solve the equation: z^ +4z+20+iz(a+1)=0 Where A is constant, has complex conjuget root. if one of roots this quadratic is z=B+2i?​

The simplified expression for the area of the rectangular table is Three-halves x squared, 3x²/2

Since the carpenter built a square table with side length x.  Next, he will build a rectangular table by tripling one side and halving the other.

To find the area of the rectangular table, we know that Area, A = LW where

Now, since the length of the square is x, and the rectangular table has one side of the square tripled and halving the other side .

So,

let

So, the area of the rectangular table A = LW

= x/2 × 3x

= 3x²/2

So, the simplified expression for the area of the rectangular table is Three-halves x squared, 3x²/2

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The value of the expression is 972

The expression is given as:

27(36)

Express 36 as 18 + 18

27(18+ 18)

Expand

486+ 486

Evaluate the sum

972

Hence, the value of the expression is 972

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Answer: (1,3)

Step-by-step explanation:

Let's solve this system of equations by elimination. We will multiply one or both equations such that when we combine the equations, one of the variables will completely cancel out.

Let's multiply the whole first equation by -2 to achieve this:

[tex]-2(x+2y=7)[/tex] now becomes [tex]-2x-4y=-14[/tex]

Now let's add both equations

[tex]-2x-4y=-14[/tex]

[tex]2x-y=-1[/tex]

[tex]-5y= -15[/tex]

Since we got y into a form we can solve it for, lets divide both sides by -5 to isolate it.

[tex]\frac{-5y}{-5} = \frac{-15}{-5}[/tex]

[tex]y=3[/tex]

Now that we have the value of y, we can substitute it into any equation to solve for x. Only if we have both x and y can we make an ordered pair. Let's use the second equation and substitute 3 for y.

[tex]2x-3=-1[/tex]

We can now solve for x.

[tex]2x=2[/tex] [Adding 3 to both sides]

[tex]x=1[/tex] [Dividing by 2 on both sides]

We now have both x and y, so we can put it in an ordered pair to answer the question.

[tex](1,3)[/tex]

Based on the information given about the equation, y will be 0.5x + 2.

From the information given, it should be noted that the equation of the line it represents was given and the y intercept is = (0, 2).

The function to represent y will be:

y = mx + b

y = (1/2)x + 2

y = 0.5x + 2

In conclusion, y = 0.5x + 2.

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Answer:

The function has 4 roots.

Step-by-step explanation:

Since the degree of the polynomial has is 4, there are a total of 4 roots (both real and complex).

Answer:

4 roots, two real and two complex.

Step-by-step explanation:

The degree of the polynomial indicates the number of solutions

Hope this helps

The height of the cylinder is 3.82 m

2. The surface area is 316.5 ft²

The volume is 406.5 ft³

The volume of a cylinder is given by the formula,

V = πr²h

Where V is the volume

r is the radius

and h is the height

From the given information,

V = 300 m³

r = 5 m

h = ?

Putting the parameters into the formula, we get

300 = π × 5² × h

300 = π × 25× h

∴ h = 300/25π

h = 3.82 m

Hence, the height of the cylinder is 3.82 m

2.

Diameter = 6 feet 6 inches = 6.5 feet

∴ Radius = 3.25 feet

Height = 12 feet 3 inches = 12.25 feet

Surface area of a cylinder is given by

Surface area = 2πr(r + h)

Where r is the radius

and h is the height

Surface area = 2π×3.25(3.25 + 12.25)

Surface area = 316.5 ft²

For the volume

V = πr²h

V = π × 3.25² × 12.25

V = 406.5 ft³

Hence, the volume is 406.5 ft³

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If no less than 100000 packets must be packed each week, the minimum number of packets needed to be packed each day for the remaining days is 21250.

An equation is an expression that shows the relationship between two or more variables and numbers.

There are 6 days from Monday to Saturday. The factory is closed on Tuesday and 15000 packets were packed on Monday. If no less than 100000 packet must be packed, hence:

4x + 15000 ≥ 100000

x ≥ 21250

If no less than 100000 packets must be packed each week, the minimum number of packets needed to be packed each day for the remaining days is 21250.

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Answer:

1777777777888876332222233

Answer: Option C   [tex]\boldsymbol{7^6}[/tex]

Work Shown:

[tex]\frac{7^{13}}{7^{7}}\\\\\\7^{13-7}\\\\\\\boldsymbol{7^6}[/tex]

Subtract the exponents to get the answer. The rule is [tex]\frac{a^{b}}{a^{c}} = a^{b-c}[/tex]. This rule only works when the bases are the same.

The probability that a student attended the game, given that the student is from North Beach is 0.65.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that a student attended the game, given that the student is from North Beach = number of North beach students that attended the game / total number of students who attended the game

110 / 170 = 0.65

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The coefficients in the expression are -1 and 9

The expression is given as:

-x^2 + 9x

In an expression ax, the coefficient is a.

Using the above as a guide, we have:

-x^2 + 9x

The coefficients in the above expression are -1 and 9

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The monthly payments for each add-on interest loan is computed to be $29.71.

Given Information and Formula Used

Principal Amount of the loan, P = $1150

Rate of Interest of the loan, R = 6%

Term of loan in years, T = 4

The formula for simple interest is given as follows,

I = (P × R × T)/100

The formula for amount of add-on interest loan is given by, A = P + I

Calculating the Interest of the Loan

Interest of the loan, I = (P × R × T)/100

Now, substituting the given values of P, R, and T in the above formula, we get,

I = $ (1150 × 6 × 4)/100

I = $ 27600/100

I = $276

Calculating the Total Monthly Payment for the Loan

Amount of loan, A = P+I

A = $1150 + $276

A = $1426

Monthly payment of the loan with interest = A/(4×12)

= $ 1426/48

= $29.71

Thus, the monthly payments for each add-on interest loan comes out to be $29.71.

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The attached line is a parallel line that goes through C and parallel to AB

Parallel lines are lines on the same plane that have the same slope, they do not intersect even when they are extended indefinitely

From the question, we have the following points and line:

The following steps would create the parallel line that goes through C and parallel to AB

See attachment for the parallel line that goes through C and parallel to AB

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Answer:

x is equal to 5

Step-by-step explanation:

Based on the dataset given, the first quartile is 38.75, and the third quartile is 45.25. This interquartile range is 6.5. The lower fence is 29 and the upper fence is 55.

Order the sets:

31, 38, 39, 40, 41, 45, 45, 45,46, 58

First quartile position:

= 1(10 + 1) / 4

= 2.75th position

= 38 + 0.75 x (39 - 38)

= 38.75

Third quartile:

= 3(10 + 1) / 4

= 8.25th position

= 45 + 0.25 x (46-45)

= 45.25

Interquartile range:

= 45.25 - 38.75

= 6.5

Upper fence:

= 45.25 + (1.5 x 6.5)

= 55

Lower fence:

= 38.75 - (1.5 x 6.5)

= 29

59 is an outlier.

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Answer:

[tex](-\infty, -1) \cup (0, \infty)[/tex]

Step-by-step explanation:

The function is decreasing if, as x increases, the value of the function (y) gets smaller.  This means as you read the graph from left-to-right, the function is decreasing if the graph is falling.

From -infinity to -1, the graph is falling, then the graph rises (f is increasing) until x =0, then the graph falls again from x = 0 to infinity.

❄ Hi there,

let us start by considering this: What should we do to get x all by itself?

Since it's

we should

So, let's start.

[tex]\sf{\dfrac{-x}{4}\times4 < 2\times4}}[/tex]

[tex]\sf{-x < -8}[/tex]

[tex]\sf{x > 8}[/tex]

When we divide both sides of an inequality by a negative number, we do "the inequality flip" and flip the inequality sign.

❄

The arc length of the partial circle is 7.5π

From the question, we are to determine the arc length of the partial circle

The length of an arc can be calculated by using the formula

[tex]l = \frac{\theta}{360^\circ} \times 2\pi r[/tex]

Where [tex]l[/tex] is the length of the arc

[tex]\theta[/tex] is the angle subtended

and r is the radius

From the diagram,

θ = 270°

r = 5

Putting the values into the equation, we get

[tex]l = \frac{270 ^\circ}{360^\circ} \times 2\pi \times 5[/tex]

[tex]l = \frac{3}{4} \times 2\pi \times 5[/tex]

[tex]l = \frac{30\pi}{4}[/tex]

[tex]l = \frac{15}{2}\pi[/tex] OR 7.5π

Hence, the arc length of the partial circle is 7.5π

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The regression equation is y =  3.002 + 0.5x and the scatterplot is illustrated.

It should be noted that a scatterplot simply means a type of data that shows the relationship between two numerical variables.

From the information, summation is X is 99, summation Y is 82.5, summation XY is 797.47, and summation X² is 1001.

Now the value of a will be:

= 82.5 - 1001 - 99 - 797.47/(11.1001 - 99²)

= 3.002

b = (11 × 797.47 - 99 × 82.5)/11.1001 - 99²

= 0.5

The regression equation will be:

y = a + bx.

y = 3.002 + 0.5x

There's positive linear correlation between x and y.

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The solution to the given system of equation is (3, 3, 3)

Given the following system of equation expressed as:

2x-y+5z=16

X-6у +2z=-9

3x+4y- z=32

Multiply equation 2 by 2 to have:

2x-y+5z=16

2X-12у +4z=-18

Subtract

10y+z = 34 .........4

Similarly

3X-18у +6z=-27

3x+4y- z=32

Subtract

-22y+7z = -59 ........... 5

Equate 4 and 5

10y+z = 34 .........4 * 7

-22y+7z = -59 ........... 5 * 1

_______________________

70y+7z = 238

-22y+7z = -59

Subtract

92y = 297

y = 3

Recall that

10y+z = 34

10(3) + z = 34

z = 3

Since x - 6y +2z = -9

x-6(3)+2(3) = -9
x - 18 + 6 = -9
x = 3

Hence the solution to the given system of equation is (3, 3, 3)

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Answer:

x = ±√10i (i outside the radical), or approximately ±3.62i, or no solution depending on your class.

Step-by-step explanation:

x^2 + 10 = 0

x^2 = -10

x = ±√-10

x = ±√10i (i outside the radical), or approximately ±3.62i.

The solution is not real.

If you meant x^2 - 10 = 0 then x = ±√10 or approximately ±3.62. This solution is real.

Answer: 23,5%

Step-by-step explanation:

[tex]23\frac{1}{2} %[/tex]% = [tex]\frac{47}{200}[/tex] = 0,235 = 23,5%

Answer:

x² + 1 = 0

a = 1

b = 0

c = 1

[tex]x1.2 = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

[tex]x1.2 = \frac{ - 0 ±\sqrt{ {0}^{2} - (4.1.1) } }{2.1} [/tex]

[tex]x1.2 = \frac{0± \sqrt{0 - 4} }{2} [/tex]

[tex]x1.2 = \frac{± \sqrt{ - 4} }{2} [/tex]

There is no real solution because the discriminant is negative

Note.

Formula diskriminan

√b² - 4ac.

if the diskrimanan is negatif, so the quadratic equatoin dont have solution

The value of CE = 18.3

According to the statement

Here we have given the value of tangents AE = 8 and BC = 3

we have to find the value of CE and

It is given that AE is the tangent to the circle.

Now we make a equation to find the CE then

(8)^2 = 3(x+3)

In this equation the value of AE is 8. and

In this x is the value of CE and BC have value 3.

And the total value of BE becomes the 3(x+3) and 3 is the parts by which  BE is formed.

Then solve the equation

64= 3x +9

3x = 64-9

x = 18.3

So, The value of CE = 18.3

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Answer:

sin (- 135°)= – sin 135°= – sin (1 × 90°+ 45°) = – cos 45° = – 1√2

cos (- 135°)= cos 135°= cos (1 × 90°+ 45°) = – sin 45°= – 1√2

tan (- 135°) = – tan 135° = – tan ( 1 × 90° + 45°) = – (- cot 45°) = 1

csc (- 135°)= – csc 135°= – csc (1 × 90°+ 45°)= – sec 45° = – √2

sec (- 135°)= sec 135°= sec (1 × 90°+ 45°)= – csc 45°= – √2

cot (- 135°) = – cot 135° = – cot ( 1 × 90° + 45°) = – (-tan 45°) = 1

Step-by-step explanation:

hope this helps

The z score corresponding to the sample is -6.25

The formula for calculating the z-score is expressed as

z = x- μ/σ

Given the following parameters

x = 22 (sample size)

Mean  μ = 72

standard deviation σ = 8

Substitute

z = 22-72/8

z = -50/8

z = -6.25

Hence the z score corresponding to the sample is -6.25

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Step-by-step explanation:

Find the slope between the two points given. Then, use the slope and point ONE to write the

equation of the

13) 120 + 1.5 + 0.25 = 121.75 pounds

14) 4 - 1.5 = 2.5 pints

15) (2.25)(32)= $72

13. Mrs. Smith's current weight is 121.75 pounds.

14. The students should consume an additional 2.5 pints of water.

15. The nurse's overtime earnings amount to $72.00.

Given are words problems based on mixed numbers:

13. To find Mrs. Smith's current weight, we need to add the weight gained over the last two months to her weight last month.

Weight gained in the first month: 1 1/2 pounds

Weight gained in the second month: 1/4 pounds

Total weight gained over the last two months: 1 1/2 + 1/4 = 1 3/4 pounds

Now, to find Mrs. Smith's current weight, we add the total weight gained to her weight last month:

Current weight = Weight last month + Total weight gained

Current weight = 120 pounds + 1 3/4 pounds

Hence, Mrs. Smith's current weight is 121.75 pounds.

14. To calculate the additional water the students should consume to meet the school nurse's recommendation of at least 4 pints daily, we need to find the difference between the recommended amount and the average amount the students currently drink.

The recommended amount is 4 pints, and the average amount the students currently drink is 1 1/2 pints, which can be written as 1.5 pints.

Additional water needed = Recommended amount - Current average amount

Additional water needed = 4 pints - 1.5 pints

Additional water needed = 2.5 pints

Therefore, the students should consume an additional 2.5 pints of water daily to meet the school nurse's recommendation.

15. To calculate the nurse's overtime earnings, you can use the formula:

Overtime Earnings = Overtime Hours × Overtime Pay Rate

First, let's convert the mixed number of overtime hours into an improper fraction:

2 1/4 hours = 2 + 1/4 = 9/4 hours

Now, we can calculate her overtime earnings:

Overtime Hours = 9/4 hours

Overtime Pay Rate = $32.00/hour

Overtime Earnings = (9/4) hours × $32.00/hour

To simplify the calculation, you can convert the fraction to a decimal:

Overtime Earnings = (9/4) hours × $32.00/hour

Overtime Earnings = 2.25 hours × $32.00/hour

Overtime Earnings = $72.00

So, the nurse's overtime earnings amount to $72.00.

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Answer:

300

Step-by-step explanation:

30+30+w+x+y+z = 360 (all angles round a point add up to 360)

Simplifying :

60 + w+x+y+z = 360

Subtracting 60 from both sides :

w+x+y+z = 300

Hope this helped and brainliest ?

Sum of entire angle=360°

so