3. the width and length of a rectangle are
consecutive integers. if the perimeter of
the rectangle is 142 inches, find the width
and length of the rectangle.

35 and 36

Step-by-step explanation:

If the smaller dimension is x, then the larger dimension is x + 1.  Therefore:

2x + 2(x + 1) = 142

2x + 2x + 2 = 142

4x = 140

x = 35

One dimension is 35, and the other dimension is 36.

The dimensions of the rectangle are 35 inches by 36 inches.

Step-by-step explanation:

If the length and width are consecutive integers and L=n, then W=n+1 assuming the width is larger.

We are given the perimeter is 142 inches so: 2L+2W=142.

Substituting L=n and W=n+1 we have:   2(n)+2(n+1)=142.

Let's solve it:

2(n)+2(n+1)=142

Distribute:

2n+2n+2=142

Combine like terms:

4n+2=142

Subtract 2 on both sides:

4n=140

Divide both sides by 4:

n=140/4

n=35

Since L=n, then the length is 35 inches.

Since W=n+1, then the width is 36 inches.

The dimensions of the rectangle are 35 inches by 36 inches.

y=3n + 1

step-by-step explanation:

this is wrong because it says the second number is one less and i added one instead

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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