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AnnyKZ [126]
3 years ago
6

Can someone help me please!.

Mathematics
1 answer:
garik1379 [7]3 years ago
5 0

Answer:

f I used to know this one

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Find the 12th term of the geometric sequence 5, -25, 125, ...5,−25,125,...
katovenus [111]

Answer:

  • a_{12}=-244140625

Step-by-step explanation:

Considering the geometric sequence

5,-25,\:125,\:...

a_1=5

As the common ratio 'r' between consecutive terms is constant.

\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}

r=\frac{-25}{5}=-5

r=\frac{125}{-25}=-5

The general term of a geometric sequence is given by the formula:  

a_n=a_1\cdot \:r^{n-1}

where a_1 is the initial term and r the common ratio.

Putting n = 12 , r = -5 and a_1=5 in the general term of a geometric sequence to determine the 12th term of the sequence.

a_n=a_1\cdot \:r^{n-1}

a_n=5\left(-5\right)^{n-1}

a_{12}=5\left(-5\right)^{12-1}

      =5\left(-5^{11}\right)

\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a

       =-5\cdot \:5^{11}

\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}

        =-5^{1+11}     ∵ 5\cdot \:5^{11}=\:5^{1+11}

        =-244140625

Therefore,

  • a_{12}=-244140625
6 0
3 years ago
Consider the following equations: f(x) = 2x – 2 and g(x) = 5 - x
zysi [14]

Answer:

The difference in slopes of f(x)\ and\ g(x) is = 3

We can say slope of f(x) is positive  and 3 more than slope of g(x) while slope of g(x)  is negative.

Difference of y-intercepts of f(x)\ and\ g(x) is = -7

We can say the y-intercept of g(x) is positive and 7 units above f(x) while y-intercept of f(x)  is negative.

Step-by-step explanation:

Given equation:

f(x) =2x - 2

g(x) =5-x

We need to find the difference of slopes and y-intercepts of the given equations.

The standard form of a slope intercept equation of line is given by:

y=mx+b

where m represents slope and b represents y-intercept of line.

Writing the given equations in standard form to find slope and y-intercept.

f(x) =2x +(-2)

Slope = 2 and y-intercept =-2

g(x) =(-1)x+5

Slope = -1 and y-intercept =5

The difference in slopes of f(x)\ and\ g(x) is = 2-(-1)=2+1=3

We can say slope of f(x) is positive  and 3 more than slope of g(x) while slope of g(x)  is negative.

Difference of y-intercepts of f(x)\ and\ g(x) is = -2-5=-7

We can say the y-intercept of g(x) is positive and 7 units above f(x) while y-intercept of f(x)  is negative.

5 0
3 years ago
State the extremes of the proportion below. 4/7=12/x
yKpoI14uk [10]

\frac{4}{7}  =  \frac{12}{x}  \\  \\ 1. \:  \frac{4}{7}x  = 12 \\  \\ 2. \:  \frac{4x}{7}  = 12 \\  \\ 3. \: 4x = 12 \times 7 \\  \\ 4. \: 4x = 84 \\  \\ 5. \: x =  \frac{84}{4}  \\  \\ 6. \: x = 21

7 0
3 years ago
Read 2 more answers
One step inequalities.... 9x&lt;18<br> how to solve
Nuetrik [128]
So 9x<18 can be factored out into 
9(x)<9(2)
you can divide both sides by 9
x<2 

so the solution is any number more than 2, but not 2
5 0
3 years ago
Read 2 more answers
25% of 176 is what number in equation forms
harina [27]
25% divided by 176=44
7 0
3 years ago
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