Simplify: (4xy^-2) / [ 12x^(-1/3) y^5]

The simplest radical form of the expression 5√28 + √63 will be 29√7.

If the power of the variable "a" is b/c.

Then the simplest radical form of the expression will be

[tex]\rm \left ( a \right )^{\rm \frac{b}{c}} = \rm \sqrt[\rm c]{\rm a^b}[/tex]

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 5√28 + √63

Simplify the expression, then we have

⇒ 5√28 + √63

⇒ 5√(4 x 7) + √(9 x 7)

⇒ 5 x 4√7 + 9√7

⇒ 20√7 + 9√7

⇒ 29√7

The simplest radical form of the expression 5√28 + √63 will be 29√7.

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the answer is -14

hope this helps   : )

Final answer:

To find all cube roots of -125i in polar form, convert them to a+bi form by expressing -125i in polar form, finding the cube roots, and converting them to a+bi form.

Explanation:

To find all the cube roots of -125i in polar form and convert them to a+bi form, follow these steps:

Express -125i in polar form: -125i = 125∠-90°.

Find the cube roots by taking the cube roots of the magnitude and adding multiples of 360°/3 to the argument.

The cube roots of -125i in a+bi form are 5∠-30°, 5∠90°, and 5∠210°, which correspond to -2.5-4.33i, 0+5i, and 2.5-4.33i respectively.

Answer:

The correct answer is c.

Step-by-step explanation:

Given the equation

[tex]ax^{2}+bx+c=0[/tex]

The quadratic equation solves the values of ''x'' which satisfy the original equation (In the equation I replace ± by the symbol |):

[tex]\frac{-b|\sqrt{b^{2}-4ac}}{2a}[/tex]

The solutions of [tex]4x^{2}+x=-3[/tex] are the same that the solutions of [tex]4x^{2}+x+3=0[/tex]

With [tex]a=4\\b=1\\c=3[/tex] we replace this in the quadratic equation ⇒

[tex]\frac{-1|\sqrt{(1)^{2}-4(4)(3)}}{(2)(4)}[/tex]  ⇒

[tex]\frac{-1|\sqrt{1-48}}{8}[/tex] ⇒

[tex]\frac{-1|\sqrt{-47}}{8}[/tex]

Given that [tex]i^{2}=-1[/tex] (imaginary numbers property)

[tex]\frac{-1|\sqrt{47i^{2}}}{8}=\frac{-1|i\sqrt{47}}{8}[/tex]

The solutions are [tex]\frac{-1+i\sqrt{47}}{8}[/tex]

and [tex]\frac{-1-i\sqrt{47}}{8}[/tex]

The correct answer is c.

Answer: C

Step-by-step explanation: I just took the test and got it right <3

Answer:

Margin of error: 6%; Confidence Interval Percentage: 90%; Confidence Interval: 74% and 86%

Step-by-step explanation:

Margin of error: 6%  --  It's already given in the question.

Confidence interval is at 90%. 9/10=.90

The exam creator is saying that they are 90% confident that the seniors test scores will be between 74% and 86%.

0.8 - 0.06 = 0.74

0.8 + 0.06 = 0.86

The confidence interval is (0.74, 0.86)

Answer:

Slope-Intercept Form states that in the equation of a straight line y=mx+b the slope is the number represented by m that is multiplied on the x, and b is the y intercept i.,e the point where line cut the vertical  y-axis.

Given equation: 5x+2y=3              ......[1]

To convert this equation into slope intercept form;

Subtraction Property of equality states that you subtract the same number from both sides of an equation.

Subtract 5x from both sides in equation [1];

[tex]5x+2y-5x=3-5x[/tex]

Simplify:

[tex]2y=3-5x[/tex] or we can write this as;

[tex]2y=-5x+3[/tex]                 ......[2]

Division property of equality states that you divide the same number from both sides of an equation:

Divide by 2 from both sides of an equation in [2]

[tex]\frac{2y}{2} =\frac{-5x+3}{2}[/tex]

On simplify:

[tex]y=-\frac{5}{2}x+\frac{3}{2}[/tex]

Therefore, the given equation in slope intercept form is: [tex]y=-\frac{5}{2}x +\frac{3}{2}[/tex]

Answer: 7/12

Explaintion: Write at least 20 characters to explain it well.

Answer:

D is your answer :)

Step-by-step explanation:

With the given conditions of angle A being 30 degrees, side a being 1.5 cm, and side b being 2 cm in a triangle, only one possible triangle satisfies these properties according to the Law of Sines.

The question relates to determining the number of possible triangles given certain conditions. Specifically, it refers to a triangle with an angle A of 30 degrees, a side a of 1.5 cm opposite to A, and another side b of 2 cm. To decide the number of possible triangles that fit these criteria, we make use of the Law of Sines. This law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

In the given scenario, since side a (1.5 cm), opposite to angle A (30 degrees), is shorter than side b (2 cm), it is possible that two different triangles could exist, often referred to as the ambiguous case in the Law of Sines. However, the fact that side a is shorter than side b coupled with angle A being acute (30 degrees) leaves us with only one possible triangle. This is because the side opposite the smallest angle (A) cannot form a valid triangle if it's longer than the other given side. Therefore, there is just one solution to this problem.

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Answer: A: one or more points of interest.

Step-by-step explanation:

The rule says that an image should be divided into 9 equal squares by two horizontal and two vertical lines and that the important objects of the image should be placed between the lines (in the centers of the squares) or in the intersections of the lines.

In this way, the eye is dragged to the different points that the artist wants the viewer to focus on the image, then the correct option is option A:  one or more points of interest.

The correct answer is:

D) The amount a person pays for gas compared with the number of gallons purchased

Explanation:

A constant rate of change means that for every x, y increases the same amount.

In the situation "The amount a person pays for gas compared with the number of gallons purchased ," the independent quantity, or x-value, is the number of gallons, and the dependent quantity, or y-value, is the amount paid.  Since gas has a set price per gallon, for every gallon purchased, the total amount paid goes up the same amount.  This means it has a constant rate of change.

Answer:

D on edge

Step-by-step explanation:

Answer:

a.  Essential (flexible) expense

Step-by-step explanation:

Most people consider a cell phone an essential expense, since they are used in power outages or emergencies while traveling.

This is a flexible expense, since there are extra fees for extra usage.  

The phone bill expense is an Essential (flexible) expense so option (A) will be correct.

The procedure of utilizing logical reasoning to analyze a condition to determine the best problem-solving approach for a particular issue, then using this approach to create and explain a resolution.

In another word, reasoning is a tricky but interesting problem in mathematics that required relations of variables to solve.

The mobile cost is an essential cost because it is can be used in an emergency situation or it is very useful for calling massaging or video calling.

Since the plan for mobile recharge varies higher or lower according to benefits so it will be a flexible expense.

Hence "The phone bill expense is an Essential (flexible) expense".

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Answer:

B

Step-by-step explanation:

hope this helps

To find out how much 250 envelopes would cost, set up a proportion using the given information that 100 envelopes cost 70 cents. Cross-multiply and solve for the unknown cost, which is $1.75.

To find out how much 250 envelopes would cost, you can use the concept of proportions. Since 100 envelopes cost 70 cents, you can set up a proportion to find the cost of 250 envelopes: 100/70 = 250/x, where 'x' represents the unknown cost. Cross-multiplying, you get 100x = 70 * 250. Dividing both sides by 100, you find that x = 175.

Therefore, 250 envelopes would cost 175 cents.

In decimal form, 175 cents is equal to $1.75.