According to the HL theorem if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another 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)

Now we will plug the value y+1 of equation 1 in equation 2.

2x+3 = 3y+3

2(y+1)+3=3y+3

2y+2+3=3y+3

2y+5=3y+3

Now combine the like terms:

5-3=3y-2y

2=y

y=2

Now plug the value y=2 in equation 1.

x=y+1

x=2+1

x=3

Thus the values of(x.y) are{(2,3)}

Therefore the correct option is x=3 , y=2 .....

3 0

3 years ago

Mr.Marquez had 123 eggs in his refrigerator in his restaurant.He put 32 more cartoons of eggs in the refrigerator.Each cartoon c

skad [1K]

Answer:

2790

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

The rectangle has an area of x^2-7x+10 square meters and a width of x−5 meters. What expression represents the length of the rec

Katyanochek1 [597]

Answer:

length = x - 2

Step-by-step explanation:

Area (A) of rectangle = lw ( l is the length and w the width )

A = x² - 7x + 10 = (x - 2)(x - 5) ← in factored form

l = $\frac{A}{w}$ = $\frac{(x-2)(x-5)}{x-5}$

cancel the factor (x - 5) on the numerator/ denominator, hence

l = x - 2

8 0

3 years ago

I've been on vacation this week and my math teacher just gave me a packet of makeup work to do. a lot of them are questions like

adelina 88 [10]

To visualize better, look at it like this:

$\frac{3r^3}{2r}$

First, see if you can simplify 3/2. You can't, so leave it like that.

The rule for exponents is you subtract the exponent from the bottom (r) from the exponent on the top ( $r^3$ )

$r^3 - r^1 = r^2$

Put that on the top, and you get

$\frac{3r^2}{2}$

7 0

3 years ago