<span>In here, we will use the slope formula
in order to prove that ABCD is a parallelogram. The slope of AB must be equal
to CD and the slope of BC must be equal to DA. Using the formula m = (y1-y2) /
(x1-x2), we obtain the slope for AB = 0/4, BC = 1, CD = 0/4, DA = 1. We can say that ABCD is a parallelogram as it satisfies AB = CD, and BC = DA</span>
Answer:
x = 13, y = 26
The length of the sides of Δ QRS are QR = 104, <u>QS = 468</u>, RS = 76
Step-by-step explanation:
In ΔRQS
∵ M is the mid-point of side RQ
→ That means M divide RQ into 2 equal parts RM and MQ
∴ RM = MQ
∵ RM = 4x
∵ MQ = 52
→ Equate them
∴ 4x = 52
→ Divide both sides by 4 to get x
∴ x = 13
∵ P is the mid-point of side QS
→ That means P divide QS into 2 equal parts QP and PS
∴ QP = PS
∵ QP = 9y
∵ PS = 234
→ Equate them
∴ 9y = 234
→ Divide both sides by 9 to get y
∴ y = 26
→ Find the length of each side
∵ RQ = 52 + 52
∴ RQ = 104
∵ QS = 234 + 234
∴ QS = 468
∵ RS = 38 + 38
∴ RS = 76
∴ The length of the sides of Δ QRS are QR = 104, QS = 468, RS = 76
Note: PS = 234 is wrong because it made the length of the sides QS = 468, which could not be because the sum of any 2 sides of a triangle must be greater than the 3rd side. So check it.
Answer:
The solution to the system of equations is y = -5 and x = -2.
Step-by-step explanation:
The question tells us to use substitution to solve the system. This means that the given value for x (in terms of y) should be substituted into the other equation. This is modeled below:
-4y - 5x = 30
-4y - 5(y+3) = 30
Next, we should use the distributive property to simplify the left side of the equation.
-4y -5y - 15 = 30
The next step is to combine like terms on the left side of the equation.
-9y - 15 = 30
Then, we can add 15 to both sides of the equation.
-9y = 45
Finally, we can divide both sides of the equation by -9.
y = -5
To find the value for x, we substitute in the value we just found for y into either of our original equations.
x = y + 3
x = -5 + 3
x = -2
Therefore, the correct answer is y = -5 and x = -2.
Hope this helps!
The graph shows a zero slope since the equation of this graph is y = 4. No matter what the input is, it will just give you the same output. The input doesn't really give a care to the output because the output is just the same all through out.
