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3 years ago

PLS HELP AS SOON AS POSSIBLE!!! WILL AWARD BRAINLIEST AND 20 POINTS!!! Also the answer is NOT 22.5 degrees!

Mathematics

1 answer:

olga_2 [115]3 years ago

5 0

Answer:

x=0.392 radians

Step-by-step explanation:

Since DE is parallel to AB, then ∠DEA=∠EAB=2x (Alternate angles). (1)

Also, ∠FEB+∠AEB=180°(Straight line property)

⇒4x+∠AEB=180°

⇒∠AEB=180°-4x (2)

Also, ∠EBA+∠EBC=180°

⇒∠EBA=180°-6x (3)

Now, using equations (1), (2) and (3) and the angle sum property in ΔABE, we get

∠EAB+∠AEB+∠EBA=180°

2x+180°-4x+180°-6x=180°

⇒360°-8x=180°

⇒180°=8x

⇒x=22.5°

⇒x=0.392 radians

which is the required value of x.

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What are the coordinates of the orthocenter of △JKL with vertices at J(−4, −1) , K(−4, 8) , and L(2, 8) ?

PilotLPTM [1.2K]

ANSWER

The orthocenter is $(-4,8)$

EXPLANATION

The orthocenter is the point of intersection of all the altitudes of a triangle.

If it is a right angle triangle then the orthocenter is the point at which the right angle is made.

If it is not a right angle triangle, then you have to find the equations of any two of the altitudes and solve simultaneously.

So you must first check to see if it is a right angle triangle that way you do not have to do bunch work.

The given triangle has vertices $J(-4,-1)$ , $(-4,8)$ , and $L(2,8)$ .

$Slope_{JK}=\frac{8--1}{-4--4}$

$Slope_{JK}=\frac{8+1}{-4+4}$

$Slope_{JK}=\frac{9}{0}$

Since the denominator is zero, the slope is undefined.

If the slope of a straight line is undefined, then that line is parallel to the y-axis. In other words, it is a vertical line.

$Slope_{JL}=\frac{8--1}{2--4}$

$Slope_{JL}=\frac{8+1}{2+4}$

$Slope_{JL}=\frac{9}{6}$

$Slope_{JL}=\frac{3}{2}$

$Slope_{KL}=\frac{8-8}{2--4}$

$Slope_{KL}=\frac{0}{2+4}$

$Slope_{KL}=\frac{0}{6}$

$Slope_{KL}=0$

if a straight line has a slope of zero, that line is parallel to the x-axis or it is horizontal.

From the slopes we can see that side KL of the triangle is horizontal and side JK is vertical. This two sides will meet at right angles at K.

See graph.

Therefore the coordinates of K, $(-4,8)$ is the orthocenter of the given triangle.

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3 years ago

When evaluting an expression, is it easier to combine terms first or substitute values first? PLSSSS ANSWERRR ILL GIVE BRAINLIES

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What do you mean by combining terms?

If you have an equation like y=3(2+x), then you would need to substitute for x before you combined the terms "2" and "x"

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Consider the equation below. Log Subscript 4 Baseline (x 3) = log Subscript 2 Baseline (2 x) Which system of equations can repre

swat32

Equal expressions can be taken equal to an another variable. The system of equations representing the equation is $y = x + 3\\y = 4x + 8$

<h3>What is logarithm and some of its useful properties?</h3>

When you raise a number with an exponent, there comes a result.

Lets say you get

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

Some properties of logarithm are:

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Log with base e = 2.71828... is written as $\ln(x)$ simply.

Log with base 10 is written as $\log(x)$ simply.

The given equation is:

$\log_4(x+3) = \log_2(2 +x)$

Adding $\log_2(4)$ on both the sides, we get:

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The, we get two equations as:

$y = x + 3\\y = 4x + 8$

This is the needed system of equations.

Learn more about logarithms here:

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