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

So, x=3 and y=2 make these triangles congruent.

So, the correct choice is 3. x = 3, y = 2.

7 0

3 years ago

Write the numbers -|-2|, -(8), |-3|, -7 in order from smallest to largest.

andreyandreev [35.5K]

Answer:

The order is -(8), -7, -|-2|, |-3|

Step-by-step explanation:

Absolute value makes the number positive. Therefore -8,-7 and then -|-2|, and finally -3 absolute value makes it positive.

6 0

3 years ago

Tan θ sin θ + sin θ = 0 . Solve the given equation.

VashaNatasha [74]

Here's a PDF file with the solution... Powered by Wolfram Mathematica

Download pdf

4 0

3 years ago

1/2 log2x=3log23 rewrite with out using logarithmic

Brums [2.3K]

Answer:

729

Step-by-step explanation:

$\frac{1}{2}log_{2}x=3log_{2}3 \\$

$log_{2}\sqrt{x} =log_{2}3^{3}$

$\sqrt{x} =27 \\$

x=27²=729

7 0

3 years ago