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a_sh-v [17]
3 years ago
11

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:

  • -13

Step-by-step explanation:

<u>The fifth term:</u>

  • a_5=a+4d = 11

<u>The 10th term:</u>

  • a_{10}=a+9d=41

<u>Subtract side-by-side and find d:</u>

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

<u>Find the first term:</u>

  • a = 11 - 4*6
  • a = 11 - 24
  • a = - 13
Oxana [17]3 years ago
4 0

<em><u>The common difference d is </u></em>

  • (41–11) / (10–5) = 6.

<em><u>The first term is</u></em>

  • 11 - 6(5–1) = -13.

<em>so , the first term is -13 </em>

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6
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

<em>Hence, the number of students that do not participate in both is 325</em>

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
2 years ago
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