2 years ago

The letters that we use when are writing the exponent rules are called..

Mathematics

1 answer:

konstantin123 [22]2 years ago

3 0

Laws of exponents or rules of exponents? I’m sorry if I’m wrong

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If x^2+1/x^2=3 find the value of x^2/(x^2+1)^2<br> Express answer as a common fraction.<br> 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:

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

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3 years ago

Mrs.Dimitri purchased a case of yogurt cups. Out of every 10 yogurt cups, 6 are strawberry. There are 30 guy hurt cups in the ca

miv72 [106K]

18 cups, if you triple the amount without changing the percentage of strawberry, then the amount of strawberry yoghurt is also tripled

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2 years ago

Read 2 more answers

1-Solve: m - 9 = -13

timofeeve [1]

1: m=-4
2: b=-4
3: -9=k
4: C=-11.4
5:X<10

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3 years ago

Looking for right triangle side a is 1 inch long,and side b is 2 inches long. What is the length of side c?

Sergeeva-Olga [200]

Answer:

$\sqrt{5}$

Step-by-step explanation:

$a^{2} + b^{2} = c^{2}$

In this situation a = 1, b = 2

$1^{2} + 2^{2} = c^{2}$

1 + 4 = $c^{2}$

5 = $c^{2}$

c = $\sqrt{5}$

This is an important mathematical theorem to know. It's called the Pythagorean Theorem.

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2 years ago

Help me I will really appreciate it

kotykmax [81]

Answer:

The answer is (1,-1)

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2 years ago