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Lemur [1.5K]
3 years ago
10

Solve the equation INCLUDE THE FORMULA x - 5 = 3 - 5x + 3x + 4

Mathematics
1 answer:
weeeeeb [17]3 years ago
7 0

Answer:

x = 4

Step-by-step explanation:

  • x-5 = 3-5x+3x+4
  • x = 3-5x+3x+4+5
  • x = 3-5x+3x+9
  • x = -5x+3x+12
  • x+5x =3x+12
  • 6x =3x+12
  • 6x-3x = 12
  • 3x = 12
  • x = 12/3
  • x = 4
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The area of a rectangular fountain is x2 + 9x + 20 square feet. A 3-foot walkway is built around the fountain. Find the dimensio
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Answer:

(x+11) by (x+10)

Step-by-step explanation:

We know that Area = Length x width

Given: Area = x²+9x+20

Lets sort this out first

Area = x²+5x + 4x + 20

Area = x(x+5) + 4(x+5)

Area = (x+5) (x+4)

Therefore, it is concluded that:

Length 'l' = (x+5) feet

Width 'w' = (x+4) feet

if a 3-foot walkway is built around the fountain, we'll add 3 feet on both sides

Therefore,

Outer Length = (x+5+3+3) = (x+11) feet

Outer Width = (x+4+3+3) = (x+10) feet

Answer:

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3 years ago
URGENT HELP PLEASE!
Vaselesa [24]

Answer:

(a) x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}

(b) x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}

Step-by-step explanation:

It is given that 0\leq x\leq 2\pi.

(a)

\sqrt{2}\sin 2x=1

\sin 2x=\dfrac{1}{\sqrt{2}}

\sin 2x=\dfrac{\pi}{4}

2x=\dfrac{\pi}{4},\dfrac{3\pi}{4},\dfrac{9\pi}{4},\dfrac{11\pi}{4}     [\because \sin x=\sin y\Rightarrow x=n\pi+(-1)^ny]

x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}

(b)

\csc^2 x-\csc x-2=0

\csc^2 x-2\csc x+\csc x-2=0

\csc x(\csc x-2)+1(\csc x-2)=0

(\csc x+1)(\csc x-2)=0

\csc x=-1\text{ or }\csc x=2

\sin x=-1\text{ or }\sin x=\dfrac{1}{2}         [\because \sin x=\dfrac{1}{\csc x}]

x=\dfrac{3\pi}{2}\text{ or }x=\dfrac{\pi}{6},\dfrac{5\pi}{6}

Therefore, x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}.

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