Solve the system using subtitution 3x + 2y = 23 1/2x

The three lines given below form a triangle. Find the coordinates of the vertices of the triangle.

LenKa [72]

Answer:

(3, 5), (1, 2) and (5, 1)

Step-by-step explanation:

Make three systems with pairs of lines and solve them to work out the vertices.

1) Line 1 and line 2

-3x + 2y = 1
2x + y = 11

Double the second equation and subtract equations:

-3x + 2y - 2(2x + y) = 1 - 2(11)
-3x - 4x = 1 - 22
-7x = - 21
x = 3

Find y:

2*3 + y = 11
6 + y = 11
y = 11 - 6
y = 5

The point is (3, 5)

2) Line 1 and line 3

-3x + 2y = 1
x + 4y = 9

Triple the second equation and add up equations:

-3x + 2y + 3(x + 4y) = 1 + 3(9)
2y + 12y = 1 + 27
14y = 28
y = 2

Find x:

x + 4*2 = 9
x + 8 = 9
x = 1

The point is (1, 2)

3) Line 2 and line 3

2x + y = 11
x + 4y = 9

Double the second equation and subtract the equations:

2x + y - 2(x + 4y) = 11 - 2(9)
y - 8y = 11 - 18
- 7y = - 7
y = 1

Find x:

x + 4*1 = 9
x + 4 = 9
x = 5

The point is (5, 1)

8 0

2 years ago

Mark gets picked up by the bus at 7:40 he arrives at school at 8:10 how long does it take to get to school

Elodia [21]

You could do this in two ways, you could either subtract immediately or convert the time given in hours into minutes
STEP 1:
8:10
- 7:40
which will give 0:30
STEP 2:
8 hours 10 minutes into minutes is
(8 * 60) +10 = 490 minutes
7 hours 40 minutes into minutes is
(7*40) + 40 = 460 minutes
490 - 460
= 30minutes

3 0

3 years ago

Read 2 more answers

The fraction bar represents which equation?

Vera_Pavlovna [14]

Answer:

what equation silly

Step-by-step explanation:

3 0

3 years ago

Hey guys can u tell me if the top is correct if its not can u show me step by step what to do and what the answer will be and ca

ASHA 777 [7]

You have the right idea and you are close to the correct answer. However that's not what your teacher is looking for in terms of steps.

The starting inequality is $b + 8 \ge 20$
She starts off selling 8 buckets. Then she sells b more to get a total of b+8
This total must be 20 or larger which is why I set b+8 greater than or equal to 20

Solve for b by subtracting 8 from both sides

$b + 8 \ge 20$

$b + 8-8 \ge 20-8$

$b \ge 12$

So she needs to sell at least 12 more buckets to reach her goal

If you graphed this on a number line, then you would draw a closed circle at 12. Then shade to the right of the close circle.

6 0

3 years ago

Which of the following random variables should be considered continuous? Select one: a. The number of cars owned by a randomly c

kolbaska11 [484]

The Random Variable that should be considered continuous is "The time it takes for a randomly chosen athlete to run 200 meters" , the correct option is (c) .

In the question ,

four random variables are given , we have to select the random variable that is continuous .

A Continuous Random Variable is a random variable X , which can take any value in its domain or in an interval or the union of intervals on the real line is called Continuous random variable .

For Example : weight of middle aged people lying between 40 Kg and 150 Kg .

From the given options ,

the option (c) , the time taken for a randomly chosen athlete to run 200 meters is a interval of time ,

So ,it is can be called as Continuous Random Variable .

Therefore , the option that represents Continuous Random Variable is option(c) .

The given question is incomplete , the complete question is

Which of the following random variables should be considered continuous ? Select one:

(a) The number of cars owned by a randomly chosen adult male

(b) The number of orders received by a mail-order company in a randomly chosen week

(c) The time it takes for a randomly chosen athlete to run 200 meters

(d) The numbers of brothers a randomly chosen person has .

Learn more about Continuous Random Variable here

brainly.com/question/17238189

#SPJ4

3 0

1 year ago

Solve the system using subtitution 3x + 2y = 23 1/2x - 4 = y