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3 years ago

How do I solve this I don't understand it

Mathematics

1 answer:

Free_Kalibri [48]3 years ago

7 0

Here’s how u do it ^

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(2x-7)(x+2)+(3x+7)(x+2)

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Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC . What is the leng

Thepotemich [5.8K]

Answer:

Length of side of rhombus is $x=\frac{ab}{a+b}$

Step-by-step explanation:

Given Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC. We have to find the length of side of rhombus.

It is also given that AB=a and AC=b

Let side of rhombus is x.

In ΔCEF and ΔCBA

∠CEF=∠CBA (∵Corresponding angles)

∠CFE=∠CAB (∵Corresponding angles)

By AA similarity rule, ΔCEF~ΔCBA

∴ their sides are in proportion

$\frac{EF}{AB}=\frac{CF}{AC}$

⇒ $\frac{x}{a}=\frac{b-x}{b}$

⇒ $xb=ab-ax$

⇒ $x(a+b)=ab$

⇒ $x=\frac{ab}{a+b}$

Hence, length of side of rhombus is $x=\frac{ab}{a+b}$

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3 years ago

Suppose that A = PDP-1 . Prove that det(A) = det(D)

daser333 [38]

Answer:

Check.

Step-by-step explanation:

To prove it we need to know that for two matrices A and B we have that:

det(AB) = det(A)*det(B) and $det(A^{-1}) = \frac{1}{det(A)}$ . Now:

$A = PDP^{-1}$

$det(A) = det(PDP^{-1})$

$det(A) = det(P)*det(D)*det(P^{-1})$

$det(A) = det(P)*det(D)*\frac{1}{det(P)}$

$det(A) = det(P)*\frac{1}{det(P)}*det(D)$

$det(A) = det(D)$ .

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4 years ago

There were 18 grey wolves after three years there were 27 grey wolves what is the percent increase

goldfiish [28.3K]

27-18= 9
9/18 x100= 50
There was a 50% increase in grey wolves

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3 years ago