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2 years ago

The length of a rectangle is 3 m longer than its width.

Mathematics

1 answer:

Veseljchak [2.6K]2 years ago

5 0

Step-by-step explanation:

With this question ,

The length of the rectangle is 3m longer than it's width=3 +w

then the width =w

therefore perimeter= 2L +2w

34= 2(3+w) +2w

34= 6+2w +2w

34-6 = 4w

28=4w

7= w

Area= Length x breadth

Area = (7+3) x7

Area= 10 x7

Area= 70cm square

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Shelley has a collection of dimes, nickels and quarters that is worth $5.25. There are a total of 48 coins. If there are 7 more

Mumz [18]

Answer:

25 dimes

Step-by-step explanation:

Given

Coins: Nickels (N), Quarters (Q) , and Dimes (D)

$0.05 = 1 nickel, $0.10 = 1 dime and $0.25 = 1 quarter

So, the amount implies:

$0.05N + 0.10D + 0.25Q = 5.25$

The number of coin implies:

$N + D + Q = 48$

and

$N = 7 + Q$

Required

Determine the number of Dimes

$0.05N + 0.10D + 0.25Q = 5.25$

$N + D + Q = 48$

$N = 7 + Q$

Substitute 7 + Q for N in the first and second equation

$0.05N + 0.10D + 0.25Q = 5.25$

$0.05(7 + Q) + 0.10D + 0.25Q = 5.25$

$0.35 + 0.05Q+ 0.10D + 0.25Q = 5.25$

Collect Like Terms

$0.10D + 0.25Q+0.05Q = 5.25 - 0.35$

$0.10D + 0.30Q = 4.90$ ----- (1)

$N + D + Q = 48$

$7 + Q + D + Q = 48$

Collect Like Terms

$D + Q + Q= 48 - 7$

$D + 2Q= 41$

Make Q the subject

$2Q = 41 - D$

$Q = \frac{41}{2} - \frac{D}{2}$

$Q = 20.5 - 0.50D$

Substitute 20.5 - 0.50D for Q in (1)

$0.10D + 0.30Q = 4.90$

$0.10D + 0.30(20.5 - 0.50D) = 4.90$

$0.10D + 0.30*20.5 - 0.30*0.50D = 4.90$

$0.10D + 6.15 - 0.15D = 4.90$

$0.10D - 0.15D = 4.90 - 6.15$

$-0.05D = -1.25$

Solve for D

$D = \frac{-1.25}{-0.05}$

$D = 25$

<em>Hence, there are 25 Dimes</em>

4 0

3 years ago

DELL LAPTOP WITH A RETAIL PRICE OF $525 FOR ONLY $393.75 what is the percent of change

Alex73 [517]

That is a 25% decrease.

8 0

3 years ago

Solve this system by substitution, y = 1 -3x - 4y = 14 *Remember to write your answer as a coordinate point (x, y). 1

Oksi-84 [34.3K]

Step1- substitute 1 into the y
= -3x-4 x 1=14
=-3x -4=14
=-3x=14+4
=-3x=18
X=18/-3
X=-6

8 0

3 years ago

The radius of a circle is 10. Using π, which equation expresses the ratio of the circumference of the circle to the circle's dia

Ede4ka [16]

Answer:

$\frac{circumference\ }{diameter}=\pi$

Step-by-step explanation:

Given that radius of the circle = 10

Using π, we need to find about which equation expresses the ratio of the circumference of the circle to the circle's diameter.

diameter of the circle = 2(radius) = 2(10)=20

circumference of the circle = 2 π r = 2 π (10) = 20 π

then ratio of the circumference of the circle to the circle's diameter is given by: $\frac{circumference\ }{diameter}=\frac{20\pi}{20}=\pi$ .

Hence required equation is $\frac{circumference\ }{diameter}=\pi$

3 0

4 years ago

What is a real-world situation that can be modeled by the equation | x - 14 | = 3?

Anna [14]

Absolute value is the distance/difference from a number to the standard number. In this case, the standard value is 14. Let's say 7-year-old Mike is riding his bike up and down the neighborhood street. Mike's house is located on 14th Avenue. Mom told Mike to stay within 3 blocks from home, so Mike can go as far north the 17th street and as far south to 11th street.
x-14=3 or x-14=-3
x=17 or x=11

I hope this makes sense to you.

5 0

3 years ago