write the sum and then write an equivalent expression by collecting like terms and removing parentheses the opposite of (5x - 1) and 5x

[tex]\dfrac{ 2+ 2i}{5+4i}\\\\\\=\dfrac{(2+2i)(5-4i)}{(5+4i)(5-4i)}\\\\\\=\dfrac{10-8i + 10i -8i^2}{5^2 -(4i)^2}\\\\\\=\dfrac{10+2i +8}{25+16}~~~~;[i^2 =-1]\\\\\\=\dfrac{18+2i}{41}\\\\\\=\dfrac{18}{41} + \dfrac{2}{41}i[/tex]

Answer:

2.5

Step-by-step explanation:

3 1/2 - 9 3/4 =

3 2/4 - 9 3/4 = -6 1/4

-6 1/4 = -6.25 ÷ (-2.5) = 2.5

Answer:

Step-by-step explanation:

(4+3i)(12-2i)

48 - 8i + 36i - 6i^2

48 + 28i +6

54 + 28i

Answer:

The answer for your problem will be 0.0625

Answer:

2 lines are used fro their respected two centers one Is vertical or one is horizontal it's dice into 4 squares

A rigid transformation is one in which the distance between pairs of points

are preserved, and the image and preimage have the same dimensions.

Reasons:

The vertices of the trapezoid GHIZ are G(0, 0), H(-1, 2), I(3, 2), and J(2, 0)

The given transformations are;

1. GHIJ is reflected in the x-axis and the image is reflected in the y-axis

The above transformation is a double reflection.

2. GHIJ is rotated about the origin 90° counterclockwise. The resulting

image is translated up 2 units.

3. GHIJ is dilated by a scale factor of [tex]\mathbf{\frac{1}{2}}[/tex], with the center of dilation at the

origin. The resulting image is translated 2 units left.

Required:

The transformations that produce an image that is congruent to the given figure:

Solution:

Two figures are congruent if they have the same size and shape.

With the given figure being the trapezoid GHIJ, we have that a

transformation that will give an image that is congruent to the preimage

which is the trapezoid GHIJ is a rigid transformation.

Rigid transformations are;

The combinations of transformation given within the scenario that consists

of only rigid transformations are scenario 1 and scenario 2.

Therefore, the correct option is; Numbers 1 and 2.

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Answer: Choice A.   sqrt(116)

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Explanation:

If we were to view a vertical cross section of the cone, then we get a triangle. This triangle splits along the vertical height line to form two congruent right triangles.

The horizontal piece of each triangle is the radius r = 4.

The vertical piece is the height h = 10.

Apply the pythagorean theorem to find the slant height, which is the hypotenuse of the right triangle.

a^2 + b^2 = c^2

r^2 + h^2 = x^2

4^2 + 10^2 = x^2

16 + 100 = x^2

116 = x^2

x^2 = 116

x = sqrt(116)

Answer:

The odds for are 50% and the odds against are 50%.

Step-by-step explanation:

On a die, there is 6 possibilities 2, 3, and 5, are 3 of them.

This means there is a 3/6 chance that it will land on one of those numbers, and there is also a 3/6 chance it will land on 1, 4, or 6.

3/6 is equivalent to 50% and 1/2.

P(A and B) = P(A) + P(B) - P(A or B)

P(A and B) = 0.3 + 0.6 - 0.8

P(A and B) = 0.1

Because this result is nonzero, the two events A and B are not mutually exclusive. It is possible for the two events to happen at the same time.

Mutually exclusive events always have P(A and B) = 0, which means A and B cannot happen simultaneously.

The probability of A or B equals the probability of A plus the probability of B. so, the event is not mutually exclusive because of the P(A and B) = 0.1, not 0.

The probability for event A is 0.3, the probability for event B is 0.6,

and the probability of events A or B is 0.8.

Why are the events not mutually exclusive?

The probability for event A is 0.3, the probability for event B is 0.6,

and the probability of events A or B is 0.8.

P(A) = 0.3

P(B) = 0.8

and P(A∪B) = 0.8

When two events are said to be mutually exclusive when both the events cannot take place simultaneously.

Mutually exclusive events always undergo different outcomes.

These events are also known as disjoint events.

Mutually exclusive events prevent the second event to take place when the first event appears.

The probability of A and B together equals 0,

P(A and B) = 0

The probability of A or B equals the probability of A plus the probability of B,

P(A or B) = P(A) + P(B)

Therefore,

P(A or B) = P(A) + P(B) = 0.3 + 0.6 = 0.9

Here, 0.9 ≠ 0.8

Thus, the events are not mutually exclusive.

Hence, The event is not mutually exclusive because the P(A and B) = 0.1, not 0.

For more details about Probability refer to the link given below.

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The value of x is 5. The value of y is 8.66.

The image attached is that of a right triangle. In order to determine the value of x and y, SOHCAHTOA would be used.  x is he opposite side and y in the adjacent side to the angle 30 degrees.

Sin 30 = opposite / hypotenuse

0.5 = x / 10

x = 5

Cos 30  = adjacent / hypotenuse

0.8660 = y / 10

y = 8.66

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Answer:yes, additional training is necessary because if the employee does not have training they will mess up and ur stores reputation will be ruined

Step-by-step explanation:

The answer is A since the tip of the triangle points to the smallest number

Answer:

a

Step-by-step explanation:

it says 46 is more than that cetain number

Answer:

9

Step-by-step explanation:

pemdas

9-3÷1/3+1

division

3 and 1/3 becomes 1

we have 9-1+1

which simplifies to 9

Answer:

9

Step-by-step explanation:

9 pillows per hour i believe

Answer: 147 votes

Beacause they need to find out what to do with the beach house

The greatest value in the range for this situation is $2,675.

A function has an input and an output.

A function can be one-to-one or onto-one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Let the number of days the beach house is rented be represented by the variable "d".

If d is less than or equal to 7, then the total cost can be calculated as:

Total Cost = 375d + 100

If d is greater than 7, then the maximum cost would be reached by renting the house for 7 days and adding the $100 cleaning fee.

In this case, the total cost can be calculated as:

Total Cost = 375(7) + 100 = 2,675

Therefore,

The greatest value in the range for this situation is $2,675.

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#SPJ2

Answer:

y=49/9

Step-by-step explanation:

Distribute 3 with 3y and -5

3 times 3y is 9y

3 times -5 is -15

So the equation now looks like this:

9y-15=34

Add 15 on both sides:

9y=49

Divide 9 on both sides

So y=49/9

Since there is no common value to divide by y is 49/9

If you want the decimal version it is 5.44=> (=> meaning continuing forever)

Hope this helps!

Answer:

i found this so srry if its wrong i saw no one answering this so i wanna help

Step-by-step explanation:

so,  x*(7/100) + (3500 - x)*(4/100) = 197

=> 3x + 14000 = 19700

=> 3x = 19700 - 14000

=> x = 5700/3 = 1900

Answer:

16z

Step-by-step explanation:

z = the unknown number of pounds

16 ounces in 1 pound.

So  z pounds =  16z    

or   it can be given as a proportion;

[tex]\frac{16 ounces}{1 pound} (z)[/tex]

Answer:

5 and 25

Step-by-step explanation:

let the son's age be x then the father's age is x + 20

In 5 years

son = x + 5 and father = x + 20 + 5 = x + 25

Then

x + 25 = 3(x + 5) ← father is three times as old as son

x + 25 = 3x + 15 ( subtract x from both sides )

25 = 2x + 15 ( subtract 15 from both sides )

10 = 2x ( divide both sides by 2 )

5 = x and x + 20 = 5 + 20 = 25

si=on is 5 and father is 25

Answer:

The son is 5 and the father is 25.

Step-by-step explanation:

We can do this using  Algebra.

Let the son be x years old.

Then the father's age is x + 20 years.

After 5 years the father's age is x + 25 and the son is x + 5 years.

So we can write the equation:

x + 25 = 3(x + 5)

x + 25 = 3x + 15

25 - 15 = 3x - x

10 = 2x

x = 5.

So the father's present age is 20 + 5 = 25 and the son is 5 years old.

Answer:

5

Step-by-step explanation:

just had this question

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Explanation:

Since 300 is a multiple of some number, this means that mystery number is a factor of 300.

So for instance, she could have picked 60 since 60*5 = 300. Or she could have picked 50 because 50*6 = 300.

To find out if you have a factor or not, divide the 300 over each answer choice. If you get a whole number, then it is a factor.

Choices B through D lead to whole number results, which shows that the numbers 50, 60 and 75 are factors of 300. Flipping things around, this means that 300 is a multiple of 50, 60, and 75.

Only 45 is the one that isn't a factor of 300, which means that 300 is not a multiple of 45.

--------------

Another way to see this is to list out the multiples of 45

and we don't land on 300. The closest we get is 315.

In contrast, let's list out the multiples of 50

The value 300 is in the list, allowing us to cross off choice B. Choices C and D are similar.

Answer:

LR = 17

Step-by-step explanation:

RP is one section of LP (the whole section). Since R is the midpoint of the segment, RP = LR. Hope this helps!

Based on the definition of a parallel line and the Midsegment Theorem the following are the right answers:

1. a.) BD║AE

b.) BF ║CE

c.) DF║CA

2. a.) YZ║RT

b.) RS ║XZ

c.) XY║TS

3. a.) FH = 24

b.) JL = 74

c.) KJ = 60

d.) FJ = 30

4. a.) AE = 26

b.) AN = 58

c.) CT = 21.5

d.) Perimeter of ΔAEN = 127

5. x = 15

6. x = 6

Parallel lines coplanar straight lines that do not meet each other and are equal distance from each other.

Applying the definition of a parallel line and the Midsegment Theorem the following can be solved as shown below:

1. The pairs of parallel lines in ΔAEC (i.e. the midsegment is parallel to the third side) are:

a.) BD║AE

b.) BF ║CE

c.) DF║CA

2. The segment parallel to the given segments are:

a.) YZ║RT

b.) RS ║XZ

c.) XY║TS

3. Given:

FG = 37; KL = 48; GH = 30

a.) FH = ½(KL)

FH = ½(48)

FH = 24

b.) JL = 2(FG)

JL = 2(37)

JL = 74

c.) KJ = 2(GH)

KJ = 2(30)

KJ = 60

d.) FJ = ½(KJ)

FJ = ½(60)

FJ = 30

4. Given:

PT = 13

EN = 43

CP = 29

a.) AE = 2(PT)

AE = 2(13)

AE = 26

b.) AN = 2(CP)

AN = 2(29)

AN = 58

c.) CT = ½(EN)

CT = ½(43)

CT = 21.5

d.) Perimeter of ΔAEN = EN + AN + AE

Perimeter of ΔAEN = 43 + 58 + 26

Perimeter of ΔAEN = 127

5. 10x + 44 = 2(8x - 23) (midsegment theorem)

10x + 44 = 16x - 46

10x - 16x = -44 - 46

-6x = -90

Divide both sides by -6

x = 15

6. 19x - 28 = 2(6x + 7) (midsegment theorem)

19x - 28 = 12x + 14

19x - 12x = 28 + 14

7x = 42

x = 6

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Answer:

Step-by-step explanation:

A= h(x + 10)^2

27 = 4(x + 10)^2

(x + 10)^2 = 27/4

x + 10 = √27/2

x + 10 = 3√3/2

x = 3√3/2 - 10

= -7.40 to nearest hundredth.

Answer: 40BC and 766AD

Step-by-step explanation:

Answer:

n-1, n, n+1

Step-by-step explanation:

n - 1    +   n    +   n +1  = 3n

The middle number is n, the first is n-1 and the third is n+1

Based on the information given, the three consecutive numbers will be n-1, n, and n+1.

It should be noted that consecutive numbers simply mean the numbers that follow themselves in a particular order.

In this case, the three consecutive numbers will be n-1, n, and n+1. Their addition will be:

= n - 1 + n + n + 1

= 3n

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Answer:

x= 0

y= 2

explanation in the picture attached (tap the image to view it fully)

Answer:

1000

Step-by-step explanation:

Answer:$1000

Step-by-step explanation:

Divide 1200 by 6 then multiply that number by 5