Order the simplification steps of the expression below using the properties of rational exponents.​

Answer:

[tex]\frac{\sqrt[4]{3x^2} }{2y}[/tex]

Step-by-step explanation:

We can simplify the expression under the root first.

Remember to use  [tex]\frac{a^x}{a^y}=a^{x-y}[/tex]

Thus, we have:

[tex]\sqrt[4]{\frac{24x^{6}y}{128x^{4}y^{5}}} \\=\sqrt[4]{\frac{3x^{2}}{16y^{4}}}[/tex]

We know 4th root can be written as "to the power 1/4th". Then we can use the property  [tex](ab)^{x}=a^x b^x[/tex]

So we have:

[tex]\sqrt[4]{\frac{3x^{2}}{16y^{4}}} \\=(\frac{3x^{2}}{16y^{4}})^{\frac{1}{4}}\\=\frac{3^{\frac{1}{4}}x^{\frac{1}{2}}}{2y}\\=\frac{\sqrt[4]{3x^2} }{2y}[/tex]

Option D is right.

Answer:

The oven mitts cost

$13.80

But, Cook-n-Serve buys from a wholesaler, so they receive a discount of 40%

This means that they pay

(1-0.4)*($13.80) = 0.6*($13.80) = $8.28 for each pair

The markup rate on cost is 60%

And they sell for

$13.80/$8.28 = 1.67 times the price

1.67*100% = 167%

The markup rate on selling price is  167%

Answer:

The reflected point is (3,6)

Step-by-step explanation:

we know that

The reflection Ry = 5, means a reflection is across the line y= 5

we have

the point P(3,4)

Since the point P has y-coordinate  4, its distance to the line y= 5 is equal to 1 units (P is located 1 units down the line y=5).

therefore

The reflection of the y-coordinate will be 1 units above the line y=5, which is  equal to

5+1=6

Hence

the y-coordinate of the image is 6.

The reflected point is (3,6)

To reflect a point about the y-axis, negate the x-coordinate while keeping the y-coordinate the same.

In this question, you are given the point P(3,4) and asked to find Ry=5(P). The notation Ry=5(P) represents the reflection of point P about the y-axis. To reflect a point about the y-axis, you need to replace the x-coordinate with its opposite (negate it) while keeping the y-coordinate the same.

So, P(3,4) reflected about the y-axis becomes (-3,4). The x-coordinate changes from 3 to -3, but the y-coordinate remains the same at 4.

Therefore, Ry=5(P) is (-3,4).

Answer: y=-8-4/1

Step-by-step explanation:

Answer:

The slope is  m= 4.

Step-by-step explanation:

Do Rise over run method. Then divide the two numbers.

Answer:

That is < 3.

Step-by-step explanation:

It is the angle between the (dotted)  horizontal  from B and the line going B and C.

All real numbers.

[tex]\boxed{TRUE}[/tex]

Step-by-step explanation:

Distributive property: a(b+c)=ab+ac

Expand: 4(a+2)=4a+8

Expand again: 14-2(3-2a)=4a+8

4a+8=4a+8

You subtract by 8 from both sides of an equation.

4a+8-8=4a+8-8

Simplify.

4a=4a

Then, subtract by 4a from both sides of an equation.

4a-4a=4a-4a

Finally, simplify.

4a-4a=0

0=0

True

All real numbers is the final answer.

Hope this helps you!

Have a nice day! :)

Answer:

D. All real numbers except 0.

Step-by-step explanation:

The figure show a particular case of a hyperbola, which is continuous for all values of x, except the value of x where discontinuity exists. Hence, the domain of the function is all real numbers except 0.

Answer:

Westmoreland County, VA

Answer:

Yhe equation that jas the steepest gradient is D

Step-by-step explanation:

look at the numbers infront of the 'x' without looking at the negative sign. The

larger the number the steeper the gradient. Negative gradient only means that it is a downward slope

Answer:

Step-by-step explanation:

D

Answer:

Step-by-step explanation:

1 unit = 14 pence

and

1 times 942 = 942 so 14 times 942 = 13,188

therefore

942 units cost £131.88!!hope it help:):)

Final answer:

To calculate the total cost for 942 units at 14p each, multiply the cost per unit by the number of units [tex](942 imes 14p)[/tex]resulting in 13,188p, which is £131.88.

Explanation:

If each unit costs 14p, to find the total cost of 942 units, we need to multiply the cost per unit by the total number of units. The calculation is as follows:

[tex]942 units imes 14p per unit = 13,188p[/tex]

Since there are 100 pence in a pound, we need to convert pence into pounds:

[tex]13,188p \/ 100 = \£131.88\[/tex]

[tex]Therefore, the total cost for 942 units is \£131.88\.[/tex]

Answer:

A. Scalene since all sides have different lengths

E. Right since it has a right angle

Answer:

Exponential growth is called growth because its curve increases really fast, so that's the main characteristic of exponential growth. I'm attaching an example of a function with exponential growth, which is the change of population size over time.

To find the midpoint, add the 2 x values together and divide by 2, then add the 2 Y values together and divide by 2.

(5-13)/2, (-4+12)/2

-8/2 , 8/2

-4,4

The answer is (-4,4)

Answer:

a = 80°

Step-by-step explanation:

Since PS and QR are parallel lines, then

a = 80° ( alternate angles )

Answer:

a = 80°

Step-by-step explanation:

Since PS and QR are parallel lines, then

a = 80° ( alternate angles )

Answer:

x = 3

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠QRT is an exterior angle of the triangle

∠RTS and ∠RST are the 2 opposite interior angles, thus

45x = 25x + 57 + x

45x = 26x + 57 ( subtract 26x from both sides )

19x = 57 ( divide both sides by 19 )

x = 3

Answer:

Brown's experimental probability is closest to it's theoretical probability.

Step-by-step explanation:

Theoretical:

There are 5 colors so the probability of getting orange is 1/5

The probability of getting purple is 1/5

and so on... each color has the probability of 1/5 of being used

We just need to see what experimental probability is closest to .2

Experimental probability:

So Orange 118/625=.1888

Purple 137/625=.2192

Brown 122/625=.1952

Yellow 106/625=.1696

Green 142/625=.2272

So the closest from below .2 is .1952 (which is brown)

The closest from above .2 is .2192 (which is purple.

If you aren't sure which one is closer.. you can see which difference is closer to 0.

.2-.1952=.0048

.2192-.2=.0192

.1952 is the winner since .0048 is closer to 0 than .0192 is

So Brown !

Answer:

73

Step-by-step explanation:

F(c)= 9/5 c + 32

Let C = 23

F(23) = 9/5 (23) +32

          = 41.4 +32

        =73.4

To the nearest degree

73

Answer:

2

Step-by-step explanation:

1/2 is the same as saying 0.5

0.5 x 4     is the same as saying      0.5 + 0.5 + 0.5 + 0.5

0.5 + 0.5 + 0.5 + 0.5 = 2

Answer:

D

Step-by-step explanation:

Given

- 1(x + 7)(x - 4)

each term in the second factor is multiplied by each term in the first factor, that is

leaving the multiplier of - 1 for the time being

x(x- 4) + 7(x - 4) ← distribute both parenthesis

= x² - 4x + 7x - 28 ← collect like terms

= x² + 3x - 28

Hence

- 1(x² + 3x - 28) = - x² - 3x + 28 → D

Answer:

D

Step-by-step explanation:

The expression below is the factorization of what trinomial?

-1(x+ 7)(x-4)

A. -x^2 + 3x+ 28

B. -x^2 + 3x-28

C. -x^2 - 3х - 28

D. -x^2 - 3x+ 28

Answer:

1152

Step-by-step explanation:

First we need to find the area of the wall in square inches

8 ft = 8*12 = 96 inch tall

36 ft = 36 * 12 = 432 inches wide

The area = 96 * 432 =41472 in^2

Each ounce of paint cover 72 in^2 so divide by 72

41472/72 =576

We need 576 ounces to cover the wall

At 2 dollars per ounces

576*2 =1152 dollars to paint the wall

For this case we must find the product of the following expressions:[tex](-2x ^ 2 + x-5) (x ^ 3-3x-4) =[/tex]

We must apply distributive property, that is, multiply each term:

We must bear in mind that:

[tex]+ * - = -\\- * - = +[/tex]

[tex]-2x ^ {2 + 3} + 6x^{2 + 1} + 8x ^ 2 + x^{3 + 1} -3x^{1 + 1} -4x-5x ^ 3 + 15x + 20 =\\-2x ^ 5 + 6x ^ 3 + 8x ^ 2 + x ^ 4-3x ^ 2-4x-5x ^ 3 + 15x + 20[/tex]

If we multiply[tex](x ^ 3-3x-4) (- 2x ^ 2 + x-5)[/tex] we would obtain the same result according to the commutative property of the multiplication:

[tex]a * b = b * a[/tex]

Answer:

[tex]-2x ^ 5 + 6x ^ 3 + 8x ^ 2 + x ^ 4-3x ^ 2-4x-5x ^ 3 + 15x + 20[/tex]

Answer:

The CORRECT answer is  -2x^6 + 7x^4 + 3x^3 – 3x^2 + 11x + 20

Step-by-step explanation:

I go to k12 and all the other answers are incorrect. I had this on my test.  

MY WORK:

-2x^6 + 6x^4 + 8x^3 + x^4 – 3x^2 – 4x – 5x^3 + 15x + 20

= -2x^6 + 7x^4 + 3x^3 – 3x^2 + 11x + 20  

b) Yes, it would be equal because of the rule of the commutative property. (basically, the order in which you multiply won’t matter.)            

Answer:

[tex]P(x\:<\:50)=0.0918[/tex]

Step-by-step explanation:

To  find the probability that a randomly selected test taker scored below 50, we need to first of all determine the z-score of 50.

The z-score for a normal distribution is given by:

[tex]z=\frac{x-\bar x}{\sigma}[/tex].

From the question, the mean score is [tex]\bar x=70[/tex], the standard deviation is, [tex]\sigma=15[/tex], and the test score is [tex]x=50[/tex].

We substitute these values into the formula to get:

 [tex]z=\frac{50-70}{15}[/tex].

 [tex]z=\frac{-20}{15}=-1.33[/tex].

We now read the area that corresponds to a z-score of -1.33 from the standard normal distribution table.

From the table, a z-score of -1.33 corresponds to and area of 0.09176.

Therefore the probability that a randomly selected test taker scored below 50 is [tex]P(x\:<\:50)=0.0918[/tex]

The next step is to add (b/2a)^2 to both sides to complete the square, then balance the equation by adding the inverse of that value outside the parentheses.

The student has asked for the next step in solving the quadratic equation 0 = −2x2 + 2x + 3 by completing the square.

After rewriting the equation and factoring out the coefficient of the x2 term, the next step is to add a specific value to both sides to form a perfect square trinomial.

This value is found by taking (b/2a)2, where a is the coefficient of x2 and b is the coefficient of x. For this equation, we therefore add −(2/2*(-2))2 = 1 to both sides inside the parentheses.

The completed equation becomes −3 + 1 = −2*(x2 − x + 1/4). Finally, we must balance the equation by adding the inverse of −<strong>2*1/4</strong> outside the parentheses.

Then, we can continue solving for x.

([tex]x^{2}[/tex] + 4)([tex]x^{2}[/tex] - 4)

To solve this question you must FOIL (First, Outside, Inside, Last) like so

First:

(x^2 + 4)(x^2 - 4)

x^2 * x^2

x^4

Outside:

(x^2 + 4)(x^2 - 4)

x^2 * -4

-4x^2

Inside:

(x^2 + 4)(x^2 - 4)

4 * x^2

4x^2

Last:

(x^2 + 4)(x^2 - 4)

4 * -4

-16

Now combine all the products of the FOIL together like so...

x^4 - 4x^2 +4x^2 - 16

Combine like terms:

x^4 - 4x^2 +4x^2 - 16

- 4x^2 +4x^2 = 0

x^4 - 16 <<<This is your answer

Hope this helped!

~Just a girl in love with Shawn Mendes

ANSWER

[tex]y = 2x - 8[/tex]

EXPLANATION

To find the equation of a straight line, we need the slope and a point on that line.

We were given the equation of another line that will help us determine the slope . The given line has equation:

[tex]y = 2x + 4[/tex]

This equation is of the form

[tex]y = mx + b[/tex]

where

[tex]m = 2 \: \: is \: the \: \: slope.[/tex]

Since our line of interest is parallel to this line, their slopes are the same.

The line also contains the point (3,-2).

So we substitute the slope and point into the slope-intercept formula:

[tex] - 2= 2(3)+ b[/tex]

[tex] - 2 =6 + b[/tex]

[tex] \implies \: b = - 2 - 6 = - 8[/tex]

The required equation is

[tex]y = 2x - 8[/tex]

Final answer:

The equation of a line parallel to y = 2x + 4 and passing through the point (3, −2) is y = 2x − 8.

Explanation:

To find the equation of a line parallel to line AB with the equation y = 2x + 4 that passes through the point (3, −2), we need to use the fact that parallel lines have the same slope. Line AB has a slope of 2, so our new line will also have a slope of 2. Now, we use the point-slope form of a line: y − y1 = m(x − x1), where (x1, y1) is the point the line passes through and m is the slope. Substituting our point and slope in, we get y − (−2) = 2(x − 3). Simplifying, we get y + 2 = 2x − 6, and after moving the 2 to the other side, the final equation in slope-intercept form is y = 2x − 8.

Answer: The approximate distance is 14.76

Step-by-step explanation:

You can use the following formula for calculate the distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

For the points (3, 5) and (-4, -8) you can identify that:

[tex]x_2=-4\\x_1=3\\y_2=-8\\y_1=5[/tex]

Now you need to substitute these values into the formula.

Therefore, the approximate distance between the given points is:

 [tex]d=\sqrt{(-4-3)^2+(-8-5)^2}\\\\d=\sqrt{(-7)^2+(-13)^2}\\\\d=\sqrt{49+169}\\\\d=\sqrt{218}[/tex]

[tex]d[/tex]≈[tex]14.76[/tex]

Final answer:

To find the distance between the points (3, 5) and (-4, -8), the distance formula is used, resulting in an approximate distance of 14.76 when rounded to the nearest hundredth.

Explanation:

To determine the approximate distance between two points with coordinates (3, 5) and (-4, -8), we use the distance formula which is derived from the Pythagorean theorem. The distance formula is: d = √((x2 - x1)² + (y2 - y1)²). Plugging in the values, we get d = √((-4 - 3)² + (-8 - 5)²) = √(7² + 13²) = √(49 + 169) = √218. The approximate distance is thus the square root of 218, which when calculated gives us approximately 14.76. This result should be rounded to the nearest hundredth, which would give us 14.76 as the final answer.

Recall that

[tex]1-x^n=(1-x)(1+x+x^2+\cdots+x^{n-1})[/tex]

So we have

[tex]x^2+x+1=0\implies\dfrac{1-x^3}{1-x}=0\implies x^3=1[/tex]

Then for any [tex]n[/tex], we have

[tex]x^{3n}=(x^3)^n=1^n=1[/tex]

For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We need two points through which the line passes to find the slope:

[tex](0, -4)\\(1,0)[/tex]

We found the slope:

[tex]m = \frac {y2-y1} {x2-x1}\\m = \frac {0 - (- 4)} {1-0} = \frac {4} {1} = 4[/tex]

So, the equation is of the form:

[tex]y = 4x + b[/tex]

We substitute a point to find "b":

[tex]-4 = 4 (0) + b\\-4 = b[/tex]

Finally, the equation is:

[tex]y = 4x-4[/tex]

Answer:

Option D

The expressions (x-5)/(x+3) and 4/(x-3) can be rewritten with a common denominator of (x+3)(x-3) to become ((x-5)(x-3))/((x+3)(x-3)) and 4(x+3)/((x+3)(x-3)).

The expressions stated are: (x-5)/(x+3) and 4/(x-3). In order to rewrite these expressions with a common denominator, you need to multiply the denominators together to create a common denominator. Therefore, the common denominator would be (x+3)(x-3).

Next, each expression must be rewritten so that they have this common denominator. For the first expression, we multiply the numerator and denominator by (x-3) so we get: ((x-5)(x-3))/((x+3)(x-3)).

For the second expression, we multiply the numerator and denominator by (x+3) so we get: 4(x+3)/((x+3)(x-3)). So, the expressions rewritten with a common denominator are ((x-5)(x-3))/((x+3)(x-3)) and 4(x+3)/((x+3)(x-3)).

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To find a common denominator for the given expressions, multiply the denominators together. The expressions, rewritten with the common denominator, are [tex](x-3)*(x-5)/(x+3)(x-3)[/tex] and [tex]4*(x+3)/(x+3)(x-3).[/tex]

The goal here is to find a common denominator for the expressions x-5/x+3 and 4/x-3. A common denominator can be found by multiplying the denominators of both expressions together. So for these expressions, the common denominator would be [tex](x+3)*(x-3).[/tex]

Then you multiply the top and bottom of each fraction by the missing factor from the other denominator. The expressions rewritten with a common denominator would then be:

So the expressions with a common denominator are: [tex](x-3)*(x-5)/(x+3)*(x-3)[/tex]and [tex]4*(x+3)/(x+3)*(x-3).[/tex]

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Answer:

The third option (C) Yes, because there is enough water in the cooler for about 81 cups total.Step-by-step explanation:

The radius and height of the cooler of 6 and 20 inches respectively, can

contain approximately only 81 cups, the correct option is therefore;

The dimensions of the cooler are;

Radius = 6 inches

Height = 20 inches

The possible dimensions of a cup are;

Diameter = 4.4 inches

Height = 5.5 inches

Required:

If each of the 38 players have 2 paper cups filled with water.

Solution;

The volume of the cooler, V₁, is found as follows;

V₁ = π × 6² × 20 = 720·π

The volume of the cooler, V₁ = 720·π in.³

The volume of the paper cup, V₂, is; [tex]V_2 = \dfrac{1}{3} \times \pi \times \left(\frac{4.4}{2} \right)^2 \times 5.5 = 8\frac{131}{150} \cdot \pi[/tex]

The volume of the paper cup, V₂ = [tex]8\frac{131}{150} \cdot \pi[/tex] in.³

The number of cups, n, in the cooler of water is therefore;

The number of cups of water in the cooler ≈ 81 cups

The number of cups required for each of the 38 player to have two full cups is, Cups = 38 × 2 = 76 cups

Given that the water available, (approximately 81 cups) is more than the

number of cups required (76 cups), the correct option is option;

Learn more about the volume of a cone here:

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