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2 years ago

If an orthocenter lies inside of a triangle, then the triangle must be

Mathematics

1 answer:

Black_prince [1.1K]2 years ago

8 0

Answer:

<h2><u><em>acute</em></u></h2>

Step-by-step explanation:

Remember :the orthocenter of a triangle is the point of concurrency of the 3 altitudes.

$\large \text{If an orthocenter lies inside of a triangle, then the triangle must be}\ :\\\\\large isosceles. \\\\\large obtuse. \\\\\large right. \\\\\large acute \checkmark$

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(03.05 MC) Solve the rational equation x divided by 2 equals x squared divided by quantity x minus 2 end quantity, and check for

ycow [4]

Answer:

x = 0 and x = -2 are solutions of the given rational equation.

Step-by-step explanation:

We must solve the following rational equation:

$\frac{x}{2} = \frac{x^{2}}{x-2}$

Now we present the procedure:

1) $\frac{x}{2} = \frac{x^{2}}{x-2}$ Given

2) $x\cdot (x-2) = 2\cdot x^{2}$ Compatibility with multiplication/Existence of the multiplicative inverse/Definition of division/Modulative property.

3) $x^{2}-2\cdot x = 2\cdot x^{2}$ Distributive property/ $a^{b}\cdot a^{c} = a^{b+c}$

4) $x^{2} + 2\cdot x = 0$ Compatibility with addition/Existence of the additive inverse/Modulative property/Reflexive property

5) $x \cdot (x+2) = 0$ Distributive property/ $a^{b}\cdot a^{c} = a^{b+c}$

6) $x = 0\, \lor\, x = -2$ Result

Now we check the rational equation with each root:

x = 0

$\frac{x}{2} = \frac{x^{2}}{x-2}$

$\frac{0}{2} = \frac{0^{2}}{0-2}$

$0 = \frac{0}{-2}$

$0 = 0$

x = 0 is a solution of the rational equation.

x = -2

$\frac{x}{2} = \frac{x^{2}}{x-2}$

$\frac{-2}{2} = \frac{(-2)^{2}}{-2-2}$

$-1 = -1$

x = -2 is a solution of the rational equation.

4 0

2 years ago

There are three dials on a combination lock. Each dial can be set to one of the numbers 1, 2, 3, 4, 5 The three digit number 553

Anika [276]

The number of different three-digit numbers that can be set for the combination lock is 125

<h3>How to determine the number of different locks?</h3>

The digits are given as

Digit = 1, 2, 3, 4, 5

Each digit can be repeated on the number lock.

So, the individual digit of the lock can be any of the 5 digits.

So, we have:

Locks = 5 * 5 * 5

Evaluate

Locks = 125

Hence, the number of different three-digit numbers that can be set for the combination lock is 125

Read more about combination at:

brainly.com/question/11732255

#SPJ1

8 0

2 years ago

What does the numerator of the fraction 1 /2 fraction mean?

olya-2409 [2.1K]

Answer:

1/2

2 is the total parts. you can visualise it as a circle or another form of a diagram. so theres 2 parts. 1 might mean one segmented is shaded or cut depending on the context

7 0

2 years ago

Read 2 more answers

Jill mixed 3/8 cup of water with 1 5/6 cups of sugar.how many more cups of sugar did he use in his mixture

kherson [118]

Jill had 1 11/24 more cups of sugar in his mixture that he used.
1 5/6 1 20/24
- → -
3/8 9/24
_____ _______
1 11/24

4 0

2 years ago

A bag with 8 marbles is shown below. (The 8 marbles are red.) A marble is

Degger [83]

Answer:

Step-by-step explanation: