Mathematics, 08.12.2020 05:40 jiminpark12

Just number 7 would be fine but if you could also number 8 would help a lot

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Answer from: richellemjordan

7. r = -5

8. x = -1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define

r + 2 - 8r = -3 - 8r

Step 2: Solve for r

Combine like terms: -7r + 2 = -3 - 8rAdd 8r to both sides: r + 2 = -3Subtract 2 on both sides: r = -5

Step 3: Check

Plug in r into the original equation to verify it's a solution.

Substitute in r: -5 + 2 - 8(-5) = -3 - 8(-5)Multiply: -5 + 2 + 40 = -3 + 40Add: -3 + 40 = -3 + 40Add: 37 = 37

Here we see that 37 does indeed equal 37.

∴ r = -5 is a solution of the equation.

Step 4: Define equation

-4x = x + 5

Step 5: Solve for x

Subtract x on both sides: -5x = 5Divide -5 on both sides: x = -1

Step 6: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x: -4(-1) = -1 + 5Multiply: 4 = -1 + 5Add: 4 = 4

Here we see that 4 does indeed equal 4.

∴ x = -1 is a solution of the equation.

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

Answer from: Quest

B. because the 7 represents "seven times", x represents "a number", 12 represents "plus twelve", and -4 represents "minus four"
Which of the following best describes an algebraic expression 7 (x+ 12) -4

Which of the following best describes an algebraic expression 7 (x+ 12) -4

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Just number 7 would be fine but if you could also number 8 would help a lot
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