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What is the fifth term of the geometric sequence 5,15,45,...

denpristay [2]

Answer:

405

Step-by-step explanation:

This is a geometric sequence, so we need the common ratio and the first term

To find the common ratio, we take the second term and divide by the first term

15/5 =3

The common ratio is 3

We are multiplying by 3 each time

The first term is 5

The formula is

an = a1 * (r) ^ (n-1) where n is the term number

We want the 5th term

a5 = 5 * (3) ^ (5-1)

a5 = 5 *3^4

= 5 *81

= 405

7 0

4 years ago

I cannot find the answer to this can someone please help me

dlinn [17]

Answer:

A = 1,144 ft²

Step-by-step explanation:

The base of the quadrilateral is also x. We know this since there are 2 90° angles, there fore the other 2 angles are also 90°, making the top and bottom sides of the quadrilateral parallel to each other, and equal in measure.

Since the entire base of the yard is 2x, the base of the triangle is x.

The area of the triangle is

A = (1/2)bh where b is the base, and h is the height

For this example...

A = (1/2)x(44) (x is the base, and 44 is the height)

So

A = (1/2)(44)x

A = 22x

The area of the quadrilateral is

A = LW

A = 44x

The total area of the yard is

A = 22x + 44x

A = 66x

We are told that the entire area is 3,462. so

3,462 = 66x now solve for 'x'

3,462/66 = x (divide both sides by 66)

52 = x

So the area of the picnic tables is the area of the triangle, which is

A = 22(52) = 1,144 ft²

5 0

4 years ago

The volume of a rectangular prism is 3,240 ft3. The prism is 9ft long and 12ft wide. How tall is the rectangular prism? Please h

Softa [21]

3.5*10^5
''''''''''''''''

5 0

4 years ago

Marcus walks 9 miles in 2 hours. At what unit rate does Marcus walk.

Sonja [21]

Answer:

He walks 4.5 miles per hour

Step-by-step explanation:

5 0

4 years ago

Read 2 more answers

Which equation represents a line that passes through (4,1/3) and has a slope of 3/4?

velikii [3]

We can use the point-slope equation:
$y = mx + b$
m, the slope, is 3/4:
$y = \frac{3}{4} x + b$
To find b, we plug in the point (4,1/3):
$( \frac{1}{3} ) = \frac{3}{4} (4) + b \\ \frac{1}{3} = 3 + b \\ \frac{1}{3} = \frac{9}{3} + b$
$- \frac{8}{3} = b$

Therefore, the point-slope equation is
$y = \frac{3}{4} x - \frac{8}{3}$

Now we have to see which answer matches.

$y - \frac{3}{4} = \frac{1}{3} (x - 4) \\ y - \frac{3}{4} = \frac{1}{3} x - \frac{4}{3} \\ y - \frac{9}{12} = \frac{1}{3} x - \frac{16}{12}$
$y = \frac{1}{3} x - \frac{7}{12}$
Since this is not the same, we try the next one.

$y - \frac{1}{3} = \frac{3}{4} (x - 4) \\ y - \frac{1}{3} = \frac{3}{4} x - 3 \\ y - \frac{1}{3} = \frac{3}{4} x - \frac{9}{3}$
$y = \frac{3}{4} x - \frac{8}{3}$

This is the same, so this is the answer. We should still double-check the other answers.

$y - \frac{1}{3} = 4(x - \frac{3}{4} ) \\ y - \frac{1}{3} = 4x - 3 \\ y - \frac{1}{3} = 4x - \frac{9}{3}$
$y = 4x - \frac{8}{3}$
This one is not equivalent.

$y - 4 = \frac{3}{4} (x - \frac{1}{3} ) \\ y - 4 = \frac{3}{4} x - \frac{1}{4} \\ y - \frac{16}{4} = \frac{3}{4} x - \frac{1}{4}$
$y = \frac{3}{4} x + \frac{15}{4}$
This one also does not work.

The answer is the second one:
$y - \frac{1}{3} = \frac{3}{4} (x - 4)$

3 0

3 years ago

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