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2 years ago

In rectangle ABCD, AB = 10 cm and BC = 14 cm. If rectangle EFGH is the image after a dilation, which could be its side lengths?

Mathematics

1 answer:

kakasveta [241]2 years ago

3 0

Answer:

EF = 25 cm and FG = 35 cm

Step-by-step explanation:

After finding each scale factor for each of the 4 answers, only the last option is relatable. Every other option resulted in different numbers of EF and FG.

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Find (f −1)'(a).<br><br> f(x) = 4 + x2 + tan(πx/2), −1 < x < 1, a = 4

Vinvika [58]

Answer:

The solution is $(f^{-1})'(a) = \frac{2}{\pi }$

Step-by-step explanation:

From the question we are told that

The function is $f(x) = 4 + x^2 + tan [\frac{ \pi x}{2} ]$ , -1 < x < 1 a = 4

Here we are told find $(f^{-1}) (a)$

Let equate

$f(x) = a$

$4 + x^2 + tan[\frac{\pi x }{2} ] = 4$

$x^2 + tan[\frac{\pi x }{2} ] = 0$

For the equation above to be valid x must be equal to 0

Now when x = 0

$f(0) = 4+0^2 + tan [\frac{ \pi * 0}{2} ]$

=> $f(0) = 4$

=> $0 = f^{-1} (4)$

Differentiating f(x)

$f(x)' = 0 + 2x + sec^2 (\frac{\pi x}{2} )\cdot \frac{\pi}{2}$

Now

since $0 = f^{-1} (4)$

We have

$f(0)' = 0 + \frac{\pi }{2} sec^2 (0)$

$f(0)' = \frac{\pi }{2}$

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$(f^{-1})'(a) = \frac{1}{(\frac{\pi}{2} )}$

$(f^{-1})'(a) = \frac{2}{\pi }$

3 0

3 years ago

Simplify . 7(8-1)+(-1) ^)2/1+2^2

kodGreya [7K]

Answer:

$\frac{50}{5} = 10$

Step-by-step explanation:

$\frac{7(8 - 1) + ( - 1 {)}^{2} }{1 + {2}^{2} }$

$\frac{7 \times 7 + ( - 1 {)}^{2} }{1 + {2}^{2} } = \frac{7 \times 7 + 1}{1 + {2}^{2} }$

$\frac{7 \times 7 + 1}{1 + 4} = \frac{49 + 1}{1 + 4} = \frac{49 + 1}{5}$

$= \frac{50}{5} = 10$

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3 years ago