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Harlamova29_29 [7]
3 years ago
10

19 – 5x = 9(1+x) solve

Mathematics
2 answers:
Maurinko [17]3 years ago
7 0

\Large\boxed{\tt Answer:~x=\frac{5}{7} }

\tt Step-by-step~explanation:

Remember: PEMDAS - Parentheses, exponents, multiply/divide, add/subtract

Distribute: 9(1+x) = 9+9x

19 - 5x = 9 + 9x

Add 5x to both sides of the equation and subtract 9 from both sides.

19 - 5x + (5x) = 9 + 9x + (5x)

19 - (9) = 9 - (9) + 14x

10 = 14x

Divide both sides by 14 to get the variable on its own.

10/14 = 14x/14

10/14=x

5/7 = x

viva [34]3 years ago
7 0
<h3>Given Equation:</h3>

\boxed{ \sf19 - 5x = 9(1+x)}

<h3>Step-by-step explanation:</h3>

⇢ 19 - 5x = 9(1+x)

⇢ 19 - 5x = 9 × 1 + 9(x)

⇢ 19 - 5x = 9 × 1 + 9x

⇢ 19 - 5x = 9 + 9x

⇢ 19 = 9 + 9x +5x

⇢ 19 = 9 + 14 x

⇢ 19 - 9 = 14x

⇢ 10 = 14x

⇢ 14x = 10

⇢ x = \sf\frac{10}{14}

⇢ x = \sf\frac{2\times 5}{2\times 7}

⇢ x = \sf\frac{\cancel2\times 5}{\cancel2\times 7}

⇢ x = \sf\frac{1\times 5}{1\times 7}

⇢ x = \sf\frac{5}{7}

⇢ x = 0.71 (approx)

Now Let's verify value of x

↬ 19 - 5x = 9(1+x)

put value of x in this equation

↬ 19 - 5 × 0.71 = 9(1+0.71)

↬ 19 - 5 ×0.71 = 9 ×1 + 9 × 0.71

↬ 19 - 5 × 0.71 = 9 + 9 × 0.71

↬ 19 - 5 × 0.71 = 9 + 6

↬ 19 - 3 = 9 + 6

↬ 19 - 3 = 9 + 6

↬ 19 - 3 = 15 + 6

↬ 15 = 15

LHS = RHS

HENCE VERIFIED!

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Cos^2x+cos^2(120°+x)+cos^2(120°-x)<br>i need this asap. pls help me​
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Answer:

\frac{3}{2}

Step-by-step explanation:

Using the addition formulae for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

---------------------------------------------------------------

cos(120 + x) = cos120cosx - sin120sinx

                   = - cos60cosx - sin60sinx

                   = - \frac{1}{2} cosx - \frac{\sqrt{3} }{2} sinx

squaring to obtain cos² (120 + x)

= \frac{1}{4}cos²x + \frac{\sqrt{3} }{2}sinxcosx + \frac{3}{4}sin²x

--------------------------------------------------------------------

cos(120 - x) = cos120cosx + sin120sinx

                   = -cos60cosx + sin60sinx

                   = - \frac{1}{2}cosx + \frac{\sqrt{3} }{2}sinx

squaring to obtain cos²(120 - x)

= \frac{1}{4}cos²x - \frac{\sqrt{3} }{2}sinxcosx + \frac{3}{4}sin²x

--------------------------------------------------------------------------

Putting it all together

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= cos²x + \frac{1}{2}cos²x + \frac{3}{2}sin²x

= \frac{3}{2}cos²x + \frac{3}{2}sin²x

= \frac{3}{2}(cos²x + sin²x) = \frac{3}{2}

                 

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Step-by-step explanation:

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