Since 
are linearly dependent, there exist coefficients 
such that
Now, a linear combination of the new vectors would look like this:
Which simplifies to
So, any linear combination of 
is also a linear combination of . This implies that we can choose the coefficients for a linear combination that will give the zero vector.
In particular, if are the coefficients such that
we can choose
And we have
Answer:
x = 12 degrees
Step-by-step explanation:
m < LNM = (70+136)/2
= 206 / 2
= 103 degrees
So 7x + 19 = 103
7x = 103 - 19 = 84
x = 84/7
x = 12.
Answer:
(-9/2,2)
Step-by-step explanation:
Midpoint equals (x1+x2)/2, (y1+y2)/2
Answer: Ryan drove at 81.67 miles per hour.
Janelle drove at 65 miles per hour.
Step-by-step explanation:
The formula for determining speed is expressed as
Speed = distance/time
When they each stopped for lunch, they called each other on their cell phones. Ryan had traveled 245 miles in 3hours. This means that the speed at which Ryan is driving is
245/3 = 81.67 miles per hour.
Janelle had driven 260 miles in 4 hours. This means that the speed at which Janelle is driving is
260/4 = 65 miles per hour.
Answer:
30 Chairs
Step-by-step explanation:
I will solve this problem using algebra and try to explain in detail.
We can form two equations with the information given to us.
Firstly, 5 times a length of chairs (I will call this unknown length of chairs x), plus 5 left over chairs, equals the total number of chairs (I will call the total number of chairs y).
5x + 5 = y
Secondly, 3 times a length of chairs (I will call this unknown length of chairs x), plus 15 left over chairs, equals the total number of chairs (I will call the total number of chairs y).
3x + 15 = y
Since both equations are equal to y, they are equal to each other
5x + 5 = 3x + 15
Take 5 away from both sides of the equals, and take away 3x from both sides of the equals
5x - 3x = 15 - 5
2x = 10
Divide both sides by 2
x = 5 chairs
Put this back into either the first equation or the second to solve for y
3 (5) + 15 = y
15 + 15 = y
y = 30 chairs
