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alexira [117]
3 years ago
15

Yelp............................

Mathematics
1 answer:
exis [7]3 years ago
3 0

Answers:

f(2) = \textbf{1}\\\\f^{-1}(1) = \textbf{2}\\\\f^{-1}(f(2)) = \textbf{2}

===================================================

Explanation:

Replace x in f(x) with 2. Then simplify

f(x) = \frac{1}{2}x\\\\f(2) = \frac{1}{2}(2)\\\\f(2) =1\\

Then plug x = 1 into the inverse function and simplify

f^{-1}(x) = 2x\\\\f^{-1}(1) = 2(1)\\\\f^{-1}(1) = 2\\

Lastly,

f^{-1}(f(2)) = f^{-1}(1) = 2

is the result of combining the two parts above.

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. Use the quadratic formula to solve each quadratic real equation. Round
Liono4ka [1.6K]

Answer:

A. No real solution

B. 5 and -1.5

C. 5.5

Step-by-step explanation:

The quadratic formula is:

\begin{array}{*{20}c} {\frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} \end{array}, with a being the x² term, b being the x term, and c being the constant.

Let's solve for a.

\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {5^2 - 4\cdot1\cdot11} }}{{2\cdot1}}} \end{array}

\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {25 - 44} }}{{2}}} \end{array}

\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {-19} }}{{2}}} \end{array}

We can't take the square root of a negative number, so A has no real solution.

Let's do B now.

\begin{array}{*{20}c} {\frac{{ 7 \pm \sqrt {7^2 - 4\cdot-2\cdot15} }}{{2\cdot-2}}} \end{array}

\begin{array}{*{20}c} {\frac{{ 7 \pm \sqrt {49 + 120} }}{{-4}}} \end{array}

\begin{array}{*{20}c} {\frac{{ 7 \pm \sqrt {169} }}{{-4}}} \end{array}

\begin{array}{*{20}c} {\frac{{ 7 \pm 13 }}{{-4}}} \end{array}

\frac{7+13}{4} = 5\\\frac{7-13}{4}=-1.5

So B has two solutions of 5 and -1.5.

Now to C!

\begin{array}{*{20}c} {\frac{{ -(-44) \pm \sqrt {-44^2 - 4\cdot4\cdot121} }}{{2\cdot4}}} \end{array}

\begin{array}{*{20}c} {\frac{{ 44 \pm \sqrt {1936 - 1936} }}{{8}}} \end{array}

\begin{array}{*{20}c} {\frac{{ 44 \pm 0}}{{8}}} \end{array}

\frac{44}{8} = 5.5

So c has one solution: 5.5

Hope this helped (and I'm sorry I'm late!)

4 0
3 years ago
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Viktor [21]

Answer:

subtract 3m from both sides

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
370 second song is divided into three parts, the beginning, the middle, and the end. The beginning is one sixth as long as the e
Alex777 [14]

Answer:

Step-by-step explanation:

The main part of the song is the end.  The beginning length is based on the end and so is the middle length.  The beginning length is 1/6 as long as the end, so if the end is our main unknown, x, the beginning is 1/6x.  The middle is one-half as long as the end, so if the end is our main unknown, x, the middle is 1/2x.  The sum of the 3 parts is 370, so:

x+\frac{1}{6}x+\frac{1}{2}x=370

The GCF of those denominators is 6, so multiply through every term by 6 to get rid of the fractions:

(6)x+(6)\frac{1}{6}x+(6)\frac{1}{2}x=(6)370

Simplifying gives us

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10x = 2220 so

x = 222

That means that the end is 222 seconds, the bginning is 37 seconds, and the middle is 111 seconds.

3 0
3 years ago
Please tell me the ans fast ​
katrin2010 [14]

Answer:

B

Step-by-step explanation:

mgh=PE

(5)(9.8)(2.5)=pe

122.5j=pe

6 0
2 years ago
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White raven [17]

Answer: -6

Step-by-step explanation: 8-2= 6 and 3-4= -1. So 6/-1 is -6

3 0
2 years ago
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