Answer:
(-60/11,111/11)
Step-by-step explanation:
Solving simultaneously, 4x - 3y=6
-3(6x + y=42)
then it becomes, 4x - 3y=6
-18x - 3y= 126 subtracting the two equations,
22x= -120, x= -60/11 and y = 111/11
Let's recall that in a parallelogram:
1. The opposite sides are paralell
In our exercise. sides CZ and KG are paralell. And so do sides KC and GZ.
2. Those opposite sides are equal in length.
3. The opposites angles are equal. In our exercise, angle C and G are equal and so do angles K and Z.
4. That also mean that the angles at the top of the figure are supplementary. It means they add up to 180 degrees. We have the same situation with the two angles at the bottom of the parallelogram.
In our case then:

Now, we can find the measure of angles K and Z, as follows:

Answer:
B. The vectors v and w are orthogonal because their dot product is <u> 0 </u>
Step-by-step explanation:
Given that :
v= - i - j
w= - i + j
Therefore;
vw = ( - i - j ) ( - i + j )
Taking each set of integer of the vector into consideration:
vw = ( -1 × - 1) ( -1 × 1)
vw = 1 - 1
vw = 0
Hence, we can conclude that :
The vectors v and w are orthogonal because their dot product is <u> 0 </u>
How fast did he run each mile, that is to say how fast did he run 1 mile.
We can simply find the time it took him to run 1 mile.
He ran 7 miles in 57 3/4 minutes = 57.75 minutes.
In 1 mile he would run = 57.75/7 minutes = 8.25 minutes.
He ran 1 mile, that is each mile in 8.25 minutes.
I hope this helped.
The equation of parabola is y = -8(x -3)² - 9.
<h3>Define parabola.</h3>
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
Given Data
Focus = (3, -9)
Directrix: y = -5
The focus-passing line has an equation of x = -5 that is perpendicular to the directrix. The symmetry line of a parabola is seen here.
The parameter of the parabola is the separation between the focus and the directrix, so
p = -9 - 3
p = -12
p = 12
The distance between the focus and the directrix is divided into two equal portions by the parabola's vertex, which is located on the line of symmetry. Its coordinates are as follows: (3,-9).
Since a parabola moves in the opposite direction of y, its equation is
y -(-9) = -2(4(x -3)²)
y + 9 = -8(x-3)²
y = -8(x -3)² - 9
The equation of parabola is y = -8(x -3)² - 9.
To learn more about parabola, visit:
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