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3 years ago

9. Only 12 students can be in the next school play.

Mathematics

1 answer:

Sunny_sXe [5.5K]3 years ago

5 0

T-42=12 so the is 54 and 54-42=12

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Helppp!! I NEED HELP PLEASE

Elodia [21]

Given:

The table of values for the function f(x).

To find:

The values $f^{-1}(f(3.14))$ and $f(f(-7))$ .

Solution:

From the given table, it is clear that the function f(x) is defined as:

$f(x)=\{(-14,11),(-7,-12),(-12,-5),(9,1),(10,-2),(-2,13)\}$

We know that if (a,b) is in the function f(x), then (b,a) must be in the function $f^{-1}(x)$ . So, the inverse function is defined as:

$f^{-1}(x)=\{(11,-14),(-12,-7),(-5,-12),(1,9),(-2,10),(13,-2)\}$

And,

$f^{-1}(f(a))=f^{1}(b)$

$f^{-1}(f(a))=a$ ...(i)

Using (i), we get

$f^{-1}(f(3.14))=3.14$

Now,

$f(f(-7))=f(-12)$

$f(f(-7))=5$

Therefore, the required values are $f^{-1}(f(3.14))=3.14$ and $f(f(-7))=5$ .

5 0

3 years ago

The triangles are similar

hoa [83]

Answer:

Part 1) $x=16\ units$

Part 2) $x=23\ units$

Part 3) $AE=20\ units$

Part 4) $x= 6.25\ units$

Part 5) $x=26.67\ in$

Step-by-step explanation:

Part 1) we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

In this problem

$\frac{12}{3}=\frac{x}{4}\\\\3x=12*4\\ \\x=48/3\\ \\x=16\ units$

Part 2) we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

In this problem

$\frac{36}{12}=\frac{39}{(x-10)}\\\\3(x-10)=39\\ \\x=(39/3)+10\\ \\x=23\ units$

Part 3) we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

In this problem

$\frac{AB}{CD}=\frac{AE}{ED}$

substitute the values

$\frac{10}{4}=\frac{2x+10}{x+3}$

$2.5(x+3)=2x+10$

$2.5x+7.5=2x+10$

$2.5x-2x=10-7.5$

$0.5x=2.5$

$x=5\ units$

$AE=2x+10=2*5+10=20\ units$

Part 4) we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

In this problem

$\frac{4}{5}=\frac{5}{x}\\ \\4x=5*5\\ \\ x=25/4\\ \\ x= 6.25\ units$

Part 5) we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

In this problem

$\frac{30}{x}=\frac{45}{40}\\ \\45x=30*40\\ \\x=1,200/45\\ \\ x=26.67\ in$

3 0

3 years ago

Read 2 more answers

If A+B+C=<img src="https://tex.z-dn.net/?f=%5Cpi" id="TexFormula1" title="\pi" alt="\pi" align="absmiddle" class="latex-formula"

seraphim [82]

Answer:

$a + b + c = \pi \\ = > c= \pi - a - b \\ < = > \tan(c) = \tan(\pi - a - b) = -\tan(a + b)$

Step-by-step explanation:

we have:

$\tan(a) + \tan(b) + \tan(c) \\ = \tan(a) + \tan(b) - \tan(a + b) \\ = \tan( a) + \tan(b) - \frac{ \tan(a) + \tan(b) }{1 - \tan(a) \tan(b) } \\ = \frac{ ( \tan(a) + \tan(b) ) \tan(a) \tan(b) }{ \tan(a) \tan(b) - 1 } (1)$

we also have:

$\tan(a) \tan(b) \tan(c) \\ = - \tan(a) \tan(b) \tan(a + b) \\ = \frac{ -(\tan( a ) + \tan(b) ) \tan(a) \tan(b) }{1 - \tan(a) \tan(b) } \\ = \frac{( \tan(a) + \tan(b)) \tan(a) \tan(b) }{ \tan(a) \tan(b) - 1 } (2)$