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Alchen [17]
3 years ago
7

Solve the inequality.show work. (r+3)>7

Mathematics
1 answer:
skelet666 [1.2K]3 years ago
6 0
First you subtract 3 from both sides. 3-3 and 7-3, that cancels out 3 which leaves you with r>4.


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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
Hunter-Best [27]

Answer:

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
What is the measure of angle c in degrees? *<br> 150<br> 30<br> 90<br> 60
Dmitry [639]

Answer:

Option (2)

Step-by-step explanation:

Measure of angle formed by two tangents from a point outside the circleis half the difference of the measures of the intercepted arcs.

From the figure attached,

m∠C = \frac{1}{2}[m(\text{major arc AB})-m(\text{minor arc AB)}]

        = \frac{1}{2}[(360-m\widehat{AB})-m(\widehat{AB})]

        = \frac{1}{2}[360-2m(\widehat{AB})]

        = 180-m\widehat{AB}

        = 180 - 150

        = 30°

Therefore, measure of angle C will be 30°.

Option (2) is the answer.

4 0
3 years ago
10. What is the distance between (8,7) and (3,-5)?
Anarel [89]

Answer:

distance between points=13 units

Step-by-step explanation:

distance between points=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

put (x_1,x_2)=(8,7) and (y_1,y_2)=(3,-5)

distance between points=\sqrt{(3-8)^2+(-5-7)^2}

distance between points=\sqrt{(-5)^2+(-12)^2}

distance between points=\sqrt{25+144}

distance between points=\sqrt{169}

distance between points=13 units answer

8 0
3 years ago
If f(x) = 3x + –, what is f(a+ 2)?
svetlana [45]

Answer:

C

Step-by-step explanation:

3 0
3 years ago
G=3t^2−5t+6<br><br> P=−8t^2+7t−9<br><br> G+P=
kotykmax [81]

Answer:

  -5t^2 +2t -3

Step-by-step explanation:

Collect terms in the sum:

  G+P = (3t^2 -5t +6) +(-8t^2 +7t -9) = (3-8)t^2 +(-5+7)t +(6-9)

  = -5t^2 +2t -3

3 0
3 years ago
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