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4 years ago

PLEASE HELP 25 PTS AND BRAINLIEST!!!

Mathematics

1 answer:

masya89 [10]4 years ago

3 0

A. X=16

Work

2x+3x-6=10+4x

5x-6=10+4x

5x-4x=10+6

----------------

B. 18+5x

Work

17+5x-23+4x6

Multiply the Numbers

17+5x-23+24

Calculate

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C. 2(7x-1)

Work

7x+5x+8+2x-10

Collect the like terms

Calculate

14x-2

Factor the expression

Hope this Helps

✔Dante✔

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Tom has read the first 40 pages of a book. He plans to read another 12 pages each day Write an equation that represents the rela

DaniilM [7]

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The equation that represents the relationship between , and the number of days he has been reading , d is p = 40 + (12 × d)

Step-by-step explanation:

Tom has read the first 40 pages of a book.

He plans to read another 12 pages each day

Since the total number of pages is p

And the Number of days required to read the book is d

if Tom read 12 pages per day, then in d days he would read 12 × d pages

h/e has already read 40 pages of the book

Then total pages of the book

p = 40 + (12 × d)

Hence, The equation that represents the relationship between , and the number of days he has been reading , d is p = 40 + (12 × d)

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3 years ago

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3 years ago

The sum of the first n terms of a geometric series is 364? The sum of their reciprocals 364/243. If the first term is 1, find n

Afina-wow [57]

If the geometric series has first term $a$ and common ratio $r$ , then its $N$ -th partial sum is

$\displaystyle S_N = \sum_{n=1}^N ar^{n-1} = a + ar + ar^2 + \cdots + ar^{N-1}$

Multiply both sides by $r$ , then subtract $rS_N$ from $S_N$ to eliminate all the middle terms and solve for $S_N$ :

$rS_N = ar + ar^2 + ar^3 + \cdots + ar^N$

$\implies (1 - r) S_N = a - ar^N$

$\implies S_N = \dfrac{a(1-r^N)}{1-r}$

The $N$ -th partial sum for the series of reciprocal terms (denoted by $S'_N$ ) can be computed similarly:

$\displaystyle S'_N = \sum_{n=1}^N \frac1{ar^{N-1}} = \frac1a + \frac1{ar} + \frac1{ar^2} + \cdots + \frac1{ar^{N-1}}$

$\dfrac{S'_N}r = \dfrac1{ar} + \dfrac1{ar^2} + \dfrac1{ar^3} + \cdots + \dfrac1{ar^N}$

$\implies \left(1 - \dfrac1r\right) S'_N = \dfrac1a - \dfrac1{ar^N}$

$\implies S'_N = \dfrac{1 - \frac1{r^N}}{a\left(1 - \frac1r\right)} = \dfrac{r^N - 1}{a(r^N - r^{N-1})} = \dfrac{1 - r^N}{a r^{N-1} (1 - r)}$

We're given that $a=1$ , and the sum of the first $n$ terms of the series is

$S_n = \dfrac{1-r^n}{1-r} = 364$

and the sum of their reciprocals is

$S'_n = \dfrac{1 - r^n}{r^{n-1}(1 - r)} = \dfrac{364}{243}$

By substitution,

$\dfrac{1 - r^n}{r^{n-1}(1-r)} = \dfrac{364}{r^{n-1}} = \dfrac{364}{243} \implies r^{n-1} = 243$

Manipulating the $S_n$ equation gives

$\dfrac{1 - r^n}{1-r} = 364 \implies r (364 - r^{n-1}) = 363$

so that substituting again yields

$r (364 - 243) = 363 \implies 121r = 363 \implies \boxed{r=3}$

and it follows that

$r^{n-1} = 243 \implies 3^{n-1} = 3^5 \implies n-1 = 5 \implies \boxed{n=6}$

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2 years ago

A box of oats cereal measures 24 cm long by 5 cm wide 25 cm high. A box of rice cereal measures 26 cm long by 4 cm wide by 28 mm

Tanzania [10]

Answer:

Box of oat:

24*5*25(all in cm)=3000 cm3

cereal:

26*4*2.8=291.2 cm3

oat is grater by 2708.8

Step-by-step explanation:

28mm was changed to 2.8 cm

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2 years ago