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neonofarm [45]
2 years ago
10

A ​30-inch board is to be cut into three pieces so that the second piece is 4 times as long as the first piece and the third pie

ce is 5 times as long as the first piece. If x represents the length of the first​ piece, find the lengths of all three pieces.
Mathematics
1 answer:
Arte-miy333 [17]2 years ago
6 0

Answer:

Step-by-step explanation:

Length of:

First piece = x

Second piece = 4x

Third piece = 5x

Equation: 30 = 4x + 5x + x

Solving the Equation:

10x = 30  

x = 3

Lengths of:

First piece = 3 inches

Second piece = 12 inches

Third piece = 15 inches

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jeka94

Answer:

The rental cost of one movie is $2.25 and the rental cost of one video game is $6.25

Step-by-step explanation:

Let the rental cost of 1 movie be m.

Let the rental cost of 1 video game be v.

One month, Tammy rented 2 movies and 6 video games for a total of $42. This means that:

2m + 6v = 42 ________ (1)

The next month she rented 5 movies and 3 video games for a total of $30. This means that:

5m + 3v = 30 _________(2)

We now have two simultaneous equations:

2m + 6v = 42 ________ (1)

5m + 3v = 30 _________(2)

Multiply (2) by 2, and we have:

2m + 6v = 42 __________ (1)

10m + 6v = 60 _________ (3)

Subtract (1) from (3):

 10m + 6v = 60

-<u> 2m + 6v = 42</u>

 <u>  8m     =     18</u>

=> m = 18 / 8

m = $2.25

Put the value of m back in (1):

2(2.25) + 6v = 42

4.5 + 6v = 42

=> 6v = 42 - 4.5 = 37.5

v = 37.5 / 6

v = $6.25

Therefore, the rental cost of one movie is $2.25 and the rental cost of one video game is $6.25

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Answer:

-7, -8 , -9 and -10 are such four integers.

Step-by-step explanation:

Let the first integer = k

So, the next three consecutive integers are ( k+1), ((k + 1) + 1)  and (((k + 1) + 1) +1)

or, k , (k +1), (k +2) and (k +3) are four consecutive integers.

Now, their sum is -34.

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