Please help me I have been stuck

Mathematics

1 answer:

Mnenie [13.5K]2 years ago

8 0

I think you have to pay attention in class for this

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Simplify: 4(3x^2y^4)^3 / 2x^3y^5)^4

Semenov [28]

Step by step solution :Step 1 :Equation at the end of step 1 : (((3•(x2))•(y4))3) 4•—————————————————— ((2x3•(y5))4) Step 2 :Equation at the end of step 2 : ((3x2 • (y4))3) 4 • ——————————————— 24x12y20 Step 3 : 33x6y12 Simplify ———————— 24x12y20 Dividing exponential expressions :

3.1 x6 divided by x12 = x(6 - 12) = x(-6) = 1/x6

Dividing exponential expressions :

3.2 y12 divided by y20 = y(12 - 20) = y(-8) = 1/y8

Equation at the end of step 3 : 27 4 • —————— 16x6y8 Step 4 :Final result : 27 ————— 4x6y8

6 0

2 years ago

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Write 0.6 as a fraction ?

satela [25.4K]

Answer:

6/10 ; 3/5 (simplified form)

Step-by-step explanation:

To solve, note the decimal place value. Move the decimal point to the right two place values, and set it over 100

0.6 = 60/100

Simplify the fraction. Divide common factors from the numerator & denominator (20 in this case)

(60/100)/(20/20) = 3/5

3/5 is your answer

7 0

2 years ago

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If x^2+1/x^2=3 find the value of x^2/(x^2+1)^2 Express answer as a common fraction. Thanks!!

timama [110]

$x^2+\dfrac1{x^2}=3\implies x^4+1=3x^2\implies x^4-3x^2+1=0$

By the quadratic formula,

$x^2=\dfrac{3\pm\sqrt5}2\implies x^2+1=\dfrac{5\pm\sqrt5}2$

Then

$(x^2+1)^2=\dfrac{25\pm10\sqrt5+5}4=\dfrac{15\pm5\sqrt5}2$

$\implies\dfrac{x^2}{(x^2+1)^2}=\dfrac{\frac{3\pm\sqrt5}2}{\frac{15\pm5\sqrt5}2}=\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}$

Multiply numerator and denominator by the denominator's conjugate:

$\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}\cdot\dfrac{15\mp5\sqrt5}{15\mp5\sqrt5}=\dfrac{45\pm15\sqrt5\mp15\sqrt5-25}{15^2-(5\sqrt5)^2}=\dfrac{20}{100}=\dfrac15$