Answer:
I) f + g = 10/3
II) 4f + 2g = 20/3
III) f = 2 and g = 4/3
Step-by-step explanation:
From the chart,
P = 25
q = 40
The total number of one centimeter lines in the first n diagrams is given by the expression
2/3n^3 + fn^2 + gn.
When n = 1, the total number of line = 4. So,
2/3(1)^3 + f(1)^2 + g(1) = 4
2/3 + f + g = 4
Make f+g the subject of formula
f + g = 4 - 2/3
f + g = (12 - 2)/3
f + g = 10/3 ......(1)
When n = 2
Total number of line = 12
2/3(2)^3 + f(2)^2 + g(2) = 12
2/3×8 + 4f + 2g = 12
16/3 + 4f + 2g = 12
4f + 2g = 12 - 16/3
4f + 2g = (36 - 16)/3
4f + 2g = 20/3 ......(2)
(iii) To find the values of f and g, solve equation 1 and 2 simultaneously
f + g = 10/3 × 2
4f + 2g = 32/3
2f + 2g = 20/3
4f + 2g = 32/3
- 2f = - 12/3
f = 12/6
f = 2
Substitutes f in equation 1
f + g = 10/3
2 + g = 10/3
g = 10/3 - 2
g = (10 - 6)/3
g = 4/3
First find the slope
Slope formula: (y2-y1)/(x2-x1)
(-4-(-6))/(-2-2) = 2/-4 = -1/2
Slope intercept formula: y = mx + b
Y = -1/2x + b (solve for b)
Plug in any point
-6 = -1/2(2) + b
-6 = -1 + b, b = -5
Solution: y = -1/2x - 5
Im not quite sure but i think the unit rate is 150. Hope this helps!!
Answer:
C. Construction X because point C is the incenter of triangle LMN.
Step-by-step explanation:
The construction requires that the school must be at equal distance to cities of the triangle town. Thus, it must be located at the point of intersection of the straight path from the three cities L, M, and N.
To be able to construct the school with the specification, option C is the most suitable. Construction X describe the appropriate method because point C is the incenter of triangle town of cities L, M, and N.
Answer:
P = 350 feet
Step-by-step explanation:
P = 2L + 2W
W = 70 feet
L = 105 feet
plug in values:
P = 2(105) + 2(70)
P = 210 + 140
P = 350 feet