How is the product of a complex number and a real number represented on the complex plane?

Consider the product of 2−4i and 3.

The speed of the boat against the current is (13+x)mph and with the current is (13-x) mph.

If boat goes along the stream flow (downstream), then the speed of boat will be increased as stream will help boat go faster. In contrast, the upstream flow of boat will be slower than its speed in normal flow due to stream resistance.

Speed of boat with the current = Speed of boat + Speed of current

Speed of boat against the current = Speed of boat - Speed of current

Given that the speed of a boat in still water is 13 mph. Also, the speed of the water current is x mph. Therefore, the speeds in the given cases can be written as,

a.) The of speed going against a current with a rate of x mph can be written as,

Speed of boat with against the water current

= Speed of Boat - Speed of water current

= 13 mph - x mph

= (13-x) mph

b.) The of speed going with a current with a rate of x mph can be written as,

Speed of boat with the water current

= Speed of Boat + Speed of water current

= 13 mph + x mph

= (13+x) mph

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The value of the function F(3) will be 1/125. It is obtained by putting the value 3 in the place of x.

A connection between independent variables and the dependent variable is defined by the function. Functions help to represent graphs and equations.

A function is represented by the two variables one is dependent and another one is an independent function. The relation between them is shown as y if dependent and x is the independent variable.

F(x)=(1/5)ˣ

F(3)=(1/5)³

F(3)=1/125

Hence, the value of the function F(3) will be 1/125.

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The form that most quickly reveals the y intercept is

The y intercept is (0, 21/2)

The y-intercept is the point where a function or a curve intersects the y-axis. In other words, it is the value of the dependent variable (y) when the independent variable (x) is equal to zero.

In the form,  f(x) = 1/2 x² - 5x + 21/2 it is easier to see that eliminating x by plugging in 0 leaves 21/2 which is the y intercept

hence we can easily say that the y intercept is (0, 21/2)

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Answer:

Lest then 5/8

Step-by-step explanation:

Lest then 5/8

Answer:

Ext angle = 93°

Step-by-step explanation:

The angle marked 4x + 9 is the exterior angle. The other two marked angles are interior angles. They are, moreover, "remote interior angles" because they are away from the exterior angle.

So here's how to set up an equation:

the two remote interior angles added together equal the exterior angle.

2x + 3x - 12 = 4x + 9

Combine like terms.

5x - 12 = 4x + 9

Subtract 4x

x - 12 = 9

Add 12

x = 21

The exterior angle is:

4x + 9

= 4(21) + 9

= 84 + 9

= 93

During halftime of a basketball game, a slingshot launches T-shirts at the crowd.

What is the maximum height?

Generally, To find the time it takes the T-shirt to reach its maximum height, we need to find the time when the height of the T-shirt stops increasing and starts decreasing. At this point, the velocity of the T-shirt will be 0, since it is not moving up or down.

The velocity of the T-shirt at any time t can be found by taking the derivative of the equation for height:

v(t) = dh/dt = -32t + 72

Setting the velocity to 0 and solving for t, we get:

0 = -32t + 72 32t = 72 t = 72/32 t = 9/4

So it takes the T-shirt 9/4 seconds, or approximately 2.25 seconds, to reach its maximum height.

To find the maximum height, we plug this value back into the equation for height:

h(t) = -16(9/4)^2 + 72(9/4) + 4 h(t) = -81 + 162 + 4 h(t) = 77

The maximum height of the T-shirt is 77 feet.

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Answer:

15

Step-by-step explanation:

a square root multiplied by itself equals the number inside the box, right?

(/~15~)2 = 15

Answer:

15

Step-by-step explanation:

Squaring a square root of a number will just give you back the number since the square and the square root will cancel each other.

Answer:

Part A: $3,415.50

B: 11.34%

Step-by-step explanation:

Part A: $31,000 is within the values 10,276≤x≤41,175, so use f(x)=0.12x-205.50

Part B: For the effective tax rate, divide the amount in part A by the taxable income

Part C: Compare both the taxable income and the effective tax rate to the income domains given and the % multiplier. This one is mostly about how you describe the situation, so I'll leave that up to you.

To calculate the taxes owed on a taxable income of $31,000, we use the appropriate equation for the tax bracket it falls into and substitute the value of x. The effective tax rate is calculated by dividing the amount of taxes owed by the taxable income and multiplying by 100. The piecewise function represents the marginal tax rate chart by using different equations for each tax bracket.

Part A:

To calculate the amount of taxes owed on a taxable income of $31,000, we need to determine which tax bracket it falls into. Since $31,000 is greater than $10,275 but less than $41,175, it falls into tax bracket 2. To find the amount of taxes owed, we use the equation for tax bracket 2: f(x) = 0.12x - 205.50. Plugging in $31,000 for x, we get:

f(x) = 0.12 * 31000 - 205.50 = $3,574.50

Therefore, the amount of taxes owed on a taxable income of $31,000 is $3,574.50.

Part B:

To determine the effective tax rate, we divide the amount of taxes owed by the taxable income. Using the result from Part A (taxes owed = $3,574.50) and the taxable income of $31,000, we have:

Effective tax rate = (taxes owed / taxable income) * 100 = (3,574.50 / 31,000) * 100 ≈ 11.52%

Therefore, the effective tax rate on a taxable income of $31,000 is approximately 11.52%.

Part C:

The piecewise function represents the amount of taxes owed as a function of the taxable income. Each part of the function corresponds to a different tax bracket, with the equation for that tax bracket. The marginal tax rate chart is represented in the piecewise function by the different equations for each tax bracket. For example, the equation in part 1 of the function (f(x) = 0.10x) corresponds to the 10% marginal tax rate for the tax bracket $0-$10,275.

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Answer:

A. 1
B. 3
C. 2
D. 5
E. 4
F. 6

Answer:

pi rad/s

Step-by-step explanation:

360 degrees = 2pi radians

thus 180 deg = pi radians

Answer:

a.

Step-by-step explanation:

\(d = \sqrt{( y _2 - y) {}^{2} + ( x_2 - x ) {}^{2} } \)

\(d = \sqrt{( - 1 - 4) {}^{2} + \sqrt{ - 4 + 1) {}^{2} } } \)

\(d = \sqrt{ - 5 {}^{2} +( - 3 {}^{2} )} \)

\(d = \sqrt{25 + 9} \)

\(d = \sqrt{34} \)

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Answer:

Step-by-step explanation:

Answer:

$2.24

Step-by-step explanation:

To find the unit cost, you divide 6.72 by 3, which is 2.24.

The estimate of the sum of the points is 47/45

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

Points = 6/10 and 4/9

Using the given number line (see attachment), we have the sum expression to be

Sum = 6/10 + 4/9

Evaluate the sum

So, we have the following representation

Sum = 94/90

Simplify

Sum = 47/45

Hence, the sum of the points is 47/45

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hope this helps!everything is explained step by step

T) 7(2m+6) + 8m = 22m + 42

A) 3(1 + 4m)+ 5m= 17m + 3

E) 6m+7(7m+9)= 55m+ 63

H) 4+6(3m+2)= 18m+16

D) 9+9(5+4m)= 36m+54

I) 2+(6m+3)7= 42m+23

U) (4m+3)9+6m= 42m+27

0.5  is the probability that a driver is having a conversation while driving.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given, 6/10 drivers look at their phones while driving. 3/10 drivers are having a conversation and looking at their phones while driving.

Let P(A) be the probability of drivers looking at their phones while driving.

and P(B) be the probability of drivers looking at their phones while driving.

Since:

P(A) = 0.6

P(A ∩ B) = 0.3

P(B) = (P(A ∩ B))/ P(A)

P(B) = 0.3/0.6

P(B) = 1/2

therefore, the probability that a driver is having a conversation while driving is 0.5.

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Step-by-step explanation:

T = (1,7) → T' = (1-5,7-10) = (-4,-3)

S = (1,0) → S' = (1-5,0-10) = (-4,-10)

U = (8,7) → U' = (8-5,7-10) = (3,-3)

V = (8,0) → V' = (8-5,0-10) = (3,-10)

Answer:

Angle 6 = 70

Step-by-step explanation: Using vertical angles if you look across from angle 6 you would see the angle of 70 degrees which means they are equal because they're across from each other.

Answer:

x <> -3, 8

Step-by-step explanation:

x² - 5x - 24 (the denominator of the fraction) must not be 0, because n/0 is not defined for any n.

since this is a quadratic equation, it must have 2 solutions.

therefore, the second answer must be right.

let's check.

a quadratic equation

ax² + bx + c = 0

has the solutions

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (5 ± sqrt((-5)² - 4×1×-24))/(2×1) =

= (5 ± sqrt(25 + 96))/2 = (5 ± sqrt(121))/2 =

= (5 ± 11)/2

x1 = (5 + 11)/2 = 16/2 = 8

x2 = (5 - 11)/2 = -6/2 = -3

correct.

Answer: around -$0.77

Step-by-step explanation:

To calculate the expected value of this lottery game, we need to find the probability of winning the game and the probability of losing the game.

Probability of winning:

There are a total of C(25, 6) possible combinations of choosing 6 numbers out of 25, where C(n, k) represents the number of combinations of choosing k items from a set of n items. The formula for combinations is:

C(n, k) = n! / (k!(n-k)!)

C(25, 6) = 25! / (6!19!) = 177100

So, there are 177,100 possible combinations. Since there's only 1 winning combination, the probability of winning is:

P(Winning) = 1 / 177,100

Probability of losing:

Since there's only 1 winning combination, the probability of losing is:

P(Losing) = 1 - P(Winning) = 1 - (1 / 177,100) = 177,099 / 177,100

Expected value:

Now, we can calculate the expected value (EV) by multiplying the probabilities of each outcome by their respective values and then summing up these products:

EV = P(Winning) * Value(Winning) + P(Losing) * Value(Losing)

EV = (1 / 177,100) * $40,000 + (177,099 / 177,100) * (-$1)

EV ≈ ($40,000 / 177,100) - ($177,099 / 177,100)

EV ≈ $0.2256 - $1

EV ≈ -$0.7744

The expected value of this lottery game is approximately -$0.7744. This means that, on average, a player would lose about 77.44 cents per game.

Answer:

x=40/33

Step-by-step explanation:

Let's solve your equation step-by-step.

25(4x−3)−2x=45−x

Step 1: Simplify both sides of the equation.

25(4x−3)−2x=45−x

(25)(4x)+(25)(−3)+−2x=45+−x(Distribute)

100x+−75+−2x=45+−x

(100x+−2x)+(−75)=−x+45(Combine Like Terms)

98x+−75=−x+45

98x−75=−x+45

Step 2: Add x to both sides.

98x−75+x=−x+45+x

99x−75=45

Step 3: Add 75 to both sides.

99x−75+75=45+75

99x=120

Step 4: Divide both sides by 99.

99x

99

=

120

99

x=

40

33

Answer:

x=40/33

Answer:

x=1.2121212121212....

Step-by-step explanation:

25(4x-3)-2x=45-x

            +x          +x

25(4x-3)-x=45

      /25     /25

4x-3-(x/25)=1.8

(99x/25)-3=1.8

            +3+3

99x/25=4.8

     *25 *25

99x=120

/99   /99

x=1.2121212121212....

Answer:

2nd choice

Step-by-step explanation:

Answer:

\( y - 8 = -7(x - 6) \) or \( y - 1 = -7(x - 7) \)

Step-by-step explanation:

The point-slope form equation is \( y - b = m(x - a) \), where,

(a, b) = a point on the line.

\( m = slope = \frac{y_2 - y_1}{x_2 - x_1} \)

Given the two points, (6, 8) and (7, 1), find the slope of the line:

\( m = \frac{1 - 8}{7 - 6} \)

\( m = \frac{-7}{1} \)

\( m = -7 \)

There are two possible point-slope equation we can come up with using each points on the line given.

Using the point (6, 8) and m = -7,

Substitute m = -7, a = 6, and b = 8 into \( y - b = m(x - a) \)

\( y - 8 = -7(x - 6) \)

Using the point (7, 1) and m = -7,

Substitute m = -7, a = 7, and b = 1 into \( y - b = m(x - a) \)

\( y - 1 = -7(x - 7) \)

The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Answer:

The image is (-16,-14)

Step-by-step explanation:

Given

Represent the point with A

\(A = (-8,-7)\)

\(Scale\ factor = 2\)

Required

Determine the image (A')

The image is calculated as:

\(A' = A * Scale\ factor\)

\(A' = (-8,-7) * 2\)

So, we have:

\(A' = (-8* 2,-7* 2)\)

\(A' = (-16,-14)\)

Hence, the image is (-16,-14)

The calculated measure of m∠PNM is 87 degrees

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

The circle

Where, we have

PM = 360 - 64 - 122

Evaluate

PM = 174

Next, we have

m∠PNM = 1/2 * 174

So, we have

m∠PNM = 87

Hence, the measure of m∠PNM is 87 degrees

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Answer:

In a 30°-60°-90° right triangle, the length of the longer leg is √3 times the length of the shorter leg.

A = (1/2)Pa

= (1/2)(2)(8/√3)(6)(8)

= (384√3)/3 = 128√3 = 221.7 units^2

Answer:

Step-by-step explanation:

JOB A: 40*15=600 PER WEEK

600*4=2400 PER MONTH

JOB B; 1375*2=2750 PER MONTH

JOB A PAYS MORE 2750-2400=350.00

WITH 350.00 DOLLARS