On which of the following lines does the point (7, 1) lie?

1 answer:

6 0

We have that
the point (7, 1)

case A.) y = 5x + 4
if the point (7, 1) lie to the line
so
for x=7 the value of y must be 1
y=5*7+4------> y=39
39 is not 1---------> the point does not belong to the line

case B.) y = -x + 8
if the point (7, 1) lie to the line
so
for x=7 the value of y must be 1
y=-7+8------> y=1--------> the point belongs to the line

case C.) y = x - 10
if the point (7, 1) lie to the line
so
for x=7 the value of y must be 1
y=7-10------> y=-3
-3 is not 1---------> the point does not belong to the line

case D.) y = -4x + 3
if the point (7, 1) lie to the line
so
for x=7 the value of y must be 1
y=-4*7+3------> y=-25
-25 is not 1---------> the point does not belong to the line

the answer is the option
B.) y = -x + 8

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Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5

zaharov [31]

Answer:

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}$ or $\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

$\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}$

Therefore, the solution is 31.

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as $\displaystyle \large{a_{n-1} \cdot r = a_n}$ meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as: