please select the best answer from the choices provided

Using the properties of exponents, the expression is simplified as (4/3)x⁵y².

To simplify the given expression, we need to use properties of exponents

Taking the numerator;

[(2x³y)⁴] = (2⁴)(x³)⁴(y)⁴ = 16x¹²y⁴

Next, let's simplify the denominator:

3x²(4x⁵y²) = 3 * 4 * x² * x⁵ * y² = 12x⁷y²

This can be expressed as;

[(2x³y)⁴] / [3x²(4x⁵y²)] = (16x¹²y⁴) / (12x⁷y²)

Take the common factors and divide both of them;

(16x¹²y⁴) / (12x⁷y²) = (4/3)(x¹² / x⁷)(y⁴ / y²) = (4/3)x¹²⁻⁷y⁴⁻² = (4/3)x⁵y²

Therefore, the simplified expression is (4/3)x⁵y².

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The following inequality are matched with their graphical solution;

6. 4y + 3 ≤ y + 6. graph C

7. -2y > 2. graph A

8. y/3 < -1. graph D

9. 3y < 2y + 3. graph B

6.

4y + 3 ≤ y + 6

Combine like terms

4y - y ≤ 6 - 3

3y ≤ 3

Divide both sides by 3

y ≤ 3/3

y ≤ 1

7.

-2y > 2

Divide both sides by -2

y < 2/-2

y < -1

8.

y/3 < -1

cross product

y < -1 × 3

y < -3

9.

3y < 2y + 3

Subtract 2y from both sides

3y - 2y < 3

y < 3

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Answer:

The average age is 30.4.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Edge 2021

Measurement of the bookcase on the scale drawing using the scale 3cm:2 feet is width =19.5 cm and height = 36 cm

Scaling an object means multiplying every linear dimension of it by the same factor

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given,

Width of the bookcase = 13 feet

Height of the bookcase = 24 feet

Given scale is 3cm : 2 feet

Therefore for 1 feet = 1.5 cm

Then,

Width of the bookcase = 13×1.5= 19.5 cm

Height of the bookcase = 24×1.5= 36 cm

Hence, the measurements of the bookcase after scaling is width =19.5 cm and height = 36 cm

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The dimensions of the rooms in the blueprint will be Living room ([tex]5\times2[/tex]), Kitchen ([tex]4\times4[/tex]), Office ([tex]2\times4[/tex]), Bedroom ([tex]2\times4[/tex]), Bedroom ([tex]5\times5[/tex]), Bathroom ([tex]1.5\times2[/tex]).

Given information:

A house blueprint has a scale of 1 in : 4 ft.

The length and width of each room in the actual house are shown in the table below:

  Living room  Kitchen  Office  Bedroom  Bedroom     Bathroom

Length  20             16    8              8                      20                6

width 8             16    16              16              20                8

The scale factor is of 1 in: 4 ft. So, 4 ft of actual length is equivalent to 1 inch in the blueprint.

So, the length and width of the different rooms in te house in the blueprint will be,

  Living room  Kitchen  Office  Bedroom  Bedroom       Bathroom

Length(in) 5             4            2              2                      5                        1.5

width(in)   2             4            4              4                      5                          2

Therefore, the dimensions of the rooms in the blueprint will be Living room ([tex]5\times2[/tex]), Kitchen ([tex]4\times4[/tex]), Office ([tex]2\times4[/tex]), Bedroom ([tex]2\times4[/tex]), Bedroom ([tex]5\times5[/tex]), Bathroom ([tex]1.5\times2[/tex]).

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Answer:

C)82 Degrees F

Step-by-step explanation:

The formula we have is F = 9/5C + 32.  Substituting the value for Celsius, 28, into the formula,

F = 9/5(28) + 32

F = 1.8(28) + 32

F = 50.4 + 32

F = 82.4

To the nearest whole number, this is 82 degrees.

The converted temperature in degrees Fahrenheit is 82 Degrees F

Temperature conversion is the process of changing the value of temperature from one unit to another. We measure temperature on scales like Kelvin, Celsius, and Fahrenheit, etc.

Given that, the temperature in Australia, is 28 degrees C, Ed wasn’t sure if that was hot or cold, so he converted the temperature to degrees in Fahrenheit.

We know that,

The formula to convert the temperature into Fahrenheit is:

F = 9/5C + 32.  

Substituting the value for Celsius, 28, into the formula,

F = 9/5(28) + 32

F = 1.8(28) + 32

F = 50.4 + 32

F = 82.4

Hence, the converted temperature in degrees Fahrenheit is 82 Degrees F

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Answer:

Dalai have 45 marbles.

Step-by-step explanation:

Consider the provided information.

Dalai bought a few swirl marbles and divided it equally among four of her friends and her brother, Jake. while playing, Jake lost two marbles and has only 7 marbles at present.

Let x is the number of marbles Dalai have.

She divide x number of marbles into 5 equal part (Four of friend and her brother)

That means each of them have [tex]\frac{x}{5}[/tex] marbles.

Jake lost two marbles out of [tex]\frac{x}{5}[/tex] and now he has only 7 marbles,

This can be represented as:

[tex]\frac{x}{5}-2=7[/tex]

Solve the equation for x.

[tex]\frac{x}{5}=7+2[/tex]

[tex]\frac{x}{5}=9[/tex]

[tex]x=45[/tex]

Hence, Dalai have 45 marbles.

Answer:

the answer would be A

Step-by-step explanation:

I hope  this is helpful

Answer: The expression that is quivalent to to 0.2n + 2n + 4 is

2.2n +4

Hope this helped! -mojo jojo x

Solution:

we are given that

In the image, shape ABCD is similar to shape WXYZ.

we have been asked to find the measure of side ZW.

As we know that when two shapes are similar then the ratios of their corresponding sides are equal.

So we can write

[tex] \frac{zw}{6}= \frac{18}{24}\\ \\ ZW=6*\frac{18}{24}\\ \\ ZW=\frac{18}{4}\\ \\ ZW=4.5\\ [/tex]

Hence ZW=4.5 Inches.

Answer:

4.5

Explanation:

Got it right on Imagine math.

Final answer:

The jogger is approximately 7 miles from his house after running 3 miles east and then 5 miles at a 30° angle east of north, calculated using trigonometric functions and the Pythagorean theorem.

Explanation:

The question asks how far a jogger is from his house after running a total of 8 miles, initially 3 miles due east and then 5 miles at a 30° angle east of north. To solve this, we can use trigonometric functions to find the resultant displacement. The first leg of the journey is straightforward, 3 miles directly east. The second leg can be broken into its northward and eastward components using sine and cosine functions, with the length of the leg being the hypotenuse.

Northward component: 5 miles × cos(30°) = 4.33 miles

Eastward component: 3 miles (initial) + (5 miles × sin(30°)) = 3 + 2.5 = 5.5 miles

To find the total displacement, we calculate the straight-line distance from the starting point to the end point using the Pythagorean theorem.

Displacement = √(northward component² + eastward component²) = √(4.33² + 5.5²) = √(18.7489 + 30.25) = √(48.9989) = 7 miles approximately.

Therefore, the jogger is approximately 7 miles from his house.

To find the distance and direction from the starting point after the jogger's two separate runs, we apply vector addition by decomposing the second leg into its components with trigonometry and then use the Pythagorean theorem and arctangent function to find the resultant magnitude and direction.

The question involves determining the distance from the starting point after a two-leg journey with given directions and distances. To solve this, we need to apply principles of vector addition to combine the two displacements into one resultant displacement. The first displacement is due east, and can be represented as a straight line on a horizontal axis. The second displacement, at a 30° angle east of north, requires us to decompose it into its northward and eastward components. These components are found using trigonometry: by multiplying the distance by the cosine (for the eastward part) and sine (for the northward part) of the angle.

After computing the respective components of the second displacement, we add both eastward displacements together and both northward displacements together to find the total displacement in the east and north directions. The final step is to use the Pythagorean theorem to determine the magnitude of the resultant vector, and trigonometry (specifically, the arctangent function) to find the direction of the resultant vector from the origin, which provides the required distance and direction from the jogger's house after running.