<span>–36, –32, –28, –24 This is an arithmetic sequence because each term has the same difference from the preceding term, called the common difference, d...
-32--36=-28--32=-24--28=4 So 4 is d, the common difference.
The sequence of any arithmetic sequence has the form:
a(n)=a+d(n-1), a=first term, d=common difference, n=term number...in this case we have:
a(n)=-36+4(n-1)
a(n)=-36+4n-4
a(n)=4n-40 so the 29th term is:
a(29)=4(29)-40
a(29)=116-40
a(29)=76
...
distance=velocity * time
d=vt we want to find t so
t=d/v and in this case:
t=234/70
t=(210+24)/70
t=3hr+(60*24)/70
t=3hr+20min+34sec so
t≈3hr 20min
...
This is an arithmetic sequence...100,150,200...
The sum of an arithmetic sequence will always be the average of the first and last terms times the number of terms....
the rule for the sequence is:
a(n)=a+d(n-1), a(n)=100+50d-50, a(n)=50n+50
Now we know the nth term is 50n+50, and we also know the first term is 100 so:
s(n)=n(100+50n+50)/2 and we want to know the sum of the first 10 terms so
s(10)=10(100+500+50)/2
s(10)=$3250
...
The first two terms are 2 and 4 so:
a(n)=2+2(n-1)
a(n)=2+2n-2
a(n)=2n
a(10)=20
...
You could do synthetic or long division, but you also could just use the fact that the factor being (x+8) should indicate a zero for the function when x=-8. If f(x) could be divided by (x+8) the value of y(-8) would equal zero, however calculating y(-8)=-10 so that would be the remainder if you did the division.</span>
Answer:
p=4
Step-by-step explanation:
distance b/n points is given by formula
Given : The Area of the Rectangle = x⁴ - 100
We know that : (a + b)(a - b) = a² - b²
⇒ x⁴ - 100 can be written as : (x²)² - (10)²
⇒ (x²)² - (10)² can be written as : (x² + 10)(x² - 10)
We know that, Area of a Rectangle is given by : Length × Width
Comparing (x² + 10)(x² - 10) with Area of the Rectangle formula, We can notice that :
⊕ Length = x² + 10
⊕ Width = x² - 10
Given : Length of the Rectangle is 20 units more than Width
⇒ Width + 20 = Length
⇒ x² - 10 + 20 = x² + 10
⇒ x² + 10 = x² + 10
<u>Answer </u>: x² - 10 represents the width of the rectangle. Because the area expression can be rewritten as (x² - 10)(x² + 10) which equals
(x² - 10)((x² - 10) + 20)
⇒ Option A
Answer: 50.48
Step-by-step explanation:
You subtract $186.45 by $35 and you will get $151.45
Then you divide $151.45 by 3 (Savion,Carter and Jojo)
Answer:
4 miles per hour
Step-by-step explanation:
So we have bike speed, b, and run speed, r. We also have an amount of time t where running that amount of time gets 6 miles, while biking that same time gets 19.5. Let's write these out as equations.
rt = 6
bt = 19.5
We are also told that b is 9 more than r so writing that out is b = 9 + r. So it's basically a system of equations.
rt = 6
bt = 19.5
b = 9 + r
Since we have b = 9 + r let's replace b with that in bt = 19.5
rt = 6
(9 + r)t = 19.5
b = 9 + r
With rt = 6 we can get that r = 6/t, so we can plug hat into (9 + r)t = 19.5
rt = 6
(9 + 6/t)t = 19.5
b = 9 + r
Expanding (9 + 6/t)t = 19.5 will get us an equation to solve for t
rt = 6
9t + 6 = 19.5
b = 9 + r
So let's solve for t in 9t + 6 = 19.5
rt = 6
t = (19.5 - 6)/9 = 1.5
b = 9 + r
Now we can plug this new value for t into rt = 6 to find r. I'm just gonna write that part since this will get us the answer.
rt = 6
r*1.5 = 6
r = 4
So she runs at 4 miles per hour
