Answer:
The factors of given expression are 10+10√2 and 10-10√2.
Step-by-step explanation:
We have given a quadratic expression.
s²-20s-100
We have to find factors of given expression.
We use quadratic formula to find factors.
x = (-b±√b²-4ac) / 2a
From given expression, a = 1 , b = -20 and c = -100
Putting values in above formula, we have
x = (-(-20)±√(-20)²-4(1)(-100) ) / 2(1)
x = (20±√400+400 ) / 2
x = (20±√800) / 2
x = (20± √400×2) / 2
x = (20±20√2) / 2
x = 10±10√2
Hence, the factors of given expression are 10+10√2 and 10-10√2.
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)
-----------------------------
-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
It can be x = 3 and x = -15
Answer:
(-3,5)
Step-by-step explanation:
If you start at the origin (0), going up 5 spaces will leave you at 5 for your y plot. Then, 3 spaces <em>left</em> leaves you at -3 for your x. However, when writing down plots, you write x before y. So, you are left with (-3,5) as your coordinate plot for the final answer.
