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3 years ago

Consider the sequence shown.

Mathematics

1 answer:

Semmy [17]3 years ago

3 0

Given:

The sequence is

436, 218, 109, 54.5, 27.25,...

To find:

The explicit formula for the given sequence.

Solution:

We have,

436, 218, 109, 54.5, 27.25,...

It is a GP because the two consecutive terms have common ratio.

Here,

First term : a=436

Common ratio : d = $\dfrac{218}{436}$

= $\dfrac{1}{2}$

= $0.5$

Now, the explicit formula for a GP is

$g_n=ar^{(n-1)}$

Where, a is the first term and r is the common ratio.

Putting a=436 and r=0.5, we get

$g_n=436(0.5)^{(n-1)}$

Therefore, the correct option is c.

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Pls help is it A. B. C. D.

Ivenika [448]

Answer:

Step-by-step explanation:

Hope I was able to help!! :)

7 0

3 years ago

How do you solve this?

puteri [66]

Answer:

Width: 7

Length: 14

Step-by-step explanation:

The area of a rectangle can be found my multiplying the length by the width. We do not know neither the length nor the width. However, we do know that the length is 7 feet longer than the width. Because we do not know the value of either side, let's let $x$ represent the width.

Since the length is 7 feet longer, we can represent the length by $x+7$ .

Now that we have our values for the length and the width we can multiply them together to find our area.

$(x)(x+7)=x^{2} +7x$

Now we have our equation, so we can address the changes made by the original question. The original question states that when 7 is added to both the length and width the area becomes 3 times larger. To do so simply increase each side by 7 by adding 7 to the original values.

$(x+7)(x+14)$

And multiply our area by 3.

$3(x^{2} +7x)$

set these equal to each other to find your new equation.

$(x+7)(x+14)=3(x^{2} +7x)$

Now you need to solve for $x$ . To do this first muliply $(x+7)$ and $(x+14)$ .

$(x+7)(x+14)=\\x^{2} +14x+7x+98=\\x^{2} +21x+98$

Then multiply $3(x^{2} +7x)$

$3(x^{2} +7x)=\\3x^{2} +21x$

Now you can begin solving for $x$ .

$x^{2} +21x+98=3x^{2} +21x$

Subtract $x^{2}$ from both sides.

$21x+98=2x^{2} +21x$

Subtract $21x$ from both sides.

$98=2x^{2}$

Divide by 2.

$49=x^{2}$

And finally take the sqaure root of both sides.

$\sqrt{x^{2} }=\sqrt{49}\\x=7$

Remember, because we are dealing with length, there cannot be negative. So while normally we would get both +7 and -7, in this case we only get +7.

Now that we have the value of $x$ , we can plug it into our original values.

For width we simply get 7.

For length we get 7+7=14

To check our answer we cna multiply 7 by 14 to get 98. Then we can add 7 to our length and width to get 14 and 21. Multiply these together and we get 294. 294 divided by 3 is 98, proving our answer correct.

7 0

3 years ago

PLEASE HELP WILL GIVE BRAINLIEST TO CORRECT ANSWER

nlexa [21]

Answer:

B. 6.000000 g

Step-by-step explanation:

The reason why its B is due to it having more 'sigs' than 'figs'

Hope this helped <3

6 0

3 years ago

Vector bought 15.6 pounds of paintballs. Ali together, the balls cost 35.99. About how much did the paintball cost per pound

Igoryamba

Answer:

about $2.31 per pound

Step-by-step explanation:

35.99/15.6 = 2.30705128205

2.31

Have a good day! :)

5 0

2 years ago

Eth enlarged the triangle below by a scale of 5.

levacccp [35]

Answer:

She should have multiplied one half (4)(3.5) by 5 squared.

Step-by-step explanation:

We are given that

Base of triangle=b=4 cm

Height of triangle=h=3.5 cm

Area of triangle= $\frac{1}{2}bh=\frac{1}{2}(4)(3.5) cm^2$

After enlarged

Scale factor=5

New base of enlarged triangle=b'=4(5) cm

Height of enlarged triangle=h'=3.5(5) cm

Area of enlarged triangle= $\frac{1}{2}4(5)(3.5\times 5)=\frac{1}{2}(4)(3.5)(5^2) cm^2$

But Beth wrote

Area of enlarged triangle= $\frac{1}{2}(4)(3.5)(5)=35 cm^2$

She should have multiplied one half (4)(3.5) by 5 squared.

3 0

3 years ago