a) ∠PQR=65° (alternate interior angles theorem)
∠PRQ = 60° (linear pair)
x = 55° (angles in a triangle add to 180°)
b) ∠APQ and ∠PQR are congruent alternate interior angles.
To find the mean of a set, add up all of the data points and divide by the number of data points.
For the first set:
(14+18+21+15+17) ÷ 5 = 85 ÷ 5 = 17
For the second set:
(15+17+22+20+16) ÷ 5 = 90 ÷ 5 = 18
To find the MAD (mean absolute deviation) of a set, find the mean of the distances of each data point from the mean.
For the first set:
(3+1+4+2+0) ÷ 5 = 10 ÷ 5 = 2
For the second set:
(3+1+4+2+2) ÷ 5 = 12 ÷ 5 = 2.4
To find the means-to-MAD ratio of a set, divide its mean by its MAD.
For the first set:
17 ÷ 2 = 8.5
For the second set:
18 ÷ 2.4 = 7.5
Answer:
2x⁴+x³-x²+54x+56
Step-by-step explanation:
Given the expression length of dylan room = (x² – 2x + 8) and width = (2x² + 5x – 7), assuming the shap of the room is rectangular in nature, the formula for calculating area of a triangle is given as;
Area of rectangle = Length *Width
Area of the rectangle = (x² – 2x + 8)(2x² + 5x – 7)
Area of the rectangle = x²(2x² + 5x – 7) - 2x (2x² + 5x – 7) + 8(2x² + 5x – 7)
= (2x⁴+5x³-7x²)-(4x³+10x²-14x)+(16x²+40x-56)
expanding the bracket
= 2x⁴+5x³-7x²-4x³-10x²+14x+16x²+40x-56
Collecting the like terms;
= 2x⁴+5x³-4x³-7x²-10x²+16x²+40x+14x+56
= 2x⁴+x³-x²+54x+56
Hence, the expression that represents the area (lw) of Dylan's room is 2x⁴+x³-x²+54x+56
Step-by-step explanation:
y = cost, m = miles driven
y = 2m +33