Is 6 and 9 like terms or unlike terms

40, 10, 5/2 5/8... (fractions) is it arithmetic or geometric and what are the next two terms PLZ HELP DUE IN 10 MINS

patriot [66]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the sequence

$40,\:10,\:\frac{5}{2},\:\frac{5}{8}$

A geometric sequence has a constant ratio 'r' and is defined by

$\:a_n=a_0\cdot r^{n-1}$

Computing the ratios of all the adjacent terms

$\frac{10}{40}=\frac{1}{4},\:\quad \frac{\frac{5}{2}}{10}=\frac{1}{4},\:\quad \frac{\frac{5}{8}}{\frac{5}{2}}=\frac{1}{4}$

The ratio of all the adjacent terms is the same and equal to

$r=\frac{1}{4}$

Thus, the given sequence is a geometric sequence.

As the first element of the sequence is

$a_1=40$

Therefore, the nth term is calculated as

$\:a_n=a_0\cdot r^{n-1}$

$a_n=40\left(\frac{1}{4}\right)^{n-1}$

Put n = 5 to find the next term

$a_5=40\left(\frac{1}{4}\right)^{5-1}$

$a_5=40\cdot \frac{1}{4^4}$

$a_5=\frac{40}{4^4}$

$=\frac{2^3\cdot \:5}{2^8}$

$a_5=\frac{5}{2^5}$

$a_5=\frac{5}{32}$

now, Put n = 6 to find the 6th term

$a_6=40\left(\frac{1}{4}\right)^{6-1}$

$a_6=40\cdot \frac{1}{4^5}$

$a_6=\frac{40}{4^5}$

$=\frac{2^3\cdot \:5}{2^{10}}$

$a_6=\frac{5}{2^7}$

$a_6=\frac{5}{128}$

Thus, the next two terms of the sequence 40, 10, 5/2, 5/8... is:

$a_5=\frac{5}{32}$

$a_6=\frac{5}{128}$

7 0

3 years ago

Ms. Potts washed 1/4 of her laundry. Her son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still nee

LenaWriter [7]

Answer:

Son washed more
Remaining 9/28 of the laundry

Step-by-step explanation:

Make denominators common to see the difference in fractions:

1/4 = 7/28
3/7 = 12/28

Son washed more laundry as 12/28 > 7/28

Together they washed:

7/28 + 12/28 = 19/28 of the laundry

Remaining part is:

1 - 19/28 =
28/28 - 19/28 =
9/28 of the laundry

7 0

3 years ago

Read 2 more answers

Identify which line from the graph the following right triangles could lie on.

qaws [65]

Answer:

Step-by-step explanation:

Slope of line A = $\frac{\text{Rise}}{\text{Run}}$

= $\frac{9}{3}$

= 3

Slope of line B = $\frac{9}{6}$

= $\frac{3}{2}$

Slope of line C = $\frac{6}{8}$

= $\frac{3}{4}$

5). Slope of the hypotenuse of the right triangle = $\frac{\text{Rise}}{\text{Run}}$

= $\frac{90}{120}$

= $\frac{3}{4}$

Since slopes of line C and the hypotenuse are same, right triangle may lie on line C.

6). Slope of the hypotenuse = $\frac{30}{10}$

= 3

Therefore, this triangle may lie on the line A.

7). Slope of hypotenuse = $\frac{18}{24}$

= $\frac{3}{4}$

Given triangle may lie on the line C.

8). Slope of hypotenuse = $\frac{21}{14}$

= $\frac{3}{2}$

Given triangle may lie on the line B.

9). Slope of hypotenuse = $\frac{36}{24}$

= $\frac{3}{2}$

Given triangle may lie on the line B.

10). Slope of hypotenuse = $\frac{48}{16}$

= 3

Given triangle may lie on the line A.

7 0

3 years ago

Needs answered ASAP What is the volume of the triangular prism below?

neonofarm [45]

Answer:

172.5 inches cubed

Step-by-step explanation:

5 0

4 years ago

Y=-|x+3| domain and range

Serjik [45]

Answer:

the domain is that x is a set of real numbers.

the range is y ≤ -3

Step-by-step explanation:

y = -|x + 3|

y is either positive or equal to zero.

Now, x is all real numbers because any value of x used will yield a valid value of y.

Thus, we can say that the domain is that x is a set of real numbers.

Now, for the range:

The minus sign in front of the absolute value indicates that the function has a maximum value.

Thus, the range is y ≤ -3

6 0

3 years ago