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.

Drag a value or phrase into each box to correctly complete the statements

The area of the figure composed of two rectangles is 99 mi²

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

For the first rectangle:

Area = 11 mile * 5 mile = 55 mi²

For the second rectangle:

Area = 11 mile * 4 mile = 44 mi²

The area of figure = 55 mi² + 44 mi² = 99 mi²

The area of the figure is 99 mi²

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Answer:

150

Step-by-step explanation:

divide the percentage by 100 to make it decimal form,
75/100= .75

The multiple .75 by the total amount to find the 75%,

200 x .75 = 150

Which means 75% of 200 is 150

1. The force they must apply is 2256.3 N

2. The amount of work done = 3835.71 J

3. The work done using the ramp = 4500 J

4.  The efficiency of the ramp = 85.24%

5. When the people use inclined ramp, they don't have worry about the gravitational force that is acting on the piano. The trade off with with less force, the ramp is able to cover more distance.

1. To find force applied, used the formula; F = mg

230 x 9.8N

=2256.3N

2. To find the amount of work done, we use the formula;

W = Fd

2256.3 x 1.7 m

= 3835.71J

3. o calculate the work done using the ramp, you use the same formula you used in step 2

300N x 15m

= 4500J

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The difference in the length of dogs jump is 24 inches.

Given that, Mackenzie's dog can jump [tex]2\frac{1}{2}[/tex] =5/2 feet off the ground. Jordyn's dog can jump 1/2 foot off the ground.

We know that, 1 feet = 12 inches

Here, 5/2 feet = 5/2 ×12

= 30 inches

1/2 foot = 1/2 ×12

= 6 inches

Now, difference = 30-6 = 24 inches

Therefore, the difference in the length of dogs jump is 24 inches.

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Answer:

Second number line

Step-by-step explanation:

(h-3)^2 <= 25

h^2 - 6h + 9 <= 25

h^2 - 6h - 16 <= 0

(h-8)(h+2) <=0

Using the graph of (x-8)(x+2),

-2 <= h <= 8

Hence, the answer is the second one (as it has shaded circles)

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The solution of equation is (2, 3).

We have,

x= 3y -7.........(1)

y= x + 1.........(2)

Solving equation (1) and (2) we get

y = 3y - 7 + 1

y - 3y = -7 + 1

-2y = -6

y = -6/(-2)

y = 3

and, x = 3(3) - 7

x = 9 - 7

x = 2

Thus, the solution of equation is (2, 3).

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Answer: D 36л

Step-by-step explanation:

s = θr

where r is the radius of the circle.  given that the arc length is 6, and the central angle is π/3 radians r:

6 = (π/3)r

r = 6/(π/3) = 18/π

the circumference of the circle is given by:

C = 2πr

Substituting r = 18/π, we get:C = 2π(18/π) = 36

Answer:

Step-by-step explanation:

1 -E (102/234) *100 =43.6%

2- F

3-C

4-A

The image is attached of the graph of the inequality y < 4x - 5.

What is the inequality equation?

An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

To graph the inequality y < 4x - 5 using the slope-intercept form, follow these steps:

Rewrite the inequality in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.

y = 4x - 5

Plot the y-intercept on the y-axis.

The y-intercept is -5, so plot the point (0, -5).

Use the slope to find a second point on the line.

The slope is 4, so start at the y-intercept and move up 4 units and to the right 1 unit to find the point (1, -1).

Draw a dashed line through the two points.

Since the inequality is y < 4x - 5, use a dashed line to indicate that the line itself is not part of the solution.

Shade the region that satisfies the inequality.

To do this, pick a test point that is not on the line and plug its coordinates into the inequality. If the inequality is true for that point, shade the region that contains the test point. If the inequality is false for that point, shade the region that does not contain the test point.

Let's use the test point (0, 0). Plug its coordinates into the inequality to get:

0 < 4(0) - 5

This simplifies to 5 < 0, which is false. Therefore, we need to shade the region that does not contain the test point.

Since the inequality is y < 4x - 5, we need to shade the region below the dashed line.

Label the shaded region with the inequality symbol.

The inequality is y < 4x - 5, so label the shaded region below the dashed line with the symbol "<".

hence, The image is attached of the graph of the inequality y < 4x - 5.

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Based on the above, about  174 people out of the sample of 600 people indicated Bluetooth capability.

To know the number of individuals who shown Bluetooth capability, we have to to begin with calculate the division of individuals who chose this choice from the circle chart.

Note that:

People who Bluetooth capability =29%

Number of people = Percentage × Total sample size

= 0.29 × 600

= 174

So,  174 individuals shows that the Bluetooth capability is their favored option for the family trip.

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Answer: ∠BDA

Step-by-step explanation:

Complementary: Either of two angles whose sum is 90°.

Starting Angle: ∠BDC

Possible Complement: ∠BDA

Answer: ∠ACD

Step-by-step explanation:

Complementary angles are angles which have a sum of 90 degrees when added together.

Angle ∠ADB is 90°

So ∠BDC and another angle should give you ∠ADB

The angle that when added to ∠BDC give you ∠ADB is ∠ACD

Answer:  x = 6 and y = -5.

Step-by-step explanation: Multiply the second equation by -2 to eliminate the y term:

-2(x + y) = -2(1) -> -2x - 2y = -2

Add the resulting equation to the first equation to eliminate the y term:

2x + y = 7

-2x - 2y = -2

0x - y = 5

Solve for y:

-y = 5

y = -5

Substitute y = -5 into either of the original equations and solve for x:

x + y = 1

x + (-5) = 1

x = 6

Therefore, the solution to the system of equations is x = 6 and y = -5.

Answer:

After half hour=30 min you have 2×2500=5000 bacteria so you can use this into your equation to write:

and:

Apply the natural logarithm ln to both sides and get:

so  in units of

so your equation is now:

1] it t= 50 min substituting you get:

bacteria

2] if t= 8 h = 480 min you get:

bacteria

Step-by-step explanation:

We can begin by focusing on c on one side of the equation to help us solve it. Craig's height is 44 as a result.

A mathematical equation is a claim that two expressions are equivalent. It is divided into two sections, the left and the right, by the equal sign (=). Equation's left and right sides each have the potential to include variables, constants, and operators.

Finding the value(s) of the variable(s) necessary to make an equation true is the aim of equation solving. Algebraic techniques like simplification, substitution, and elimination can be used to solve equations.

An equation can be used to represent the following sentence:

c + 24 = 68

Craig's height is represented by c in this equation. The equal sign (=) is used to symbolise the phrase "is 68," while the phrase "is 24 more than Craig's height" is symbolised by c + 24. The formula for the problem can be solved to find the value of c, which corresponds to Craig's height.

We can begin by concentrating c on just one side of the equation in order to solve it:

c + 24 - 24 = 68 - 24

c = 44

Therefore, Craig's height is 44.

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question 9.

Based on a cubic modeling equation, the  prediction about this data that is  most reliable is a $70k house would have 1,354 square ft.

Option A is correct.

Question 10.

The second coordinate in a scatterplot of the linearized data and  rounding the answer to the tenth place is 0.8

Option A is correct.

Question 11.

The approximate value when x=4 and rounding the answer to the nearest whole number is 1,168

Option C is correct.

The equation is given as

Log y= 0.75821x+0.03442

We substitute x = 4 into the given equation and solve for y:

log y = 0.75821(4) + 0.03442

log y = 3.07286 + 0.03442

log y = 3.10728

We take the antilogarithm of both sides,

y = 10^(3.10728)

y = 1,168.66

Rounding off, the closest answer is option  (c) 1,168.

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Answer:

the answer is none of the answer choices

Answer:

the answer is none of the answer choices

The residual plot shows that the regression equation is a good model of the data because it shows a random scatter of points around a horizontal line at zero, with no pattern or trend

A residual plot is a scatter plot of the residuals against the predictor variable(s) or the fitted values. It is used to verify whether the regression equation fits the data well.

In the event that the residual plot shows a random scatter of points around a horizontal line at zero, with no pattern or trend, it shows that the regression equation is a good model of the data.

On the other hand, supposing the residual plot shows a pattern or trend, such as a curve, a U-shape, or a funnel shape, it shows that the regression equation is a bad model of the data.

Therefore, from the graph given, the residual plot shows that the regression equation is a good model of the data.

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Answer:

According to the model. the weight of the candle after S hours of burning would be about 15.05 ounces

Step-by-step explanation:

If the burn rate is believed to be constant, determine the average burn rate for the eight candles as the ratio of weight loss per hour.

ounces lost over three hours

0.5+0.6+0.5÷0.7÷0.7÷0.5÷0.5÷0.6

8

* 0.575

0.575

ounces lost per hour on average

= 0.19

For 0 hours, the weight of each candle is 16 ounces. Therefore, w 16 - 0.19h.

This model can be used to predict the weight of the candle when h, the number of hours of burning, is 5.

W * 16 - 0.19(5)

W = 16 - 0.95

W = 15.05

According to the model. the weight of the candle after S hours of burning would be about 15.05 ounces.

Answer: n^6-25

Step-by-step explanation:

Use the distributive property to obtain: n^6-5n^3+5n^3-25

Simplify: n^6-25

Answer: n^6-25

The product of the given expression [tex](n^{3} + 5) (n^{3} - 5)[/tex] will be the second option  [tex]n^{6} - 25[/tex].

This is a simple math problem that can be solved using algebraic identities. Algebraic identities are mathematical formulas that hold true regardless of the value assigned to each of the variables. They can be used to resolve equations and simplify expressions.

In the above question, we have used the following identity:

[tex](a^{2} - b^{2} ) = (a + b) (a - b)[/tex]

In the given question, a = [tex]n^{3}[/tex] and b = 5

So putting values in the identity, we get

[tex][(n^{3})^{2} - 5^{2}] = (n^{3} + 5) (n^{3} - 5)[/tex]

On solving the left side of the equation, we get

[tex]n^{6} - 25[/tex] which is our answer to the given question.

Note: [tex](n^3)^2 = n^6[/tex] because the powers get multiplied.

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c) Population [tex]\sigma = 48[/tex]

Z = [tex]\frac{68-60 }{\frac{48 }{\sqrt{64}}}[/tex]

Z-score= 1.3333

According to the question , sample size n=64 , mean M = 68 , population mean [tex]\mu= 60[/tex]

Z = [tex]\frac{M-\mu }{\frac{\sigma }{\sqrt{n}}}[/tex]

where M = Sample Mean

[tex]\mu[/tex] = Population Mean

[tex]\sigma[/tex] = Population Standard Deviation

n = Sample Size

a) Population [tex]\sigma[/tex] = 16

Z = [tex]\frac{68-60 }{\frac{16 }{\sqrt{64}}}[/tex]

Z-score = 4

b) Population [tex]\sigma[/tex] = 32

Z = [tex]\frac{68-60 }{\frac{32 }{\sqrt{64}}}[/tex]

Z-score = 2

c) Population [tex]\sigma[/tex]= 48

Z = [tex]\frac{68-60 }{\frac{48 }{\sqrt{64}}}[/tex]

Z-score= 1.3333

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The monthly payments will thus be $1,612.81.

The annual effective rate on this loan is 5.78%.

We can use the following loan payment formula to determine the loan payment:

Loan Payment  = [tex]\\\frac{p * \frac{r}{n} }{1 - (1 + \frac{r}{n} )^{-n *t} }[/tex]

where P = borrowed amount = $69,300

r = yearly interest rate (decimal) = 0.056

n = number of times compounded per year = 12

t = number of years = 4

When we plug in the values, we get:

Loan Payment = [69300 x (0.056/12)] / [1 - (1 + 0.056/12)^(-12*4)]

= $1,612.81 (to the nearest cent)

The monthly payments will thus be $1,612.81.

We can use the following calculation to obtain the effective annual rate:

Annual Effective Rate =[tex](1 + r/n)^{n-1}[/tex]

When we plug in the values, we get:

Annual Effective Rate =[tex](1 + 0.056/12)^{12 - 1}[/tex]= 0.0578 or 5.78%

As a result, the annual effective rate on this loan is 5.78%.

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The value of k include the following: B. k is equal to one third.

In Mathematics, the vertex form of a quadratic function can be modeled by this formula:

y = a(x - h)² + k

Where:

Based on the information provided about the quadratic function f(x), we can logically deduce that its vertex is at (0, 0);

f(x) = a(x - h)² + k

2 = a(1 - 0)² + 0

2 = a

f(x) = 2(x - 0)² + 0

f(x) = 2x²

For the quadratic function g(x), we have;

g(x) = f(kx)

g(x) = 2(kx)²

g(x) = 2k²x²

By using the point (3, 2) from the table, we have:

2 = 2k²3²

1 = k²9

k² = 1/9

k = √(1/9)

k = 1/3 i.e one third.

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Answer:

incomplete question bru

Answer:

The given expression is a polynomial:

f(x) = x^2 + 7x - 9 + 2x - 1

Combining like terms, we get:

f(x) = x^2 + 9x - 10

The degree of the polynomial is 2, since the highest power of x is 2.

10x² + 13x + 11 is the sum of linear equation .

What is a linear equation in mathematics?

The algebraic equation y=mx+b is known as a linear equation. All of its terms are constant, first-order linear ones. where m denotes the slope and b the y-intercept.

                             The aforementioned is occasionally referred to as a "linear equation in two variables" where y and x are variables. One or more variables may be present in a linear equation. The term "bivariate linear equation" refers to a linear equation with two variables.

two equations are  10x² + 7x + 6 and 6x + 5.

now add both equations

= (10x² + 7x + 6 )+ (6x + 5)

=  10x² + 7x + 6 + 6x + 5

= 10x² + 13x + 11

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Answer:

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

(7+2x)(9+2x)= 143 (area= length x width)

63+14x+18x+4x^2=143

4x^2+32x−80=0

x^2+8x−20=0

(x−2)(x+10)=0

x = 2 or -10

Since the length of the walkway can't be negative, the answer is 2.