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2 years ago

Can somebody please help me with these

Mathematics

1 answer:

Softa [21]2 years ago

8 0

The first pic is A. because 1.2 x 10=12

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. Find the inverse of the function below on the given interval and write it in the form yequalsf Superscript negative 1 Baseline

Elena L [17]

Answer:

The inverse of the function is $f^{-1}(x)=\frac{x-5}{3}$ .

Step-by-step explanation:

The function provided is:

$f (x)=3x+5$

Let $f(x)=y$ .

Then the value of <em>x</em> is:

$y=3x+5\\\\3x=y-5\\\\x=\frac{y-5}{3}$

For the inverse of the function, $x\rightarrow y$ .

⇒ $f^{-1}(x)=\frac{x-5}{3}$

Compute the value of $f[f^{-1}(x)]$ as follows:

$f[f^{-1}(x)]=f[\frac{x-5}{3}]$

$=3[\frac{x-5}{3}]+5\\\\=x-5+5\\\\=x$

Hence proved that $f[f^{-1}(x)]=x$ .

Compute the value of $f^{-1}[f(x)]$ as follows:

$f^{-1}[f(x)]=f^{-1}[3x+5]$

$=\frac{(3x+5)-5}{3}\\\\=\frac{3x+5-5}{3}\\\\=x$

Hence proved that $f^{-1}[f(x)]=x$ .

8 0

2 years ago

Solve the quadratic equation 3x^2+x-5=0

irinina [24]

-1 <span>± </span><span><span>√61 / 6. Negative 1, plus or minus square root of 61 divide by 6</span></span>

5 0

3 years ago

Another plan to secure the roller coaster involves placing two concrete struts on either side of the center of the leg of the ro

skelet666 [1.2K]

Answer:

The beam should be placed 8 feet from the center.

Step-by-step explanation:

The struts are y = √(x + 8) and y = √(x − 4). The struts are 2 feet apart at the location of the beam:

√(x + 8) − √(x − 4) = 2

Solving:

√(x + 8) = 2 + √(x − 4)

x + 8 = 4 + 4√(x − 4) + x − 4

8 = 4√(x − 4)

2 = √(x − 4)

x − 4 = 4

x = 8

8 0

2 years ago

If 32 teams participate in a standard single elimination tournament, how many games must be played to decide a champion?

SCORPION-xisa [38]

<h3>Answer: 31 games</h3>

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

Explanation:

32/2 = 16 games will happen in round 1. Afterward, 16 teams are left.
16/2 = 8 games will happen in round 2. Afterward, 8 teams are left.
8/2 = 4 games happen in round 3.
4/2 = 2 games in round 4.
2/2 = 1 game as the final championship.

Count the number of times you divide by two and we have five occurrences of this. So there five rounds overall.

To get the total number of games played, we add up the quotients

16+8+4+2+1 = 31

----------------

Or as a shortcut we can simply subtract off 1 since 1+2+4+...+2^n = 2^(n+1)-1

We can write that rule as

$\displaystyle \sum_{k=1}^{n}2^k = 2^{n+1}-1$

which is equivalent to

$\displaystyle \sum_{k=1}^{n}2^{k-1} = 2^n-1$

3 0

3 years ago

Okay so this is for my math homework that I wasn't able to do earlier.

WITCHER [35]

What is the question?????

4 0

2 years ago