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3 years ago

Position to term rule of 2, 6, 10, 14, 18 multiply by _ and subtract by _

Mathematics

1 answer:

andreyandreev [35.5K]3 years ago

4 0

Answer:

Please check the explanation.

Step-by-step explanation:

Given the sequence

2, 6, 10, 14, 18

An arithmetic sequence has a constant difference and is defined as

$\:a_n=a_1+\left(n-1\right)d$

compute the differences of all the adjacent terms

$6-2=4,\:\quad \:10-6=4,\:\quad \:14-10=4,\:\quad \:18-14=4$

The difference between all the adjacent terms is the same.

Thus,

$d=4$

and

$a_1=2$

Therefore, the nth term is computed by:

$a_n=4\left(n-1\right)+2$

$a_n=4n-2$

Thus, position to term rule of 2, 6, 10, 14, 18 multiply by __4___ and subtract by __2__.

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Glen is planting square flower gardens surrounding a triangular fishpond as shown. If the sides of the triangular fishpond are 5

weqwewe [10]

Answer:

$h=\sqrt{106} \approx 10.3$ feet

Step-by-step explanation:

We will use the Pythagorean Theorem to solve this. Which states that:

One Length^2 + Another Length^2 = Hypotenuse^2

We can take one length as 5 ft and another length as 9 ft and we call the hypotenuse "h", so we have:

$5^2+9^2=h^2$

Now, let us solve for "h":

$5^2+9^2=h^2\\25 + 81 = h^2\\106=h^2\\h=\sqrt{106} \approx 10.3$

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3 years ago

The wavelength of a wave of frequency 100 Hz is 3.3m. Find it's speed

Natasha_Volkova [10]

Step-by-step explanation:

Given:

Wavelength of wave : 3.3m

Frequency of wave : 100Hz.

speed/velocity : ?

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= 3.3 × 100

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5 0

1 year ago

Read 2 more answers

f the pattern in the table is extended to represent more equivalent ratios for 2:6, which pair of numbers would be in the column

olasank [31]

The pair of numbers that would be in the columns, considering the proportional relationship, is given as follows:

20 would be in the column for 2, and 60 would be in the column for 6.

<h3>What is a proportional relationship?</h3>

A proportional relationship is a special linear function, with intercept having a value of zero, in which the output variable is obtained with the multiplication of the input variable and the constant of proportionality k, as shown as follows:

y = kx

The table is extended to represent more equivalent ratios for 2:6, hence the constant of the relationship is given as follows:

k = 6/2 = 3.

Hence the equation is:

y = 3x.

The values given by each column are given as follows:

Column 2: values of x.

Column 6: values of y.

When x = 20, the numeric value of the relationship is of:

y = 3 x 20 = 60.

Hence the first option is correct.

More can be learned about proportional relationships at brainly.com/question/10424180

#SPJ1

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1 year ago

Jeff goes to a theme park to ride the roller coaster. The theme park charges an entry fee in addition to a fee for each roller c

Damm [24]

Entry fee $15 Roller coasters costs $4 each

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4 years ago

Read 2 more answers

Three friends met for a book club at a coffee shop, each friend ordered a cup of coffee and two donuts. the total of the order w

4vir4ik [10]

Answer:

$Cost\ of\ donut=\frac{49}{24}\approx \$2.042\\\\cost\ of\ donuts=\frac{49}{4}\approx \$12.25$

Step-by-step explanation:

$Let\ cost\ of\ coffee=y\\\\cost\ of\ one\ donut=x\\\\Each\ friend\ buy\ one\ coffee\ and\ two\ donuts\\\\Amount\ for\ 1\ friend=Cost\ of\ coffee+2\times cost\ of\ donut\\\\Amount\ for\ 1\ friend=y+2x\\\\Amount\ required\ for\ 3\ friend=3\times Amount\ for\ 1\ friend\\\\Amount\ required\ for\ 3\ friend=3\times (y+2x)\\\\Amount\ required\ for\ 3\ friend=3y+6x\\\\Total\ bill=\$ 22\\\\3y+2x=22\\\\Given\ cost\ of\ coffee=\$3.25\\\\y=\$3.25$

$Hence\ solution\ of\ following\ system\ of\ equation\ will\ give\ cost\ of\ donut:\\\\3y+6x=22\\\\y=3.25\\\\\\Substitute\ y=3.25\ in\ first\ equation\\\\3\times 3.25+6x=22\\\\9.75+6x=22\\\\6x=22-9.75\\\\6x=12.25\\\\x=\frac{12.25}{6}\\\\x=\frac{49}{24}\approx \$2.042\\\\Cost\ of\ donut=\frac{49}{24}\approx \$2.042$

See attached diagram.

$Each\ friend\ takes\ 2\ donuts\\\\Total\ donuts=Number\ of\ friends\times 2\\\\Total\ donuts=3\times 2=6\\\\cost\ of\ donuts=number\ of\ donuts\times cost\ of\ 1\ donut\\\\cost\ of\ donuts=6\times \frac{49}{24}\\\\cost\ of\ donuts=\frac{49}{4}\approx \$12.25$

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3 years ago

Position to term rule of 2, 6, 10, 14, 18 multiply by _____ and subtract by _____

Position to term rule of 2, 6, 10, 14, 18 multiply by _ and subtract by _