For what values of x and y are the triangles to the right congruent by HL?

Answers

Answer 1

Answer:

Based on the Hypotenuse-LengthTheorem of Congruence (HL), the values of x and y that will make both right triangles congruent are:

x = 8
y = 4

Recall:

Two right triangles are congruent to each other by the Hypotenuse-Length Congruence Theorem (HL) if the hypotenuse length and one leg of a right triangle is congruent to the hypotenuse length and leg of the other right triangle.

Thus, for both right triangles to be congruent, it means that their hypotenuse and one of their corresponding legs must be equal to each other.

Use this to create two equations and solve to get the value of x and y.

Equal Hypotenuse:

$x + 4 = 3y\n\nx + 4 - 4 = 3y - 4\n\nx = 3y - 4$ (eqn. 1)

Equal legs:

$x = y + 4\n\n$ (eqn. 2).

Find the value of y, by substituting x = (y + 4) into eqn. 1.

$x = 3y - 4$ (eqn. 1)

Substitute

$y + 4 = 3y - 4\n\ny - 3y = -4 - 4\n\n-2y = -8\n\ny = 4$

Find the value of x, by substituting y = 4 into eqn. 2.

$x = y + 4\n\nx = 4 + 4\n\nx = 8$

Therefore, based on the Hypotenuse-LengthTheorem of Congruence (HL), the values of x and y that will make both right triangles congruent are:

x = 8
y = 4

Learn more here:

brainly.com/question/9525809

Answer 2

Answer:

Answer:

x = 8 and y = 4

Step-by-step explanation:

For congruency the hypotenuse and a leg must be congruent, that is

3y = x + 4 → (1) ( Equating the hypotenuse )

x = y + 4 → (2) ( equating corresponding legs )

Substitute x = y + 4 into (1)

3y = y + 4 + 4

3y = y + 8 ( subtract y from both sides )

2y = 8 ( divide both sides by 2 )

y = 4

Substitute y = 4 into (2)

x = 4 + 4 = 8

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a rectangle is 22 feet long and has a perimeter of 56 feet what is the width of this rectangle And how do I show work if I’m showing my kid

Answers

Answer:

Step-by-step explanation:

(22+x)2=56

22+x=28

x=6

How many times does 72 go into 533

Answers

The answer is 7.40277777778

Six friends share 2 pizzas equally how much of a pizza does each friend get

Answers

6/2=3...
They each get 1/3 of the pizza.
hope this helps.

so if there are six people and they buy two pizza pies. You will have to divide 6 and 2 and get three.

The floor of a hall has an area of 48 dm.The floor is to be tiled by triangular tiles.of sides 20 cm,30 cm and 40 cm. Find the total cost of tiles if cost of each tile is Rs.200.

Answers

The triangle is an obtuse triangle. No sides are equal.
convert cm to dm

1 dm = 10 cm

side a: 20 cm ⇒ 20cm * 1dm/10cm = 20dm/10 = 2 dm
side b: 30 cm ⇒ 30cm * 1dm/10cm = 30dm/10 = 3 dm
side c: 40 cm ⇒ 40cm * 1dm/10cm = 40dm/10 = 4 dm

We need to get the area of a triangle, but first we need to solve for its height using Heron's formula

s = (a+b+c)/2 = (2+3+4)/2 = 9/2 = 4.5
Area = √(s(s-a)(s-b)(s-c)
h3/2 = √4.5(4.5-2)(4.5-3)(4.5-4)
h3/2 = √4.5(2.5)(1.5)(0.5)
h3/2 = √8.44
h3/2 = 2.91
h = (2.91*2)/3
h = 1.94

A = hb/2 = (1.94*3)/2 = 5.82/2 = 2.91 dm²

48 dm² / 2.91dm² = 16.5 or 17 tiles needed

17 x Rs200 = Rs3,400 is the total cost

A 100-pound person on Earth would weigh about 4 x 4 x 4 x 4 pounds on Jupiter. Evaluate the expression to determine how much a 100-pound person would weigh on Jupiter.

Answers

Answer:

$\text{Weight on Jupiter} = (25)/(64)* (\text{Weight on earth})$

Step-by-step explanation:

A 100 pound person on earth weigh 4×4×4×4 pounds on Jupiter.

4×4×4×4 pounds weight = 256 pounds

Therefore ratio of the weights on earth and Jupiter = 100 : 256

= 25 : 64

Let a person weigh x pounds on Earth therefore the expression which represents the weight of the person on Jupiter will be

$\frac{\text{Weight on Jupiter}}{\text{Weight on Earth}}=(25)/(64)$

$\text{Weight on Jupiter} = (25)/(64)* (\text{Weight on earth})$

he would weigh 25,600 pounds on Jupiter
100 * 4*4*4*4 gives you 25,60p

Can someone explain the steps of how to solve number 13 please!!

Answers

Answer:

-5/10

Step-by-step explanation:

change -4/5 to -8/10 so the denominator is the same.

since its minus negative the negative sign can be changed to a plus sign, so -8/10+3/10=-5/10