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adoni [48]
3 years ago
15

The fourth and fifth grade classes at James Madison Elementary School are going on a field trip. There are 87 students in fourth

grade, 96 students in the fifth grade, and 8 teachers. Each bus can hold up to 26 people. How many buses are needed to hold all the students and teachers?
Mathematics
1 answer:
Anna11 [10]3 years ago
6 0

Answer:

about 7

Step-by-step explanation:

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The third term of an arithmetic sequence is equal to 9 and the sum of the first 8 term is 42. Find the first term and the common
zloy xaker [14]

Answer:

The first term is 14

The common difference is -2.5

Step-by-step explanation:

we know that

The rule to calculate the an term in an arithmetic sequence is

a_n=a_1+d(n-1)

where

d is the common difference

a_1 is the first term

we have that

The third term of an arithmetic sequence is equal to 9

so

a_3=9

n=3

substitute

9=a_1+d(3-1)

9=a_1+2d ----> equation A

The rule to find the sum of the the first n terms of the arithmetic sequence is equal to

S=\frac{n}{2} [2a_1+(n-1)d]

we have

The sum of the first 8 term is 42

so

S=42

n=8

substitute

42=\frac{8}{2} [2a_1+(8-1)d]

42=4[2a_1+7d]

10.5=2a_1+7d ----> equation B

Solve the system of equations

9=a_1+2d ----> equation A

10.5=2a_1+7d ----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

the solution is (14,-2.5)

see the attached figure

therefore

a_1=14\\d=-2.5

The first term is 14

The common difference is -2.5

8 0
3 years ago
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