Answer:
cost of system is $175 and cost of the games is $525
Step-by-step explanation:
Let us take the cost of the system to be X.The games cost 3 times as much as the system and are therefore given 3X. The total cost of the system and the games is $700.Therefore,we form the equation 3X+X=$700.Meaning that 4X=$700 and X is equal to $175.The cost of the system is X therefore it is $175 and the cost of the games is 3X and is therefore $525.
In an arithmetic sequence:
Tn=t₁+(n-1)d
t₄=t₁+(4-1)d=t₁+3d
t₅=t₁+(5-1)d=t₁+4d
t₆=t₁+(6-1)d=t₁+5d
t₄+t₅+t₆=(t₁+3d) +(t₁+4d)+(t₁+5d)=3t₁+12d
Therefore:
3t₁+12d=300 (1)
t₁₅=t₁+(15-1)d=t₁+14d
t₁₆=t₁+(16-1)d=t₁+15d
t₁₇=t₁+(17-1)d=t₁+16d
t₁₅+t₁₆+t₁₇=(t₁+14d)+(t₁+15d)+(t₁+16d)=3t₁+45d
Therefore:
3t₁+45d=201 (2)
With the equations (1) and (2) we make an system of equations:
3t₁+12d=300
3t₁+45d=201
we can solve this system of equations by reduction method.
3t₁+12d=300
-(3t₁+45d=201)
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-33d=99 ⇒d=99/-33=-3
3t₁+12d=300
3t₁+12(-3)=300
3t₁-36=300
3t₁=300+36
3t₁=336
t₁=336/3
t₁=112
Threfore:
Tn=112+(n-1)(-3)
Tn=112-3n+3
Tn=115-3n
Now, we calculate T₁₈:
T₁₈=115-3(18)=115-54=61
Answer: T₁₈=61
Since you have an angle and at least one side you can use either sine, cosine or tan. For this question, you would use sine like above. Hope this helps!
The properties of exponents would help solve exponential equations by creating an expression that can be simplified easily. It elps in simplfying a certain equation. It tells us how are terms that contain exponents can be added, subtracted, divided and multiplied. For addition, terms having the same can only be added. This would be also true for subtraction. For example, we have x^2 + y^3, these terms could not be added since they have different base. For multiplication, we can readily multiply these terms and add the exponents of the terms with the same base, x^2(y^2)(x) = x^3y^2. For division, they can also be divided readily but, terms with the same base, the exponents are to be subtracted, x^3 / x^2 = x.
