zz* + 3iz = p + 9i
where z is a complex number and p is a real constant.
Given that this equation has exactly one root, determine the complex number z

Step-by-step explanation:

The given quadratic equation is :

[tex]13x^2 +1 = -10x\\\\or\\\\13x^2+10x+1=0[/tex]

The formula to solve a quadratic equation is :

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]

Put a = 13, b = 10 and c = 1

So,

[tex]x=\dfrac{-10\pm \sqrt{10^2-4(13)(1)} }{2(13)}\\\\x=-0.118, -0.651[/tex]

Hence, this is the required solution.

Answer:

0.1638

Step-by-step explanation:

P(A and B) or simply the probability of both events happening is the product of their individual probabilities.

P(A and B)= (0.42×0.39)= 0.1638

Answer:

The surface of the area is 320 cm. :D

Step-by-step explanation:

Answer:

the answer would be false

Answer:

Step-by-step explanation:

4(3x-5)^2+5=13

4(3x-5)^2+5-13=0

As  (a-b)^2=a^2-2ab+b^2

4((3x)^2-2(3x)(5)+(5)^2)-8=0

4(9x^2-30x+25)-8=0

36x^2-120x+100-8=0

36x^2-120x+92=0

using the Quadratic Formula where

a = 36, b = -120, and c = 92

x=(−bc± sqrt(b^2-4ac))/2a

x=(-(-120)±sqrt((−120)^2−4(36)(92))/2(36)

=120±sqrt(14400−13248−)/72

=120±sqrt(1152)/72

The discriminant b2−4ac>0

so, there are two real roots.

x=(120±24sqrt(2))/72

x=(120/72)±24sqrt(2)/72

implify fractions and/or signs:

x=5/3±sqrt(2)/3

hich becomes

x=2.13807

x=1.19526

Answer:

v = -3i - 2j

Step-by-step explanation:

Vector given two points:

Given two points, a vector is the subtraction of the terminal point by the initial point.

In this question:

Initial point: (-1, 4)

Terminal point: (-4, 2)

So

v = (-4,2) - (-1, 4) = (-4 - (-1), 2 - 4) = (-3,-2)

The vector is v = (-3,-2)

In component form:

xvalue is i, yvalue j. So

v = -3i - 2j

Answer:

bro just search it on mathaway or calculator soup

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Answer:

363 portions can be made with one case.

Step-by-step explanation:

Since I buy tomatoes in 25-pound cases, and one batch of Cobb salad requires 1.1 ounces of tomatoes, to determine how many portions can be made with one case, the following calculations must be performed:

1 pound = 16 ounces

25 pounds = 400 ounces

400 / 1.1 = 363.63

Therefore, 363 portions can be made with one case.

Answer: angles HIL and MLI are supplementary angles.

Hope this helps! :D

9514 1404 393

Answer:

  1.3

Step-by-step explanation:

The two points are on the same vertical line, so the distance between them is the distance between their y-coordinates:

  2.5 -1.2 = 1.3

The distance between the two points is 1.3 units.

Answer:13058

Step-by-step explanation:

Answer:

A = 22 and B = 35

Step-by-step explanation:

The proportional value of x and y is simply

x times 3 1/2 = y

Answer:

-3/1

Step-by-step explanation:

The rise is 1 and the the run is 3 but the line goes from top left to top right so its negative.

Answer:

Slope

Step-by-step explanation:

Hope it helps you in your learning process

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Answer:

  672 m²

Step-by-step explanation:

There are several ways you can do this.

It appears you are intended to divide the isosceles triangle into halves that are right triangles with a leg of 14 and a hypotenuse of 50. The height can then be found from the Pythagorean theorem:

  h² = 50² -14² = 2304

  h = √2304 = 48

Then the area is ...

  A = 1/2bh

  A = (1/2)(28 m)(48 m) = 672 m² . . . triangle area

_____

Additional comment

You may recognize the right triangle as a (7, 24, 25) Pythagorean triple, multiplied by 2.

Answer:

A

Step-by-step explanation:

Answer:

Her gross earnings for that week were $ 363.24.

Step-by-step explanation:

Since Stacy Arrington is paid $ 0.73 for sewing a jacket collar, $ 0.86 for a sleeve with cuffs, and $ 0.94 for a lapel, and one week she sewed 318 jacket collars, 112 sleeves with cuffs, and 37 lapels, to find her gross earnings you must perform the following calculations:

(318 x 0.73) + (112 x 0.86) + (37 x 0.94) = X

232.14 + 96.32 + 34.78 = X

363.24 = X

Therefore, her gross earnings for that week were $ 363.24.

Answer:

Step-by-step explanation:

It is 4:9   and 4.5:2

Answer:

Radius is 9

Formula of a circumference is:

2πr

we can use pie/π as 3.14

3.14 x 2 x 9 (radius) = 56.52

Step-by-step explanation:

If there is a diameter only do half of that and that would be your radius.

Answer:

18π inches (or approximately 56.549 inches)

Step-by-step explanation:

The formula to find circumference is 2πr (or πd). Since we are given the radius (which is half of a circle), we will use 2πr, and the radius (or r) is equal to 9. So you just plug that into the circumference formula, and get:

2*π*9 = 18π

So, the circumference is 18π inches or approximately 56.549 inches (when rounded to the nearest thousandths).

Answer:

Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)

answer:

2y(x³+4x-2x²-8)

Part B: Factor the entire expression completely. Show the steps of your work. (6 points)

answer:

2y(x³+4x-2x²-8)

2y(x³-2x²+4x-8)

2y(x²(x-2)+4(x-2))

2y(x²+4)(x-2)

Answer:

Mean x¯¯¯ 5.8888888888889

Median x˜ 6

Mode 7

Range 3

Minimum 4

Maximum 7

Count n 9

Sum 53

Quartiles Quartiles:

Q1 --> 5

Q2 --> 6

Q3 --> 7

Interquartile

Range IQR 2

hope i helped:) can u plz mark me brainlest

Answer:

the mean is 5.88888888889

Step-by-step explanation:

to find the mean, add all the data results together and divide by how many results you have.  

for example:  5+4+5+7+7+7+5+7+6= 53

53 divided by 9= 5.88888888889

have a good day

Answer:

2nd one and the last one

Step-by-step explanation:

Step-by-step explanation:

Use Pythagoras' theorem

[tex] {a}^{2} = b {}^{2} + c {}^{2} [/tex]

52² = 33.6² + x²

solve for x

Answer:

1575.04

Step-by-step explanation:

Using Pythagoras theorem,

a^2+b^2=C^2

52^2-33.6^2=1575.04

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Answer:

  53

Step-by-step explanation:

Their average is the sum divided by 2: 108/2 = 54. This average is the even number between the two odd numbers of interest.

The smaller number is 53.

Answer:

3^81 is bigger

Step-by-step explanation:

3^81=4.43426488e38

9^27=5.8149737e25

Answer: 13

Step-by-step explanation: subtract 22 from 9