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n200080 [17]
3 years ago
5

Here is a diagram and its corresponding equation. Find the solution to the equation and explain your reasoning 38 x+7 x+7 x+7 x+

7 4(x + 7) = 38​
Mathematics
1 answer:
QveST [7]3 years ago
5 0

Answer:

x = (-158)/87

Step-by-step explanation:

Solve for x:

38 x + 7 x + 7 x + 7 x + 7×4 (x + 7) = 38

Hint: | Multiply 7 and 4 together.

7×4 = 28:

38 x + 7 x + 7 x + 7 x + 28 (x + 7) = 38

Hint: | Group like terms in 38 x + 7 x + 7 x + 7 x + 28 (x + 7).

Grouping like terms, 38 x + 7 x + 7 x + 7 x + 28 (x + 7) = 28 (x + 7) + (38 x + 7 x + 7 x + 7 x):

28 (x + 7) + (38 x + 7 x + 7 x + 7 x) = 38

Hint: | Add like terms in 38 x + 7 x + 7 x + 7 x.

38 x + 7 x + 7 x + 7 x = 59 x:

28 (x + 7) + 59 x = 38

Hint: | Distribute 28 over x + 7.

28 (x + 7) = 28 x + 196:

28 x + 196 + 59 x = 38

Hint: | Add like terms in 59 x + 28 x + 196.

28 x + 59 x = 87 x:

87 x + 196 = 38

Hint: | Isolate terms with x to the left hand side.

Subtract 196 from both sides:

87 x + (196 - 196) = 38 - 196

Hint: | Look for the difference of two identical terms.

196 - 196 = 0:

87 x = 38 - 196

Hint: | Evaluate 38 - 196.

38 - 196 = -158:

87 x = -158

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 87 x = -158 by 87:

(87 x)/87 = (-158)/87

Hint: | Any nonzero number divided by itself is one.

87/87 = 1:

Answer: x = (-158)/87

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SpyIntel [72]

y=2x so replacr the -y with -2x so 2x+6 is 8x. :)

7 0
3 years ago
1. What are the first five terms of the sequence given by the formula an = 5n + 1?
Dvinal [7]

The correct answers are:

(1) 6, 11, 16, 21, 26 (Option B)

(2)~a_1 = 8; ~a_n = a_{n-1} - 2~ (Option A)

(3)~a_n = -2 + 3(n-1)~~~~ (Option D)

Explanations:

(1) Given Sequence:

a_n = 5n + 1

Now in order to find the first 5 terms, we need to put n=1,2,3,4,5 in the above sequence and solve.

For n=1: a_1 = 5(1) + 1 = 6

For n=2: a_2 = 5(2) + 1 = 11

For n=3: a_3 = 5(3) + 1 = 16

For n=4: a_4 = 5(4) + 1 = 21

For n=5: a_5 = 5(5) + 1 = 26

Hence, the first five terms are: 6, 11, 16, 21, 26 (Option B)

(2) Given Sequence:

8, 6, 4, 2, …

Now to find the recursive definition, we need to adopt trial-and-error approach.

As, a_1 = 8 (meaning the first element of the sequence is 8), the second or nth value of the sequence can be found by using the following formula:

a_n = a_{n-1} - d --- (1)

Where, n = the index of the number in a sequence

d = difference between two consecutive numbers = 8-6 = 2

Now,

The second number of the sequence has to be 6 by using (1). Put n = 2 and d = 2 in (1):

a_2 = a_{2-1} - 2

a_2 = a_{1} - 2

Since a_1 = 8, therefore,

a_2 = 8 - 2 = 6 (correct)

Hence the correct answer is a_1 = 8; ~a_n = a_{n-1} - 2~ (Option A)

(3) Given Sequence:

−2, 1, 4, 7, …

To find the explicit definition, use the following formula:

a_n = a_1 + (n-1)*d --- (X)

Where,

a_n = nth~term~of~the~sequence \\a_1 = 1st~term~of~the~sequence = -2 \\d = common~difference = 4-1 = 7-4 = 3 \\n = index~of~a~number~in~a~sequence \\

Plug in the values in (X):

(X)=> a_n = -2 + (n-1)*3~~~~ (Option D)

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Answer:

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Step-by-step explanation:

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