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natali 33 [55]
2 years ago
9

Choose the equation that represents the line passing through the point (2,-4) with a slope of 1/2? y=1/2x+5, y=1/2x-3, y=1/2x-5,

y=1/2x+3
Mathematics
1 answer:
LUCKY_DIMON [66]2 years ago
3 0
Correct answer: <span>y=1/2x-5
</span>
given: point = (2,-4)
slope = 1/2 

Explanation: equation of line is: y = mx + c
where, m is the slope
c is the y-intercept

Now, 
here, y = 1/2x + c
put, x = 2, y = -4
we get, -4 = (1/2).2 + c
or c = -4 - 1
or c = -5 

Hence, equation of line is : y = 1/2x-5
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Answer:

1

Step-by-step explanation:

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We can think of 5.6 x 10-9 as the product of two numbers: 5.6 (the digit term) and 10-9 (the exponential term).

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Find the 12th term of the geometric sequence 5, -25, 125, ...5,−25,125,...
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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
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Step-by-step explanation:

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