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ivanzaharov [21]
2 years ago
15

Two more than 16 times a number is the same as 21 less than the product of -7 and the number

Mathematics
2 answers:
slava [35]2 years ago
7 0

Answer:

  • -1

Step-by-step explanation:

<u>Let the number be x, and we have equation:</u>

  • 16x + 2 = -7x - 21
  • 16x + 7x = - 21 - 2
  • 23x = - 23
  • x = -1

The number is -1

lara31 [8.8K]2 years ago
5 0

Answer:

-1

Step-by-step explanation:

"a number" = x

-- <u>"Two more</u> than <u>16 times</u> <u>a number</u>." | 16 times a number means "16x" | Two more than just means add 2.

(16x + 2)

-- "Is the same as" means equals.

(16x + 2) =

-- <u>21 less than</u> <u>the product of -7</u> and <u>the number</u> | The product of -7 and the number means "-7x" | 21 less than means subtract 21.

(16x + 2) = (-7x - 21)

-- solve for x.

(16x + 7x) = (-21 - 2)

-- combine like terms.

23x = -23

-- Divide.

x = -1

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4 0
3 years ago
Read 2 more answers
Find the 13th term of the arithmetic sequence -3x – 1,42 + 4,112 + 9, ...
Strike441 [17]

Answer:

The 13th term is 81<em>x</em> + 59.

Step-by-step explanation:

We are given the arithmetic sequence:

\displaystle -3x -1, \, 4x +4, \, 11x  + 9 \dots

And we want to find the 13th term.

Recall that for an arithmetic sequence, each subsequent term only differ by a common difference <em>d</em>. In other words:

\displaystyle \underbrace{-3x - 1}_{x_1} + d = \underbrace{4x + 4} _ {x_2}

Find the common difference by subtracting the first term from the second:

d = (4x+4) - (-3x - 1)

Distribute:

d = (4x + 4) + (3x + 1)

Combine like terms. Hence:

d = 7x + 5

The common difference is (7<em>x</em> + 5).

To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:

\displaystyle x_n = a + d(n-1)

Where <em>a</em> is the initial term and <em>d</em> is the common difference.

The initial term is (-3<em>x</em> - 1) and the common difference is (7<em>x</em> + 5). Hence:

\displaystyle x_n = (-3x - 1) + (7x+5)(n-1)

To find the 13th term, let <em>n</em> = 13. Hence:

\displaystyle x_{13} = (-3x - 1) + (7x + 5)((13)-1)

Simplify:

\displaystyle \begin{aligned}x_{13} &= (-3x-1) + (7x+5)(12) \\ &= (-3x - 1) +(84x + 60) \\ &= 81x + 59 \end{aligned}

The 13th term is 81<em>x</em> + 59.

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L am sure this is a answer of this question

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