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3 years ago

Tell whether the equation has one, zero, or infinitely many solutions.

1 answer:

4 0

−(8x + 1) − 3 = −7x − (x + 4)
-8x - 1 - 3 = -7x - x - 4
-8x - 4 = -8x - 4
0 = 0

answer
infinitely many solutions.

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Prove that the triangle EDF is isosceles. Give reasons for your answer.

Gekata [30.6K]

Answer:

$\triangle EDF$ is isosceles.

Step-by-step explanation:

Please have a look at the attached figure.

We are given the following things:

$\angle EDF = y$

$\text{External }\angle DFG = 90 +\dfrac{y}{2}$

Let us try to find out $\angle E$ and $\angle DFE$ . After that we will compare them.

Finding  $\angle DFE$ :

Side EG is a straight line so $\angle GFE = 180$

$\angle GFE$ is sum of internal $\angle DFE$ and external $\angle DFG$

$\angle GFE = 180 = \angle DFE + \angle DFG\\\Rightarrow 180 = \angle DFE + (90+\dfrac{y}{2})\\\Rightarrow \angle DFE = 180 - 90 - \dfrac{y}{2}\\\Rightarrow \angle DFE = 90 - \dfrac{y}{2} ....... (1)$

Finding  $\angle E$ :

Property of external angle: External angle in a triangle is equal to the sum of two opposite internal angles of a triangle.

i.e. external $\angle DFG$ = $\angle E + \angle EDF$

$\Rightarrow 90+\dfrac{y}{2} = \angle E + y\\\Rightarrow \angle E = 90+\dfrac{y}{2} -y\\\Rightarrow \angle E = 90-\dfrac{y}{2} ....... (2)$

Comparing equations (1) and (2):

It can be clearly seen that:

$\angle DFE = \angle E =90-\dfrac{y}{2}$

The two angles of $\triangle EDF$ are equal hence $\triangle EDF$ is isosceles.

8 0

3 years ago

The theory that it is reasonable to chose the simpler theory when choosing between two competing theories of equal explanatory v

Vesnalui [34]

Answer:

Occam’s razor theory.

Step-by-step explanation:

This theory is known as Occam’s razor theory.

It's a theory based on the principle whereby we give precedence to simplicity. It states that out of two competing theories, the one with the simpler explanation of an object should be embraced over the other. The reason is that the philosopher William of Ockham said that "objects are not meant to be multiplied beyond absolute necessity.”

This definition resonates with what is explained in the question.

Thus, the theory is as explained.

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3 years ago

HELP ME I NEED HELP QUICK

vova2212 [387]

Answer:

Step-by-step explanation:

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3 years ago

What is the mode of the data?

Luden [163]

Answer:

Step-by-step explanation:

Mode means most, so it's the number you see most.

5 0

3 years ago

What are the coordinates of the endpoints of the midsegment for △JKL that is parallel to KL⎯⎯⎯⎯⎯? Enter your answers in the boxe

algol [13]

The points you are looking for are the midpoints of segments JL and JK.
J(-2, -1), K(4, -5), L(0, -5)

The midpoint of segment JL is

(-2 + 0)/2, (-1 + (-5))/2) = (-2/2, -6/2) = (-1, -3)

The midpoint of segment JK is

(-2 + 4)/2, (-1 + (-5))/2) = (2/2, -6/2) = (1, -3)

Answer: The coordinates are (-1, -3), (1, -3)

6 0

3 years ago

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