Answer:
X=2
Step-by-step explanation:
Step-by-step explanation:
a triangular number n is the sum of all natural numbers <= n.
t1 = 1
t2 = 1+2 = 3
t3 = 1+2+3 = 6
t4 = 1+2+3+4 = 10
...
so,
tn = tn-1 + n
47.
1×8 + 1 = 9 is a square number.
3×8 + 1 = 25 is a square number
6×8 + 1 = 49 is a square number
10×8 + 1 = 81 is a square number
48.
1/3 = 0 remainder 1
3/3 = 1 remainder 0
6/3 = 2 remainder 0
10/3 = 3 remainder 1
15/3 = 5 remainder 0
21/3 = 7 remainder 0
28/3 = 9 remainder 1
so, there seems to be a pattern 1 0 0 1 0 0 1 0 0 1 ...
49.
1/4 = 0 remainder 1
4/4 = 1 remainder 0
9/4 = 2 remainder 1
16/4 = 4 remainder 0
25/4 = 6 remainder 1
36/4 = 9 remainder 0
49/4 = 12 remainder 1
so, there seems to be a pattern 1 0 1 0 1 0 1 0 1 0 1 ...
50.
polygonal numbers is the real name for this.
the formula for dimensions = 5 is
(3n² − n)/2
for dimensions = 6 it is
2n² - n
so, dimensions=5 (and therefore dividing also by 5) we get the remainders
1/5 = 0 remainder 1
5/5 = 1 remainder 0
12/5 = 2 remainder 2
22/5 = 4 remainder 2
35/5 = 7 remainder 0
51/5 = 10 remainder 1
70/5 = 14 remainder 0
92/5 = 18 remainder 2
117/5 = 23 remainder 2
145/5 = 29 remainder 0
here the pattern is 1 0 2 2 0 1 0 2 2 0 1 0 2 2 0 ...
dimensions=6 (and therefore dividing also by 6) we get the remainders
1/6 = 0 remainder 1
6/6 = 1 remainder 0
15/6 = 2 remainder 3
28/6 = 4 remainder 4
45/6 = 7 remainder 3
66/6 = 11 remainder 0
91/6 = 15 remainder 1
120/6 = 20 remainder 0
153/6 = 25 remainder 3
190/6 = 31 remainder 4
231/6 = 38 remainder 3
276/6 = 46 remainder 0
325/6 = 54 remainder 1
here the pattern is 1 0 3 4 3 0 1 0 3 4 3 0 1 0 3 4 3 0 ...
Answer:
<u>The correct answer is C. 14.6 feet</u>
Step-by-step explanation:
Information given to solve the case:
Length of the ladder = 15 feet
Distance from the base of the wall = 3.5 feet
Using the Pythagorean theorem for finding the height, because this is a right triangle:
h² = Length of the ladder ² - Distance from the base of the wall ²
h² = 15 ² - 3.5 ²
h² = 225 - 12.25
h² = 212.75
h = √ 212.75
h = 14.59
<u>h = 14.6 feet (Rounding to one decimal place)</u>
The area and arc length of each piece can be found using the
relationship between a circle and a sector of the circle.
Responses (b, c, and d are approximated):
a. 120°
b. 10.6 square inch
c. 28.3 in.
d. Area: 15.8 in.², Central angle: 89.1°
<h3>How can the pie pieces dimensions be evaluated?</h3>
Given:
Diameter of the pan, d = 9-inch
Number pie pieces cut from the apple pie = 6
The pie pieces are sectors of a circular pie.
a. The central angle of one pie pieces = 
= 60°
Therefore;
- The central angle of two pie pieces = 2 × 60° = <u>120°</u>
b. Area of circular pie = π·r²
Where;
Therefore;
- The area covered by each pie piece is approximately <u>10.6 square inch</u>
c. The circumference of a circle = 2·π·r
The circumference of the original pie = 2 × π × 4.5 in. ≈ <u>28.3 in.</u>
d. Let the arc length of the pie piece = 7 inches
- The area of the pie piece is approximately <u>15.8 in.²</u>
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Learn more about circumference, area and sector of a circle here:
brainly.com/question/12985985
