To get to the next term in this sequence, multiply the last term by 2.5. What is the value of the next term?
1 answer:
The question is incomplete. Here is the complete question:
To get the next term in the sequence,multiply the last term by 2.5 . What is the value of the next term?
1 , 2.5 , 6.25, 15.625, ...
Answer:
39.0625
Step-by-step explanation:
Let the next term of the sequence be
Given:
The terms of the given sequence are 1, 2.5, 6.25, 15.625,..
Here, we can conclude that the next term is obtained by multiplying the previous term by 2.5 and is verified below.
2.5 = 1 2.5 = 2.5
6.25 = 2.5 2.5 = 6.25
15.625 = 6.25 2.5 = 15.625
Therefore, the next term is given as:
Therefore, the next term of the given sequence is 39.0625.
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Answer:
The equation relates the variables is y = 8x ⇒ D
Step-by-step explanation:
If x and y vary directly (y ∝ x), then y = k x, where
- k is the constant of variation
- k can be found using the initial value of x and y
∵ The variable x and y vary directly
∴ y ∝ x
→ By using the rule above
∴ y = k x
∵ y = 40 when x = 5
∴ The initial values of x and y are x = 5 and y = 40
→ Substitute them in the equation above to find k
∵ 40 = k(5)
∴ 40 = 5k
→ Divide both sides by 5
∵ =
∴ 8 = k
→ Substitute the value of k in the equation above
∴ y = 8x
∴ The equation relates the variables is y = 8x
Assuming a diagram similar to the one I've attached, ∠<em>YVZ</em> is a vertical angle to ∠<em>WVX</em>, which means they have an equal measure. Additionally, ∠<em>WVZ</em> and ∠<em>WVX</em> form a linear pair, which means they are supplementary (sum to 180°). That means we start out with the equation
We combine our like terms (the <em>x</em>'s get combined, then the constants get combined) and have:
Cancel the 9 first by subtraction:
Cancel the 19 by division:
Since we know that our angle we're looking for, ∠<em>YVZ</em>, is the same measure as ∠<em>WVX</em>, we substitute 9 in for <em>x</em>:
8(9)+28=72+28=100°
We combine our like terms (the <em>x</em>'s get combined, then the constants get combined) and have:
Cancel the 9 first by subtraction:
Cancel the 19 by division:
Since we know that our angle we're looking for, ∠<em>YVZ</em>, is the same measure as ∠<em>WVX</em>, we substitute 9 in for <em>x</em>:
8(9)+28=72+28=100°