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3 years ago

How to right a radical in exponential form

Mathematics

1 answer:

Law Incorporation [45]3 years ago

3 0

Answer:

$\sqrt[n]{x}=x^{\frac{1}{n}}$

Step-by-step explanation:

The index of a radical is the denominator of a fractional exponent, and vice versa. If you think about the rules of exponents, you know this must be so.

For example, consider the cube root:

$\sqrt[3]{x}\cdot \sqrt[3]{x}\cdot \sqrt[3]{x}=(\sqrt[3]{x})^3=x\\\\(x^{\frac{1}{3}})^3=x^{\frac{3}{3}}=x^1=x$

That is ...

$\sqrt[3]{x}=x^{\frac{1}{3}} \quad\text{radical index = fraction denominator}$

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The equation 4x2 – 24x + 4y2 + 72y = 76 is equivalent to

DerKrebs [107]

Answer:

Option 4 is correct.

The equation $4x^2 -24x + 4y^2 + 72y = 76$ is equivalent to $4(x-3)^2 + 4(y+9)^2 =436$

Step-by-step explanation:'

Given equation: $4x^2 -24x + 4y^2 + 72y = 76$

First group the terms with x and those with y;

$(4x^2-24x)+(4y^2+72y) = 76$

Next, we complete the squares.

We can do this by adding a third term such that the x terms and the y terms are perfect squares.

For this we must either add the same value on the other side of the equation or subtract the same value on the same side so that the equality is maintained.

⇒ $4(x^2-6x) +4(y+18y) = 76$

$4(x^2 -6x +3^2 -3^2) + 4(y^2 +18y +9^2 -9^2) = 76$

$4(x^2-6x + 3^2) - 36 + 4(y^2+18y +9^2) - 324 = 76$

$4(x-3)^2 + 4(y+9)^2 - 360 =76$

Add 360 on both sides we get;

$4(x-3)^2 + 4(y+9)^2 =360 +76$

Simplify:

$4(x-3)^2 + 4(y+9)^2 =436$

Therefore, the given equation is equivalent to $4(x-3)^2 + 4(y+9)^2 =436$

5 0

3 years ago

The 70th term of an arithmatic sequence is 121.5 the common difference is 1.5. Find a12. (write a rule to find a12)

Katen [24]

Answer:

$a_{12}$ = 34.5

Step-by-step explanation:

The n th term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given $a_{70}$ = 121.5, then

a₁ + (69 × 1.5) = 121.5

a₁ + 103.5 = 121.5 ( subtract 103.5 from both sides )

a₁ = 18

Hence

$a_{12}$ = 18 + (11 × 1.5) = 18 + 16.5 = 34.5

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2 years ago

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stira [4]

Answer:29,400 ft^3

Step-by-step explanation:

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2 years ago

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Your writing an essay describing a famous Painting. Which pattern of organization would be BEST for this essay.

skad [1K]

<span>C. order of importance </span>

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3 years ago

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the vertices of PQR are P(-5,1), Q(-4,6), and R(-2,3), graph P"Q"R" after a composition of the transformations in the order they

horsena [70]

SOLUTION

We are told to translate; (x, y) to (x -8, y). This means we have to add - 8 to each value of x in P(-5,1), Q(-4,6), and R(-2,3).

In P(-5,1), x = -5 and y = 1

In Q(-4,6), x = -4 and y = 6 and

In R(-2,3), x = -2 and y = 3

$\begin{gathered} P(-5,\text{ 1) translates to (-5 -8, 1) }\rightarrow P^i(-13,\text{ 1)} \\ Q(-4,\text{ 6) translates to (-4 -8, 6) }\rightarrow Q^i(-12,\text{ 6)} \\ R(-2,\text{ 3) translates to (-2 -8, 3) }\rightarrow R^i(-10,\text{ 3)} \end{gathered}$

For the dilation centered at the origin k =2, simply multiply the value of k, which is 2 into the translations.

$\begin{gathered} At\text{ K = 2, }P^i(-13,\text{ 1) }\rightarrow\text{ }2(-13,\text{ 1) }\rightarrow\text{ }P^{ii}(-26,\text{ 2)} \\ Q^i(-12,\text{ 6) }\rightarrow\text{ }2(-12,\text{ 6) }\rightarrow\text{ Q}^{ii}(-24,\text{ 12)} \\ R^i(-10,\text{ 3) }\rightarrow\text{ }2(-10,\text{ 3) }\rightarrow\text{ R}^{ii}(-20,\text{ 6)} \end{gathered}$

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1 year ago