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Simplification of the given expression to single complex number are as follow :

1. 3i

2. 4i

3. 24

4. 15

5. 1 + √3 i

6.  2 + [tex]\sqrt{5}i[/tex]

As given,

Simplify the following expression to a single complex number,

1) [tex]\sqrt{-9}[/tex] = [tex]\sqrt{9}\sqrt{-1}[/tex] = 3i

where i is the complex number representing [tex]\sqrt{-1}[/tex]

2) √-16 = 4i

3) √-6 √-24

= √6 ×6 ×4

= 6 ×4

= 24

4) √-3 √-75

=√ 3×75

= √3 × 3 ×25

= 3 ×5

=15

5) [tex]\frac{2 +\sqrt{-12} }{2}[/tex]

= (2 + 2√-3) /2

= 1 + √3 i

6) [tex]\frac{4+\sqrt{-20}}{2}[/tex] = [tex]\frac{4+\sqrt{20}\sqrt{-1}}{2}[/tex] = [tex]\frac{4+(2\sqrt{5}\sqrt{-1})}{2}[/tex] = [tex]\frac{4+(2\sqrt{5}i)}{2}[/tex] = [tex]\frac{2(2+\sqrt{5}i)}{2}[/tex] = 2 + [tex]\sqrt{5}i[/tex]

where i is the complex number representing [tex]\sqrt{-1}[/tex]

Therefore, simplification of  the given expression to single complex number are as follow :

1. 3i

2. 4i

3. 24

4. 15

5. 1 + √3 i

6.  2 + [tex]\sqrt{5}i[/tex]

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Han is therefore mistaken in what he claims. The area is 8640 [tex]feet^{2}[/tex]

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given Data

Let "x" represent the restaurant's actual space.

You are aware that the map's scale is 1 inch to 12 feet. As a fraction, this is written as follows:

[tex]\frac{1inch}{12feet}[/tex]

Calculate the restaurant's scale drawing area. Such is:

([tex]\frac{1inch}{12feet}[/tex]) ² = [tex]\frac{1inch^{2} }{144feet^{2} } }[/tex]

We can set up this percentage and then solve for "x" to determine the precise location of the restaurant because the restaurant's location is indicated on the map.

Such is:

[tex]\frac{144}{1}[/tex] = [tex]\frac{x}{60}[/tex]

60 (144) = x

x = 8640 [tex]feet^{2}[/tex]

Han is therefore mistaken in what he claims.

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Answer: the andwer to that is C

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

If the slope is undefined, it is a vertical line. Since the slope-intercept equation is y=mx+b, but the slope is undefined, the equation would have to be the x coordinate, because that is the unchanging variable in a vertical line. So, the answer is x=5.

Answer:

3/16

We assume that the marbles are drawn without replacement.

P(blue and yellow)

= P(b1 and y2) + P(y1 and b2)

= P(b1) P(y2) + P(y1) P(b2)

= (1/4)(1/2) + (1/4)(1/4)

= 1/8 + 1/16 = 2/16 + 1/16 = 3/16

The absolute value function as piecewise function of y = -3(x + 24)/4 and y = 3(x - 38)/4

The absolute value function is commonly understood as a function providing the distance the number is from zero on a number line.

y = 3/4|x-6|-8

y = 3/4(-(x-6))-8

y= 3/4( -x + 6) -8

y = 3(-x + 6 - 32)/4

4y = -3x - 24

y = -3(x + 24)/4

For another function of y

y = 3/4|x-6|-8

y= 3/4( x - 6) -8

y = 3(x - 6 - 32)/4

4y = 3(x - 38)

y = 3(x - 38)/4

The absolute value function as piecewise function of y = -3(x + 24)/4 and y = 3(x - 38)/4

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For the given function f(x) = 7 , the value of x is 5.

We have a linear function in the figure, and linear functions have the same slope for all values of. We can determine the value of f using the secant line equation:

(yB -yA) / (xB - xA) = (yC - yA) / (xC - xA)

Where:

(xA , yA) , (xB , yB)  given

to find ,  (xC , yC)

(xA , yA) = (2,0) , (xB , yB) = (5,7)  and yC = 7

to find xC ,

xC - xA = (yC - yA) / (yB - yA) . (xB - xA)

xC =  xA + (yC - yA) / (yB - yA) . (xB - xA)

xC = 2 + (7-0)/(7-0) x (5 - 2)

xC = 2 + (5 - 2)

xC = 2 + 3

xC = 5

so the value of x in given function f(x) = 7 is 5.

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Answer:

an = -4n +12

Step-by-step explanation:

the nth term in this arithmetic sequence is : an = a1 + (n -1 )d

a1 = 8 d = a2-a1 = 4-8 = -4 ( common difrence)

an = 8 + (n -1 )(-4) = 8 - 4n +4

an = -4n +12

Answer: (-9/2,-53/4)

Step-by-step explanation:

Answer:

[tex]y=\left(x+\dfrac{9}{2}\right)^2-\dfrac{53}{4}[/tex]

Step-by-step explanation:

Vertex form of a quadratic equation:  

[tex]\boxed{y=a(x-h)^2+k}[/tex]

where:

To find the vertex form of a quadratic equation, complete the square.

Given quadratic equation:

[tex]y=x^2+9x+7[/tex]

Add and subtract the square of half the coefficient of the term in x to the right side of the equation:

[tex]\implies y=x^2+9x+\left(\dfrac{9}{2}\right)^2+7-\left(\dfrac{9}{2}\right)^2[/tex]

[tex]\implies y=x^2+9x+\dfrac{81}{4}+7-\dfrac{81}{4}[/tex]

[tex]\implies y=x^2+9x+\dfrac{81}{4}-\dfrac{53}{4}[/tex]

Factor the perfect square trinomial formed by the first 3 terms:

[tex]\implies y=\left(x+\dfrac{9}{2}\right)^2-\dfrac{53}{4}[/tex]

Answer:

Equation of the parabola:

The height of the arch 18 meters from the center is 6.75m

Explanation:

The arch feet are 72m apart and the origin half way between them. This means that the axis of symmetry (or the x.coordinate of the vertex) is x = 0

Since it's an arch, the parabola is concave down, with it's maximum at the vertex, y = 9. This means that the vertex is at (0, 9). Also, we can see that the y-intercept is y = 9

Finally, we know the two roots of the parabola: x = -36 and x = 36. This is because the points x = -36 and x = 36 are 72m apart, with the center at the original, as the problem says. SInce x = 36 is a root, this means that at that point the y value is 0.

With all this, we can try to find the general form of a parabola. The general form is:

c is the y-intercept. We know that c = 9

We can find the value of b, because we know the coordinates of the vertex. The x-coordinate of the vertex is:

SInce the x-coordinate of the vertex is x = 0

If we solve:

So far we have:

Finally, to find a, we can use the point (36, 0) (one of the roots)

And solve:

Thus, the equation of the arch is:

Evaluating this equation for x = 18, we can find the height of the arch:

Answer:Explanation:

The average rate of change = 3

The average rate of change for a function f(x) is an intervale a < x < b can be calculated using the following equation:

Therefore, the average rate of change of the function h(x) = x^2 – 7x + 6 in the interval 3 < x < 7 is:

Where h(7) and h(3) are equal to:

So, the average rate of change is:

Therefore, the answer is 3.

-3/2 (option A)

The line of green and red are perpendicular.

For two lines to be perpendicular, the slope of one line will be the negative reciprocal of the second line.

slope of one line (green) = 2/3

slope of red line = negative reciprocal of green line

slope = 2/3

reciprocal of line = 3/2

negative reciprocal of the line = -3/2

The slope of the red line = -3/2 (option A)

The difference of the values is -12.9 while the product of the expression is 45.9

We have to solve for

2.4 x 10/8

= 2.4 x 1.25

= 3

(9.2 x 10/6)

= 9.2 x 1.667

= 15.3

The difference between the values wpuld be

3 - 15.3

= -12.3

The product of the expressions would be solved by

3 x 15.3

= 45.9

Hence we would say that the difference that is in the values that we have here is -12.9 while the product of these values is given as 45.9

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The result of the indicated operations are:

(a) -4.324.

(b)  4.324.

(c) 0.9

(a) -1.424-2.9

Calculate the sum of the decimals,

The result is -4.324.

(b) 1.424-(-2.9)

Remove the bracket and change the sign in the middle and add the decimals to get the sum,

1.424 + 2.9 = 4.324.

(c) -1.424-(-2.9) -0.576

Remove the parentheses and change the sign,

-1.424 + 2.9 - 0.576

Add the negative decimal numbers and subtract them from the positive decimal number.

-2 + 2.9 = 0.9

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Answer:

There were 24 cookies in the jar at the beginning.

Step-by-step explanation:

There is 1 cookie left add the one susan took that is two. Two is 1/4 of 8. Eight is 2/3 of 12. Twelve is 1/2 of 24. 24 is the answer. You can also check it by going back.

SOLUTION:

Step 1:

In this question, we are given the following:

Can you give me two examples of an absolute value parent function?

Step 2:

What is the parent function for absolute value?

An absolute value function is a function that contains an algebraic expression within absolute value symbols. Recall that the absolute value of a number is its distance from 0 on the number line.

Examples include:

1. The absolute value parent function, written as: f(x)=| x |, is defined as:f(x)={x if x>00 if x=0−x if x<0.

, is defined as:

2. The second example of absolute value function is:

Answer:

13 correct me if i am wrong

Step-by-step explanation:

The two pairs of conjugates are ([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]).

In mathematics, a pair of binomials with identical phrases that part opposite arithmetic operators in the midst of these similar terms are referred to as conjugates. Below are a few more instances of conjugate pairs: p + q, p - q. 3 + 1, 3 - 1. 4 - 3i, 4 + 3i.

Let the two pair of conjugates is

([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex])

Use the formula,

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

Then,

([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]) = [tex]\sqrt{2} ^{2}-i^{2}[/tex]

We know that,

[tex]i^{2}=-1[/tex]

([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]) = 2-(-1)

 ([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]) =  3

Hence, The two pairs of conjugates are ([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]) with a product 3 .

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According to the solving the  two pairs of conjugates with a product of 3:

(√2 - i ) & (√2 + i ).

When two binomials are identical except for the signs separating the terms, they are said to be conjugates. You only need to rephrase a binomial and alter the sign of the second term to create its conjugate.

given number = 3.

lets the two pair of conjugates is:

(√2 - i ) & (√2 + i )

Use the formula:

a² - b² = (a + b) and  (a - b)

So,

(√2 - i ) & (√2 + i ) = (√2)² -( i )²

We know that,

i² = -1

So,

(√2 - i ) & (√2 + i ) = 2 - (-1)

(√2 - i ) & (√2 + i ) = 3

According to the solving the  two pairs of conjugates with a product of 3:

(√2 - i ) & (√2 + i ).

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Given:

Required:

Find (fg)(4)

Explanation:

Given functions are

Final answer:

The value of (fg)(4) = 4

The other endpoint of the segment is (7, 14)

From the question, we have:

On the segment, we have the following endpoints

Endpoint 1, A = (-3,-2)

Midpoint, M = (2,6)

The midpoint of the segment is calculated using

Midpoint (x, y) = 1/2 * (x1 + x2, y1 + y2)

Where

(x1, y1) = (-3,-2)

(x, y) = (2,6)

Substitute the known values in the above equation

So, we have

(2, 6) = 1/2 * (-3 + x, -2 + y)

Multiply both sides of the equation by 2

So, we have

(4, 12) = (-3 + x, -2 + y)

By comparison, we have

-3 + x = 4

-2 + y = 12

Evaluate the like terms in the above equation

So, we have

x = 7

y = 14

When the above solution is represented as a coordinate, we have the following

(x, y) = (7, 14)

Hence, the other endpoint of the segment where the segment has the endpoint (-3,-2) and midpoint (2,6) is (7, 14)

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The value of x comes to 78.808 after solving the given expression 1.25x + 1.49 = 100.

So, 1.25x + 1.49 = 100:

Now, solve as follows:

Therefore, the value of x comes to 78.808 after solving the given expression.

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1) If  A = {U, S, T, A, C}, then the Subsets of  {U, S, T, A, C} are;

as detailed below

2) If B = {red, blue, yellow}. then the Subsets of {red, blue, yellow} are;

as detailed below

Subsets are a part of one of the mathematical concepts called Sets. For example If a set A is a collection of odd numbers and set B consists of {1,3,5}, then B is said to be a subset of A.

Thus;

1) Subsets of  {U, S, T, A, C} are;

{U}, {S}, {T}, {A}, {C},

{U, S}, {U, T}, {S, T}, {U, A}, {S, A}, {T, A}, {U, C}, {S, C}, {T, C}, {A, C},

{U, S, T}, {U, S, A}, {U, T, A}, {S, T, A}, {U, S, C}, {U, T, C}, {S, T, C}, {U, A, C}, {S, A, C}, {T, A, C},

{U, S, T, A}, {U, S, T, C}, {U, S, A, C}, {U, T, A, C}, {S, T, A, C},

{U, S, T, A, C}

2) Subsets of {red, blue, yellow} are;

{Red}, {Yellow}, {Blue},

{Red, Yellow}, {Red, Blue}, {Yellow, Blue},

{Red, Yellow, Blue}

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The probability that the average person has a time faster than Usain Bolt’s record of 9.58 seconds

P(x>9.58)=1

This is further explained below.

Mean[tex](\mu)[/tex]=14 seconds

Standard deviation[tex](\sigma)[/tex]=0.8 seconds

To determine the likelihood that the average individual will beat Usain Bolt's record of 9.58

To express the statement "the probability that the average person has a time faster than Usain Bolt’s record of 9.58 seconds" in a mathematical equation we have:

[tex]&P(x > 9.58)=P\left(\frac{x-\mu}{\sigma} > \frac{9.58-14}{0.8}\right) \\\\&P(x > 9.58)=P\left(z > -\frac{4.42}{0.8}\right) \\\\ &P(x > 9.58)=P(z > -5.525)[/tex]

P(x>9.58)=1

Note: we would make use of the normal table in reading z>-5.525

In conclusion, By using standard normal distribution we get

P(x>9.58)=1

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Answer:

17

Step-by-step explanation:

To find k, we use

∫∞−∞∫∞−∞fXY(x,y)dxdy=1.

Thus, we have

1=∫∞−∞∫∞−∞fXY(x,y)dxdy=∫10∫10x+cy2dxdy=∫10[12x2+cy2x]x=1x=0dy=∫1012+cy2dy=[12y+13cy3]y=1y=0=12+13c.

Therefore, we obtain c=32.

To find P(0≤X≤12,0≤Y≤12), we can write

P((X,Y)∈A)=∬AfXY(x,y)dxdy,for A={(x,y)|0≤x,y≤1}.

Thus,

P(0≤X≤12,0≤Y≤12)=∫120∫120(x+32y2)dxdy=∫120[12x2+32y2x]120dy=∫120(18+34y2)dy=332.

We can find marginal PDFs of X and Y from their joint PDF. This is exactly analogous to what we saw in the discrete case. In particular, by integrating over all y's, we obtain fX(x). We have

Marginal PDFs

fX(x)=∫∞−∞fXY(x,y)dy, for all x,fY(y)=∫∞−∞fXY(x,y)dx, for all y.

Example

In Example 5.15 find the marginal PDFs fX(x) and fY(y).

Answer:

17

Step-by-step explanation:

okokokomokokokokokoko

60 and 274.

Step-by-step explanation:

1. The simple interest rate is 80%

2. The interest earned on the account after 10 years is $75

Simple interest can be defined as a mathematical or arithmetic method of calculating the charge of interest on a given loan.

The formula for simple interest is expressed as;

I = PRT/100

Where;

From the information given, we are to determine the interest rate, R

Substitute the values into the formula, we have;

320 = 200 × R × 2/100

Now, cross multiply, we have;

320(100) = 400R

Find the product of the values

400R = 32000

Divide both sides by the coefficient of the interest rate, we get

R = 32000/400

Find the quotient

R = 80%

If the interest for 2 years is $15

Then in 10 years = $x

cross multiply

x = 150/2

Find the quotient

x = $75

Hence, the rate is 80%

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The value of the average price per square foot in 2002 is  $101. 5

A function can simply be defined as a rule, a law, an equation or an expression that is made up of two variables and shows or explains the relationship between them.

The variables are;

Given the function;

P(t) = 0. 018t³ - 0. 294t² + 3. 065t + 55. 190

Where;

For the year 2002 , the value of t would be 10

Substitute the value into the formula

P(10) = 0. 018(10)³ - 0. 0294(10)² + 3. 05(10) + 55. 190

expand the bracket, we have

P(10) = 0. 018(1000) - 0. 0294(100) + 30. 5 + 55. 90

multiply through

P(10) = 18 - 2.  + 30. 5 + 55. 90

Add the values

P(10) = $101. 5

Hence, the value is  $101. 5

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To determine which is the best buy, we need to first find the unit price of each

8 oz $2.40

Unit price

$2.40/8 = $0.3

1 oz = $0.3

24 oz $6.48

Unit price

$6.48/24 =$0.27

1 oz = $0.27

64 oz $14.08

Unit price

$14.08/64 =$0.22

From the above the best best buy is the one with the lowest price which is $0.22

The best buy is;

64 oz $14.08

and the unit rate is $0.22 per oz

Answer:

x = 0

Step-by-step explanation:

A line that has undefined slope is a vertical line. A vertical line has an equation in the form "x = anumber"

In the given information, (0,5), x is 0 and y is 5. What we need is the information on x.

x is 0.

x = 0 is the equation of the line.

Answer:

x=0.

Step-by-step explanation:

undefined slope is a vertical line. if it passes through (0,5) it means its on the y line