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3 years ago

50 POINTS! The fifth term of an arithmetic sequence is 11 and the tenth term is 41. What is the first term?

Mathematics

2 answers:

marshall27 [118]3 years ago

8 0

Answer:

Step-by-step explanation:

The fifth term:

$a_5=a+4d = 11$

The 10th term:

$a_{10}=a+9d=41$

Subtract side-by-side and find d:

9d - 4d = 41 - 11
5d = 30
d = 6

Find the first term:

a = 11 - 4*6
a = 11 - 24
a = - 13

Oxana [17]3 years ago

4 0

The common difference d is

(41–11) / (10–5) = 6.

The first term is

11 - 6(5–1) = -13.

so , the first term is -13 

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denis23 [38]

Answer:

$B = 325$

Step-by-step explanation:

Given

Total = 900

Singing = 600

Dancing = 500

None = 125

Required

Determine the number of students that participate in both

Representing; Singing with S, Dancing with D, Both singing and dancing with B and None with N;

In Set Notation;

$Total = (S - B) + (D - B) + N + B$

Substitute 900 for Total, 600 for S, 500 for D and 125 for N

$900 = (600 - B) + (500 - B) + 125$

Open Brackets

$900 = 600 - B + 500 - B + 125 + B$

Collect Like Terms

$900 = 600 + 500 + 125 - B - B + B$

$900 = 1225- B - B + B$

$900 = 1225- B$

Collect Like Terms

$900 - 1225 = -B$

$-325 = -B$

Multiply both sides by -1

$-1 * -325 = -B * -1$

$325 = B$

Reorder

$B = 325$

Hence, the number of students that do not participate in both is 325

4 0

3 years ago

If you double a number and then add 1616, you get two fifths 2 5 of the original number. what is the original number?

Scilla [17]

Let the original number be x.

Acc. to the question,
2x+1616=(2/5)x
or, 10x+8080=2x
or, 10x-2x= -8080
or, 8x= -8080
or, x= -8080/8
or, x = -1010

Therefore, the original number is -1010

4 0

3 years ago

What’s missing reason in the proof

svetlana [45]

Answer:

SSS congruence theorem.

Step-by-step explanation:

We have proved that the 3 sides of the triangles are congruent.

6 0

3 years ago

Can you solve it, please

weeeeeb [17]

Answer:20

Step-by-step explanation:

3.1 *4.2=13.02 12.4*21=260.4 260.4/13.02=20

8 0

2 years ago

Read 2 more answers

Q.1 Thee are five girls and three boys in a group. The teacher chose one person at random. How could the teacher make a random c

Hatshy [7]

Answer:

Q1: She can write names of each Student on separate Papers and choose one Randomly, the Result may be 5:3 Girls to Boys

Q2: 75/100

4 0

3 years ago