The length of a rectangle is 9.7 cm more than 4 times the width. If the perimeter of the rectangle is 91.4 cm, what are its dimensions?

Answer 1

Let the width of the rectangle be x cm.
The length of the rectangle is 9.7 cm more than 4 times the width, so it is (4x + 9.7) cm.
The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
Plugging in the given values, we get 91.4 = 2((4x + 9.7) + x).
Expanding the equation, we get 91.4 = 2(5x + 9.7).
Simplifying further, we get 91.4 = 10x + 19.4.
Subtracting 19.4 from both sides, we get 72 = 10x.
Dividing both sides by 10, we get x = 7.2.
So, the width of the rectangle is 7.2 cm.
The length of the rectangle is 4(7.2) + 9.7 = 28.8 + 9.7 = 38.5 cm.
Therefore, the dimensions of the rectangle are 7.2 cm by 38.5 cm.

Answer 2

Solve the system using elimination.5x + 4y = 123x – 3y = 18

Answer 3

To solve the system using elimination, we'll multiply the second equation by 5 to make the coefficients of x in both equations equal:

5(3x - 3y) = 5(18)
15x - 15y = 90

Now, we can subtract the first equation from the second equation to eliminate x:

(15x - 15y) - (5x + 4y) = 90 - 12
15x - 5x - 15y - 4y = 78
10x - 19y = 78

Now, we have a new equation: 10x - 19y = 78.

Multiplying the first equation by 3, we get:

3(5x + 4y) = 3(123)
15x + 12y = 369

We can subtract the equation 10x - 19y = 78 from the equation 15x + 12y = 369 to eliminate x again:

(15x + 12y) - (10x - 19y) = 369 - 78
15x - 10x + 12y + 19y = 291
5x + 31y = 291

Now, we have a new equation: 5x + 31y = 291.

We now have a system of equations:

10x - 19y = 78
5x + 31y = 291

We can multiply the first equation by 5 and the second equation by 10 to further eliminate x:

5(10x - 19y) = 5(78)
50x - 95y = 390

10(5x + 31y) = 10(291)
50x + 310y = 2910

Now, we can subtract the equation 50x - 95y = 390 from the equation 50x + 310y = 2910 to eliminate x once more:

(50x + 310y) - (50x - 95y) = 2910 - 390
50x - 50x + 310y + 95y = 2520
405y = 2520

Dividing both sides by 405, we get:

y = 2520/405
y = 6.22

Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the second equation:

3x - 3(6.22) = 18
3x - 18.66 = 18
3x = 18 + 18.66
3x = 36.66
x = 36.66/3
x = 12.22

Therefore, the solution to the system of equations is x = 12.22 and y = 6.22.

Answer 4

Solve the system by substitution.{−4.5x−2y=−12.53.25x−y=−0.75 show little work

Answer 5

From the first equation, we have -4.5x - 2y = -12.5.
Solving for x, we get x = (12.5 - 2y) / -4.5.

Substituting this value of x into the second equation, we have:
3.25[(12.5 - 2y) / -4.5] - y = -0.75.

Now we can solve for y:
3.25(12.5 - 2y) - 4.5y = -0.75.
40.625 - 6.5y - 4.5y = -0.75.
40.625 - 11y = -0.75.
-11y = -0.75 - 40.625.
-11y = -41.375.
Dividing both sides by -11, we get:
y = -41.375 / -11.
y ≈ 3.761.

Substituting this value of y back into x = (12.5 - 2y) / -4.5, we have:
x = (12.5 - 2(3.761)) / -4.5.
x = (12.5 - 7.522) / -4.5.
x = 4.978 / -4.5.
x ≈ -1.106.

Therefore, the solution to the system of equations is x ≈ -1.106 and y ≈ 3.761.