All categories

3 years ago

Identify all of the real fifth roots of 1024.

Mathematics

2 answers:

V125BC [204]3 years ago

8 0

Answer:

Real fifth root of 1024 is 4.

Step-by-step explanation:

We have to find the value of real fifth root of 1024.

For this let fifth root of 1024 = x

Therefore $x^{5} = 1024 = 4^{5}$

Or $x^{5}=4^{5}$

Therefore x = 4

X= 4 is the right answer.

muminat3 years ago

4 0

Answer:

$\large\boxed{\sqrt[5]{1024}=4}$

Step-by-step explanation:

$\begin{array}{c|c}1024&2\\512&2\\256&2\\128&2\\64&2\\32&2\\16&2\\8&2\\4&2\\2&2\\1\end{array}\\\\1024=\underbrace{2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2}_{10}=2^{10}\\\\\sqrt[5]{1024}=\sqrt[5]{2^{10}}\\\\\text{Use}\ (a^n)^m=a^{nm}\\\\=\sqrt[5]{2^{2\cdot5}}=\sqrt[5]{(2^2)^5}=\sqrt[5]{4^5}\\\\\text{Use}\ \sqrt[n]{a^n}=a\\\\=\boxed4$

You might be interested in

Quadrilateral ABCD with vertices A(0, 6), B(-3, -6), C(-9, -6), and D(-12, -3): a) dilation with scale factor of 1/3 centered at

Oksanka [162]

a) The points of the new quadrillateral are $A'(x,y) = (0, 2)$ , $B'(x,y) = (-1, -2)$ , $C'(x,y) = \left(-3,-2\right)$ and $D'(x,y) = (-4, -1)$ , respectively.

b) The points of the new quadrillateral are $A'(x,y) = (-5, 5)$ , $B'(x,y) = (-8,-7)$ , $C'(x,y) = (-13, -7)$ and $D'(x,y) = (-17, -4)$ , respectively.

<h3>How to perform transformations with points</h3>

a) A dillation centered at the origin is defined by following operation:

$P'(x,y) = k\cdot P(x,y)$ (1)

Where:

$P(x,y)$ - Original point
$P'(x,y)$ - Dilated point.

If we know that $k = \frac{1}{3}$ , $A(x,y) = (0,6)$ , $B(x,y) = (-3,-6)$ , $C(x,y) = (-9, -6)$ and $D(x,y) = (-12, -3)$ , then the new points of the quadrilateral are:

$A'(x,y) = \frac{1}{3}\cdot (0,6)$

$A'(x,y) = (0, 2)$

$B'(x,y) = \frac{1}{3} \cdot (-3,-6)$

$B'(x,y) = (-1, -2)$

$C'(x,y) = \frac{1}{3}\cdot (-9,-6)$

$C'(x,y) = \left(-3,-2\right)$

$D'(x,y) = \frac{1}{3}\cdot (-12,-3)$

$D'(x,y) = (-4, -1)$

The points of the new quadrillateral are $A'(x,y) = (0, 2)$ , $B'(x,y) = (-1, -2)$ , $C'(x,y) = \left(-3,-2\right)$ and $D'(x,y) = (-4, -1)$ , respectively. $\blacksquare$

b) A translation along a vector is defined by following operation:

$P'(x,y) = P(x,y) +T(x,y)$ (2)

Where $T(x,y)$ is the transformation vector.

If we know that $T(x,y) = (-5,-1)$ , $A(x,y) = (0,6)$ , $B(x,y) = (-3,-6)$ , $C(x,y) = (-9, -6)$ and $D(x,y) = (-12, -3)$ ,

$A'(x,y) = (0,6) + (-5, -1)$

$A'(x,y) = (-5, 5)$

$B'(x,y) = (-3, -6) + (-5, -1)$

$B'(x,y) = (-8,-7)$

$C'(x,y) = (-9, -6) + (-5, -1)$

$C'(x,y) = (-13, -7)$

$D'(x,y) = (-12,-3)+(-5,-1)$

$D'(x,y) = (-17, -4)$

The points of the new quadrillateral are $A'(x,y) = (-5, 5)$ , $B'(x,y) = (-8,-7)$ , $C'(x,y) = (-13, -7)$ and $D'(x,y) = (-17, -4)$ , respectively. $\blacksquare$

To learn more on transformation rules, we kindly invite to check this verified question: brainly.com/question/4801277

7 0

2 years ago

Check the following pair of linear equations is consistent or inconsistent

alexandr1967 [171]

Answer:

Consistent

Step-by-step explanation:

It was a solution.

8 0

3 years ago

Read 2 more answers

Solve the equation<br>algebra 2<br><br>-6=3x-6y<br>4x=4+5x

Talja [164]

3x = 6y - 6
x = 2y - 2

4 ( 2y - 2 ) = 4 + 5 ( 2y - 2 )
8y - 8 = 4 + 10y - 10
2y = - 2
y = - 1

x = 2 ( - 1 ) - 2
x = - 4

i am a mathematics teacher. if anything to ask please pm me

6 0

3 years ago

What is the solution for x in the equation?<br><br> 10x − 4.5 + 3x = 12x − 1.1

Aleksandr [31]

Answer:in first part of equation add 10x and 3x (like terms)

13x-4.5=12x-1.1

move all terms containing x to left side of equation

13x-4.5-12x= -1.1

x-4.5= -1.1

Subtract 4.5 from both sides

x=3.4

Step-by-step explanation: