Answer:
a) one solution(x = 9)
b) no solution
c) infinite solutions
Step-by-step explanation:
a) To solve this equation, we can add 4 on both sides in order to isolate x:
x - 4 =5
+ 4 + 4
x = 9
Since x equals 9, that counts as only one solution, as there is only one value of x that makes the equation true.
b) We start by subtracting 2x from both sides to combine the variable terms:
2x - 6 = 2x + 5
-2x -2x
-6 = 5
The statement, -6 = 5 is never true and it is not dependent on the value of x. This means there are no solutions to this equation.
c) We can start by subtracting 3x from both sides to combine the terms with x:
3x + 12 = 3x + 12
-3x -3x
12 = 12
The statement above is always true, and no matter the value of x, it will always be true. This means there are infinite solutions to the equation.
Answer is 8671/6 which is the third choice
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Work Shown:
Find the first term of the sequence by plugging in n = 1
a_n = (5/6)*n + 1/3
a_1 = (5/6)*1 + 1/3 replace n with 1
a_1 = 5/6 + 1/3
a_1 = 5/6 + 2/6
a_1 = 7/6
Repeat for n = 58 to get the 58th term
a_n = (5/6)*n + 1/3
a_58 = (5/6)*58 + 1/3 replace n with 58
a_58 = (5/6)*(58/1) + 1/3
a_58 = (5*58)/(6*1) + 1/3
a_58 = 290/6 + 1/3
a_58 = 145/3 + 1/3
a_58 = 146/3
Now we can use the s_n formula below with n = 58
s_n = (n/2)*(a_1 + a_n)
s_58 = (58/2)*(a_1 + a_58) replace n with 58
s_58 = (58/2)*(7/6 + a_58) replace a_1 with 7/6
s_58 = (58/2)*(7/6 + 146/3) replace a_58 with 146/3
s_58 = (58/2)*(7/6 + 292/6)
s_58 = (58/2)*(299/6)
s_58 = (58*299)/(2*6)
s_58 = 17342/12
s_58 = 8671/6
Answer:
Answer for A
Step-by-step explanation:
I don't know about B , Sorry for that.
Answer:
5x + 2y = 12
Step-by-step explanation:
Direction factor = (2, 1) - (0, 6) = (2, -5)
So, normal factor = (5, 2)
Line: 5x + 2y = k
(0, 6) -> L: 0 + 12 = 12 = k
L: 5x + 2y = 12