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Anastaziya [24]
3 years ago
11

The length of a rectangle is 5 in longer than its width.

Mathematics
1 answer:
NeTakaya3 years ago
5 0

Answer:

Length = 21

Width = 16

Step-by-step explanation:

We know that the formula for perimeter is:

P=2W+2L

And we also know that:

L=W+5

So then we put all that we know in the formula:

74=2W+2(W+5)

Now we expand the brackets and do some algebra:

74=4W+10 (-10)

64=4W (÷4)

16=W

Now that we know the width we can pop that into the length equation:

L=16+5

L=21

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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
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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

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so

a_3=9

n=3

substitute

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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
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