Given: <span>9=(1/27)^(a+3)
[Note: Please review rules of PEMDAS.
The question posted as is means
</span><span>9=[(1/27)^a]+3 which is probably not what you mean. It has been interpreted with (a+3) as the exponent, please check.]
</span><span>
Need to find value of a that satisfies above.
We will first isolate a in order to solve for its value.
</span>9=(1/27)^(a+3)
Switch unknown to the left
(1/27)^(a+3) = 9
Since both 27 and 9 are powers of 3, we can take log to base 3.
take log (base 3) on both sides, applying rule of logarithm of exponents.
(a+3)log_3(1/27)=log_3(9)
(a+3)log_3(3^(-3))=log_3(3^2)
Apply definition of logarithm [log_a(a^k)=k]
(a+3)(-3)=2
(a+3)=-2/3
a=-3 2/3=-11/3
Check: (1/27)^(-11/3+3)=(1/27)^(-2/3)=(3^(-3))^(-2/3)=3^(-3(-2/3))=3^2=9 ok
Answer: a=-11/3 or a=-3.667 (approx.)
ANSWER
Option D
EXPLANATION
The parent radical function is
The transformed function is
This is a transformation of the form.
which shifts the parent function horizontally by k units to the right and stretches the parent function vertically by a factor of 'a'.
In this case a=2 and k=3,
there is a horizontal shift of 3 units to the right and a vertical stretch by a factor of 2.
The last choice is correct.
Hi there! The domain of a function refers to the values that can be validly input for x. In laymen's terms, domain is the x-values that exist on a graph of the equation.
If we were to plug in y=-2x+5 into a calculator that shows an infinite graph, we would see that the line of the equation would extend both ways infinitely! This means that all real numbers can be inputs for x, because for every x value that exists there is a corresponding y value.
This means that D. All real numbers, is your answer.
Hope it helps! :)
Answer:
Answer: 3
Step-by-step explanation:
Use BODMAS
<u>Step 1: Open bracket (1 2/5 +3.5÷1 1/4 )</u>
<em>Convert mixed fractions into improper fractions</em>
7/5 + 3.5 ÷ 5/4
<em>Divide 3.5 by 5/4</em>
7/5 + 2.8 = 4.2
<u>Step 2: Carry out all divisions</u>
<em>Convert mixed fraction into improper fractions</em>
4.2 ÷2 2/5 +3.4÷2 1 /8 −0.35
4.2 ÷ 12/5 + 3.4 ÷ 17/8 - 0.35
1.75 + 1.6 - 0.35
<u>Step 3: Solve</u>
1.75 + 1.6 - 0.35
3.35 - 0.35
Answer = 3
Answer:
Hi, There!
Option B 125% Is the Most Accurate Answer
Step-by-step explanation:
Circumference is the distance around a plane shape. So, it also measures length.
Length and area of two similar shapes are related by the formula
Where the A in both cases represents area and the L represents length. But here the Ls will represent circumference.
Since the circumference of the circle increased by 50%, then the new circumference becomes
Now subtracting from the original area then
This means that the area was increased by 1.25, which means 125%
Hence option B is the correct answer
