Express 23/7 in decimal form
1 answer:
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Answer:
The area of a parallelogram is 360 in.²
Step-by-step explanation:
Where DG = GH
GP = 12 in.
AB = 39 in.
∠DAB + ∠ABC = 180° (Adjacent angles of a parallelogram)
Whereby ∠DAB is bisected by AG and ∠ABC is bisected by BH
Therefore, ∠GAB + ∠HBA = 90°
Hence, ∠BPA = 90° (Sum of interior angles of a triangle)
We note that ∠AGD = ∠GAB (Alternate angles of parallel lines)
∴ ∠AGD = ∠AGD since ∠AGD = ∠GAB (Bisected angle)
Hence AD = DG (Side length of isosceles triangle)
The bisector of ∠ADG is parallel to BH and will bisect AG at point Q
Hence ΔDAQ ≅ ΔDGQ ≅ ΔGPH and AQ = QG = GP
Hence, AP = 3 × GP = 3 × 12 = 36
∠GAB = 22.62°
GH = 13 in.
∴ AD 13 in.
BP = 39 × sin(22.62°) = 15 in.
GH = √(GP² + HP²)
∠DAB = 2 × 22.62° = 45.24°
The height of the parallelogram = AD × sin(∠DAB) = 13 × sin(45.24°)
The height of the parallelogram = 120/13 = 9.23 in.
The area of a parallelogram = Base × Height = (120/13) × 39 = 360 in.²
Answer:
y = 1.5x + 1.5
Step-by-step explanation:
First, plot 2x + 3y = 15 on a graph. Then plot (1,3) on a graph. After that, draw a line that passes through (1,3) and forms 90 degrees angles with 2x + 3y = 15. Then find the equation of that line by finding the y-intercept (0, 1.5). Then head up to the intersection point (1.6153846153846, 3.9230769230769). Subtract 1.5 from y. (2.4230769230769) Then divide by 1.5 (1.6153846153846). Reverse the operations you just did (in reverse order) to get the equation y = 1.5x + 1.5.
(I don't know how to explain this too well. Here's a graph to make more sense of it.)
