well the two polynomials in the series are 1 and n^8 (I'm assuming the +7 is not in the decimal but it seems to not matter). The degree of the polynomial 1 is 0 which can be represented by 1x^0. The second polynomial in the denominator has a degree of 8. So j = 0 and k = 8. Since 0 < (8-1)

0 < 7 the series converges

6 0

1 year ago

which of the following gives an equation of a line that passes through the point (6 over 5, -19 over 5) and is parallel to the l

victus00 [196]

One equation for this would be

$y = \frac{41}{16} x-\frac{55}{8}$

We start by finding the slope between the two points:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-12-\frac{-19}{5}}{-2-\frac{6}{5}}
\\
\\=(-12+\frac{19}{5}) \div (-2-\frac{6}{5})
\\
\\=(\frac{-60}{5}+\frac{19}{5}) \div (\frac{-10}{5}-\frac{6}{5})
\\
\\=\frac{-41}{5} \div \frac{-16}{5}=\frac{-41}{5} \times \frac{-5}{16}=\frac{41}{16}$

A line parallel to this one will have the same slope. We will use point-slope form to write our equation:

$y-y_1=m(x-x_1)
\\
\\y-\frac{-19}{5}=\frac{41}{16}(x-\frac{6}{5})
\\
\\y+\frac{19}{5}=\frac{41}{16}x- \frac{41}{16} \times \frac{6}{5}
\\
\\y+\frac{19}{5}=\frac{41}{16}x-\frac{246}{80}
\\
\\y+\frac{304}{80}=\frac{41}{16}x-\frac{246}{80}
\\
\\y=\frac{41}{16}x-\frac{246}{80}-\frac{304}{80}
\\
\\y=\frac{41}{16}x-\frac{550}{80}
\\
\\y=\frac{41}{16}x-\frac{55}{8}$

6 0

2 years ago

Tanya's father travels every week for business. He has traveled around the

Nikitich [7]

The correct answer would be: 4.6 x 10^5

8 0

1 year ago

the larger of two positive numbers is 5 more then the smaller. The product of the numbers is 66. find the numbers

Serjik [45]

Answer: 30.5 and 35.5

Step-by-step explanation:

We can use a system of linear equations to find out the answer to this problem. The larger number will be x and the smaller number will be y.

x=y+5

x+y=66

Substitute y+5 in for the bottom equation to get y+5+y=66. Simplify to get 2y+5=66. Subtract 5 from both sides and get 2y=61. Divide by 2 to get y=30.5. This is the smaller number. Add 5 to get the bigger number, which is 35.5

7 0

2 years ago