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Nimfa-mama [501]
3 years ago
14

Evaluate the expression when y = 5 and x = 4 x + 7y

Mathematics
1 answer:
Alex3 years ago
3 0

y = 5 and x = 4

x + 7y =

4 + 7(5) =

4 +35 =

39

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8 0
4 years ago
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
How do I write 5 7/8 as an improper fraction
uysha [10]
5 7/8 as an improper fraction would be 47/8!

To convert a mixed number into an improper fraction, you need to do this:

1. Multiply the whole number to the denominator (lower number of the fraction), which in this case is 8. So 5 X 8 = 40.

2. Add the resulting number to the numerator (also known as the top fraction value). 7 + 40 = 47.

3. Take away the whole number and leave the fraction with the previous number as the numerator and the denominator the same!

So we end up with 47/8!

Hope that helps!

:D®
6 0
3 years ago
Read 2 more answers
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