Answer:
(3, 1)
Step-by-step explanation:
(a) Algebraic solution
(1) y = -⅔x + 3
(2) y = 2x - 5
Set Equation (1) equal to Equation (2)
-⅔x + 3 = 2x - 5
Multiply each side by 3
-2x + 9 = 6x - 15
Add 15 to each side
-2x + 24 = 6x
Add 2x to each side
24 = 8x
Divide each side by 3
(3) x = 3
Substitute (3) into (2)
y = 2×3 - 5 = 6 - 5 = 1
The ordered pair that makes both equations true is (3, 1).
(b) Graphical solution
In the diagram below, the red line is the graph of Equation (1). The blue line is the graph of Equation (2). The point of intersection is at (3, 1).
Hi, I actually just took the test and got 100%
Remember: When plotting the points for this equation, make sure to always first plot the ones that correspond to the first linear equation, and then plot the ones that correspond to the second linear equation.
The points on the line should be for the first linear equation, (4,0) and (8,0). I got this answer by first converting the linear equation, 2x+y=8 from standard form to slope-intercept form. To do this, I subtracted 2x from both sides of the equation. So now it reads as y=8-2x. After this step was completed, I then graphed my first linear equation.
The points on the line should be for the first linear equation, (2,4) and (6,6).
I got this answer by first converting the linear equation, -x+2y=6 into slope-intercept form. To do this, I subtracted -x from both sides of the equation. Then I had to divide the 2 into both -x and 6. So now it reads as y= 6/2-x/2. After this step was completed, I then graphed my second and final linear equation.
I hope this helps!
Step-by-step explanation:
Pythagoras Theorem
If the sum of the squares of the smaller two sides is equal to the square if the third side then it is a right triangle
So, (5)^2 + (12)^2
is 25 + 144 = 169
Which is equal to (13)^2 which is also 169
The sides of the given triangle follows pythagoras theorem, therefore it is a right triangle
Hope it helps:)
100 times is the answer to the question
Answer:
The answer is below
Step-by-step explanation:
Triangle FCD is cut from parallelogram ABCD moved with left-hand side. What are the dimensions of the resulting rectangle AEFD?
A parallelogram is a quadrilateral (has four sides and four angles) in which opposite sides are parallel to each other.
A rectangle is a quadrilateral with opposite sides which are parallel and equal to each other. All the angles in a rectangle are at 90 degrees.
From the image, AD = z, FC = x, BF = w and BC = y. Hence:
EB = FC = x.
EF = AD = length = z; AE = FD = height = w
Therefore the dimensions of rectangle AEFD is length z and height w
