Complete the equation of the line through (4,-8)(4,−8)

The life spans of elephants in a Columbus zoo are normally distributed. The average elephant lives 60 years: the standard deviat

Marta_Voda [28]

did u ever get the answer l need it

5 0

3 years ago

The figure below shows two triangles EFG and KLM.

grandymaker [24]

A right triangle is a triangle that has a right angle of 90 degrees. In this exercise, we have two of this type of triangles. To solve this problem, we will apply some properties of triangles, so:

1. Which step can be used to prove that triangle EFG is also a right triangle?

To prove this, we need to use Pythagorean Theorem. So, for triangle EGF, if the formula:

$c^{2}=a^{2}+b^{2}$

is true, then EFG is also a right triangle. The steps are:

Square a

Square b

Square c

If the sum of the square of a and the sum of the square of b equals the square of c, then this is a right triangle.

2. Prove that the sum of a and c is greater than b.

We need to prove that:

$a+c>b$

From trigonometry, we know that:

$a=c \times sin(\theta) \\ \\ b=c \times cos(\theta) \\ \\ where \ \theta=\angle EFG \\ \\$

By substituting these values in the previous inequality:

$c \times sin(\theta)+c>c \times cos(\theta) \\ \\ Since \ c>0 \\ \\ sin(\theta)+1>cos(\theta) \\ \\ 1>cos(\theta)-sin(\theta)$

Since $\theta$ is an angle greater than 0 and less than 90 degrees, $cos(\theta) \ and \ sin(\theta)$ are numbers between 0 (greater than) and 1. Therefore, this inequality is always true. So, the statement has been proved.

3. Prove that the sum of a and b is greater than c.

We need to prove that:

$a+b>c$

Applying the same reasoning as in 2:

$c \times sin(\theta)+c \times cos(\theta)>c \\ \\ Since \ c>0 \\ \\ sin(\theta)+cos(\theta)>1$

This inequality is always true. So, the statement has been proved.

4. Prove that triangles are congruent by SSS property and hence angle EGF is equal to angle KML.

SSS means that we know the three sides of the triangle and want to find the missing angles. For ΔEGF, we know the three sides, and for KML, since this is a right triangle KL = c, therefore the corresponding sides of these two triangles are equal. Accordingly, these two triangles are congruent by SSS and angle EGF is equal to angle KML.

5. Prove that the ratio of EF and KL is greater than 1 and hence the triangles are similar by AA postulate.

The ratio of EF and KL is:

$\frac{EF}{KL}$

The statement is true if and only if EF > KL. Then, according to AA postulate, two triangles are similar if they have two corresponding angles congruent. So:

EGF is congruent to KML and equals 90 degrees
GEF is congruent to MKL
EFG is conguent to KLM

Accordingly, the triangles are similar.

3 0

4 years ago

Read 2 more answers

What do you get when you combine like terms what answer <br> −2k−(−5)+1

Alchen [17]

Answer:

-2k+6

Step-by-step explanation:

-2k-(-5)+1

multiply negative to negative 5 and get a positive

-2k+5+1=

-2k+6 or 6-2k

5 0

3 years ago

Which of these values of x is NOT a solution of the equation tanx= 1?

Kobotan [32]

The tangent ratio is an illustration of the trigonometry identity

The value of x that is not a solution of tan(x) = 1 is 3 $\pi$ /4

<h3>How to determine the value that is not a solution</h3>

The trigonometry identity is given as:

tan(x) = 1

Next, we test the x values using a calculator.

When $x = -7\pi/4$ , we have:

tan(-7 $\pi$ /4) = 1

When x = 3 $\pi$ /4, we have:

tan(3 $\pi$ /4) = -1

When x = 5 $\pi$ /4, we have:

tan(5 $\pi$ /4) = 1

When x = $\pi$ /4, we have:

tan( $\pi$ /4) = 1

Hence, the value of x that is not a solution of tan(x) = 1 is 3 $\pi$ /4

Read more about trigonometry identity at:

brainly.com/question/7331447

5 0

3 years ago

Supongamos que estás en el infierno y el diablo te reta a un juego. Él piensa en un número natural.Cada día, tú tendrás una opor

Blababa [14]

Answer:

En síntesis, se inicia con el número natural más pequeño en el primer y se prosigue con los números siguientes en caso de no dar con $n$ , de modo que el participante pasará en el infierno únicamente $n$ días, algo pequeño en comparación con la eternidad.

Step-by-step explanation:

Los números naturales comprenden el subconjunto más pequeño de los números reales conformado por los siguientes elementos:

$\mathbb{N} = \{1,2,3,4,...\}$

Sea $n \in \mathbb{N}$ el número que tiene el diablo en su mente, tal que $n \geq 1$ . Comenzamos el primer día con 1, si este no corresponde con $n$ . Entonces se utiliza 2 al día siguiente y este no corresponde, se emplea al día siguiente y así sucesivamente hasta conseguir $n$ .

En síntesis, se inicia con el número natural más pequeño en el primer y se prosigue con los números siguientes en caso de no dar con $n$ , de modo que el participante pasará en el infierno únicamente $n$ días, algo pequeño en comparación con la eternidad.

6 0

3 years ago