Factor this expression

The algebraic expression [tex]x^{10/3}[/tex] is equivalent to the algebraic expression [tex]x^{3}\cdot \sqrt[3]{x}[/tex]. Thus, the right choice is option D.

In this question we must apply the following set of algebraic properties to simplify a given expression:

[tex]x^{m/n} = \sqrt[n]{x^{m}} = \left(\sqrt[n]{x}\right)^{m}[/tex]   (1)

[tex]x^{m+n} = x^{m}\cdot x^{n}[/tex]   (2)

[tex]x^{m\cdot n} = \left(x^{m}\right)^{n} = \left(x^{n}\right)^{m}[/tex]   (3)

Where:

And also by apply the definition of power.

If we know that the given expression is [tex]x^{10/3}[/tex], then the equivalent expression is:

[tex]x^{10/3} = \sqrt[3]{x^{10}} = \sqrt[3]{x^{9}\cdot x} = \sqrt[3]{x^{9}}\cdot \sqrt[3]{x} = x^{3}\cdot \sqrt[3]{x}[/tex]

The algebraic expression [tex]x^{10/3}[/tex] is equivalent to the algebraic expression [tex]x^{3}\cdot \sqrt[3]{x}[/tex]. Thus, the right choice is option D.

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Answer:

53.3 somewhere like that

Step-by-step explanation:

Answer:

4 less (less than or Equal to) X (less than or Equal to) 13

Step-by-step explanation:

Note:-

Here

we can see

Hence domain

Answer:

tan is opposite over adjacent soo 12/15=4/5

Step-by-step explanation:

soo the answer is C

Answer:

option d

Step-by-step explanation:

(-3)²=9

(-3)²≠(-9)

Answer:

Explanation:

So you want to start by finding the area of the big square.

We know the width of the big square is 60cm. The length of the big square is

19

+

24

+

13

=

56

Big square

A

r

e

a

=

L

⋅

W

=

56

⋅

60

=

3360

Now let’s find the little square inside the bigger square. We see from the picture that the width is 34 and the length is 24cm. Using the same formula, we can find the area of the little square.

Little square

A

r

e

a

=

L

⋅

W

=

24

⋅

34

=

816

The area enclosed in the area of the big square minus the area of the little square.

3360

−

816

=

2544

So the area enclosed is

2544

c

m

2

Step-by-step explanation:

A product is the outcome of multiplication. Brad can put 144 balls in the box.

A product is the outcome of multiplication or an expression that indicates the elements that will be multiplied.

Given that the bottom layer of the box has 6×6 balls, while the box has 5 layers. Since one layer is already arranged, therefore, there are only 4 layers left in which each layer will have 6×6 balls. Therefore, the total number of balls is,

[tex]\text{Total number of ball} = 4 \times 6\times 6 = 144[/tex]

Hence, Brad can put 144 balls in the box.

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Answer:

100

Step-by-step explanation:

If x is 6 and y is 2 the new equation would look like this: 5(3x6 + 2). 3 times 6 is 18 and add 2 is 20. Therefore you would get 20 times 5. 20x5 is 100

Answer:

Hope that helps

Step-by-step explanation:

Brainliest would be much appreciated

The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².

The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines

b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°)   ⇒   b = 96√3 cm

Call b the base of this triangle.

The vertex angle is 120°, so the other two angles have measure θ such that

120° + 2θ = 180°

since the interior angles of any triangle sum to 180°. Solve for θ :

2θ = 60°

θ = 30°

Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find

tan(30°) = h / (b/2)   ⇒   h = 48 cm

Then the area of the triangle is

1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²

and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:

3072π cm² - 2304√3 cm² ≈ 5660.3 cm²

Answer:

Option C, There are about 3.75 times as many people as pet dogs

Step-by-step explanation:

Step 1:  Determine the ratio

[tex](Amount\ of\ People) / (Amount\ of\ Dogs)[/tex]

[tex](3 * 10^8) / (8 * 10^7)[/tex]

[tex]3.75[/tex]

Answer: Option C, There are about 3.75 times as many people as pet dogs

If we have 360 degrees and need to divide it into 12 equal angles, then all we have to do is a simple division problem.

360 / 12 = 30

There are 30 degrees in each angle.

Hope this helps!

Answer:

30 i think ???

Step-by-step explanation:

Answer:

| Drink (x ml) |   200 |       100 |    500|   1000|  

| Sugar (y g)  | 20      |  10       |    50   |  100   |

Step-by-step explanation:

Formula :  y=k/x

Solve:

Before we find the answer chart =

| Drink (x ml) |   200 |       100 |    500|   1000|  

| Sugar (y g)  | 20     |      ?        |    ?     |      ?      |

20 = ? / 200

? = 10

Thus,

100/10 = 10

500/10 = 50

1000/10 = 100

So the chart now is:

| Drink (x ml) |   200 |       100 |    500|   1000|  

| Sugar (y g)  | 20      |  10       |    50   |  100   |

~lenvy~

Step-by-step explanation:

The lines meet at (6,0)

That is the solution to the system of equations.

Answer:

20

Step-by-step explanation:

4*5-(2-2) =

(Make sure to use BODMAS to solve correctley in order)

4*5=

20

Answer:

0 ones + 18 tenths + 3 hundredths

Step-by-step explanation:

Answer:

yes it's O ones + 18 tenths + 3 hundredths

Step-by-step explanation:

I took the test

Answer:

75%

Step-by-step explanation:

You turn the information into a fraction which is 15/20.

20x 5= 100, and everything you do in the bottom you have to do the top and 15 times 5 is 75.

Hope it helps

Answer:

The answer my good friend is 7776 because if you do 6 to the 5th power  or 6x6x6x6x6 you will get 7776.

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

we'll make x the number of hours and set up the following equation:

59km x + 67km x = 1008km

Now we solve for x(hours)

126x = 1008

x = 8

Answer:

[tex]\fbox{length= 10 \: in}

[/tex]

Step-by-step explanation:

Given:

Length to Width Ratio = 2:3

Area of Rectangle= 150 in²

To find:

Length of rectangle=?

Solution:

Assume the length of rectangle is 2x

and the width of rectangle is 3x

Now,

we know that,

[tex]\sf\: Area \: of \: Rectangle = Length \times Width \\ \sf \: 150 = 2x \: \times 3x \\ \sf \: 150 =6 {x}^{2} \\ \sf \: {x}^{2} = \frac{150}{6} \\ \sf {x}^{2} = \cancel\frac{150}{6} \\\sf {x}^{2} = 25 \\\sf \sqrt{ {x}^{2} } = \sqrt{ {25} } \\ \sf \sqrt{ {x}^{2} } = \sqrt{ {5}^{2} } \\ \sf \: \fbox{x = 5 \: in}[/tex]

Substituting the value of x in assumption,

[tex] \sf \: length= 2x \\ \sf \: length= 2 \times 5 \\ \sf \: \fbox{length= 10 \: in}

[/tex]

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Step-by-step explanation:

area of inner rectangle = 10*8 = 80 units^2

area of outer rectangle = 12*10 = 120 units^2

area of shaded portion = 40units^2

The root of the system of equations is x = -1

That is, the lines intersect at (x,y)= (-1,-5)

Answer:

234

Step-by-step explanation:

If reflected over y = x

then use

[tex]\left[\begin{array}{ccc}0&1\\1&0\end{array}\right][/tex]

=====================

[tex]\left[\begin{array}{ccc}0&1\\1&0\end{array}\right] \left[\begin{array}{ccc}3&6&3\\-3&3&3\end{array}\right][/tex]

similar as (x, y) → (y, x)

multiply the matrixes to get the final answer

[tex]\left[\begin{array}{ccc}(3*0+1*-3)&(6*0+1*3)&(3*0+1*3)\\(3*1+(-3*0)&(1*6+0*3)&(1*3+0*3)\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-3&3&3\\3&6&3\end{array}\right][/tex]

Answer:

[3,-3,-3] [-3,-6,3]

Step-by-step explanation:

jus got it right

byAnswer: doing the trials/tests

Step-by-step explanation: Learn With Brainly