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swat32
3 years ago
5

How do you determine if 5x-7y=14 is a function?

Mathematics
2 answers:
Tasya [4]3 years ago
6 0
You can type that function in a graphing calculator and either see the graph or the table. If you put that function in a table, then you have to make sure that x isn't repeating itself. If you look at the graph, then you have to do the vertical line test
Pavlova-9 [17]3 years ago
3 0
One way is to graph it and do the vertical line test
it is not a function if we can draw a vertical line in the graph that passes through 2 points of the graph

if we graph this function, we see there is no place we can draw a vertical line and hit the line twice
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Given the sequence, 26, 13, 6.5, ..... find a) the 10th term and b) the sum of the first 18 terms
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a) 10th term is 0.051

b) The sum of first 18 terms of given sequence is 51.48

Step-by-step explanation:

We are given the sequence 26, 13, 6.5, ..... we need to find

a) 10th term

b) Sum of first 18 terms

Before solving we need to determine if the sequence is arithmetic or geometric

The sequence is arithmetic if common difference d is same.

The sequence is geometric if common ratio r is same.

Finding common difference d: 13-26 = -13, 6.5-13= -6.5

As common difference is not same so, the sequence is not arithmetic.

Finding common ratio r : 13/26 =0.5, 6.5/13= 0.5

As common ratio is same so, the sequence is geometric.

a) Finding common difference: 13-26 = -13, 6.5-13= -6.5

As common difference is not same so, the sequence is not arithmetic.

a) 10th term

The formula to find 10th term is: a_n=a_1r^{n-1}

We have a₁=26 and r = 0.5 n=10

a_n=a_1r^{n-1}\\a_{10}=26(0.5)^{10-1}\\a_{10}=26(0.5)^{9}\\a_{10}=0.051

So, 10th term is 0.051

b) Sum of first 18 terms

The formula to find sum of geometric series is: S_n=\frac{a(1-r^n)}{1-r}

where a= 1st term, r = common ratio and n= number of terms

In the given sequence we have

a=26, r=0.5 and n=18

Finding sum of first 18 terms

S_n=\frac{a(1-r^n)}{1-r}\\S_{18}=\frac{26(1-(0.5)^{18}}{1-0.5}\\S_{18}=\frac{26(0.99)}{0.5}\\S_{18}=\frac{25.74}{0.5}\\S_{18}=51.48

So, sum of first 18 terms of given sequence is 51.48

6 0
3 years ago
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