Fill in each square with a digit 1-9, and fill in
each circle with an operator +, -, *, -. Use each
digit and each operator exactly once. The
resulting equation should be true. Use the
standard order of operations (PEMDAS).


What is the largest possible three-digit result
that can be obtained on the right side of the
equation?​

Answer:

x =5

Step-by-step explanation:

3.1x−16.3=−0.8

Add 16.3 to each side

3.1x−16.3+16.3=−0.8+16.3

3.1x = 15.5

Divide each side by 3.1

3.1x = 15.5/3.1

x =5

Answer:

$9.00

Step-by-step explanation:

4x + 12 = 48   - First, subtract 12 from both sides.

4x = 36           - Then, divide each side by 4 to get x by itself.

x = 9                - After getting x by itself, we see that x = 9, so one ticket will

                         cost $9.00

For this case we have the following equation:

[tex]4x + 12 = 48[/tex]

Where the variable "x" represents the cost of a performance ticket.

Clear "x" of the equation to know the cost of a ticket.

Subtracting 12 on both sides of the equation:

[tex]4x = 48-12\\4x = 36[/tex]

Dividing between 4 on both sides of the equation:

[tex]x = \frac {36} {4}\\x = 9[/tex]

So, the cost of a ticket is $ 9.00

Answer:

Option C

Answer:

8^5

Step-by-step explanation:

Answer:A

Step-by-step explanation:

Y varies directly as x

Y = kx

When y = 2.5, x = 5

Substitute the value of y and x

2.5 = k * 5

Make k the subject of the formula

k = 2.5/5

k = 1/2

:. The equation connectin y and x is

Y = 1/2x

When x = 10

Y = 1/2*10

Y = 10/2

Y = 5

Answer:

c

Step-by-step explanation:

just took the test

Answer:

B

Step-by-step explanation:

The domain of the function are the input values on the left and the corresponding values on the right are the output values, the range

domain is { 1, 2, 3, 4 }

Answer:

Step-by-step explanation:

A function is a relation in which each element of the  domain is paired with exactly one element of the  range.

A relation is a set of ordered pairs. The set of the first components of each ordered pair is called the domain and the set of the second components of each ordered pair is called the range. Consider the following set of ordered pairs. The first numbers in each pair are the first five natural numbers. The second number in each pair is twice that of the first.

{(1,2),(2,4),(3,6),(4,8),(5,10)}

The domain is{1,2,3,4,5} and the range is{2,4,6,8,10}

So, this relation is a function.

Answer: The equation of the circle whose center is at (2, 1) and radius is 3 is [tex](x-2)^2+(y-1)^2=9[/tex]

Step-by-step explanation:

We know that the equation  of a circle having center at (h,k) and radius r is given by :-

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Given : The center of the circle :  (2, 1)

The radius of the circle : 3 units

Then the equation of a circle with center at (2, 1) and radius is 3 is will be :-

[tex](x-2)^2+(y-1)^2=3^2\\\\\Rightarrow\ (x-2)^2+(y-1)^2=9[/tex]

Answer:

11.4

Step-by-step explanation:

Step 1: Calculate the mean.

40, 55, 35, 60, 20, 50, 55

=

315

divided by 7

=

45

Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.

40 - 45 = 5

55 - 45 = 10

35 - 45 = 10

60 - 45 = 15

20 - 45 = 25

50 - 45 = 5

55 - 45 = 10

Step 3: Add those deviations together.

= 80

Step 4: Divide the sum by the number of data points.divided by 7

= 11.428

Step 5: Round to the nearest tenth.

= 11.4

Answer:

Step-by-step explanation:

The means absolute deviations is define by:

[tex]D_{x} =\frac{\sum |x_{i}-x| }{N}[/tex]

From the formula, we observe that we need to find the mean, and then find the different between that mean and each element. Then, we have to sum all those differences and divide this by the total number of elements.

So, the mean is

[tex]x=\frac{\sum x_{i} }{N}\\ x=\frac{40+55+35+60+20+50+55}{7}=45[/tex]

Now, each difference would be

[tex]40-45=-5\\55-45=10\\35-45=-10\\60-45=15\\20-45=-25\\50-45=5\\55-45=10[/tex]

The sum of all differences, using their absolute value, would be:

[tex]5+10+10+15+25+5+10=80[/tex]

Then, we divide this result by the total number of elements which is 7:

[tex]\frac{80}{7} \approx 11.43[/tex]

Therefore, the mean absolute deviation is approximately is 11.43.

Final answer:

The algebraic expression for the cost of purchasing a hockey stick and a puck, where the stick costs $7 less than twice the cost of the puck, and using x to represent the cost of the puck, is x + (2x - 7).

Explanation:

To translate the given phrase into an algebraic expression using the variable x to represent the cost of the puck, let's follow the instructions provided in the phrase very carefully. The cost of the hockey stick is described as "$7 less than twice the cost of the puck." Therefore, we first consider "twice the cost of the puck" which is 2x, and then subtract 7 from it to account for the phrase "$7 less than." Hence, the final expression for the cost of the hockey stick is 2x - 7.

Now, to find the cost of purchasing both the hockey stick and the puck, we simply add the cost of the puck (x) to the expression for the cost of the hockey stick (2x - 7), giving us a total cost expression of x + (2x - 7).

Notice that we are not simplifying the expression; we're just writing the combined cost as requested. So the final untranslated expression for the cost of purchasing a hockey stick and a puck based on the given conditions is x + (2x - 7).

Answer:

B) [tex](x^2 - 5x + 13) +(x^2 + 3x - 6)\\[/tex]

Step-by-step explanation:

Let's simplify the given options and find the correct answer.

The given expression is [tex]2x^2 - 2x + 7[/tex]

Let's take the option A and simplify.

[tex]-(4x + 12) + (2x^2 - 6x + 5)[/tex]

Distributing the negative sign and simplify.

[tex]-4x - 12 + 2x^2 -6x + 5[/tex]

Simplify the like terms.

[tex]2x^2 -10x - 7[/tex]

Which is not equal to the given expression.

Let's take the option B and simplify.

[tex](x^2 - 5x + 13) +(x^2 + 3x - 6)\\[/tex]

Simplify the like terms, we get

[tex]x^2 + x^2 -5x +3x +13 -6[/tex]

[tex]2x^2 -2x +7[/tex]

Which is equal to the given expression [tex]2x^2 -2x +7[/tex]

Therefore, the answer is B) [tex](x^2 - 5x + 13) +(x^2 + 3x - 6)\\[/tex]

Answer:

77 inches

Step-by-step explanation:

1 foot=12 inches so what you have to do is 12x6=72 and since he is 6 foot 5 inches you add 5 to get 77.

Please mark brainliest and have a great day!

Step-by-step explanation:

They drove 12 out of 25, so the remaining is 13/25.  To convert to percent:

13 / 25 = x / 100

x = 52

52% of the distance remains.

Answer:

The IQR = 4.

Step-by-step explanation:

The median is the middle number so it is 8.

The lower quartile is 6  (the middle number of those less than 8).

In a similar way the upper quartile is 10.

The interquartile range is 10 - 6 = 4.

Final answer:

To find the interquartile range of the data set 5, 6, 7, 8, 9, 10, 11, we calculate Q3 (10) - Q1 (6), which results in an IQR of 4.

Explanation:

The question asks for the interquartile range (IQR) of the data set 5, 6, 7, 8, 9, 10, 11. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1) in a data set, representing the spread of the middle 50 percent of the data.

Step-by-step Calculation

First, arrange the data in ascending order, which has already been done: 5, 6, 7, 8, 9, 10, 11.

To find Q1, calculate the median of the lower half. Here, Q1 is 6 (the median of 5, 6, 7).

To find Q3, calculate the median of the upper half. Here, Q3 is 10 (the median of 9, 10, 11).

Finally, calculate the IQR by subtracting Q1 from Q3: IQR = Q3 - Q1 = 10 - 6 = 4.

Thus, the interquartile range of this data set is 4.

Answer:

Step-by-step explanation:

Part A

Cost = T - (15/100) * T

Cost = (85/100)*T

Part B

You are asked to take 15% off the cost of something. The first equation is very clear how to do that -- just take 15% of T away from T

The second part is not so obvious if you are not familiar with it, but the result will be the same.

Start with the first equation

Cost = T - (15/100) T  Change 1 T to 100 / 100

Cost = 100*T/100T - 15/100T

Cost = 85 /100 * T

Part C

Cost = Phone - 14            at Top quality.     Red in Graph below

Cost = 75/100 * Phone    at Big value.        Blue in Graph belos

The graph below is a good way to answer this. I won't solve it algebraically when the graph will give you a much better idea which phone to get.

Answer: Up to a phone cost of 55 dollars, the red phone is the better buy.

After 55$ the blue phone is better.

Try this with a couple of values for phone,

Answer:

1.  x=±4

2. t=±9

3. r=±10

4. x=±12

5. s=±5

Step-by-step explanation:

1. x^2 = 16

Taking square root on both sides

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

x=±4

2. t^2=81

Taking square root on both sides

[tex]\sqrt{t^2}=\sqrt{81}\\\sqrt{t^2}=\sqrt{(9)^2}[/tex]

t=±9

3. r^2-100=0

[tex]r^{2}-100=0\\r^2 =100\\Taking\ Square\ root\ on\ both\ sides\\\sqrt{r^2}=\sqrt{100}\\\sqrt{r^2}=\sqrt{(10)^2}[/tex]

r=±10

4. x²-144=0

x²=144

Taking square root on both sides

[tex]\sqrt{x^2}=\sqrt{144}\\\sqrt{x^2}=\sqrt{(12)^2}[/tex]

x=±12

5. 2s²=50

[tex]\frac{2s^2}{2} =\frac{50}{2}\\s^2=25\\Taking\ Square\ root\ on\ both\ sides\\\sqrt{s^2}=\sqrt{25}\\\sqrt{s^2}=\sqrt{(5)^2}[/tex]

s=±5 ..

Answer:

[tex]1.+4,-4\\2. +9,-9\\3. +10,-10\\4. +12, -12\\5. +5, -5[/tex]

Step-by-step explanation:

IN order to solve the quadratic equations you just have to solve the square root of the numeric part of the equation:

[tex]x^{2} =16\\x=\sqrt{16}\\ x= +4, -4[/tex]

[tex]t^{2} =16\\t=\sqrt{81}\\ x= +9, -9[/tex]

[tex]r^{2} =100\\r=\sqrt{100}\\ x= +10, -10[/tex]

[tex]x^{2} -144=0\\x=\sqrt{144}\\ x= +12, -12[/tex]

[tex]2s^{2}=50\\s^{2}=\frac{50}{2} \\s=\sqrt{25}\\ s= +5, -5[/tex]

Just remember that the solution for any square root will always be a negative and a positive number.

Answer:General Formula of Scientific Notation. The general from of a number in scientific notation is: a ×10n where 1 ≤ a ≤ 10 and n is an integer. In other words the number that we'll call "a" is is multiplied by 10, raised to some exponent n.

Step-by-step explanation:

Final answer:

The formula for scientific notation involves expressing a number as the product of a coefficient (a number between 1 and 10) and a power of ten. The sign of the exponent is determined by the direction the decimal point is moved to create the coefficient.

Explanation:

The formula for scientific notation is a method of writing very large or very small numbers as a product of two parts: a coefficient and a power of ten. The coefficient must be a number greater than or equal to 1 and less than 10, while the power of ten reflects how many places the decimal point is moved to convert the number to the coefficient. In scientific notation, for example, the Earth's distance from the Sun, which is 150,000,000,000 meters, is expressed as 1.5 × 1011 m.

When converting a number to scientific notation, count the number of places you moved the decimal point to get a number between 1 and 10 for your coefficient. If the decimal point is moved to the left, the exponent will be positive, and if moved to the right, it will be negative. For instance, 2386 can be converted to 2.386 × 103 because the decimal is moved 3 places to the left.

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (1, 1)

m = [tex]\frac{1-3}{1-0}[/tex] = - 2

note the line crosses the y- axis at (0, 3) ⇒ c = 3

y = - 2x + 3  → A

Answer:

Part 1) The diameter is [tex]D=6\ units[/tex]   and the radius is equal to [tex]r=3\ units[/tex]

Part 2) The center of the circle is (1+6i)

Part 3) The point (1+9i) lies on the circle

Part 4) The point (2-i) does not lies on the circle

Step-by-step explanation:

Part 1) Show me how you would determine the length of the diameter and radius.

we have that

The circle has a diameter with end points: (4 + 6i) and (-2 + 6i)

we know that

The distance between the end points is equal to the diameter

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

(4 + 6i) ----> (4,6)

(-2 + 6i) ---> (-2,6)

substitute the values

[tex]d=\sqrt{(6-6)^{2}+(-2-4)^{2}}[/tex]    

[tex]d=\sqrt{(0)^{2}+(-6)^{2}}[/tex]    

[tex]d=6\ units[/tex]    

therefore

The diameter is [tex]D=6\ units[/tex]    

The radius is equal to [tex]r=6/2=3\ units[/tex]    ---> the radius is half the diameter

Part 2) Show me how you would determine the center of the circle

we know that

The center of the circle is equal to the midpoint between the endpoints of the diameter

The circle has a diameter with end points: (4 + 6i) and (-2 + 6i)

The formula to calculate the midpoint between two points is equal to

[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

substitute

[tex]M(\frac{4-2}{2},\frac{6+6}{2})[/tex]

[tex]M(1,6})[/tex]

therefore

(1,6) ----> (1+6i)

The center of the circle is (1+6i)

Part 3) Determine, mathematically, if (1+9i) lies on the circle. Show how you proved it mathematically

Find the equation of the circle

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

we have

The center is (1+6i) -----> (1,6)

r=3 units

substitute

[tex](x-1)^{2}+(y-6)^{2}=3^{2}[/tex]

[tex](x-1)^{2}+(y-6)^{2}=9[/tex]

Verify if the point (1+9i) lies on the circle

Remember that

If a point lies on the circle, then the point must satisfy the equation of the circle

Substitute the value of x and the value of y in the equation and then compare the results

we have

the point (1+9i) -----> (1,9)

[tex](1-1)^{2}+(9-6)^{2}=9[/tex]

[tex](0)^{2}+(3)^{2}=9[/tex]

[tex]9=9[/tex] -----> is true

therefore

The point (1+9i) lies on the circle

Part 4) Determine, mathematically, if (2-i) lies on the circle. Show how you proved it mathematically

The equation of the circle is equal to

[tex](x-1)^{2}+(y-6)^{2}=9[/tex]

Verify if the point (2-i) lies on the circle

Remember that

If a point lies on the circle, then the point must satisfy the equation of the circle

Substitute the value of x and the value of y in the equation and then compare the results

we have

the point (2-i) -----> (2,-1)

[tex](2-1)^{2}+(-1-6)^{2}=9[/tex]

[tex](1)^{2}+(-7)^{2}=9[/tex]

[tex]50=9[/tex] -----> is not true

therefore

The point (2-i) does not lies on the circle

To determine the length of the diameter and radius, use the distance formula. The center of the circle can be found by finding the midpoint of the diameter's end points. To determine if a point lies on the circle, use the distance formula to compare the distance between the point and the center to the radius.

1. Determining the length of the diameter and radius:

To find the length of the diameter, we can use the distance formula. The distance between two complex numbers (a + bi) and (c + di) is given by the formula √((c-a)^2 + (d-b)^2). In this case, the two end points of the diameter are (4 + 6i) and (-2 + 6i). Using the formula, the distance is √((-2-4)^2 + (6-6)^2) = √((-6)^2 + 0) = √(36) = 6.

The radius of a circle is half the length of the diameter. Therefore, the radius of this circle is 6/2 = 3.

2. Determining the center of the circle:

The center of the circle is the midpoint between the two end points of the diameter. To find the midpoint, we can take the average of the x-coordinates and the average of the y-coordinates. In this case, the x-coordinates of the end points are 4 and -2, and the y-coordinates are 6. Taking the averages, the x-coordinate of the center is (4 + (-2))/2 = 1 and the y-coordinate of the center is (6 + 6)/2 = 6. Therefore, the center of the circle is the complex number 1 + 6i.

3. Determining if (1 + 9i) lies on the circle:

To determine if a point lies on the circle, we can check if the distance between the center of the circle and the point is equal to the radius. Using the distance formula again, the distance between the center (1 + 6i) and the point (1 + 9i) is √((1-1)^2 + (9-6)^2) = √(0 + 9) = √(9) = 3. Since the distance is equal to the radius, we can conclude that (1 + 9i) does lie on the circle.

4. Determining if (2 - i) lies on the circle:

Using the same process, we find that the distance between the center (1 + 6i) and the point (2 - i) is √((2-1)^2 + (-1-6)^2) = √(1 + 49) = √(50). Since √(50) is not equal to the radius (3), we can conclude that (2 - i) does not lie on the circle.

Answer:  23.58

Step-by-step explanation:

[tex]cos\theta=\dfrac{adjacent}{hypotenuse}\\\\\\cos(32^o)=\dfrac{20}{x}\\\\\\x=\dfrac{20}{cos(32^o)}\\\\\\x=23.58[/tex]

Answer:

23.97 ft

Step-by-step explanation:

In this question apply the expression for determining cosine of an angle.

Cosine of an angle x°=length of the adjacent side÷hypotenuse

[tex]Cos\alpha =\frac{A}{H}[/tex]

where α is the angle in degrees, A is the adjacent side length, and H is the hypotenuse

Given α=32° and A=20ft  H=?

Applying the expression

[tex]Cos\alpha =\frac{A}{H} \\\\Cos32=\frac{20}{H} \\\\0.8342=\frac{20}{H}\\ \\H=\frac{20}{0.8342} =23.97[/tex]

In this case, the length of the ladder represents the hypotenuse side of the triangle which will be 23.97 ft

Answer:

1.5

Step-by-step explanation:

m=80-65/84-74

=15/10

1.5

*Since this is an application problem, we can use decimals.*

Answer:

The slope of the line is 1.5

Step-by-step explanation:

To know the slope of a line we can have the equation or to know points of the line. In this case from the graph we have to points (84,80) and (74,65). Having this and using the equation to calculate the slope, we have:

[tex]m=\frac{y2-y1}{x2-x1} \\[/tex]

Defining:

[tex](x1=84,y1=80)[/tex] and [tex](x2=74,y2=65)[/tex]

Now using the equation:

[tex]m=\frac{65-80}{74-84}[/tex]

[tex]m=\frac{-15}{-10} \\m=\frac{15}{10} =1.5[/tex]

The slope of the line is 1.5

Answer:

6 + 0.7 + 0.04 + 0.001 = 6.741

6 x 1 + 0.1 x 7 + 0.01 x 4 + 0.001 x 1 = 6.741

Answer:

x-2 dollars is the lunch money

The expression x-2 represents the spending amount on the lunch.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

Mahimi has x dollars for food.

She wants to buy lunch and still have $2 left over to buy a snack later.

To find the spending amount on the lunch:

She spent on the lunch,

= $(x - 2).

Therefore, x -2 is the expression.

To learn more about the expression;

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Answer:

12 guest walk

Step-by-step explanation:

Total number of people that went to the party= 24 (let this be represented as y)

Half of the people walk, this means 1/2 × y   ----------- walk, where y=24 people

Hence half of 24= [tex]\frac{24}{2} =12[/tex]

12 people walked.

Answer: 12

Step-by-step explanation:

Triangle JKL is dilated by a scale factor of 1.5 to get triangle XYZ. You can find this out by dividing 9 by 6, which will give you 1.5. To get the answer, you multiply 8 by 1.5 to get 12

ANSWER

EXPLANATION

We have that ΔJKL is similar to ΔXYZ.

The corresponding sides will therefore

be in the same proportion.

This implies that,

[tex] \frac{XY}{JK} = \frac{YZ}{KL} [/tex]

From the diagram,XY=9, JK=6, KL=8, and YZ=x.

We plug in the known values into the formula to get:

[tex] \frac{9}{6} = \frac{x}{8} [/tex]

Multiply both sides by 8

[tex] \frac{9}{6} \times 8=\frac{x}{8} \times 8[/tex]

[tex]12 = x[/tex]

The correct answer is B.

To write the height of Zak as a fraction of the height of Fred, divide Zak's height by Fred's height and simplify the fraction to its simplest form.

To write the height of Zak as a fraction of the height of Fred, divide Zak's height by Fred's height. Zak's height is 1.86 metres and Fred's height is 1.6 metres. So the fraction becomes 1.86/1.6.

To simplify this fraction, find the greatest common divisor (GCD) of 1.86 and 1.6, which is 0.02. Divide both the numerator and denominator of the fraction by the GCD to write the height as a fraction in its simplest form.

The simplified fraction is 93/80.

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[tex]m=\frac{y2-y1}{x2-x1} \\ \\ m=\frac{2-(-6)}{3-(-3)} \\ \\ m=\frac{8}{6} \\ \\ m=\frac{4}{3}[/tex]

The y-intercept of the graph is -2

The graph is shaded upwards, so we will be using the greater than symbol, but since the line is dotted we will not be using any of the "equal to" symbols.

Hence, the solution of the graph is [tex]y>m=\frac{4}{3} x-2[/tex]

Option: C is the correct answer.

              C.   [tex]y>\dfrac{4}{3}x-2[/tex]

By looking at the graph we observe that the line is dotted this means that the inequality will be strict.

Also, this line passes through the point (-3,-6) and (3,2).

Hence, the equation of line is calculated by using a two point form i.e. a line passing through two  points (a,b) and(c,d) is calculated with the help of formula as:

[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]

Here (a,b)=(-3,-6) and (c,d)=(3,2)

i.e.

[tex]y-(-6)=\dfrac{2-(-6)}{3-(-3)}\times (x-(-3)}\\\\i.e.\\\\y+6=\dfrac{2+6}{3+3}\times (x+3)\\\\i.e.\\\\y+6=\dfrac{8}{6}\times (x+3)\\\\i.e.\\\\y+6=\dfrac{4}{3}\times (x+3)\\\\i.e.\\\\y+6=\dfrac{4}{3}x+4\\\\i.e.\\\\y=\dfrac{4}{3}x-2[/tex]

Also, the shaded region is towards the origin.

                    Hence, the inequality is:

                  [tex]y>\dfrac{4}{3}x-2[/tex]

Answer:

[tex] x^{\frac{28}{45}} [/tex]

Step-by-step explanation:

To multiply powers with the same base, add the exponents.

[tex] x^{\frac{2}{5}} \times x^{\frac{2}{9}} = [/tex]

[tex] = x^{\frac{2}{5} + \frac{2}{9} [/tex]

[tex] = x^{\frac{2 \times 9}{5 \times 9} + \frac{2 \times 5}{9 \times 5}} [/tex]

[tex] = x^{\frac{18}{45} + \frac{10}{45}} [/tex]

[tex] = x^{\frac{28}{45}} [/tex]

Answer:

The correct answer option is true.

Step-by-step explanation:

The given statement is true that if there is no linear equation to start with, you can isolate and substitute a variable that is squared in both the equation.

For instance, if we have a non linear equation, start by dividing both sides by coefficient of the variable.

Once you do that and isolate a variable, continue solving by substituting that variable into the other equation.

ANSWER

[tex]\sqrt[3]{- 729{a}^{9} {b}^{6} } = - 9 {a}^{3} {b}^{2} [/tex]

EXPLANATION

We want to find the cube root of

[tex] - 729 {a}^{9} {b}^{6} [/tex]

We express this symbolically as:

[tex] \sqrt[3]{- 729 {a}^{9} {b}^{6} } [/tex]

The expression under the radical called the radicand.

We need to express this radical in exponential form using the property,

[tex] {x}^{ \frac{m}{n} } = \sqrt[n]{ {x}^{m} } [/tex]

Applying this rule gives us:

[tex]\sqrt[3]{- 729 {a}^{9} {b}^{6} } = ({- 729 {a}^{9} {b}^{6}})^{ \frac{1}{3} } [/tex]

[tex]\sqrt[3]{- 729{a}^{9} {b}^{6} } = ({- {9}^{3} {a}^{9} {b}^{6}})^{ \frac{1}{3} } [/tex]

Recall that

[tex] ({a}^{m} )^{n} = {a}^{mn} [/tex]

We apply this rule on the RHS to get,

[tex]\sqrt[3]{- 729{a}^{9} {b}^{6} } = ({- {9}^{3 \times { \frac{1}{3} } } {a}^{9 \times { \frac{1}{3} } } {b}^{6 \times { \frac{1}{3} } }})[/tex]

This simplifies to

[tex]\sqrt[3]{- 729{a}^{9} {b}^{6} } = - 9 {a}^{3} {b}^{2} [/tex]

Answer:

-9a3b2

Step-by-step explanation:

Answer:

Option C. [tex]log_{2}\frac{1}{3}[/tex]

Step-by-step explanation:

The given logarithmic expression is [tex]\frac{log(\frac{1}{3} )}{log2}[/tex]

Rule of logarithm says

[tex]\frac{log_{e}a }{log_{e}b}=log_{b}a[/tex]

So by this rule,

expression [tex]\frac{log(\frac{1}{3} )}{log2}[/tex] will become [tex]log_{2}\frac{1}{3}[/tex]

Therefore, Option C. [tex]log_{2}\frac{1}{3}[/tex] will be the answer.

To solve the problem we must know about the rule to change the base of any logarithmic expression.

The solution of the given expression  [tex]\dfrac{log\dfrac{1}{3}}{log 2}[/tex]  is  [tex]\rm log_2\dfrac{1}{3}[/tex].

The formula which helps us to change the base of any logarithm expression,

[tex]\rm log_ab = \dfrac{log_cb}{log_ca}[/tex]

Given to us

[tex]\dfrac{log\dfrac{1}{3}}{log 2}[/tex]

As we have already discussed the formula for the change of the base of any logarithm expression, comparing the formula with that expression,

[tex]\rm log_ab = \dfrac{log_cb}{log_ca} = \dfrac{log\dfrac{1}{3}}{log 2}[/tex]

[tex]\rm log_2\dfrac{1}{3} = \dfrac{log\dfrac{1}{3}}{log 2}[/tex]

Hence, the solution of the given expression  [tex]\dfrac{log\dfrac{1}{3}}{log 2}[/tex]  is  [tex]\rm log_2\dfrac{1}{3}[/tex].

Learn more about Logarithm expression:

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