2. Simplify √-72 (2 points) A.) 6√2 B.) 6√-2 C.) 6√2i D.) 6i√2​

We would have to solve the equation

Step by step to determine if Timothy made a mistake.

Step 1

Expand the bracket

Hence, his step 1 is correct.

Step 2

Bring like terms together

Step 3

Simplify step 2 and find the value of x

Hence, from all the steps through 1 to 3, we can conclude that Timothy did not make a mistake. Hence the right answer is option D

Answer: the image isn't showing up for me

Step-by-step explanation:

9(5 - y)

EXPLANATION

Difference means subtraction.

This implies that the difference of 5 and y can be expressed as 5 - y.

Hence, nine times the difference of 5 and y can be represented as:

9(5 - y)

Answer:

  d. 12 cm

Step-by-step explanation:

Corresponding sides have the given ratio:

  EG/AC = 3/2 = EG/8 . . . . . . . fill in for AC

  EG = 8(3/2) = 12 . . . cm . . . . . . . multiply by 8

Answer:

12 cm

Step-by-step explanation:

Keep it simple, but correct :)

Given, Height of the cliff = 20 m Distance of the car from the foot of the cliff = 10 m.

The time taken by the car to fall from the cliff can be found using the formula:

\(`h = (1/2) g t^2`\)

Where h is the height of the cliff, g is the acceleration due to gravity and t is the time taken by the car to fall from the cliff.

Substituting the given values,`20 = (1/2) × 9.8 × t^2`

Solving for t, `t = sqrt(20/4.9)` = 2.02 s

Let the initial velocity of the car be V0 and the time taken for the car to come to rest after applying brakes be t1.

Distance covered by the car before coming to rest can be found using the formula: `\(s = V0t1 + (1/2) (-5) t1^2\)`

Where s is the distance covered by the car before coming to rest.

Simplifying the above equation,\(`2.5 = V0 t1 - (5/2) t1^2`\)

Substituting the given values,`5 = V0 - 5 t1`

Solving the above two equations,\(`V0 = 32.5/2 t1`\)

Simplifying the above equation,`V0 = 16.25 t1`

Substituting the value o\(f t1,`V0 = 16.25 × 2` = 32.5 m/s\)

Therefore, the speed of the car before the start of braking is 32.5 m/s.

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Answer:

36- degree rotation m8

Step-by-step explanation:

mark me brainliest :)

The fuel-flow indicator rotor and needle in a motor-impeller and turbine indicating system are driven by a mechanism that measures and displays the rate at which fuel is flowing to the engine.

The fuel-flow indicator rotor and needle play a crucial role in providing real-time information about the rate of fuel consumption in an engine. The rotor is typically connected to a turbine or impeller, which is driven by the flow of fuel passing through it. As the fuel flows, it causes the rotor to rotate, and this rotational motion is then translated into the movement of a needle on the indicator display. The position of the needle corresponds to the fuel flow rate, allowing the operator or pilot to monitor and control the fuel consumption.

This indicating system is important for several reasons. Firstly, it enables operators to monitor fuel usage, ensuring that the engine is receiving an appropriate amount of fuel for efficient operation. Secondly, it provides valuable information for fuel management, allowing adjustments to be made if necessary to optimize performance or conserve fuel. Additionally, the indicator system helps identify any anomalies or irregularities in fuel flow, which can be indicative of potential issues or malfunctions within the engine or fuel system. Overall, the fuel-flow indicator rotor and needle serve as critical components in maintaining engine performance, efficiency, and safety.

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Answer:

270.4 miles

Step-by-step explanation:

First we will convert the 40 liter gas tank into gallons.

There are about 0.26 gallons in 1 liter, so we can find how many gallons are in 40 liters by solving \(40 * 0.26\), which equals to \(10.4\) gallons.
We can now find how far we can travel on a full tank.

\(\mbox{26 miles per gallon } * \mbox{10.4 gallons} = \mbox{270.4 miles}\)

This means we can travel 270.4 miles on a full tank.

That is the answer

- Kan Academy Advance

Answer:

F(x) ^-1= x+3/4

Step-by-step explanation:

Exchange f(x) for y

Y=4x-3

+3

Y+3=4x

/4

Y+3/4=x

Swap y and x

F(x)^-1= x+3/4

Answer:

Here is your answer

Hope it helps

The triple integral ∫∫∫ex^2 y^2 dv in cylindrical coordinates evaluates to ∫ from 0 to 1, ∫ from 0 to 2π, and ∫ from 0 to (1-9r^2) e^r^2cos^2θsinr drdθdz.

In cylindrical coordinates, the given solid e is represented by the inequality 0 ≤ z ≤ 1-9r^2. Therefore, the limits of integration for z are 0 to 1-9r^2. The circular base of the solid is given by x^2 + y^2 ≤ 1/(9z), which can be rewritten as r^2 ≤ 1/(9z).

Thus, the limits of integration for r are 0 to √(1/(9z)). The angle θ ranges from 0 to 2π. Hence, the triple integral can be expressed as ∫ from 0 to 1, ∫ from 0 to 2π, and ∫ from 0 to √(1-9r^2) e^r^2cos^2θsinr drdθdz. Solving this integral yields the required answer.

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Answer:

D is the correct answer

Step-by-step explanation:

it honestly depends on what the numbers are

for example, 12 -6, you would get 6.

but if the question is something like 4 -8, you'd have -4

The correct answer is B. coding. Converting narrative diagnoses and procedures into numeric form is known as coding.

Coding is the process of assigning numeric or alphanumeric codes to medical diagnoses, procedures, and services for the purpose of standardized documentation, billing, and statistical analysis. It involves translating the narrative description of a diagnosis or procedure into a specific code that represents that particular condition or treatment. The codes are typically part of a standardized classification system, such as the International Classification of Diseases (ICD) for diagnoses and the Current Procedural Terminology (CPT) or Healthcare Common Procedure Coding System (HCPCS) for procedures.

Coding is essential in healthcare for various reasons. It ensures accurate and consistent documentation of patient information, facilitates proper billing and reimbursement, enables statistical analysis for research and public health purposes, and supports data exchange and interoperability between different healthcare systems and organizations. By converting narrative diagnoses and procedures into numeric codes, healthcare professionals can efficiently communicate medical information and ensure that it is interpreted and utilized correctly across different settings.

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Answer:

153

Step-by-step explanation:

discriminant = b² - 4ac

ax² + bx + c = 0

9x² - 3x - 4 = 0

a = 9

b = -3

c = -4

discriminant = (-3)² - 4(9)(-4) = 9 + 144 = 153

No Solution.

Since, the x-axis (equation y=0) does not intersect y=-7 at any point. The given pair of equations has no solution

Consider the pair of linear equations in two variables x and y.

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

Here a1, b1, c1, a2, b2, c2 are all real numbers.

Note that, a12 + b12 ≠ 0, a22 + b22 ≠ 0

1. If (a1/a2) ≠ (b1/b2), then there will be a unique solution. If we plot the graph, the lines will intersect. This type of equation is called a consistent pair of linear equations.

2. If (a1/a2) = (b1/b2) = (c1/c2), then there will be infinitely many solutions. The lines will coincide. This type of equation is called a dependent pair of linear equations in two variables

3. If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. If we plot the graph, the lines will be parallel. This type of equation is called an inconsistent pair of linear equations.

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These eight products, abc, abe, bcd, bde, acf, cdf, aef, and def, can add up to the greatest possible value of 729.

Let's give our cube's six sides the letters a, b, c, d, e, and f, with a being opposite d, a being opposite e, and b being opposite f.

As a result, we have the following products for the eight vertices:

abc, abe, bcd, bde, acf, cdf, aef, and def.

Let's calculate the total of these products:

= abc + abe + bcd + bde + acf + cdf + aef + def

We see that the first four terms are factors of b, while the last four terms are factors of f.

= b(ac + ae + cd + de) + f(ac + ae + cd + de)

Now we can factor it again:

= (b + f) (ac + ae + cd + de)

= (b + f) (a (c + e) + d (c + e))

= (b + f) (a + d) (c + e)

The given numbers for a cube's six faces are 2, 3, 4, 5, 6, and 7.

We possess the product. The factors are sums of opposite faces, as you can see. The biggest sum that may be reached by adding all three factors (7 + 2), (6 + 3), and (5 + 4) is:

= (7 + 2)(6 + 3)(5 + 4)  

= 9 x 9 x 9  

= 729

Thus, The greatest possible value of the eight products is 729.

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In the event of shortening the standard error of mean to 15 we have to increase the size to 400. Therefore, the correct answer is Option B.

The  given standard error of the mean for a sample of 100 is 30. So to cut the standard error of the mean to 15, we have to proceed by increasing the sample size to 400.

The  formula for evaluating the standard error of mean
SEM = SD / √(n)
here, SEM = standard error of the mean,
SD = standard deviation
n = sample size
Staging the values
15 = SD / √(100)
15 x √(100) = SD
SD = 150
Now evaluating for the value of n
15 = 150 / √(n)
15 x √(n) = 150
√(n) = 10
n = 100
Now looking at the formula, we need to decrease SEM by half,

So we proceed by increasing the  sample size by a factor of 4.

In the event of shortening the standard error of mean to 15 we have to increase the size to 400. Therefore, the correct answer is Option B.

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The equation of the line of best fit for this data is y = y = 15.4x + 19.6.

First, we need to enter the data into the calculator. Then, we can use the calculator's linear regression function to find the equation of the line of best fit.

The equation will be in the form y = mx + b, where m is the slope and b is the y-intercept.

Homework Average (x): 4.9, 4.6, 2.6, 3.8, 4.2, 3.9, 3.2, 4.3, 4.6, 3.8

Test Average (y): 98, 90, 62, 80, 82, 75, 68, 91, 88, 76

Using a graphing calculator to find the line of best fit gives us the equation y = 15.4x + 19.6

Therefore, the equation of the line of best fit for this data is y = y = 15.4x + 19.6.

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The equation holds true, which means the point of intersection (66/19, -37/19, 27/19) satisfies the plane equation. Therefore, the intersection point is correct.

To find the point of intersection between the line and the plane, we need to solve the system of equations formed by the line equation and the plane equation.

The line equation is given as:

r = <2, 1, -3> + t < -1, 2, -3>

And the plane equation is given as:

3x - 2y + 4z = 20

We can substitute the values of x, y, and z from the line equation into the plane equation and solve for t.

Substituting x, y, and z from the line equation:

3(2 - t) - 2(1 + 2t) + 4(-3 - 3t) = 20

Expanding and simplifying:

6 - 3t - 2 - 4t - 12 - 12t = 20

-19t - 8 = 20

-19t = 28

t = -28/19

Now, substitute the value of t back into the line equation to find the corresponding values of x, y, and z.

x = 2 - (-28/19)

= 2 + 28/19

= (38/19 + 28/19)

= 66/19

y = 1 + 2(-28/19)

= 1 - 56/19

= (19/19 - 56/19)

= -37/19

z = -3 - 3(-28/19)

= -3 + 84/19

= (-57/19 + 84/19)

= 27/19

Therefore, the point of intersection between the line and the plane is (66/19, -37/19, 27/19).

To verify if this point lies on the plane, we substitute its coordinates into the plane equation:

3(66/19) - 2(-37/19) + 4(27/19) = 20

Multiplying through by 19 to clear the fractions:

198 - (-74) + 108 = 380

198 + 74 + 108 = 380

380 = 380

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The Correct answer is 27

Odd number are the numbers that are not multiple 2 and cannot be divided into two parts equally.

For examples: 3 , 5 , 7, 9,11 . . . . .

According to the question,

If the third odd number is greater than 6, multiply 9 by 3; if it is less than 5, divide 18 by 3.

Sequence of the number is 1, 5, 4, 7, 3, 7, 9, 2

where  1 , 5 , 7 , 7 ,9 are odd numbers

The third odd number is 7 which is greater than 6

according to question we have to multiple 9 by 3

= 9 × 3

= 27

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The solution to the inequality (p² - p - 6)/(p - 1) ≥ 0 is (oo, -2) u (3, oo)

From the question, the inequality is given as

(p² - p - 6)/(p - 1) ≥ 0

Multiply both sides of the inequality by p -1

So, we have the following representation

p² - p - 6 ≥ 0

Expand

p² + 2p - 3p - 6 ≥ 0

Factorize

p(p +2) - 3(p + 2) ≥ 0

So, we have

(p - 3)(p + 2) ≥ 0

The solution to the inequality expression is then represented as

p ≥ 3 and p ≥ -2

When represented as an interval, we have

(oo, -2) u (3, oo)

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Answer:

add up all the numbers and multiply it by 32

Step-by-step explanation:

add up 32 33 34 34 36 38 38 38 40 42 amd then multiply that answer by 32

The standard form is:

Convert each equation:

1. x² + 2x = -1                        add 1 to both sides

⇒ x² + 2x + 1 = 0

2. 4 + x² = 7x                        add - 7x to both sides and rearrange

⇒ x² - 7x + 4 = 0

3. x² - x = 1                            add - 1 to both sides

⇒ x² - x - 1 = 0

4. x² + 9x = 10                       add - 10 to both sides

⇒ x² + 9x - 10 = 0

5. 4x + 3 = x²                        add -4x - 3 to both sides

⇒ x² - 4x - 3 = 0

6. x² + 5x = 5                        add -5 to both sides

⇒ x² + 5x - 5 = 0

7. 2x² + 7x = 3                      add -3 to both sides

⇒ 2x² + 7x - 3 = 0

8. x² = 3x + 8                        add -3x - 8 to both sides

⇒ x² - 3x - 8 = 0

9. x(x + 3) = 1                         distribute and add - 1 to both sides

⇒ x² + 3x - 1 = 0

10. x² - 3x = -2                       add 2 to both sides

⇒ x² - 3x + 2 = 0

11. y² - 7y = -6                        add 6 to both sides

⇒ y² - 7y + 6 = 0

12. z² - 5z = -4                       add 4 to both sides

⇒ z² - 5z + 4 = 0

Answer: ^^

1. x2 + 2x + 1 = 0

2. x^2 - 7x + 4 = 0

3. x^2 - x - 1 = 0

4. x^2 + 9x - 10 = 0

5. -x^2 + 4x + 3 = 0

6. x^2 + 5x - 5 = 0

7. 2x^5 + 7x - 3 = 0 or 2x^5 + 4x = 0

8. x^2 - 3x - 8 = 0

9. x^2 + 3x - 1 = 0

10. x^2 - 3x + 2 = 0

11. y^2 - 7y + 6 = 0

12. z^2 - 5z + 4 = 0

Step-by-step explanation:

:)

Answer:

A

Step-by-step explanation:

Random sampling is a sampling method where each sample has an equal chance of being chosen. The random sample chosen is meant to be an unbiased representation of the population.

If 30% of the sample uses the app, it means that 30% of the population are likely to use the app

The system of equations has its solutions to be x = 0 and x = -3

From the question, the system of equations is given as

f(x) = (x + 1)² - 3

g(x) = -x - 2

To determine the solution to the system of equations, we set both equations equal

i.e. f(x) = g(x)

So, we have

(x + 1)² - 3 = -x - 2

Add 3 to all sides of the equation

This gives

(x + 1)² = -x + 1

Expand

x² + 2x + 1 = -x + 1

Evaluate the like terms

x² + 3x = 0

Expand the equation

x(x + 3) = 0

Solve for x

x = 0 and x = -3

Hence, the solution to the system of equations are x = 0 and x = -3

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The lifetime cost of Ellen's dishwater is $1,030.44

What is Number system?

A system of writing to express the number is called number system.

Given that;

Cost of dishwasher before sales tax 9.22% is = $315

And, Sales tax = 9.22%

Hence, Total cost = 315 *( 1 + 0.0922) = 315 * 1.0922 = 344.043

And, Average of 10 times per week for the next 6 years before replacing it.

Since, There are 52 weeks in a year.

So, Average uses is calculated as,

10  * 52  * 6 = 3120

Since, cost for water = $0.09

Cost for electricity = $0.13

Total cost per uses = $0.22

Hence, Cost of uses = 0.22 * 3120 = $686.40

Now, Purchase cost = $344.043

And, Cost of uses =  $686.40

Hence, Lifetime cost =  $344.043 + $686.40 = $1,030.443

So, The lifetime cost of Ellen's dishwater is $1,030.44.

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To prove that if T and U are simultaneously diagonalizable operators, then T and U commute (TU = UT), we need to show that their corresponding matrices commute.

Let P be the matrix that diagonalizes both T and U, such that P⁻¹TP and P⁻¹UP are diagonal matrices.

Multiplying these diagonal matrices together, we get:
P⁻¹TP * P⁻¹UP = P⁻¹TUP

Since T and U are simultaneously diagonalizable, we have PTP⁻¹ = T and PUP⁻¹ = U.

Substituting these expressions, we have:
P⁻¹TUP = P⁻¹UTP

Multiplying both sides by P on the left and by P⁻¹ on the right, we get:
P(P⁻¹TUP)P⁻¹ = P(P⁻¹UTP)P⁻¹

Simplifying the equation, we have:
TU = UT

Therefore, if T and U are simultaneously diagonalizable operators, they commute (TU = UT).

For the second part, if A and B are simultaneously diagonalizable matrices, it means that there exists an invertible matrix P such that P⁻¹AP and P⁻¹BP are diagonal matrices.

Using a similar argument as above, we can show that A and B commute (AB = BA) by following the same steps and substituting the matrices accordingly.

Therefore, if A and B are simultaneously diagonalizable matrices, they commute.

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Area of the given triangle is 132 sqr inches.

The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina. Area is the total amount of area occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the region that its boundary encloses. The quantity of unit squares that span a closed figure's surface is its area.

Heron's formula in mathematics provides the triangle's area in terms of its three side lengths, a, b, and c. it is given by

area= \(\sqrt{s(s-a)(s-b)(s-c)}\) where s is the semi perimeter.

In the given triangle,

let a=15

b= 18

c= 21

s= \(\frac{a+b+c}{2}\)

s=\(\frac{15+18+21}{2}\)= 27

using heron's formula,

area= \(\sqrt{s(s-a)(s-b)(s-c)}\)

area= \(\sqrt{27(27-15)(27-18)(27-21)}\)

       = \(\sqrt{17496}\)= 132.27 sqr inches

        ≈132 sqr inches

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Answer: 54 sqrt 6

Step-by-step explanation: I have no clue how to get to this answer, but I got it wrong on the test and this is what it says the right answer is.

Answer:

A

Step-by-step explanation:

The products result in a sum or difference of cubes are

(x - 1)(x² + x + 1) and (x + 4)(x² - 4x + 16).

What is sum or difference of cubes?

The term "sum of cubes" refers to a polynomial with the formula a^3 + b^3. The term "difference of cubes" refers to a polynomial with the form

a^3 - b^3.

The formulas for sum of cubes and difference of cubes are given:

Sum of cubes: (a + b)(a²-ab + b²) = a³ + b³

Difference of cubes: (a-b)(a² + ab + b²)=a³-b³

We have to check which products result in a sum or difference of cubes.

Consider,

(1) (x - 4)(x^2 + 4x - 16)

(x - 4)(x^2 + 4x - 16) = x^3 - 8x^2 + 32x - 64

It is not a sum or difference of cubes.

(2) (x-1)(x²-x+1)

(x - 1)(x² - x + 1) = x^3 - 2x^2 + 2x - 1

It is not a sum or difference of cubes.

(3) (x - 1)(x² + x + 1)

(x - 1)(x² + x + 1) = x^3 - 1

This is the difference of cubes.

(4) (x + 1)(x^2 + x - 1)

(x + 1)(x^2 + x - 1) = x^3 + 2x^2 - 1

It is not a sum or difference of cubes.

(5) (x + 4)(x² - 4x + 16)

(x + 4)(x² - 4x + 16) = x^3 + 64

This is the sum of cubes.

(6) (x + 4)(x^2 + 4x + 16)

(x + 4)(x^2 + 4x + 16) = x^3 + 8x^2 + 32x + 64

It is not a sum or difference of cubes.

Hence, the products result in a sum or difference of cubes are

(x - 1)(x² + x + 1) and (x + 4)(x² - 4x + 16).

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The value of probability P( Reese's ∩ Almond Joy) is,

P( Reese's ∩ Almond Joy) = 0.08

Since, The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

He has 5 Twix, 9 Kit Kats, 12 Reese's, and 7 Almond Joys.

Hence, Total number of things are,

⇒ 5 + 9 + 12 + 7

⇒ 33

So, Probability to choose Reese's are,

P = 12 / 33

And, Probability for choose Almon Joy are,

P = 7 / 33

Thus, We can formulate;

P( Reese's ∩ Almond Joy) =  12/33 x 7/33

P( Reese's ∩ Almond Joy) = 84 / 1089

P( Reese's ∩ Almond Joy) = 0.08

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