According to HL theorem if one leg and hypotenuse of one right triangle are equal to one leg and hypotenuse of other right triangle, then the triangles are congruent.
By using this theorem we can set up the system of equations as follows:
x=y+1 ...(1)
2x+3= 3y + 3 ..(2)
By using equation (1) next step is to plug in y+1 for x in equation (2). So,
2 ( y + 1) + 3 = 3y + 3
2y + 2 + 3 = 3y + 3 By using distribution property.
2y + 5 = 3y + 3
2y + 5 - 5 = 3y + 3 - 5 Subtract 5 from each side.
2y = 3y - 2
2y - 3y = -2 Subtract 3y from each sides.
-y = -2
So, y=2
Next step is to plug in y=2 in equation (1) to get the value of x. Hence,
x= 2+1
=3
So, x=3 and y=2 make these triangles congruent.
So, the correct choice is 3. x = 3, y = 2.
The length and the width of the rectangle are 20 and 14 inches respectively
<h3>How to find the length and width?</h3>
The given parameters are:
Length = 6 + Width
Perimeter = 68 inches
The perimeter of a rectangle is calculated as:
Perimeter = 2 * (Length + Width)
So, we have:
2 * (Length + Width) = 68
Divide both sides by 2
Length + Width = 34
Substitute Length = 6 + Width in Length + Width = 34
6 + Width + Width = 34
Evaluate the like terms
2 * Width = 28
Divide both sides by 2
Width = 14
Substitute Width = 14 in Length = 6 + Width
Length = 6 + 14
Evaluate
Length = 20
Hence, the length and the width of the rectangle are 20 and 14 inches respectively
Read more about perimeter at:
brainly.com/question/24571594
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The answer would be:
6x - 7
I hope this helped you,
Have a great day
The resulting function g(x) = (x-5)^3 + 3 shows a horizontal translation to the right by 5 units and vertical translation up by 3 units
<h3>Translation of functions</h3>
Quadratic functions are functions that has a leading degree of 2.
Given the parent function as shown:
f(x) = x^3
The resulting function g(x) = (x-5)^3 + 3 shows a horizontal translation to the right by 5 units and vertical translation up by 3 units
Learn more on translation here; brainly.com/question/12861087
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