Can you name the angle pairs and type the correct code?

Mathematics

1 answer:

kompoz [17]1 year ago

6 0

$Alternate\text{ interior: 1 and 1}$ $\text{Same side exterior: 4 and 4}$ $\text{vertical: 4 and 3,1 AND 3 and 4,2}$ $Same\text{ side interior: 3 and 3}$ $\text{Obtuse angle pairs: }4\text{ and 1 AND 2 and 3}$ $\text{Adjacent pair angles: None}$ $\text{Alternate exterior: }2\text{ and 1}$ $\text{Corresponding angles: }4\text{ and 1 AND 2 and 3}$ $\text{Complementary: Non}e$

Hence, the 4-letter code is A G D B

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Solve the equation x+3/x-4 = x-5/x+4

Serga [27]

Answer:

$\large\boxed{x=\dfrac{1}{2}}$

Step-by-step explanation:

$\dfrac{x+3}{x-4}=\dfrac{x-5}{x+4}\\\\\text{Domain:}\ x-4\neq0\ \wedge\ x+4\neq0\\\\x\neq4\ \wedge\ x\neq-4\\\\D:x\in\mathbb{R}-\{-4,\ 4\}$

$\dfrac{x+3}{x-4}=\dfrac{x-5}{x+4}\qquad\text{cross multiply}\\\\(x+3)(x+4)=(x-4)(x-5)\qquad\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(x)(x)+(x)(4)+(3)(x)+(3)(4)=(x)(x)+(x)(-5)+(-4)(x)+(-4)(-5)\\\\x^2+4x+3x+12=x^2-5x-4x+20\qquad\text{combine like terms}\\\\x^2+(4x+3x)+12=x^2+(-5x-4x)+20\\\\x^2+7x+12=x^2-9x+20\qquad\text{subtract}\ x^2\ \text{from both sides}\\\\7x+12=-9x+20\qquad\text{subtract 12 from both sides}\\\\7x=-9x+8\qquad\text{add}\ 9x\ \text{to both sides}\\\\16x=8\qquad\text{divide both sides by 16}\\\\x=\dfrac{8}{16}\\\\x=\dfrac{8:8}{16:8}\\\\x=\dfrac{1}{2}\in D$