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2 years ago

Solve for Z (This should be another easy question, + there are answers you can choose from)

Mathematics

2 answers:

Delvig [45]2 years ago

8 0

Answer:

Z = 6

Step-by-step explanation:

Z/12 = Cos(60°)

Z/12 = 1/2

Liula [17]2 years ago

4 0

The answer is Z=6 hope I helped

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I need help finding slope for m

Nataly [62]

-4 + 6/-1 + 3 = 2/2

The slope is 1.

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3 years ago

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What is the sum of the geometric series in which a1 = −5, r = 3, and an = −405?

marysya [2.9K]

An = a1 * r^(n-1)

-405 = -5*3^(n-1)

3^(n-1) = 81

3^4 = 81 so n-1 = 3 and n = 4

Sn = S4 = -5 (1 - 3^4) / ( 1 - 3) = 400 / -2 = -200 Answer

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3 years ago

Find an explicit rule for the nth term of the sequence.The second and fifth terms of a geometric sequence are 18 and 144, respec

vova2212 [387]

Given:

second term = 18

fifth term = 144

The nth term of a geometric sequence is:

$\begin{gathered} a_n\text{ = ar}^{n-1} \\ Where\text{ a is the first term} \\ r\text{ is the common ratio} \end{gathered}$

Hence, we have:

$\begin{gathered} \text{ar}^{2-1}\text{ = 18} \\ ar\text{ = 18} \\ \\ ar^{5-1}=\text{ 144} \\ ar^4\text{ =144} \end{gathered}$

Divide the expression for the fifth term by the expression for the second term:

$\begin{gathered} \frac{ar^4}{ar}\text{ = }\frac{144}{18} \\ r^3\text{ = }\frac{144}{18} \\ r\text{ = 2} \end{gathered}$

Substituting the value of r into any of the expression:

$\begin{gathered} ar\text{ = 18} \\ a\text{ }\times\text{ 2 = 18} \\ Divide\text{ both sides by 2} \\ \frac{2a}{2}\text{ =}\frac{18}{2} \\ a\text{ = 9} \end{gathered}$

Hence, the explicit rule for the sequence is:

$a_n\text{ = 9\lparen2\rparen}^{n-1}$

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1 year ago

16x^7 - 8x^3 / 4x^3

Sunny_sXe [5.5K]

Answer:

4x^4-2

Step-by-step explanation:

$\dfrac{16x^7-8x^3}{4x^3}= \\\\\\\dfrac{4x^3(4x^4-2)}{4x^3}= \\\\\\4x^4-2$

Hope this helps!

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3 years ago

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There are three consecutive even integers. If twice the first integer added to the second is 268,244, find all three integers.

r-ruslan [8.4K]

Answer:

89414,89416,89418

Step-by-step explanation:

Let n bet the positive integer and then 2n is an even integer because multiplying n with 2 makes it an even integer.

Now, 2n+2, 2n+4 are the next integers.

Therefore, three consecutive integers are: 2n, 2n+2, 2n+4.

It is given that twice the first integer added to the second is 268,244 that means:

$2(2n)+(2n+2)=268244$

$4n+2n+2=268244$

$6n=268242$

$n=44707$

Therefore, three consecutive integers are:

2n=89414, 2n+2=89416, 2n+4=89418

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3 years ago