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3 years ago

What is the expanded and word form for 67.943

Mathematics

1 answer:

adell [148]3 years ago

8 0

Word : Sixty-Seven and Nine Hundred Forty-Three Thousandths
Expanded : 60 + 7 + 0.9 + 0.04 + 0.003

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The 5th term in a geometric sequence is 40. The 7th term is 10. What is (are) the possible value(s) of the 4th term?

Lena [83]

Answer:

possible values of 4th term is 80 & - 80

Step-by-step explanation:

The general term of a geometric series is given by

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

Where a(n) is the nth term, r is the common ratio (a term divided by the term before it) and n is the number of term

Given, 5th term is 40, we can write:

$ar^{5-1}=40\\ar^4=40$

Given, 7th term is 10, we can write:

$ar^{7-1}=10\\ar^6=10$

We can solve for a in the first equation as:

$ar^4=40\\a=\frac{40}{r^4}$

Now we can plug this into a of the 2nd equation:

$ar^6=10\\(\frac{40}{r^4})r^6=10\\40r^2=10\\r^2=\frac{10}{40}\\r^2=\frac{1}{4}\\r=+-\sqrt{\frac{1}{4}} \\r=\frac{1}{2},-\frac{1}{2}$

Let's solve for a:

$a=\frac{40}{r^4}\\a=\frac{40}{(\frac{1}{2})^4}\\a=640$

Now, using the general formula of a term, we know that 4th term is:

4th term = ar^3

Plugging in a = 640 and r = 1/2 and -1/2 respectively, we get 2 possible values of 4th term as:

$ar^3\\1.(640)(\frac{1}{2})^3=80\\2.(640)(-\frac{1}{2})^3=-80$

possible values of 4th term is 80 & - 80

3 0

3 years ago

Given △QRS ~ △XYZ, what is the value of tan(Q)?

VladimirAG [237]

Since the triangles are similar the ratios of the lengths of corresponding sides are equal.

tan Q = opp/adj = RS/QS = YZ/XZ = 9/12 = 3/4

8 0

3 years ago

Read 2 more answers

An amateur radio operator erects a 75-foot vertical tower for an antenna. A 117 guy wire is pulled from the top of the tower dia

vitfil [10]

Answer:

α=39.80°

Step-by-step explanation:

applying the law of sin and cos, we have:

$sin\alpha =\frac{75}{117}=0.6410\\\alpha =acs(0.64)= 39.79$

and to the nearest tenth of a degree

α=39.80°

3 0

2 years ago

Help Asap 20 points!! And Brainlist!!!

Alenkasestr [34]

Answer: 2(5c - 1x)

Step-by-step explanation: It's asking you to take out the greatest common factor (GCF).

5 0

2 years ago

Tell me the answer to the question plz

Sonja [21]

Step-by-step explanation:

(11.99+23.98+9.95)= 45.92

she has to pay = 45.92 - 20/100 (45.92)

= 45.92 - 9.18 = 36.74

so option

about 37 is right

4 0

3 years ago