Short answer: C
Let's start with the pen.
The length is x
The width is 3 more.= x + 3
Perimeter of the pen = 2L + 2W
P = 2 L + 2W
P = 2*x + 2(x + 3)
P = 2x + 2x + 6
P = 4x + 6. Leave that for now.
Area of the pen without the doghouse = x(x + 3)
Area of the pen without the doghouse = x^2 + 3x
Area with the doghouse x^2 + 3x - y = 178 (that's his running around space.
Go to the dog house for a Moment
The perimeter of the doghouse and the area are equal and we are told to make them both y.
Area = y
Perimeter = y
Combined facts.
The perimeter of the Pen is three times larger than that of the dog house.
4x + 6 = 3y
The area of the Pen - The area of the doghouse = 178
x^2 + 3x - y = 178
Now what happens is that you have to juggle these two equations so they look like your answer
x^2 + 3x - y = 178
4x + 6 = 3y Subtract 3y from both sides.
4x - 3y + 6 = 0 Subtract 6 from both sides.
4x - 3y = - 6
Answer C
The sum of the geometric series is 2199; option E.
- The 36th term of the arithmetic series is -60.5 option C
- The sum of the arithmetic series is 2547; option E
- The missing geometric sequence are; 1.614375, 3.30946875, 6.7844109375. option E
<h3>Arithmetic and Geometric series</h3>
S6 = a(rⁿ - 1) / r -1
= 1468(1/3^6 - 1) / (1/3 - 1)
= 1468(0.00137174211248 - 1) / -2/3
= 1468(-0.9986282578875) / -0.66666666666666
= -1,465.98628257885 / -0.66666666666666
= 2198.97942386829
Approximately,
S6 = 2199
Arithmetic series
Sn = n/2{2a + (n -1)d}
= 36/2 {2×27 + (36-1)-5/2}
= 18{54 + (35)-5/2}
= 18(54 + 175/2)
= 18(54 + 87.5)
= 18(141.5)
s36 = 2547
a36 = a + (n - 1) d
= 27 + (36 - 1)-5/2
= 27 + (35)-5/2
=27 + -175/2
= 27 - 87.5
= -60.5
S20 = n/2{2a + (n -1)d}
= 20/2{2×27 + (20-1)-5}
= 10(54 + (19)-5)
= 10{54 + (-95)}
= 10(54-95)
= 10(-41)
s20 = -410
Missing terms of the geometric sequence:
nth term = ar^n-1
448/135 = 63/80×r^(6-1)
448/135 = 63/80×r^5
r^5 = 448/135 ÷ 63/80
= 448/135 × 80/63
= 35,840/8,505
r = 5√35,840/5√8505
= 946.57/461.11
r = 2.05
Second term = a×r
= 63/80×2.05
= 1.614375
Third term = ar²
= 63/80×2.05²
= 63/80×4.2025
= 3.30946875
Fourth term = 63/80 × 2.05³
= 63/80×8.615125
= 6.7844109375
Therefore, none of these are correct
Learn more about sum of geometric series:
brainly.com/question/24643676
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X=27 because you would add 14 to 13
Answer: subtract
Step-by-step explanation:
look at it
