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viva [34]
3 years ago
12

The length of a rectangle is 3 centimeters less than twice the width. If the perimeter of the rectangle is 24 centimeters, find

its dimensions.
Mathematics
1 answer:
yarga [219]3 years ago
3 0

Answer:

Width = 5 cm

Length = 7 cm

Step-by-step explanation:

Width = w

Length = 2w - 3

Perimeter = 24 cm

2* (length + width ) = 24

2*(2w-3 +w) = 24

2*(3w -3) = 24

3w - 3 = 24/2

3w - 3 = 12

3w = 12+ 3

3w = 15

w = 15/3

w = 5cm

Length = 2w - 3 = 2*5 - 3 = 10-3 = 7 cm

length = 7 cm

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Anyone can help me solve this equation using cross multiplying
Natali5045456 [20]

9514 1404 393

Answer:

  x = 1 or 5

Step-by-step explanation:

The notion of "cross-multiplying" is the idea that the numerator on the left is multiplied by the denominator on the right, and the numerator on the right is multiplied by the denominator on the left. This looks like ...

  \displaystyle \frac{x-1}{7}=\frac{2x-2}{3x-1}\ \longrightarrow\ (x-1)(3x-1)=(7)(2x-2)

Then the solution proceeds by eliminating parentheses, and solving the resulting quadratic equation.

  3x^2-4x+1=14x-14\\\\3x^2-18x+15=0\qquad\text{subtract $14x-14$}\\\\x^2-6x+5=0 \qquad\text{divide by 3}\\\\(x-1)(x-5)=0\qquad\text{factor}\\\\x\in\{1,5\}

_____

<em>Comment on "cross multiply"</em>

Like a lot of instructions in Algebra courses, the idea of "cross multiply" describes <em>what the result looks like</em>. It doesn't adequately describe how you get there. The <em>one and only rule</em> in solving Algebra problems is "<em>whatever is done to one side of the equation must also be done to the other side of the equation</em>." If you multiply one side by one thing and the other side by a different thing, you are violating this rule.

What looks like "cross multiply" is really "<em>multiply by the product of the denominators</em> and cancel like terms from numerator and denominator." Here's what that looks like with the intermediate steps added.

  \displaystyle \frac{x-1}{7}=\frac{2x-2}{3x-1}\\\\\frac{x-1}{7}\times7(3x-1)=\frac{2x-2}{3x-1}\times7(3x-1)\\\\(x-1)(3x-1)=(2x-2)(7)\qquad\textit{looks like}\text{ cross multiply}

8 0
2 years ago
The equation x+53=15 can be solved by performing two operations on both sides.
Wewaii [24]
Hey!


You're right! This equation can definitely be solved by performing two operations on both sides. Let me show you how it's done.

First, let's write out our equation.

<span><em>Original Equation :</em>
</span>x + 53 = 15

Now that that's done, we'll be performing two operations on both sides. The operation we'll want to do is subtracting both sides of the equation by 53. We do this to get x on its own.

<em>Original Equation :</em>
x + 53 = 15

<em>New Equation {Added Subtract 53 to Both Sides} :</em>
x + 53 - 53 = 15 - 53

Now we have to solve the equation. Let's do the left side first.

<em>Left Side of the Equation :</em>
x + 53 - 53 

<em>Left Side of the Equation {Solved} :</em>
x

Now, we'll solve the right side of the equation.

<em>Right Side of the Equation :</em>
15 - 53

<em>Right Side of the Equation {Solved} :</em>
-38

Now we can put both solutions to both sides of the equation together.

<em>New Equation :</em>
x = -38

Since this cannot be simplified any farther, this is our final answer. And that's it!

<em>So, now we know that in the equation x + 53 = 15,</em>  x = -38

Hope this helps!


- Lindsey Frazier ♥
3 0
3 years ago
Se tiene 2 metros de tela y se corta el 85% para hacer cortinas el 50% del resto para hacer las tiras que la sujetan.¿cuantos se
zavuch27 [327]

For this case we have the following statement:

<em>"You have 2 meters of fabric and you cut 85% to make curtains, 50% of the rest to make the strips that hold it. How many centimeters of fabric were left?"</em>

So, we have:

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x ----------------------> 85%

Where "x" represents the amount of fabric meters equivalent to 85%.

x = \frac {85 * 2} {100}\\x = 1.7

Thus, 1.7 meters of fabric were used to make curtains.

There are 0.3 meters of fabric left, of which half (50%) is used to make the strips that hold the curtain. That is to say:

\frac {0.3} {2} = 0.15m

Thus, 0.15 meters of fabric remain.

0.15 m * \frac {100 cm} {1 m} = 15\ centimeters.

Thus, 15 cm of fabric remain

Answer;

15 cm

3 0
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A truck can travel 1200 miles on 80 gallons of gasoline. how far can it travel on 240 gallons of gasoline ? Show your work
pogonyaev

Answer:

3600 miles on 240 gal

Step-by-step explanation:

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7 0
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charle [14.2K]

Answer:

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Step-by-step explanation:

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2 years ago
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