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Tasya [4]
3 years ago
8

A rectangle has a perimeter of 2x^2+8x-10 the length of the rectangle is 3x-1. What is the width as an expression

Mathematics
1 answer:
4vir4ik [10]3 years ago
4 0

Answer:   The width is x^{2} + 1x -4

Step-by-step explanation:

We know to find the perimeter we have to add the distance around the rectangle.The distance can also be sought as 2 times the length  plus times the width.

So as a formula is like  P = 2l + 2w  where P is the perimeter.

We are given the perimeter so we can plot it into the formula and also plot in the length because it says the length is 3x -1  

2x^{2}+8x - 10 = 2(3x -1) + 2w    Now we have to solve for w .Break it down

(2x^{2} + 8x -10) = (6x -2 )+ 2w       subtract 6x - 2 from both sides  

(2x^{2} + 8x -10) - (6x -2) = 2w        

(  2x^{2} + 2x -8) = 2w  now divide both sides by 2  

\frac{2x^{2} +2x-8 }{2}  = w    One the left side factor the numerator  

\frac{2(x^{2} +1x-4)}{2}   = w   Now multiply both sides by 2  

  w =( x^{2} + 1x-4 )

The width is x^2 + 1x -4

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Explanation:
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4) The quantities x and y are in proportion x 4 30 8 __b__ a) b) c) y 6 45 __a__ 15 Find the value of a and b. Find the constant
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Question:

The quantities x and y are in proportion

x      y

4      6

30   45

8      b

a      15

(a) Find the values of a and b.

(b) Find the constant of variation. Is it direct variation or inverse variation?

Answer:

a = 10 and b = 12

Constant of variation is 1.5

Direct Variation

Step-by-step explanation:

Solving (a): The values of a and b

First, we determine the equation that relates x and y

From the table, we have:

(x_1,y_1) = (4,6)

(x_2,y_2) = (30,45)

The slope (m) is:

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{45 - 6}{30 -4}

m = \frac{39}{26}

m = 1.5

The equation is then calculated using:

y - y_1 = m(x - x_1)

This gives:

y - 6 = 1.5(x - 4)

y - 6 = 1.5x - 6

y = 1.5x

Solving for the value of b

From the table: x = 8, y = b

Substitute these values in y = 1.5x

b = 1.5 * 8

b = 12

Solving for the value of a

From the table: x = a, y = 15

Substitute these values in y = 1.5x

15 = 1.5 * a

Solve for a

a = \frac{15}{1.5}

a = 10

Solving (b): The constant of variation.

This has been solved in (a) above as:

m = 1.5

Direct or Inverse?

From the given table, we notice that y increases as x increases and y decreases as x decreases.

<em>This shows direct variation</em>

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