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3 years ago

Can someone help me match these too?

Mathematics

1 answer:

Furkat [3]3 years ago

7 0

ANSWER:

A is number 3

B is number 2

Step-by-step explanation:

The left side is A and B (order)

the right side is 1,2,3,4 (order)

explanation: A is number 3 because as said in A the tram already has 5 people which is what we start with a1 = 5 and we add 11 at each stop as shown in the equation.

B is number 2 for the same reason as it started with 2 but added 4 inches of rain each time.

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In a G.P the difference between the 1st and 5th term is 150, and the difference between the

liubo4ka [24]

Answer:

Either $\displaystyle \frac{-1522}{\sqrt{41}}$ (approximately $-238$ ) or $\displaystyle \frac{1522}{\sqrt{41}}$ (approximately $238$ .)

Step-by-step explanation:

Let $a$ denote the first term of this geometric series, and let $r$ denote the common ratio of this geometric series.

The first five terms of this series would be:

$a$ ,
$a\cdot r$ ,
$a \cdot r^2$ ,
$a \cdot r^3$ ,
$a \cdot r^4$ .

First equation:

$a\, r^4 - a = 150$ .

Second equation:

$a\, r^3 - a\, r = 48$ .

Rewrite and simplify the first equation.

$\begin{aligned}& a\, r^4 - a \\ &= a\, \left(r^4 - 1\right)\\ &= a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) \end{aligned}$ .

Therefore, the first equation becomes:

$a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) = 150$ ..

Similarly, rewrite and simplify the second equation:

$\begin{aligned}&a\, r^3 - a\, r\\ &= a\, \left( r^3 - r\right) \\ &= a\, r\, \left(r^2 - 1\right) \end{aligned}$ .

Therefore, the second equation becomes:

$a\, r\, \left(r^2 - 1\right) = 48$ .

Take the quotient between these two equations:

$\begin{aligned}\frac{a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right)}{a\cdot r\, \left(r^2 - 1\right)} = \frac{150}{48}\end{aligned}$ .

Simplify and solve for $r$ :

$\displaystyle \frac{r^2+ 1}{r} = \frac{25}{8}$ .

$8\, r^2 - 25\, r + 8 = 0$ .

Either $\displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}$ or $\displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}$ .

Assume that $\displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}$ . Substitute back to either of the two original equations to show that $\displaystyle a = -\frac{497\, \sqrt{41}}{41} - 75$ .

Calculate the sum of the first five terms:

$\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= -\frac{1522\sqrt{41}}{41} \approx -238\end{aligned}$ .

Similarly, assume that $\displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}$ . Substitute back to either of the two original equations to show that $\displaystyle a = \frac{497\, \sqrt{41}}{41} - 75$ .

Calculate the sum of the first five terms:

$\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= \frac{1522\sqrt{41}}{41} \approx 238\end{aligned}$ .

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3 years ago

A bag contains 18 coins consisting of quarters and dimes. The total value of the coins is $2.85. Which system of equations can b

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alukav5142 [94]

45 7 14 absolute value true the distance from 0 and -5 -3 -2 0 and 9

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Shelly and Mickelle are making a quilt . They have a piece of fabric that measures 48 inches by 168 inches . All pieces of fabri

stiv31 [10]

Answer:

Step-by-step explanation:

Given the following :

Dimension of fabric = 48 by 168

What is the length of the largest square pieces into which shelly and mickelle can cut the fabric?

To obtain this, find the greatest common factor of both numbers in the dimension:

Using the table format:

___ _48 ____168

_ 2__24 ____ 84

_2__12 _____42

_2__6 _____ 21

_3__3______ 7

Since there is no number which can divide both anymore

The greatest common factor = (2 * 2 * 2 * 3) = 24

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What is the length of BC Round to the nearest tenth

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Answer:

Step-by-step explanation :4.0148 rounded to the nearest thousand is 0, but if you meant rounded to the nearest thousandth, it would be 4.015 because the 8 in the ten thousandth column would cause the 4 in the thousandth column to round up to 5.

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