Solution:
Your problem → x + 45 = 97x
x+45=97x
⇒-96x+45=0
⇒96x=45
⇒x=45/96
⇒x=15/32
Answer:
16
x
^4 − 96
x^
3 + 216
x
^2 − 216
x + 81
Step-by-step explanation:
Use the binomial expansion theorem to find each term. ∑
∑The binomial theorem states ( a + b ) n = n ∑ k = 0 n C k ⋅ ( a n − k b k ) . 4 ∑ k = 0 4 ! ( 4 − k ) ! k ! ⋅ ( 2 x ) 4 − k ⋅ ( − 3 ) k
Expand the summation. 4 ! ( 4 − 0 ) ! 0 ! ⋅ ( 2 x ) 4 − 0 ⋅ ( − 3 ) 0 + 4 ! ( 4 − 1 ) ! 1 ! ⋅ ( 2 x ) 4 − 1 ⋅ ( − 3 ) + 4 ! ( 4 − 2 ) ! 2 ! ⋅ ( 2 x ) 4 − 2 ⋅ ( − 3 ) 2 + 4 ! ( 4 − 3 ) ! 3 ! ⋅ ( 2 x ) 4 − 3 ⋅ ( − 3 ) 3 + 4 ! ( 4 − 4 ) ! 4 ! ⋅ ( 2 x ) 4 − 4 ⋅ ( − 3 ) 4
Simplify the exponents for each term of the expansion. 1 ⋅ ( 2 x ) 4 ⋅ ( − 3 ) 0 + 4 ⋅ ( 2 x ) 3 ⋅ ( − 3 ) + 6 ⋅ ( 2 x ) 2 ⋅ ( − 3 ) 2 + 4 ⋅ ( 2 x ) ⋅ ( − 3 ) 3 + 1 ⋅ ( 2 x ) 0 ⋅ ( − 3 ) 4
Simplify each term.
= 16
x
^4 − 96
x^
3 + 216
x
^2 − 216
x + 81
Problem 23
A = 40
B = 3x+1
C = 3x+1
B and C are congruent, so they have the same angle measure
The three angles of any triangle add to 180 degrees
A+B+C = 180
40+(3x+1)+(3x+1) = 180
6x+42 = 180
6x = 180-42
6x = 138
x = 138/6
x = 23
Answer: B) 23
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Problem 24
AB is the midsegment parallel to XY
So AB is half that of XY
AB = (1/2)*XY
AB = (1/2)*28
AB = 14
Answer: B) 14
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Problem 25
Note the ratio of the given rectangle's sides: 7/12 = 0.583 roughly
Divide the answer choices in a similar fashion
A) 5/7 = 0.714
B) 14/36 = 0.389
C) 21/36 = 0.583
D) 21/48 = 0.4375
We get the same result in choice C as we did in the original rectangle
Answer: C) 21 ft x 36 ft
Answer:
108 feet^2
Step-by-step explanation:
Break it into 2 parts: 1*24 and (24*7)/2
24 + 84 = 108
Answer:
you gotta find the total score of the 5 players is by multiplying 5 by 6= 30.
the ratio is 89:30