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Fofino [41]
3 years ago
5

PLEASE HELP!!

Mathematics
2 answers:
Musya8 [376]3 years ago
6 0

Answer:

x = - 33

Step-by-step explanation:

Given

\frac{2}{3}(x + 6) = - 18

Multiply both sides by 3 to clear the fraction

2(x + 6) = - 54 ( divide both sides by 2 )

x + 6 = - 27 ( subtract 6 from both sides )

x = - 33

Whitepunk [10]3 years ago
5 0

Answer:

x= -33

Step-by-step explanation:

2/3 (x+6) = -18

(x+6)  = -18x3/2 = -9x3 = -27

x+6= -27 (if the symbols are same you need to add if symbols are different you need to subtract.) the bigger  numbers symbol  will tell if number is positive or negative.

x= -27-6

x= -33

Advice from a 5th grader!

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How is this solved using trig identities (sum/difference)?
GenaCL600 [577]
FIRST PART
We need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative

Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached

Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13

cos α = side adjacent to the angle / hypotenuse
cos α = -5/13

Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°

cos \beta = -\frac{1}{2}  \sqrt{3}

tan \beta= \frac{1}{3}  \sqrt{3}

SECOND PART
Solve the questions
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sin (α + β) = sin α cos β + cos α sin β
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Find cos (α - β)
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cos( \alpha + \beta )=(- \frac{5}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{12}{13} )( -\frac{1}{2} )
cos( \alpha + \beta )=(\frac{5}{26} \sqrt{3})+( \frac{12}{26} )
cos( \alpha + \beta )=(\frac{5\sqrt{3}+12}{26} )

Find tan (α - β)
tan( \alpha - \beta )= \frac{ tan \alpha-tan \beta }{1+tan \alpha  tan \beta }
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3}   }{1+(\frac{5}{12}) ( \frac{1}{2} \sqrt{3})}

Simplify the denominator
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3}   }{1+(\frac{5\sqrt{3}}{24})}
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }

Simplify the numerator
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{6}{12} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }
tan( \alpha - \beta )= \frac{ \frac{5-6\sqrt{3}}{12} }{ \frac{24+5\sqrt{3}}{24} }

Simplify the fraction
tan( \alpha - \beta )= (\frac{5-6\sqrt{3}}{12} })({ \frac{24}{24+5\sqrt{3}})
tan( \alpha - \beta )= \frac{10-12\sqrt{3} }{ 24+5\sqrt{3}}

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3 years ago
What the answer to this
neonofarm [45]

Answer:

D

Step-by-step explanation:

(I solved in the picture, firstly look at there)

after completing the square and factoring :

{x}^{2}  + 4x + 4 = 8 + 4

{x}^{2}  + 4x + 4 = 12

{(x  - 2)}^{2} = 12

Hope this helps ^-^

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