As we can tell, the first number is 3, so we'll have a y-intercept in our equation and overall. Secondly, we can tell it's increasing by 7 each time, so we can tell that's the rate. But, it won't just be 3+7x, if we plug 1 in, it would be 10 and not 3. We need to put in the parenthesis 3+7(x-1). If we put one in, we would receive three. Let's make sure this works.
3+7(5-1)
3+7(4)
3+28
31
31 is the fifth terms.
So the expression would be 3+7(x-1).
Let's find the 100th term.
3+7(100-1)
3+7(99)
3+693
696
So the 100th term would be 696.
This kind of exercise can be real drudgery. But it's almost all simple arithmetic, so better you than me. I'll do one of these for you, which will show you how to do the other one.
a). sin · cot / sec
You're supposed to know that [ cotangent = cosine/sine ]
and [ secant = 1/cosine ].
Then the problem becomes
sin · (cos/sin) / (1/cos) = cos²
Aw shucks, I might as well also set up 'b)' for you:
b). cos · csc / tan
You're supposed to know that [ cosecant = 1/sine ]
and [ tangent = sine/cosine ].
Then the problem becomes
cos · (1/sin) / (sin/cos) = (cos/sin)²
Now simply plug in the given values of cos A and sin A .
And may I compliment you on your nail care !
<span>8 5/9 + 1 1/5
8+1 = 9
5/9 + 1/5 = 25/45 + 9/45 = 34/45
9 34/35 is the answer</span>
Answer:
35, 35, and 50
Step-by-step explanation:
50 + x + x = n
n ÷ 3 = 40
n = 40 x 3
n = 120
50 + 2x = n
50 + 2x = 120
2x = 120 - 50
2x = 70
2x/2 = 70/2
x = 35
To check:
35 + 35 + 50 = 120
120 ÷ 3 = 40
Hope this helps
Answer:
a₄ = - 
Step-by-step explanation:
In a geometric sequence, the common ratio r is calculated as
r = 
= 
, substitute values
= 
( cross- multiply )
(2x + 2)² = x(3x + 3) ← expand both sides
4x² + 8x + 4 = 3x² + 3x ( subtract 3x² + 3x from both sides )
x² + 5x + 4 = 0 ← in standard form
(x + 1)(x + 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x + 4 = 0 ⇒ x = - 4
However x ≠ - 1 as this would make the denominator of the second term equal to zero and therefore undefined.
Thus x = - 4 and
r = 
= 
= 
= 
Then
a₁ = - 4
a₂ = - 4 × = - 6
a₃ = - 6 × = - 9
a₄ = - 9 × = -
