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Inessa05 [86]
2 years ago
5

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

Mathematics
1 answer:
stealth61 [152]2 years ago
6 0
We have that
<span>the point (7, 1)

case </span><span>A.) y = 5x + 4
if the point </span>(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 <span>B.) y = -x + 8
</span>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 <span>C.) y = x - 10
</span>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 <span>D.) y = -4x + 3
</span>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:

31

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.

__________________________________________________________

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:

\displaystyle \large{r=\frac{a_{n+1}}{a_n}}

Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:

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

Above should be applied for series that have common ratio not equal to 1.

\displaystyle \large{S_n=a_1 \cdot n}

Above should be applied for series that have common ratio exactly equal to 1.

__________________________________________________________

Topics

Sequence & Series — Geometric Series

__________________________________________________________

Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

__________________________________________________________

7 0
2 years ago
76 is what percent of 95
mario62 [17]
Take 76 over 95, and then multiply by 100% to get your answer.
(76/95) * 100%= 80%
7 0
3 years ago
Read 2 more answers
A matatu carries 14 passengers per trip. In
PilotLPTM [1.2K]

Answer:

"23,520"

Step-by-step explanation:

one trip: 14 passengers

one day: 3 trips

passengers: 80

80x14= 1,120

1,120x3= 3,360

3,360x7= 23,520

6 0
2 years ago
I WILL GIVE BRAINLIEST!!!!
spayn [35]

Answer:

first: 1/3

second: 1

third: 1/2

Step-by-step explanation:

7 0
2 years ago
Solve 10a-5b=25 for b
devlian [24]
         10a - 5b = 25
10a - 10a - 5b = 25 - 10a
                 -5b = -10a + 25
                  -5            -5
                    b = 2a - 5
6 0
3 years ago
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