Given the sequence 8, 16, 32, 64, ..., which expression would give the thirteenth term?

Answers

Answer 1

Answer: 8, 16, 32, 64,…
×2 ×2 ×2

$a_(n) = a_(1) * r^(n - 1)$
$a_(n) = 8 * 2^(13 - 1)$
$a_(n) = 8 * 2^(12)$
$a_(n) = 8 * 4096$
$a_(n) = 32768$

   First Term: 8
      Second Term: 16
      Third Term: 32
      Fourth Term: 64
       Fifth Term: 128
      Sixth Term: 256
   Seventh Term: 512
   Eighth Term: 1024
   Ninth Term: 2048
      Tenth Term: 4096
   Eleventh Term: 8192
   Twelfth Term: 16384
Thirteenth Term: 32768

$The\ expression\ that\ would\ give\ the\ thirteenth\ term\ of\ the\ problem\ would\ be\ the\ equation\ of\ the\ geometric\ sequence,\ which\ is\ equal\ to\ a_(n) = a_(1) * r^(n - 1).$

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A camp ground consists of 12 square campsites arranged in a line along a beach. The distance from the edge of a campsite to the water at the end of the beach is 5 yards. The area of the campground, including the beach, is 1,248 square yards. What is the width of one campsite/

Answers

x=side length of a campsite
12x(5+x)=1248 because each campsite has a length of x and there are 12 and from the top of the camp to the water is the 5 yds + a side length and LW=1248
60x+12x^2=1248
12x^2+60x-1248=0
x^2+5-14=0
(x+7)(x-2)=0
x+7=0 or x-2=0
x=-7 or x=2
x=2 because width can't be negative
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what is the length of the diagonal of a non-regulation tennis court with length 20 feet and width 15 feet?

Answers

Answer:

25 feet

Step-by-step explanation:

Basically that non-regulation tennis court is a rectangle. You want to know the length of the diagonal. If you draw it on paper, you'll see that this then become 2 triangles... of which you have 2 sides, and are seeking the hypotenuse. So....

H² = A² + B²

H² = 20² + 15² = 400 + 225 = 625

H = 25 feet.

Answer:

The diagonal of a non-regulation tennis court = 25 feet

Step-by-step explanation:

Pythagorean theorem

Hypotenuse² = Base² + Height²

The tennis court is like a rectangle.

We can consider the court as made of two right angled triangle

To find the length of diagonal of court

Here base = 15 feet and height = 20 feet

Diagonal or hypotenuse can be written as,

Diagonal ² = Base² + Height²

= 15² + 20²

= 225 + 400

= 625

Diagonal = √625 = 25 feet

Therefore the diagonal of a non-regulation tennis court = 25 feet

A tree 7 ft tall grows an average of 6 in. each year. Which equation models the tree’s height h after x years?

Answers

Simple...

you want to find h...

it's already 7 feet tall..and grows 6 inches per year...

h=6x+7

Thus, your answer.

what are the solutions to the quadratic equation (5y 6)2 = 24? y = and y = y = and y = y = and y = y = and y =

Answers

If you would like to find the solutions to the quadratic equation (5y + 6)^2 = 24, you can do this using the following steps:

(5y + 6)^2 = 24
25y^2 + 2 * 6 * 5y + 36 = 24
25y^2 + 60y + 36 - 24 = 0
25y^2 + 60y + 12 = 0
25 * (y + 6/5)^2 - 24 = 0
1. y = -6/5 - (2 * sqrt(6))/5
2. y = (2 * sqrt(6))/5 - 6/5

The correct result would be y = -6/5 - (2 * sqrt(6))/5 and y = (2 * sqrt(6))/5 - 6/5.

The solution to the quadratic equation is y = -2.18 and y = -0.22

How to evaluate the function?

The equation is given as:

(5y + 6)^2 = 24

Expand

25y^2 + 60y + 36 = 24

Subtract 24 from both sides

25y^2 + 60y + 12 = 0

Using a graphical tool, we have the solution to be:

y = -2.18 and y = -0.22

Hence, the solution to the quadratic equation is y = -2.18 and y = -0.22

Read more about quadratic equation at:

brainly.com/question/10449635

#SPJ5

Distance between (3,-4) and (-2,5)

Answers

26 minutes ago, I gave you a complete solution for the distance
between (-1, 2) and (7, 8). As I wrote it, I gave you a complete
explanation of every step, so that you would then know how to
find the distance between ANY two points.

Go back and review that one. Then use the same procedure to solve
this one. When you're finished, you'll have the solution to this one ...
completely on your own ... and plus, you'll LEARN something too.

If 21 and 22 are complementary angles, and m/1 = 74°; find m22.

Answers

Answer:

The measure of angle 22 is 16 degrees.

Step-by-step explanation:

Complementary angles are angles that add to 90 degrees.

m21 + m22 = 90

74+ m22 = 90

m22 = 90-74

m22 = 16

The measure of angle 22 is 16 degrees.

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