The 7th term of an AP is 4 and its common difference is -4. What is the first term?
1 answer:
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Answer:
Option C
Step-by-step explanation:
Note that the relation describing the set of ordered pairs does not change at a costing rate
Therefore the relationship is not linear.
However, the exchange rate increases by a factor of 2 units when n increases 1 unit. This allows us to conclude that the relationship is quadratic
Note that the following ordered pairs belong to the function
A = {(2, 4), (3, 9), (4, 16), (5, 25)}
The set of ordered pairs that we have is:
B = {(2, 2), (3, 7), (4, 16), (5, 23)}
Note that there is a similarity between both sets of ordered pairs.
In set B the values of y are always 2 units less than the values in y of the set A.
Then we deduce that since the function that models the set A is then the function that contains the ordered pairs of the B set is:
The correct option is option C)
The first step for solving this equation is to determine the defined range.
3㏑(2) + ㏑(8) = 2㏑(4x), x > 0
Write the number 8 in exponential form.
3㏑(2) + ㏑(2³) = 2㏑(4x)
Using ㏑(
) = x × ㏑(a),, transform the expression.
3㏑(2) + 3㏑(2) = 2㏑(4x)
Now collect the like terms on the left side of the equation.
6㏑(2) = 2㏑(4x)
Switch the sides of the equation.
2㏑(4x) = 6㏑(2)
Using x × ㏑(a) = ㏑(),, transform the expression on the left side of the equation.
㏑((4x)²) = 6㏑(2)
Using x × ㏑(a) = ㏑(),, transform the expression on the right side of the equation.
㏑((4x)²) = ㏑(
)
Since the bases of the logarithms are the same,, you need to set the arguments equal.
(4x)² =
Take the square root of both sides of the equation and remember to use both the positive and negative roots.
4x = +/- 8
Now separate the equation into 2 possible cases.
4x = 8
4x = -8
Solve the top equation for x.
x = 2
Solve the bottom equation for x.
x = 2
, x > 0
x = -2
Lastly,, check if the solution is in the defined range to find your final answer.
x = 2
This means that the correct answer to your question is x = 2.
Let me know if you have any further questions
:)
3㏑(2) + ㏑(8) = 2㏑(4x), x > 0
Write the number 8 in exponential form.
3㏑(2) + ㏑(2³) = 2㏑(4x)
Using ㏑(
3㏑(2) + 3㏑(2) = 2㏑(4x)
Now collect the like terms on the left side of the equation.
6㏑(2) = 2㏑(4x)
Switch the sides of the equation.
2㏑(4x) = 6㏑(2)
Using x × ㏑(a) = ㏑(
㏑((4x)²) = 6㏑(2)
Using x × ㏑(a) = ㏑(
㏑((4x)²) = ㏑(
Since the bases of the logarithms are the same,, you need to set the arguments equal.
(4x)² =
Take the square root of both sides of the equation and remember to use both the positive and negative roots.
4x = +/- 8
Now separate the equation into 2 possible cases.
4x = 8
4x = -8
Solve the top equation for x.
x = 2
Solve the bottom equation for x.
x = 2
, x > 0
x = -2
Lastly,, check if the solution is in the defined range to find your final answer.
x = 2
This means that the correct answer to your question is x = 2.
Let me know if you have any further questions
:)
For this case, the first thing we must do is define a variable.
We have then:
x: number of weeks
y: amount of cereal that Melanie eats
We now write the function that models the problem:
Then, for 5 weeks we have:
Answer:
A model that best represents the number of pounds of cereal she eats is:
For 5 weeks we have:
We have then:
x: number of weeks
y: amount of cereal that Melanie eats
We now write the function that models the problem:
Then, for 5 weeks we have:
Answer:
A model that best represents the number of pounds of cereal she eats is:
For 5 weeks we have: