All categories

4 years ago

Which congruence theorems can be used to prove ΔEFG ≅ ΔJHG? Select two options.

Mathematics

2 answers:

mezya [45]4 years ago

5 0

<h2><u><em>Answer: </em></u></h2><h2><u><em> </em></u></h2>

ASA and AAS

<h2><u><em>Step-by-step explanation: </em></u></h2>

We do not know if these are right triangles; therefore we cannot use HL to prove congruence.

We do not have 2 or 3 sides marked congruent; therefore we cannot use SSS or SAS to prove congruence.

We are given that EF is parallel to HJ. This makes EJ a transversal. This also means that ∠HJG and ∠GEF are alternate interior angles and are therefore congruent. We also know that ∠EGF and ∠HGJ are vertical angles and are congruent. This gives us two angles and a non-included side, which is the AAS congruence theorem.

Since EF and HJ are parallel and EJ is a transversal, ∠JHG and ∠EFG are alternate interior angles and are congruent. Again we have that ∠EGF and ∠HGJ are vertical angles and are congruent; this gives us two angles and an included side, which is the ASA congruence theorem.

choli [55]4 years ago

4 0

Answer:

ASA

Step-by-step explanation:

You might be interested in

Find the area of a square whose diagonal length is 32 CM

BigorU [14]

Answer:

512cm^2

Step-by-step explanation:

Let's imagine cutting the square down that diagonal. Now, we have two isosceles right triangles with a hypotenuse with length 32cm. Let's take one of those triangles for now and focus on it. Let's give the one of the legs of a triangle some length x. Since both legs are the same length, by the Pythagorean theorem:

$x^2+x^2=32^2\\\\2x^2=1024\\\\x^2=512\\\\x=\sqrt{512}$

Since this leg makes up one side of the square, we can use it to calculate the area of the square, which is just the side length squared:

$A=(\sqrt{512})^2 = 512$

7 0

3 years ago

Suppose <br> f '(x) = xe^−x^2

iogann1982 [59]

<h3>Answers:</h3>

(a) The function is increasing on the interval (0, infinity)
(b) The function is decreasing on the interval (-infinity, 0)

=======================================================

Explanation:

You should find that the derivative is entirely negative whenever x < 0. This suggests that the function f(x) is decreasing on this interval. So that takes care of part (b).

The interval x < 0 is the same as -infinity < x < 0 which then translates to the interval notation (-infinity, 0)

Similarly, you should find that the derivative is positive when x > 0. So the function is increasing on the interval (0, infinity)

6 0

3 years ago

yler bought snacks for his team's practice. He bought a bag of oranges for $1.94 and a 24-pack of juice bottles. The total cost

Sloan [31]

Answer:

1.94 + 24x = 43.22 ;

1.72

Step-by-step explanation:

Given :

Cost of orange = 1.94

Pack of juice = 24

Total amount spent = 43.22

Cost of orange + (number of juice * cost per bottle) = total amount spent

Let cost per bottle = x

1.94 + (24 * x) = 43.22

1.94 + 24x = 43.22

24x = 43.22 - 1.94

24x = 41.28

x = 41. 28 / 24

x = 1.72

3 0

3 years ago

Solve for x in the given equation: 1/5 x = 2/5 What would be the inverse operation you would use to solve for x?

Sindrei [870]

1/5x = 2/5
x = 2/5 * 5/1 (5/1 is the inverse of 1/5)
x = 2

6 0

2 years ago

Two trains leave towns 912 kilometers apart at the same time and travel toward each other. One train travels 12

Lady bird [3.3K]

Answer:

Step-by-step explanation:

Remark

The two trains are travelling towards each other. That means that their total distance = 912 km. Neither one has gone that distance by itself. The effect this has on the question is that you add the two rates multiplied by time.

Givens

r1 = x

r2 = x + 12

t = 3 hours

d = 912 km

Equation

d = r * t

r1 * t + r2 * t = 912

Solution

3x + 3*(x + 12) = 912 Remove the brackets

3x + 3x + 36 = 912 Combine like terms

6x + 36 = 912 Subtract 36 from both sides

6x = 876 Divide both sides by 6

6x/6 = 876/6

x = 146 km/h

Answer

Slow train = 146 km/hr

Fast train = 146 + 12 = 158 km/hr

5 0

3 years ago