Answer:
middle term = 7x
Step-by-step explanation:
in order to find the middle term, we will expand the bracket on the left hand side and compare the expressions on both sides.
(x + 2) (3x + 1) = 3x² + ___ + 2
let the unknown expression = y
(x + 2) (3x + 1) = 3x² + y + 2
Expanding the bracket on the left hand side by multiplication:
x + 2( 3x + 1) = (x × 3x) + (x × 1) + (2 × 3x) + ( 2 × 1)
= 3x² + x + 6x + 2
= 3x² + 7x + 2
Comparing with the expression on the right hand side:
3x² + 7x + 2 = 3x² + y + 2
∴ y = 7x
middle term = 7x
By taking advantage of the definition of <em>exponential</em> and <em>logarithmic</em> function and their inherent relationship we conclude that the solution is x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3).
<h3>How to solve an exponential equation by logarithms</h3>
<em>Exponential</em> and <em>logarithmic</em> functions are <em>trascendental</em> functions, these are, functions that cannot be described <em>algebraically</em>. In addition, <em>logarithmic</em> functions are the <em>inverse</em> form of <em>exponential</em> functions. In this question we take advantage of this fact to solve a given expression:
- 7ˣ = 3ˣ⁺⁴ Given
- ㏒ 7ˣ = ㏒ 3ˣ⁺⁴ Definition of logarithm
- x · ㏒ 7 = (x + 4) · ㏒ 3 ㏒ aᵇ = b · ㏒ a
- x · ㏒ 7 = x · ㏒ 3 + 4 · ㏒ 3 Distributive property
- x · (㏒ 7 - ㏒ 3) = 4 · ㏒ 3 Existence of additive inverse/Modulative and associative properties
- x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3) Existence of multiplicative inverse/Modulative property/Result
By taking advantage of the definition of <em>exponential</em> and <em>logarithmic</em> function and their inherent relationship we conclude that the solution is x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3).
To learn more on logarithms: brainly.com/question/20785664
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Answer:
-a^2
A
Step-by-step explanation:
-a/b=a/-b=-a/b to fraction
-1/a^-2
Since a slope differe, this is not linear relationship. Simply, if you connect all points on the graph, they will not lie on the same line. Two next graphs represent the linear relationships, so they represent the linear relationship.
Answer:
a. Not Divisible
b. Divisible
c. Divisible
d. Divisible
e. Divisible
Step-by-step explanation:
To find the divisibility we need to follow the PEMDAS rule and check if the total value can be divided by the selected numbers without returning a remainder.
Let's begin with a:
by 33


We now then divide the total amount with 33.

= 31,781.5454
We can see that the value has a decimal point indicating that the total value divided by 33 will return a remainder. So it is NOT Divisible by 33.
Now let's continue on with the others.
by 25


We now then divide the total amount with 25.

= 35,192,575,602
The total value did NOT return a decimal point, therefore making the equation true.
IS divisible by 25.
Next on we have:
by 7

As we know in the PEMDAS rule, that addition comes first. In this situation we have to read the equation from left to right and solve which ever comes first.


We now then divide the total amount with 7.

= 375
The total value did NOT return a decimal point, therefore making the equation true.
IS divisible by 7.
by 11



We now then divide the total amount with 11.

= 12,005
The total value did NOT return a decimal point, therefore making the equation true.
IS divisible by 11.
Last but not the least:
by 24


We now then divide the total amount with 24.

= 476,837,158,203,125
The total value did NOT return a decimal point, therefore making the equation true.
IS divisible by 24.