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
Answer:
x = 9, Angles are 54°
Step-by-step explanation:
First, we need to find x:
7x-9 = 5x+9
+9 +9
7x = 5x+18
-5x -5x
2x = 18
x = 9
Now, we plug our x value in to find our angles.
5(9) + 9 = 54
Angle B = 54°
7(9) - 9 = 54°
Angle E = 54°
(angles are the same due to AAA property)
Answer:
145°
Step-by-step explanation:
There are a couple of ways you can get there:
1. ∠ACB is a right angle, 90°. Hence, ∠BAC is the complement of ∠ABC, so is ...
... ∠BAC = 90° -∠ABC = 90° -55° = 35°
Then, ∠BAC and ∠BAD are a linear pair, so total 180°. That makes ∠BAD the supplement of ∠BAC, so ...
... ∠BAD = 180° -35° = 145°
2. ∠BAD is the exterior angle at A for the triangle ABC. It will have a measure that is the sum of the opposite interior angles: given ∠ABC = 55° and right angle ACB = 90°.
... ∠BAD = 55° +90° = 145°
We will check if y and 60cm are parallel.
If the lengths 28cm, 56cm and 15cm, 30cm are in proportion, then y and the segment 60cm are parallel.
OK. We know: y and 60cm are parallel. Therefore we have equation:
<h3>Answer: y = 90 cm.</h3>
Answer: Radius = 1,250
Step-by-step explanation: The circumference of a circle equals the 2 x radius x π.
The formula to solve the radius is 2r x 3.14 = 7,850
Divide both sides by 3.14 = 2r = 2,500
Divide both sides by 2 = r = 1,250.
The radius = 1,250
