Question 1: Select the property shown

Median AM and CN of △ABC intersect at point O. What part of area of △ABC is the area of △AON?

iogann1982 [59]

Answer:

The area of △AON is one-sixth part of △ABC.

Step-by-step explanation:

Let the total area of △ABC be x.

Median divides the area of a triangle in two equal parts.

Since AM are CN are medians, therefore the area of △ACN, △BCN, △ABM and △ATM are equal, i.e., $\frac{x}{2}$ .

The intersection point of medians is called centroid of the triangle. A centroid divides the median in 2:1.

Since CN is median and O is the centroid of the triangle, therefore CO:ON is 2:1.

Draw a perpendicular on CN from A.

$\frac{\text{Area of }\triangle ANO}{\text{Area of }\triangle ACN}=\frac{\frac{1}{2}\times ON\times h}{\frac{1}{2}\times CN\times h}=\frac{1}{3}$

Therefore the area of △AON is one-third of △ACN.

$\text{Area of }\triangle ANO=\frac{1}{3}\times\text{Area of }\triangle ACN$

$\text{Area of }\triangle ANO=\frac{1}{3}\times\frac{x}{2}$

$\text{Area of }\triangle ANO=\frac{x}{6}$

The area of ANO is $\frac{x}{6}$ . Therefore the area of △AON is one-sixth part of △ABC.

8 0

3 years ago

Solve for x: 12x+5=3x+35

elena55 [62]

Answer:

The answer would be 3.33.

Step-by-step explanation:

Simplifying 12x + 5 = 3x + 35

Reorder the terms: 5 + 12x = 3x + 35

Reorder the terms: 5 + 12x = 35 + 3x

Solving 5 + 12x = 35 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation. 5 + 12x + -3x = 35 + 3x + -3x

Combine like terms: 12x + -3x = 9x 5 + 9x = 35 + 3x + -3x

Combine like terms: 3x + -3x = 0 5 + 9x = 35 + 0 5 + 9x = 35

Add '-5' to each side of the equation. 5 + -5 + 9x = 35 + -5

Combine like terms: 5 + -5 = 0 0 + 9x = 35 + -5 9x = 35 + -5

Combine like terms: 35 + -5 = 30 9x = 30

Divide each side by '9'. x = 3.333333333

Simplifying x = 3.333333333

8 0

2 years ago

Solve the equation for a. 3a+13.61=−9.43

snow_tiger [21]

Answer: a = -7.68

STEPS:

- Subtract 13.61 from both sides

- Simplify

- Divide both sides by 3

4 0

2 years ago

Solve the system of inequalities: 3x-10<0 2x>0 HELPPP WILL MARK BRAINLIEST

son4ous [18]

Answer:

Solve each inequality and combine solutions:

3x - 10 < 0 ⇒ 3x < 10 ⇒ x < 10/3
2x > 0 ⇒ x > 0

Combination of the two is:

0 < x < 10/3

or

x ∈ (0, 10/3)

4 0

3 years ago

Read 2 more answers

Give the correct answer Solve all questions to get brainliest

beks73 [17]

Let me translate it to English before I answer your question.

Hello friend, how are you? Today I want to write about my schedule of classes.

My classes start at seven thirty in the morning. I have five classes everyday. My math class, it starts at seven thirty. Then a biology class and it starts at half past nine. I have a twenty minute break at noon. It starts at half past seven. I always have soccer practice after school, but today I have to come home early because I have to study for the biology test. Take care.

First answer: 20 mins

Second answer: 7:30

Third answer:7:30

Fourth answer:9:05

Hope this helps you!!

Stay safe.

5 0

3 years ago