Power of a power quotient rule

The terms of the expression are ab, cd, ef and gh. This shpws that the expression contains 4 terms and 0 factor.

Expression consists of terms and factors. The terms are separated by the mathematical signs.

Given the expression below

ab+cd+ef+gh

The terms of the expression are ab, cd, ef and gh. This shpws that the expression contains 4 terms and 0 factor.

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Answer:

153

Step-by-step explanation:

i = square root of -1

i = √-1

(3+12√-1) (3-12√-1)

√a times √b = √ab

a√b times c√d = (a times c) √ (b times d)

9 - (36√-1) + (36√-1) - (144(√-1)^2) =

9 - 0 - (144 * -1) =

9 - 0 - (-144) =

9 - (-144) =

9 + 144 =

153

*** funny thing is if you put

(3+12i) (3-12i)  

in a calculator

it works!

it gives you the answer 153

another way:

Expand the expression using

(a-b) (a+b) =

a²-b² :

3²-(12i)²

Simplify using exponent rule with same exponent

(a*b)^n =

a^n*b^n:

3²-12²* i²

Calculate the power:

9-144* i²

Rewrite by definition

i²=-1:

9–144×(−1)

Calculate the product or quotient: 9+144

Calculate the sum or difference: 153

Answer: 153

gathmath

The value of f⁻¹(f(58)) is 58 and the value of the function f(f(5)) is 11

As a general rule, we have:

f⁻¹(f(x)) = x

Substitute 58 for x

So, we have:

f⁻¹(f(58)) = 58

Hence, the value of f⁻¹(f(58)) is 58

Also, we have:

f(f(5))

From the table, we have:

f(5) = 9

So, we have:

f(f(5)) = f(9)

From the table, we have:

f(9) = 11

So, we have:

f(f(5)) = 11

Hence, the value of the function f(f(5)) is 11

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Since the given lines a and b are neither parallel, nor do they intersect each other. Also, they lie on two different planes, P and Q respectively, and thus, are co-planar. hence, a and b can be called skew lines.

Definition of Skew Lines

Skew lines in 3D geometry, are, by definition, a pair of lines that are neither parallel nor intersect each other. Such lines are therefore not coplanar, according to the conclusion.

Skew lines tend to occur frequently in real-world circumstances. Let's say there is a line on the ceiling and a line on the wall. These lines can be skew lines because they lie in distinct planes if they are not parallel to one another and do not meet. Skew lines go on forever in both directions.

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Answer:

Step-by-step explanation:

Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew.

[tex] {\qquad\quad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } = 34[/tex]

[ add 2 on both sides ]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } + 2 = 34 + 2[/tex]

[ form identity : a² + b² + 2ab ]

[tex]\qquad \sf  \dashrightarrow \: {(x)}^{2} + { \bigg(\cfrac{1}{ {x}^{} } \bigg) }^{2} + 2 \sdot(x) \sdot \bigg(\cfrac{1}{x} \bigg) = 36[/tex]

[ a² + b² + 2ab = (a + b)² ]

[tex]\qquad \sf  \dashrightarrow \: {\bigg (x + \cfrac{1}{x} \bigg) }^{2} = 36[/tex]

[tex]\qquad \sf  \dashrightarrow \: {\bigg (x + \cfrac{1}{x} \bigg) }^{} = \sqrt{ 36}[/tex]

[tex]\qquad \sf  \dashrightarrow \: x + \cfrac{1}{x} = \pm 6[/tex]

so, the value of required expression is 6

[usually positive value is considered, but if asked the value can be either positive or negative]

Answer:

2x - 3

Step-by-step explanation:

10x²-23x+ 12 ÷ 5x-4

Answer:

2x - 3

Step-by-step explanation:

[tex](5x-4)(2x-3)=10x^{2} -23x+12[/tex]

Hope this helps

The system of linear equations that represent the given situation is:

5x + 10y = 1750 and 1/3x + 1/2y = 100.

A linear equation is an equation with the highest degree of the variable is one. There may be one or more variables but their degree must be 1 to become a linear equation.

The general form of a linear equation is y = mx + c.

In the given situation,

Consider x as the number of short-sleeved shirts ordered and y as the number of long-sleeved shirts ordered.

It is given that,

Price for short-sleeved shirts = $5

Price long-sleeved shirts =$10

The total price for 100 shirts ordered = $1,750

So, we can write the linear equation as

5x + 10y = 1750  ...(i)

It is given that,

After the first week, they sold 1/3 of the short-sleeved shirts and 1/2 of the long-sleeved shirts. I.e.,

1/3x + 1/2y = 100  ...(ii)

Thus, from equations (i) and (ii), the system of linear equations that represent the given situation is

5x + 10y = 1750

1/3x + 1/2y = 100

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Disclaimer: The given question is incomplete. Here is the complete question.

Question:

The drama club is selling short-sleeved shirts for $5 each, and long-sleeved shirts for $10 each. They hope to sell all of the shirts they ordered, to earn a total of shirts ordered, and to earn a total of $1,750. After the first week of the fundraiser, they sold 1/3 of the short-sleeved shirts and 1/2 of the long-sleeved shirts, for a total of 100 shirts.

Let x represent the number of short-sleeved shirts ordered and let y represent the number of long-sleeved shirts ordered. which system of linear equations represents the situation?

Answer:

c

Step-by-step explanation:

46.5 is higher than 5.2

Note that:

The larger the magnitude(value) of the heights given the larger the heights

Units are not added to the values representing each height

By carefully considering the heights given:

5.2 is a lesser value than 46.5

Since 46.6 > 5.2, we can conclude that 46.5 is higher than 5.2

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(D) 200 DVD players were repaired in the first year.

Given:

The DVD player shipped 960 players last month

There is a record that out of every 24 players, the 5 would be repaired.

So we need to find the number of DVD players that were repaired in these 960 players.

So,

[tex]\frac{960*5}{24} \\=200[/tex]

Therefore, (D) 200 DVD players were repaired in the first year.

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The question you are looking for is here:

A DVD player manufacturer shipped 960 DVD players last month. According to the manufacturer's records, 5 out of every 24 players were repaired during the first year of ownership. How many of the 960 DVD players were repaired in the first year?

A: 40

B: 120

C: 192

D: 200

Answer:

Domain:[-4,∞)

Range:[0, ∞)

Thus, choice C is the exact answer

The length of the arc made by the big hand if the tip travels from 6:00pm to 6:20pm is 0.52 feet

An equation is an expression that shows the relationship between two or more variables and numbers.

The clock reads 12 hours (720). The angle if the tip travels from 6:00pm to 6:20pm (20 minutes) is:

Ф = (20/720) * 360 = 10°

The length of the arc is given as:

Length of arc = (Ф/360) * 2π * length of hand = (10/360) * 2π(3) = 0.52 feet

The length of the arc made by the big hand if the tip travels from 6:00pm to 6:20pm is 0.52 feet

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Answer:

Step-by-step explanation:

hello :

P(A ∩ B)=P(A)×P(B)=1/2×1/3 = 1/6

Step-by-step explanation:

The answer is 8 2 / 5 because ...

[tex]8 \frac{2}{5} = \frac{8 \times 5 + 2}{5} = \frac{42}{5} \\ [/tex]

Answer:

Here your ans and dont forget to say dhanwyad ok.

Answer:

3 elements

Step-by-step explanation:

Let A = solution set of x²-4

B = solution set of x²-3x+2

First, find the solution of each sets:

[tex]\displaystyle{x^2-4=0}\\\\\displaystyle{(x+2)(x-2)=0}\\\\\displaystyle{x=2,-2}[/tex]

Set B:

[tex]\displaystyle{x^2-3x+2=0}\\\\\displaystyle{(x-2)(x-1)=0}\\\\\displaystyle{x=1,2}[/tex]

Now we can write new set as:

A = {2, -2}

B = {1, 2}

The union of A and B means combine both sets together:

A ∪ B = {2, -2, 1, 2}

However, in a set, we do not write duplicate elements, so the union set will be:

A ∪ B = {2, -2, 1}

Hence, there are 3 elements in A ∪ B.

The parents could have 3 boys and 3 girls in 400 ways

The given parameters are

Children, n = 6

Boys, r = 3

Girls, r =3

The number of combination is:

[tex]Ways = ^nC_{r1} *^nC_{r2}[/tex]

So, we have:

[tex]Ways = ^6C_3 *^6C_3[/tex]

Apply the combination formula

[tex]Ways = \frac{6!}{3!3!} *\frac{6!}{3!3!}[/tex]

This gives

Ways = 400

Hence, the parents could have 3 boys and 3 girls in 400 ways

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The sum of the pulses allows us to find that the answer for the sum at a point x is

If the waves travel in the same direction, their sum gives resulting waves that can be maximum or minimum depending on the phase between them, un stationary patterns.

If the directions are coincident directions, they add place to the interference processes, in this case, stationary patterns are formed on a screen.

If the waves travel in the opposite direction the sum of the two waves gives rise to a wave that maximum is the sum of the amplitudes of the two pulses

In the case of a pulse that corresponds to a single wavelength, the result is an instantaneous maximum,  which after the pulse passes, returns to zero.

Consequently, there is no stationary pattern, so there is no interference between the two pulses.

In conclusion with the sum of the pulses, we can find that the answer is No interference pattern is produced as the amplitude does not remain constant.

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Answer: 480

Step-by-step explanation:

20(12)(2) = 480

The given exponential function exists [tex]f(x)=3(1/3)^x[/tex] . The growth value of the function is 1/3.

An exponential function exists a mathematical function of the following form: [tex]f ( x ) = a^ x[/tex].

where x exists a variable, and a exists a constant named the base of the function.

An exponential function exists of the form [tex]f(x)=ab^x[/tex]

where a ≠ 0, b > 0, b ≠1, and x exists any real number.

when b > 1, the graph increases.

when 0 < b < 1, the graph decreases.

a = initial value

r = growth or decay rate

x = number of time.

The given exponential function exists [tex]f(x)=3(1/3)^x[/tex]

The function exists a stretch of the function [tex]f(x)= (1/3)^x.[/tex]

Therefore, the correct answer is the growth value of the function is 1/3.

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Answer:

y = 120

x = 10.6

Step-by-step explanation:

Given polygons are parallelograms.

In parallelograms, consecutive angles are supplementary which means their sum is equal to 180.

Since two parallelograms are similar:

60 + y = 180 subtract 60 from both sides

y = 120

To find the value of x:

side lengths are proportional because these are similar polygons

[tex]\frac{x+4}{22} = \frac{12}{18}[/tex] cross multiply fractions

18x + 72 = 264 subtract 72 from both sides

18x = 192 divide both sides by 18

x = 10.6 approximately

Using the hypergeometric distribution, it is found that there is a 0.0232 = 2.32% probability of getting exactly two winning numbers with one ticket.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the parameters are given as follows:

N =A + B = 54, k = 4, n = 4.

The probability of getting exactly two winning numbers with one ticket is P(X = 2), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,54,4,4) = \frac{C_{4,2}C_{50,2}}{C_{54,4}} = 0.0232[/tex]

There is a 0.0232 = 2.32% probability of getting exactly two winning numbers with one ticket.

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Answer:

Step-by-step explanation:

the answer is D

This enables us to conclude that Sarita's solution is accurate, but her verification was flawed. ( 5 - 3 [tex]\neq[/tex] 2 ).

What is linear equation?

When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it.

Given the following equation:

5(x-3) + 7(x+4) = 73

The steps to solve it are:

Apply the Distributive property:

5x - 15 + 7x + 28 = 73

12x + 13 = 73

Subtract 13 from both side

12x + 13 - 13 = 73 -13

12x = 60

Divide both side by 12

12x/12 = 60/12

x = 5.

To verify it, put the x = 5 in to the equation:

5(5 - 3) + 7(5 + 4) = 73

After solving it, we get

5(2) + 7(9)  = 73

10 + 63 = 73

73 = 73  

This enables us to conclude that Sarita's solution is accurate, but her verification was flawed. ( 5 - 3 [tex]\neq[/tex] 2 ).

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Answer:

x = 19.1

Step-by-step explanation:

Because this is a right triangle, we can use trigonometry.

Thus, we must use either sine (opposite / hypotenuse), cosine (adjacent / hypotenuse), or tangent (opposite / adjacent).

If we use 33 as the reference angle, the side measuring 16 is the adjacent side and x is the hypotenuse.

Thus, we can use cosine:

[tex]cos 33=\frac{16}{x} \\x*cos33=16\\x=19.0778=19.1[/tex]

The value of s is 45 and the value of BC is 434

The given parameters are:

AB = 9s + 29

DC = 10s - 16

Opposite sides of rhombus are equal.

So, we have:

9s + 29 = 10s - 16

Evaluate the like terms

s = 45

Substitute s = 45 in AB = 9s + 29

AB = 9 * 45 + 29

Evaluate

AB = 434

This means that

BC = AB = 434

Hence, the value of s is 45 and the value of BC is 434

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The exact values of sin θ/2 and tan θ/2 given below as:

Given that tan θ = -5/12 and θ lies between 90° and 180°, the values of sin θ/2 and tan θ/2 can be found as follows:

tan θ = -5/12

θ =  180 -tan⁻¹-(5/12)

θ = 157.38

sin θ/2  = sin 157.38/2

sin θ/2 = 0.9806

tan θ/2 = tan 157.38/2

tan θ/2 = 4.99

In conclusion, the values of the sine and tangent are found from the given values.

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Answer:

Obtuse, scalene.

Step-by-step explanation:

In ΔSVU, one angle is 120° which is obtuse angle.

So, ΔSVU is a obtuse triangle.

All the sides  have different measurements. So, It is a Scalene triangle.

Multiplicative rule's probability is a rule which states that the when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

According to the statement

we have to explain about the those law which is used when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

So, For this purpose we know that the

According to multiplicative rule of probability ,

If A and B are two independent events in a probability experiment, then the probability that both events occur simultaneously is: P(A and B)=P(A)⋅P(B) In case of dependent events , the probability that both events occur simultaneously is: P(A and B)=P(A)⋅P(B | A)

and we see that these conditions are fulfilled by the definition of the multiplicative rule.

So, Multiplicative rule is a rule which states that the when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

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The derivative of the natural logarithm function is given by:

[tex]f^{\prime\prime}(x) = \cotg{x}[/tex]

Suppose we have a composite natural logarithm function given as follows:

[tex]f(x) = \ln{g(x)}[/tex]

The derivative of the function is given as follows:

[tex]f^{\prime}(x) = \frac{g^{\prime}(x)}{g(x)}[/tex]

In this problem, the function, which is already a first derivative, it given by:

[tex]f^{\prime}(x) = \ln{|\sin{x}|} + 3[/tex]

The derivative of a constant is of zero, and the derivative of sin(x) is cos(x), hence the derivative of the entire function is given as follows:

[tex]f^{\prime\prime}(x) = \frac{\cos{x}}{\sin{x}} = \cotg{x}[/tex]

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El número decimal que no es un decimal periódico es dado por:

B. [tex]\frac{11}{400}[/tex].

Un decimal periódico es un número decimal en el que la misma secuencia de dígitos se repite indefinidamente.

La conversión de las fracciones para decimales són:

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The probability that a male is selected, then a female is 0.26

The probability that a female is selected, then a male is 0.26

The probability that two males are selected is 0.18

The probability that two females are selected is 0.30.

The probability that no males are selected is 0.30.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that a male is selected, then a female = (11/25) x (14 / 24) = 0.26

The probability that a female is selected, then a male = (14/25) x (11 / 24) = 0.26

The probability that two males are selected = (11/25) x (10/24) = 0.18

The probability that two females are selected = (14/25) x (13 / 24) = 0.30

The probability that no males are selected =  (14/25) x (13 / 24) = 0.30

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