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2 years ago

Solve. -15 = -6n – 3 + 6

Mathematics

2 answers:

MrRa [10]2 years ago

6 0

Answer:

n = 3.

Step-by-step explanation:

-15 = -6n – 3 + 6

-15 + 3 - 6 = -6n

-18 = -6n

n = -18/-6

n = 3.

cestrela7 [59]2 years ago

4 0

Answer:

n = 3

Step-by-step explanation:

- 15 = - 6n - 3 + 6

- 15 + 3 - 6 = - 6n

- 18 = - 6n

n = -18 / -6

n = 3

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∆ABC ~ ∆DEF. If ∠A=35° and ∠E=55°, what is the measure of ∠C?

madam [21]

Answer:

90°

Step-by-step explanation:

ABC ~ DEF so that means E = B. A triangle has to add up to 180° so that means 180-35-55=90

7 0

3 years ago

Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

2 years ago

Evgesh-ka [11]

Answer:

He bought 20 shirts

Step-by-step explanation:

shirts -- x

pants -- 3/4 of x

Therefore,

He bought --- 28(3/4 of x) pants and 40(x) shirts.

So, 28(3/4 of x) + 40(x) = 1220

=> 21x + 40x = 1220

=> 61x = 1220

=> x = 20

He bought 20 shirts and 15 pants.

Thenks and meak me brainliest :))

3 0

2 years ago

Abbie babysits on the weekends. She charges $10 for the first hour and $6 for each

Dvinal [7]

Answer:

5 hours

Step-by-step explanation:

34-10(first hour) is 24

24/6(price per additonal hour)=4

so theres four additional hours and the one OG hour so its 5 hours total

8 0

2 years ago

there are 48 students in a school play. the ratio of boys to girls is 5:7. how many more girls than boys are in the school play?

Alex Ar [27]

We can use trial or error method here...

If we take 4 table, 4*5 = 20 and 4*7 = 28. 20+28 = 48.
20 : 28 = 5 : 7

So, there are 20 boys and 28 girls in a school play and there are 8 girls more than boys.

If you look over tables and try it out, only 4 table works for the given ratio.

3 0

3 years ago