Find the value of x then classify the triangle by its angles

A rectangle has its vertices at (-4, -3), (-4,7), (1,7), (1, -3). What part, in percent, of the rectangle is located in Quadrant

Rasek [7]

Consider the attached figure. The whole rectangle is ABCD, while AEGF is the part located in the third quadrant. In fact, this quadrant is composed by all the points with both coordinates negative.

To answer the question, let's compute the area of the two rectangles and see what part of ABCD is AEGF.

A and B have the same x coordinate, so the length of AB is given by the absolute difference of their y coordinates:

$\overline{AB} = |A_y-B_y| = |-3-7| = |-10| = 10$

Similarly, but exchanging the role of x and y, we compute the length of BC:

$\overline{BC} = |B_x-C_x| = |-4-1| = |-5| = 5$

So, the area of the rectangle is $\overline{AB} \cdot \overline{BC} = 10\cdot 5 = 50$

The same procedure allows us to compute width and height of the sub-rectangle in the third quadrant:

$\overline{AE} = |A_y-E_y| = |-3-0| = |-3| = 3$

$\overline{EG} = |E_x-G_x| = |-4-0| = |-4| = 4$

So, the area of the portion located in the third quadrant is $\overline{AE} \cdot \overline{EG} = 3\cdot 4 = 12$

This means that the ratio between the two area is

$\cfrac{\text{area }AEGF}{\text{area }ABCD} = \cfrac{12}{50}$

If we want this ratio to be a percentage, just make sure that the denominator is 100:

$\cfrac{12}{50} = \cfrac{12}{50}\cdot \cfrac{2}{2} = \cfrac{24}{100} = 24\%$

3 0

3 years ago

The ratio of 6th graders to 7th graders in a MATHCOUNTS club is 5:4. The ratio of 8th graders to 7th graders in the same club is

lorasvet [3.4K]

ANSWER
========

Ratio of 8th graders to 7th graders = 3 : 2

Let the number of graders be 3x and 2x

Number of 8th graders = 18

So , 3x = 18

x = 18/3 = 6

Number of 7th graders = 2 × 6 = 12

Ratio of 6th graders to 7th graders = 5 : 4

Let the number of graders be 5a and 4a

Number of 7th graders = 12

So , 4a = 12

a = 12/4 = 3

Number of 6th graders = 5×3 = 15 ANS

_______________________________

#BE BRAINLY

3 0

3 years ago

Read 2 more answers

True or False: A relation passing the horizontal line test is a function.

rosijanka [135]

Answer:

True.

Step-by-step explanation:

Remember that the horizontal line test checks if a function is one-to-one. If a horizontal line passes through a graph more than once, the function has more than one x-value for at least one y-value.

7 0

3 years ago

write a numerical expression for each word phrase Three less than the product of eight and six

Sergio [31]

(8*6)-3 is your answer

4 0

3 years ago

How many answers are in each of these three questions: 1. x squared minus three x plus four equals zero 2. Two x squared plus fo

vaieri [72.5K]

1. No solutions ( no answers) 2 . 2 answers 3. 1 answer

6 0

3 years ago