What are the real and imaginary parts of the complex number?
-9 + 8i
Enter your answers in the boxes.
The real part:
The imaginary part:

The approximate x-values for the local maximum and the local minimum are given as follows:

D) max ≈ -0.3 , min ≈ 2.3.

Hence the critical points of the graphed function are given as follows:

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Film cameras allow a limited number of shots per role. 36 images can a photographer typically shoot on a roll. Thus, option A is the correct option.

The most cost-effective per shot is the roll, which typically yields 36 exposures. The 35mm format comes in a few different forms. On a roll of 35mm film, half-frame cameras may capture twice as many images at a smaller size.

Rolls of film typically have 24 or 36 exposures. The number of pictures you may take before loading a new roll may be limited as a result. However, some photographers view this as a benefit since it forces them to be more deliberate and exact when creating their images.

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Using the angle addition postulate, the angle measures are:

\(m\angle RSQ = 28^{\circ}\\\\m\angle QST= 33^{\circ}\)

(See the image attached below showing the angles given.)

Recall:

The angle addition postulate states that two smaller angles within a bigger angle will add up to give the sum of the larger one.

Given:

\(m \angle RST = 3x + 7\\\\m \angle QST = 5x - 2\\\\m \angle RST = 61\)

\(m\angle RSQ + m\angle QST = m\angle RST\) (angle addition postulate)

\(3x + 7 + 5x - 2 = 61\)

\(8x + 5 = 61\\\)

\(8x + 5 = 61\\\\8x = 61 - 5\\\\8x = 56\)

\(x = 7\)

\(m\angle RSQ = 3x + 7\)

\(m\angle RSQ = 3(7) + 7\\\\m\angle RSQ = 28^{\circ}\)

\(m\angle QST= 5x - 2\)

\(m\angle QST= 5(7) - 2\\\\m\angle QST= 33^{\circ}\)

Therefore, using the angle addition postulate, the angle measures are:

\(m\angle RSQ = 28^{\circ}\\\\m\angle QST= 33^{\circ}\)

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Answer:

x = 1

Step-by-step explanation:

5(2x - 8) + 15 = -15

First, let's move the 15 to the opposite side of the equation. We'll do this by subtracting 15 from BOTH sides of the equation.

5(2x - 8) + 15-15 = -15-15

5(2x-8) + 0 = -30

5(2x-8) = -30

Now let's expand that first term.

5(2x)-5(8) = -30

10x - 40 = -30

Now let's move the -40 to the opposite side of the equation. We'll do this by ADDING 40 to both sides of the equation.

10x - 40 + 40 = -30 + 40

10x -0 = 10

10x = 10

Now to solve for x, we divide BOTH sides by 10 to "isolate the variable" aka get x alone.

10x/10 = 10/10

x = 1

The answer is x = 1.

Let's check if our answer is correct!

Original equation: 5(2x - 8) + 15 = -15

Substitute 1 for x.

5(2*1-8) + 15 =

5(2-8) + 15 =

5(-6) + 15 =

-30 + 15 = -15 >>> which is exactly what we started with! So x is 1.

Answer:

155 Units

Step-by-step explanation:

Rate of Bug (given) = 11 units PER MINUTE

It never changed direction, so it was going in positive direction (assume).

In 7:15 pm (evening), it was at Point 100,

We want the point at which it was at 7:20 pm.

7:20pm - 7:15pm = 5 minutes

So, time passed 5 minutes. It's rate is 11 units PER MINUTE, so in 5 mins:

11 * 5 = 55 units

Assuming he is going in positive direction, the bug will be at:

100 + 55 = 155 Units

Answer:

It will be at the point 155

Step-by-step explanation:

It will be at point 155 If it keeps running at the same pace and in the same direction.

I know this because if it is at point 100 at 7:15 and it goes 11 units per minute then 5 minutes later at 7:20 it would be at point 155

Answer:

16

Step-by-step explanation:

3x - 12 = 36

3x = 48

x = 16

The value of 12x in the expression is 10

You multiply 5 = 6x  by 2 to get 12x

From the question, we have the following parameters that can be used in our computation:

2x + 5 = 8x

You subtract 2X from each side to get

5 = 6x

Then multiply both sides by 2

This gives

10 = 12x

So, we have

12x = 10

Why do you multiply both sides by 2

You multiply by 2 because the question requests for the value of 12x

Since, we have solved for 6x, the next step is to multiply 6x by 2 to get 12x

i.e. 6x * 2 = 12x

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Answer:

To calculate the book value of the building, we need to calculate the annual depreciation amount and multiply it by the number of years elapsed since the building was completed.

The annual depreciation amount is calculated as: $1 million / 50 years = $20,000

In 2014, the book value of the building was: $1 million - ($20,000 * (2014 - 2010)) = $1 million - ($20,000 * 4) = $960,000

In 2022, the book value of the building will be: $1 million - ($20,000 * (2022 - 2010)) = $1 million - ($20,000 * 12) = $680,000

There are no extraneous solutions when plugging -7 into x-5=2(x+1).

So extraneous solutions means the solutions that you get by solving an equation, but after you try plugging it back into your original equation, the solution does not work.

Now we have our solutions of x=7, and we just need to check whether it is extraneous or not. We can do this by taking x=1 and plugging it back into your original equation  x - 5 = 2(x + 1)

x - 5 = 2(x + 1)

-7 - 5 = 2(-7 + 1)

-12 = -14 + 2

-14 + 14

0 = 0

We end up getting that 0 = 0 which is correct,

Thus, there are no extraneous solutions.when plugging -7 into x-5=2(x+1).

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The equation for the relationship between the number of cans of paint, x, and the total weight of the cans, y, in slope-intercept form is y = 6x + 0. This equation can be derived from the formula for the slope-intercept form of a line, y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, since the weight of each can of paint is 6 pounds and there is no y-intercept (the line passes through the origin), the slope of the line is 6 and the y-intercept is 0.

A table of possible values for the number of cans of paint, x, and the total weight of the cans, y, based on this equation is shown below:

x (number of cans of paint) y (total weight of cans)

1 6

2 12

3 18

4 24

5 30

As the table shows, for each additional can of paint, the total weight of the cans increases by 6 pounds. This is because each can of paint weighs 6 pounds, and the weight of the cans is equal to the number of cans multiplied by the weight of each can.

Answer: y = 6x

Step-by-step explanation:

       For each can of paint (x) 6 pounds is added. This is represented as;

         y = 6x

       For the table of possible values, we will plug a value in for x, and then evaluate the function for y. See attached.

y = 6(1) = 6

y = 6(2) = 12

y = 6(3) = 18

9514 1404 393

Answer:

Step-by-step explanation:

All of these exponential function problems use the same equation, but with different plug-in values. These can be easily accommodated by a spreadsheet or graphing calculator.

The general form of the value after t years is ...

  (initial value)×(1 +annual growth rate)^(years)

The growth rate is positive for an increase, negative for a decrease.

a) Initial value: 22385; growth rate: -0.14; years: 10

  value after 10 years: $22385×(1-0.14)^10 = $4953.84

__

b) initial value: 290; growth rate: 0.09; years: 5

  population after 5 years: 290(1+.09)^5 = 446

__

c) initial value: $4000; growth rate: -0.10; years: 8

  value after 8 years: $4000(1 -0.10)^8 = $1721.86

Selling the car for $1500 is selling it for less than its estimated value. That may not be a good decision.

_____

Additional comment

The property value of the car is not the only consideration when evaluating the sale. Other costs related to the car may come into play, and there may be tax implications.

The length of n for the triangle is 1778 cm

The law of sines is very useful for solving triangles. The formula is given as:

n/sinN = o/sinO = p/sinP

where

N= angle N, n = length of side n, O = angle O, o = length of side o, P = angle P and p = length side p

Given: p = 870 cm, m∠N = 127°, m∠O = 30°

m∠P = 180 - 127 - 30 = 23°   (angle sum in a triangle)

n/sinN = p/sinP

n/sin127° = 870/sin23°

n = (870 * sin127°)/sin23°

n = 1778 cm

Therefore, the length of n, to the nearest centimeter is 1778 cm

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h(x) = f(x)g(x) represents the product of two functions, combining their behaviors into a new function.

In mathematics, the expression h(x) = f(x)g(x) represents the product of two functions, f(x) and g(x). When evaluating h(x) for a given value of x, it involves multiplying the corresponding values of f(x) and g(x).

The product of two functions allows for the combination of their individual behaviors and characteristics. The resulting function, h(x), inherits properties from both f(x) and g(x). The behavior of h(x) will depend on the specific functions involved.

For example, if f(x) represents a linear function and g(x) represents an exponential function, their product h(x) = f(x)g(x) will exhibit a combined behavior reflecting both linearity and exponential growth. The specific form of the functions will determine the precise behavior of h(x) and its graph.

It is important to note that the product of two functions assumes that the functions are defined for the given values of x and that the multiplication operation is valid for the corresponding function values.

h(x) = f(x)g(x) represents the product of two functions, combining their behaviors to form a new function. The specific nature of h(x) depends on the characteristics of f(x) and g(x).

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Answer:

a < 42

Step-by-step explanation:

Question : 4a + 9a - 6a < 42

Answer :

4a + 9a - 6a < 42

Combine like terms.

13a - 6a < 42

7a < 42

Divide both sides by 7.

a < 42

Hope this helps you :-)

Let me know if you have any other questions :-)

Answer:

\(\large\boxed{\boxed{\underline{\underline{\maltese{\pink{\pmb{\sf{\: Solution :- \: a \: < \: 6 }}}}}}}}\)

Step-by-step explanation:

We need to solve the below given inequality \(\downarrow\)

For this, we need to combine all the like terms at first. So

We know that, 42 is divisible by 7. So, let's divide both the sides of the inequality by 7.

_________

Hope it helps!

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\(\mathfrak{Lucazz}\)

Answer:

y = -2/3 x - 13/3

Step-by-step explanation:

y = -2/3 x + 3/2

y = mx + b

m = -2/3

The slope of the given line is -2/3. Parallel lines have equal slopes, so our line also has slope -2/3.

m = -2/3

y = mx + b

y = -2/3 x + b

Substitute the given point for x and y and solve for b.

-7 = -2/3 (4) + b

-21/3 = -8/3 + b

b = -13/3

Answer: y = -2/3 x - 13/3

hello what's up having fun hoping that someone will answer you

Answer:

this should be the answer

here you go

b) (-3 + 5i) (1) = -3 + 5i  

Step-by-step explanation:

Answer:

151/30

Step-by-step explanation:

if you subsitute it you will get  3 1/10

Answer:

7070

Step-by-step explanation:

First, read the problem carefully.

The problem states: "so that it has only 1 nonzero digit."
This means that all the digits in the number should be zero except for one digit. The given numbers are 6988 and 67.

How do you round numbers?

If you are round to the hundreds place, look at the digit before, which is the digit in the tens place. Same if you are rounding to the thousands digit or tens digit; just look at the digit before.

How to look?

For example, if you are rounding to the nearest ten, look at your ones digit. If the ones digit is any of the numbers from 0 to 4, round down. In this case, rounding down means you keep the tens digit the same and change the digit following it into 0.

Ex.

1. Round 42 to the nearest ten.

  2 is a number from 0 to 4, so we round down.

  This yields an answer of 40.

2. Round 74 to the nearest ten.

  4 is between 0 and 4, so we round down.

  74 rounded to the nearest ten is 70.

Next, if the number following the digit you are rounding to is between 5 and 9, round up. Rounding up is taking the digit and bumping it up by 1.

Ex.

1. Round 151 to the nearest hundred.

  We are rounding to the nearest hundred so we look to the digit behind        it, the tens digit. The tens digit it between 5 and 9, so we round up, or add one to the hundreds digit. This results in an answer of 200. (151 --> 200)

How do we do this problem then?

Rounding 6988 so that it only has 1 nonzero digit means it goes up to 7000. Rounding 67 up gives us 70.

Finally, we add 7000 + 70 = 7070

Answer:

15 adult, 45 student

Step-by-step explanation:

5x+2y=165

x+y=60

x = 60-y

300-5y+2y=165

-3y = -135

x= 15

y= 45

Answer:

first answer is (3, -8); second answer is (3, -5)

Step-by-step explanation:

The general equation of the straight line that shows the temperature in degrees Fahrenheit during a given day and represents a linear function is → y = - 1.75x + 71.

The general equation of a straight line is -

y = mx + c

where -

{m} is the slope of the line.

{c} is the {y} - intercept.

Given is a graph that shows the temperature in degrees Fahrenheit during a given day and represents a linear function.

The straight line passes through the points -

(3, 65.75)

(6, 60.5)

We can write the slope as -

{m} = (60.5 - 65.75)/(6 - 3)

{m} = - 1.75

We can write the {y} - intercept as -

60.5 = - 1.75 x 6 + c

60.5 + 10.5 = c

c = 71

Therefore, the general equation of the straight line would be -

y = - 1.75x + 71

Therefore, the general equation of the straight line that shows the temperature in degrees Fahrenheit during a given day and represents a linear function is → y = - 1.75x + 71.

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Answer:

Mark has 13 marbles

Don has 40 marbles

Step-by-step explanation:

Let the number of Mark's Marbles = M

Let the number of Don's Marble = D

D = 1 + 3M - - - - (1)  (Don has 1 more than 3 times the number of marbles Mark has)

D + M = 53 - - - - - (2) (total number of marbles is 53)

puttin the value of D from equation (1) into equation (2)

(1 + 3M) + M = 53

1 + 3M + M = 53

1 + 4M = 53

4M = 53 - 1 = 52

4M = 52

M = 52 ÷ 4

M = 13

finding D by putting the value of M (M = 13) into equation 1

D = 1 + 3M - - - - (1)

D = 1 + 3 (13)

D = 1 + 39

D = 40

∴ Mark has 13 marbles

Don has 40 marbles

Step-by-step explanation:

i believe it is always true. not 100% sure though

The probability that the Yankees will lose when they score fewer than 5 runs is 0.821 (nearest to the thousandth).

For two events A and B:

The chain rule states that the probability that A and B both occur is given by:

\(P(A \cap B) = P(A)P(B|A) = P(B)P( A|B)\)

Lets suppose here that:

Suppose A' and B' are their complementary events, then we have:

Then, by the given data, we have:

\(P(A) = 0.56\\P(B) = 0.61\\P(A' \cap B') = 0.32\)

We've to find \(P(A' | B')\)

Using chain rule, we have:

\(P(A'|B') = \dfrac{P(A' \cap B')}{P(B')}\)

Since P(B') = 1-P(B) = 100.61 = 0.39, therefore, we get:

\(P(A'|B') = \dfrac{P(A' \cap B')}{P(B')} = \dfrac{0.32}{0.39} \\\\P(A'|B') \approx 0.821\)

Thus, the probability that the Yankees will lose when they score fewer than 5 runs is 0.821

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Answer:

y < 3

Step-by-step explanation:

2y + 1 < 7

~Subtract 1 to both sides

2y < 6

~Divide 2 to both sides

y < 3

Best of Luck!

Let y be the total amount of money that Gonzalo earns in a day, and x the overtime hours. We know that for his shift, he earns $60. Also, we know that the total amount he earns is the sum of what he earns for one shift (60) and what he earns for overtime.

REcall that for each overtime hour he earns $15. So, what he earns in total for the overtime is 15*x. Then, the equation we get is

Now, to know how much he would earn if he works 4 overtime hours, we simply replace the value of x by 4, then we get

So Gonzalo would earn 120 if he works 4 overtime hours.

The equatiοn οf the vertical asymptοte fοr f(x) is x = -3.

The end behaviοr οf f(x) is pοsitive οr negative infinity.

The x-intercept fοr f(x) is  (5,0).

A vertical asymptοte is a line that a curve apprοaches but never tοuches οr crοsses as the input variable apprοaches a certain value. In οther wοrds, a vertical asymptοte is a vertical line οn a graph that the functiοn apprοaches as the input variable apprοaches a specific value οr set οf values.

Tο find the equatiοn οf the vertical asymptοte fοr f(x) = (4x-20)/(x+3), we need tο identify the values οf x that make the denοminatοr οf the functiοn equal tο zerο.

Setting the denοminatοr equal tο zerο, we get:

x + 3 = 0

Sοlving fοr x, we get:

x = -3

Therefοre, the equatiοn οf the vertical asymptοte fοr f(x) is x = -3.

Tο determine the end behaviοr οf f(x) as x apprοaches infinity, we can use the fact that the degree οf the numeratοr is greater than the degree οf the denοminatοr. This means that the functiοn will apprοach infinity as x apprοaches pοsitive οr negative infinity.

Tο find the x-intercept fοr f(x), we need tο set the numeratοr οf the functiοn equal tο zerο and sοlve fοr x.

Setting the numeratοr equal tο zerο, we get:

4x - 20 = 0

Sοlving fοr x, we get:

x = 5

Therefοre, the x-intercept fοr f(x) is (5,0).

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The simplified form of the given expression is x raise to the power of one-thirty.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

Simplifying indices expressions

Given the indices expression (x^1/2/(x^1/3)^1/5

Using the indices law below:

a^m/a^n = a^m-n

(a^m)^n

Applying the law above to the given equation

(x^1/2/(x^1/3)^1/5 = (x^1/2-1/3)^1/5

(x^1/2/(x^1/3)^1/5 = (x^1/6)^1/5

(x^1/2/(x^1/3)^1/5 = x^1/30

Hence the simplified form of the given expression is x raise to the power of one-thirty.

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