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ser-zykov [4K]
3 years ago
9

I need to know how to do Solving Systems of Equations by Elimination

Mathematics
1 answer:
vredina [299]3 years ago
6 0
The point of elimination is to have one variable so example

3x + 2y = 4

7X + 3y = 5


1) Try to find a way to have one variable

7(3x + 2y = 4) ----> 21x + 14y = 28

-3(7x+ 3y = 5) -----> -21x -9y = -15


2) add

0 + 5y = 13

3) solve for the last variable

5y = 13
y = 13/5 = 2 3/5 = 2.8

4) Subsitute the variable to get the other one

3x + 2(2.8) = 4

3x + 5.6 = 4

3x = -1.6

x = 0.533333333 (continue)

The intersection would be 0.53 with a line above the 3 and 2.8. (0.5333 , 2.8)

Hope you understand!!
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Erik's disabled sailboat is floating stationary 3 miles east and 2 miles north of Kingston. A ferry leaves Kingston heading towa
sergij07 [2.7K]

Answer:

Step-by-step explanation:

Let's suppose that Ballard is an origin with coordinates (0;0)

Ballard is 8 miles south and 1 mile west of Edmonds ⇒ Edmonds is 1 mile east and 8 miles north of Ballard.

Thus, coordinates of Edmonds (0+1; 0+8) (1;8)

Edmonds is 6 miles due east of Kingston. So, is 6 miles due of Edmonds

Thus, Kingston coordinates (1-6;8) (-5:8)

Sailboat is 3 miles east and 2 miles north of kingston

So, coordinates of sailboat are (-5+3; 8+2) (-2;10)

a)

Ferry leaves Kingston towards Edmonds at mph and Edmonds is 6 miles due east of Kingston.

Initial ferry coordinates as calculated above are equal to Kingston coordinates (-5;8)

After 20 minutes the ferry turns to south.

This distance travelled (20min) is d=9mph*20/60h=3 miles

So, ferry travelled 3 miles toward east in 20 min

Then, coordinates became (-5+3;8+0) (-2;8)

Thus, we have a line connecting two points (-5;8) and (-2;8)

Line connecting them has an equation:

y-8 = (8-8)/(-2+5) * (x+5)

y-8=0

y=8 - This is the equation for the first 20 minutes of travel

Then, ferry turns due south (-2;8) and has a vertiacl line

The equation of verical line is x=a, so the equation will be x=2

b) The sailboat has a radar scope that will detect any object within 3 miles of the sailboat.

region looks like a circular disc with a center (-2;10)

(x+2)^2+(y-10)^2=3^2

(x+2)^2+(y-10)^2 <9 (interior of the circular disc)

(x+2)^2+(y-10)^2 >9 (exterior)

The equation of the line joining the Kingston and Edmonds is y=8

the point of intersection:

(x+2)^2+(8-10)^2=9

(x+2)^2=5

x is approximately 0.24; -4.24

(0.24;8) (-4.24;8) - intersection points

c) The ferry exits the radar during the trid due south long x=-2

The points of intersection of the circle and the line x=-2:

(-2+2)^2+(y-10)^2=9

0+(y-10)^2=0

y is 7.13

(-2;7)

d) Takes south turn at (-2;8), then ferry travels 0.8 miles up to point (-2;7) where it exists the radar zone

Speed is 9mph

The time taken to cover 1 mile = t=1/9hr=1/9 *60=6.667min

So, it exists after 6.67 minutes

e) Ferry enters at (-4.24;8) and takes turn due to south at (-2;8)

The distance travelled is = [-4.24+2]=2.24 miles

The time taken to cover these miles is = t=2.24/9 *60=14.93 min

After turning to south ferry remains in radar for 6.7 min

So, it remains in radar zone for 14.93+6.7=21.63min

8 0
3 years ago
Find the distance between (-4,3,-6) and the origin ((X,Y,Z) Graph)
devlian [24]

The distance between  (-4,3,-6) and the origin is \sqrt{61

<h3>How to determine the distance?</h3>

The point is given as:

(x, y, z) = (-4,3,-6)

The origin is

(x, y, z) = (0,0,0)

The distance between the point and the origin is calculated as:

d = \sqrt{x^2 + y^2 + z^2

So, we have:

d = \sqrt{(-4)^2 + (3)^2 + (-6)^2

Evaluate

d = \sqrt{61

Hence, the distance between  (-4,3,-6) and the origin is \sqrt{61

Read more about distance at:

brainly.com/question/7243416

#SPJ1

4 0
2 years ago
7 Given: -8(w + 1) = -5(w + 10); Prove: w = 14<br> Statements
LenKa [72]

Answer:

w=14

Step-by-step explanation:

-8(w + 1) = -5(w + 10)

Remove the parentheses

-8w-8+-5w-50

Move terms

-8w+5w=-50+8

Collect like terms and calculate

-3w=-42

Then divide on both sides

5 0
3 years ago
Centimeters and meters size of window
Gnom [1K]

Answer:

Tiff, hon, just measure a window, your wasting your time

Step-by-step explanation:

7 0
3 years ago
20 PTS!
mafiozo [28]

Answer:

finding the number of equal-sized parts into which a number can be split

Step-by-step explanation:

Let us split the number 80 into 10 equal parts.

80 = 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8

= 8 + 8 + 8 +...to 10 times

= 8(10)

or \frac{80}{10} =8

So, if N is any number and p is one of its equal part, then the number of parts into which N is split by p is \frac{N}{p}.

Hence, finding the number of equal-sized parts is best modeled with a division expression.

4 0
3 years ago
Read 2 more answers
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