.

\left|x+1\right|=-3

Absolute value cannot be less than 0.

Hence, |x+1|+5=2 has no solution.

|4x+12|=0

4x+12=0

x=-3

Hence, |4x+12|=0 has one solution.

|3x|=9

\mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a

3x=-9\quad \mathrm{or}\quad \:3x=9\\x=-3\quad \mathrm{or}\quad \:x=3

Hence, |3x|=9 has two solution.

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