Mathematics, 01.02.2021 14:00 rafi10

I need help on the math question if it's right I'll give brain.

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Answer from: aureliafung2p7cxoo

\frac{2}{5} ; or, write in decimal form: 0.4 .

Step-by-step explanation:

Rewrite as:

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$\frac{4x}{7} = \frac{8}{35}$ ;

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Now, "Cross-factor multiply":

that is:

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→ Given: $\frac{a}{b} =\frac{c}{d}$ ;

→ ad = bc ; (b≠0 ; d≠0) ;

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As such:

4x * 35 = 7 * 8 ;

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We can divide one side of the equatiuon by "4" ; and one side by "7" :

$\frac{4x*35}{4*7} = \frac{7*8}{4*7}$ ;

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We can simplify the "left-hand side":

"4/4 = 1 " ; and "35/7 = 5 " ; & we are left with "x * 5" ; or "5x " .

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We can simplify the "right-hand side":

"7/7 = 1 " ; and: "8/4 =2 " ; to get: "2/1" ; which equals "2".

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So; we have: " 5x = 2 " ; Solve for "x" ;

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Divide each side of the equation by "5" ; to isolate "x" on one ide of the equation; & to solve for: "x" ;

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" 5x/5 = 2/5 " ; We cancel out the "5x/5" to "1x"; which equals "x":

→ x = $\frac{2}{5}$ ; or, write in decimal format: "x = 0.4" ;

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\frac{2}{5}

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Hope this is helpful! Best wishes in your academic pursuits—and within the "" community!

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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

5\16 x 2\5 = 10/80simplify to 1/80

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