How can I factor these complex conjuages? a^2 + b^2 and a^2 - b

Answer:

[tex]\boxed{1.5}[/tex]

Step-by-step explanation:

First point is given (8, -2)

                               (x₁, y₁)

Second point is given (12, 4)

                                     (x₂, y₂)

Apply the slope formula.

[tex]slope=\frac{rise}{run}[/tex]

[tex]slope=\frac{change \: in \: y}{change \: in \: x}[/tex]

[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]slope=\frac{4-(-2)}{12-8}[/tex]

[tex]slope=\frac{6}{4}=1.5[/tex]

A slope is also known as the gradient of a line. The slope of the line through these two data points is 1.5°F per hour.

A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

slope = (y₂-y₁)/(x₂-x₁)

Given that the temperature recorded at 8 am is –2°F, while the temperature recorded at 12 pm is 4°F. The number of hours between 8:00 am to 12 pm is 4 hours. Therefore, the slope of the line through these two data points is,

Slope, m = [4°F – (–2°F)] / 4 hours = 6°F / 4 hours = 1.5°F per hour

Hence, the slope of the line through these two data points is 1.5°F per hour.

Learn more about Slope of Line here:

https://brainly.com/question/14511992

#SPJ6

Answer:

16 hours

Step-by-step explanation:

From the above question, we are given the following information

For one wall, working alone,

Amy can paint for 12 hours

Which means, in

1 hour , Amy would have painted = 1/12 of the wall

Bob can paint for 18 hours

Which means ,

in 1 hour, Bob would have painted = 1/18 of the wall.

We are told Amy painted the wall for 4 hours and then Bob took over and completed the wall.

Step 1

Find the portion of the wall Amy painted before Bob took over.

Amy painted the wall for 4 hours before Bob took over.

If:

1 hour = 1/12 of the wall for Amy

4 hours =

Cross multiply

4 × 1/12 ÷ 1

= 4/12 = 1/3

Amy painted one third(1/3) of the wall

Step 2

Find the number of hours left that Bob used in painting the remaining part of the wall

Let the entire wall = 1

If Amy painted 1/3 of the wall

Bob took over and painted = 1 - 1/3

= 2/3 of the wall

If,

Bob painted 1/18 of the wall = 1 hour

2/3 of the wall = ?? = Y

Cross multiply

2/3 × 1 = 1/18 × Y

Y = 2/3 ÷ 1/18

Y = 2/3 × 18/1

Y = 36/3

Y = 12 hours.

This means, the number of hours Bob worked when he took over from Amy = 12 hours.

Step 3

The third and final step is to calculate how many hours it took them to paint the wall

Number of hours painted by Amy + Number of hours painted by Bob

= 4 hours + 12 hours

= 16 hours

Therefore, it took them 16 hours to paint the entire wall.

Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

In the question equation is missing so, the equation and its solution can be defined as follows:

[tex]B={b_1,b_2}\\\\b_1= \left[\begin{array}{c}5&5\end{array}\right] \ \ \ \ \b_2= \left[\begin{array}{c}2&-5\end{array}\right] \ \ \ \ \x= \left[\begin{array}{c}-7&-35\end{array}\right][/tex]

[tex]\left[\begin{array}{c}a&c\end{array}\right] =?[/tex]

[tex]\to \left[\begin{array}{c}-7&-35\end{array}\right]= a\left[\begin{array}{c}5&5\end{array}\right]+c \left[\begin{array}{c}2&-5\end{array}\right] \\[/tex]

[tex]\to \left[\begin{array}{c}-7&-35\end{array}\right]= \left[\begin{array}{c}5a+2c&5a-5c\end{array}\right]\\\\\to 5a+2c=-7....(1)\\\\\to 5a-5c=-35....(2)\\\\[/tex]

subtract equation 1 from equation 2:

[tex]\to 7c=28\\\\\to c=\frac{28}{7}\\\\\to c= 4\\\\[/tex]

put the value of c in equation 1

[tex]\to 5a+2(4)=-7\\\to 5a+8=-7\\\to 5a=-7-8\\\to 5a=-15\\\to a= -3[/tex]

coordinate  value is [-3,4].

Answer:

a(n)= a(n+1)+4

Step-by-step explanation:

The first terms of this sequence are: 4,0, -4, -8, -12

Let 4 be a0 and 0 a1.

● a1-a0 = 0-4

●a1-a0 = -4

●a1 = -4+a0

So this relation links the first term with the second one.

replace 1 in a1 with n.

0 in a0 will be n-1

● an = -4+a(n-1)

Add one in n

● a(n+1) = a(n)-4

● a(n) = a(n+1)+4

Answer:

the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes is 0.4215

Step-by-step explanation:

Let consider Q to be the opening altitude.

The mean μ = 135 m

The standard deviation = 35 m

The probability that the equipment damage will occur if the parachute opens at an altitude of less than 100 m can be computed as follows:

[tex]P(Q<100) = P(\dfrac{X- 135}{\sigma} < \dfrac{100 - 135}{35}})[/tex]

[tex]P(Q<100) = P(z< \dfrac{-35}{35}})[/tex]

[tex]P(Q<100) = P(z<-1)[/tex]

[tex]P(Q<100) = 0.1587[/tex]

If we represent R to be the number of parachutes which have equipment damage to the payload out of 5 parachutes dropped.

The probability of success = 0.1587

the number of independent parachute n = 5

the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes can be computed as:

P(R ≥ 1) = 1 - P(R < 1)

P(R ≥ 1) = 1 - P(R = 0)

The probability mass function of the binomial expression is:

P(R ≥ 1) = [tex]1 - (^5_0)(0.1587)^0(1-0.1587)^{5-0}[/tex]

P(R ≥ 1) =[tex]1 - (\dfrac{5!}{(5-0)!})(0.1587)^0(1-0.1587)^{5-0}[/tex]

P(R ≥ 1) = 1 - 0.5785

P(R ≥ 1) = 0.4215

Hence, the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes is 0.4215

Answer:

A graph with a slope of -1, and a y-intercept (crosses the y-axis) at 3

Answer:

52

Step-by-step explanation:

a(n)=-5+(n-1)3

a(20)=-5+(20-1)3

a(20)=52

The 20th term of the arithmetic sequence is 52.

An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.

For example,

In an arithmetic sequence, the difference between consecutive terms is always the same. For example, the sequence 3, 5, 7, 9 ... is arithmetic because the difference between consecutive terms is always two.

The nth term of an arithmetic sequence is given by an = a + (n – 1)d.

Given:

a(n)=-5+(n-1)3

First term,

a(1)= -5 + 0

a(1)= -5

second, a(2)= -5 + 1*3

a(2)= -2

Third, a(3)= -5+6

a(3)= 1

d= 3

So, the 20th term

a(20)= -5+ (20-1)3

a(20)= -5 + 57

a(20)= 52

Hence, the 20th term is 52.

Learn more about Arithmetic Sequence here:

https://brainly.com/question/10396151

#SPJ2

Answer:

37/42 or 0.88

Step-by-step explanation:

[tex]( \frac{1}{6} + \frac{3}{7} ) + \frac{2}{7} \\ ( \frac{1}{6} + \frac{3}{7} ) = \frac{25}{42} \\ [/tex]

[tex]\frac{25}{42} + \frac{2}{7} = \frac{37}{42} \\ \\ answer = \frac{37}{42} [/tex]

Answer:

work is shown and pictured

Answer:

2/3

Step-by-step explanation:

got right n edg 2021

Answer: 78

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the shape of the equation -2(x+3) = -10. Since x is being multiplied by -2, the first step would be to divide by -2, which is equivalent to multiply by (-1/2) on both sides. Hence the answer is B

Answer:

your answer is x^2 - 16x + 64.

Answer:

x^2 - 16x + 64

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x² - 3x - 6 = 0

Using the quadratic formula

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

a = 2 , b = - 3 , c = 6

Substituting the values into the above formula

We have

[tex]x = \frac{ - - 3± \sqrt{ { - 3}^{2} - 4(2)( - 6)} }{2(2)} [/tex]

[tex]x = \frac{3± \sqrt{9 +48 } }{4} [/tex]

[tex]x = \frac{3± \sqrt{57} }{4} [/tex]

[tex]x = \frac{3 - \sqrt{57} }{4} \: \: \: \: or \: \: \: \: \: x = \frac{3 + \sqrt{57} }{4} [/tex]

We have the final answer as

Hope this helps you

Answer:

The 95 % confidence interval of the mean of the time playing video games. is

        [tex]15.67< \mu <17.52[/tex]

Step-by-step explanation:

From the question we are told that

      The sample size is [tex]n = 35[/tex]

        The sample mean is [tex]\= x = 16.6[/tex]

       The standard deviation is  [tex]\sigma = 2.8[/tex]

The confidence level is  95%  hence the level of significance is mathematically represented as

     [tex]\alpha = 100 - 95[/tex]

     [tex]\alpha = 5[/tex]%

      [tex]\alpha = 0.05[/tex]

Now the critical value of half of this level of significance obtained from the normal distribution table is  

       [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

The  reason for the half is that we are considering the two tails of the normal distribution curve which we use to obtain the interval

Now the standard error of the mean is mathematically evaluated as

       [tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values  

     [tex]\sigma _{\= x} = \frac{2.8 }{\sqrt{35} }[/tex]

      [tex]\sigma _{\= x} = 0.473[/tex]

the 95 % confidence interval of the mean of the time playing video games.

is mathematically evaluated as

    [tex]\= x - (Z_{\frac{\alpha }{2} } * \sigma_{\= x }) < \mu < \= x - (Z_{\frac{\alpha }{2} } * \sigma_{\= x })[/tex]

substituting values

    [tex]16.6 - (1.96 * 0.473) < \mu < 16.6 + (1.96 * 0.473)[/tex]

     [tex]15.67< \mu <17.52[/tex]

Answer:

Step-by-step explanation:

Triangle ABC is a right angled triangle. A right angle triangle has three sides (The hypotenuse which is the longest side and the other two sides which are the adjacent and the opposite).

The side facing the angle of a right angled triangle is the opposite side depending on the angle in consideration.

According to the triangle, AB = hyp = 5, BC = 3 and AC = 4

Side AB is facing the right angle, side BC is opposite to the angle A while side AC is opposite to the angle B.

Based on the conclusion in the last paragraph, it can be concluded that the  length of the side opposite Angle B is AC and since the measurement of AC is 4 units, then the length we are looking for is 4 units.

Answer:

B. 4 units

Step-by-step explanation:

Answer:

The inverse is ±sqrt((x-1))/ 4

Step-by-step explanation:

y = 16x^2 + 1

To find the inverse, exchange x and y

x = 16 y^2 +1

Then solve for y

Subtract 1

x-1 = 16 y^2

Divide by 16

(x-1)/16 = y^2

Take the square root of each side

±sqrt((x-1)/16) = sqrt(y^2)

±sqrt((x-1))/ sqrt(16) = y

±sqrt((x-1))/ 4 = y

The inverse is ±sqrt((x-1))/ 4

Answer:

D

Step-by-step explanation:

Answer:

1,500

Step-by-step explanation:

[tex]6*(\frac{25,000}{100} )=1,500[/tex]

Answer:

0.343

Step-by-step explanation:

First, find the different ways one can chose a professor or instructor. In this case, there are 8 professors and 4 instructors. So there are a total of 12 ways you can choose a professor or instructor.

Second, you want to find the different ways you can choose any member of the faculty. In this example, since you are only choosing one person, then you just find the total number of people in the faculty, which is 8 + 11 + 12 + 4 = 35.

Third, all you do is divide the different ways you can get a professor or instructor by the total different ways you can choose. So it's 12/35, or 0.343.

Step-by-step explanation:

5 log₅ x − ¼ log₅ (8−x)

log₅ x⁵ − log₅ (8−x)^¼

log₅ x⁵ − log₅ ∜(8−x)

log₅ (x⁵ / ∜(8−x))

The expression 5 log₅ x - 1/4 log₅ (8 - x) can be condensed to [tex]log_{5} \frac{x^5}{\sqrt[4]{8-x} }[/tex] , using the laws of logarithms and exponents.

A logarithmic expression x = logₐb, implies that aˣ = b.

Some properties used to solve logarithmic expressions are:

In the question, we are asked to condense the expression:

5 log₅ x - 1/4 log₅ (8 - x)

= [tex]log_{5}x^{5} - log_{5}(8 - x)^{1/4}[/tex], (using the power law: logₐ xⁿ = n.logₐ x)

= [tex]log_{5}x - log_{5}\sqrt[4]{8 - x}[/tex], (since, [tex]x^{1/a} = \sqrt[a]{x}[/tex])

= [tex]log_{5} \frac{x^5}{\sqrt[4]{8-x} }[/tex] , (using the quotient law: logₓ a - logₓ b = logₓ a/b).

∴ The expression 5 log₅ x - 1/4 log₅ (8 - x) can be condensed to [tex]log_{5} \frac{x^5}{\sqrt[4]{8-x} }[/tex] , using the laws of logarithms and exponents.

Learn more about the logarithms and exponents at

https://brainly.com/question/2141799

#SPJ2

Answer:

b

Step-by-step explanation:

Answer:

A. The model under-predicts the price of this diamond because the residual is positive.

Step-by-step explanation:

The diamond seller has listed its 0.8 weighting diamonds at a price of $10,999. The price of the diamond is set as the market maker. The model is used to predict the price of the diamonds. This model has under predicted the value of diamonds and actual price of diamonds must be higher.

The correct answer is C) 0.56

Explanation:

In general terms, the probability of two or more events can be calculated by adding the probability of each event. This rule applies when an event is considered as mutually exclusive. Age is considered as a mutually exclusive event because if a random individual is selected he/she will be only one age. In this context, if you need to know the probability that a student is 15 or younger it is necessary to add the probability that a student is 15, the probability that the student is 14, and the probability that the student is 13. The process is shown below:

P (A or B or C) = P(A) + P(B) + P(C)

P =  P(13) + P(14) + P(15)

P= 0.001 + 0.25 + 0.30

P= 0.56

Answer:

0.59

Step-by-step explanation:

add the probabilities of 13, 14, and 15

0.01 + 0.28 + 0.3 = 0.59

Answer:

The  probability is   [tex]P(A') = 0.485[/tex]

Step-by-step explanation:

Let assume that the number of computer produced by factory C is  k = 1  

 So  From the  question we are told that

       The number produced by  factory A is  4k =  4

        The  number produced by factory B is  7k  = 7

        The  probability of defective computers from A is  [tex]P(A) = 0.04[/tex]

        The  probability of defective computers from B is  [tex]P(B) = 0.02[/tex]

        The  probability of defective computers from C is [tex]P(C) = 0.03[/tex]

Now the probability of factory A producing a defective computer out of the 4 computers produced is  

       [tex]P(a) = 4 * P(A)[/tex]

substituting values

        [tex]P(a) = 4 * 0.04[/tex]

        [tex]P(a) = 0.16[/tex]

The probability of factory B producing a defective computer out of the 7 computers produced is  

       [tex]P(b) = 7 * P(B)[/tex]

substituting values

        [tex]P(b) = 7 * 0.02[/tex]

        [tex]P(b) = 0.14[/tex]

The probability of factory C producing a defective computer out of the 1 computer produced is  

       [tex]P(c) = 1 * P(C)[/tex]

substituting values

        [tex]P(c) = 1 * 0.03[/tex]

        [tex]P(b) = 0.03[/tex]

So the probability that the a computer produced from the three factory will be defective is  

     [tex]P(t) = P(a) + P(b) + P(c)[/tex]

substituting values

     [tex]P(t) = 0.16 + 0.14 + 0.03[/tex]

     [tex]P(t) = 0.33[/tex]

Now the probability that the defective computer is produced from factory A is

      [tex]P(A') = \frac{P(a)}{P(t)}[/tex]

       [tex]P(A') = \frac{ 0.16}{0.33}[/tex]

        [tex]P(A') = 0.485[/tex]

Answer:

Step-by-step explanation:

You have the following function:

[tex]f(x)=-3x+7[/tex]

The y-intercept of the function is given by the independent coefficient, which is 7.

y-intercept = 7

To obtain the x-intercept you equal the function to zero and solve for x, as follow:

[tex]0=-3x+7\\\\3x=7\\\\x=\frac{7}{3}\approx2.33[/tex]

x-intercept = 2.33

Due to the coefficient of x is negative, the slope of the function is negative.

The function is a straight line, then, its domain all all real numbers and its range are all real numbers.

The graph of the function is attached in the image below.

Answer:

 A-2, B-DNE*, C-3, D-DNE, E-4, F-1

---------------------

The first attachment shows the solutions to A and C.

The second attachment shows the solutions to E and F.

There are no real number solutions to systems B and D.

_____

In general, you can solve the linear equation for y, then substitute that into the quadratic. You can subtract the x-term on the left and complete the square to find the solutions.

A.

 (3-x) +12 = x^2 +x

 15 = x^2 + 2x

 16 = x^2 +2x +1 = (x +1)^2 . . . . add the square of half the x-coefficient to complete the square; next take the square root

 ±4 -1 = x = {-5, 3) . . . . . identifies the second solution set for system A

__

B.

 (x -1) -15 = x^2 +4x

 -16 = x^2 +3x

 -13.75 = x^2 +3x +2.25 = (x +1.5)^2

roots are complex: -1.5 ±i√13.75

__

C.

 (1-2x) +5 = x^2 -3x

 6 = x^2 -x

 6.25 = x^2 -x + .25 = (x -.5)^2

 ±2.5 +.5 = x = {-2, 3} . . . . . identifies the third solution set for system C

__

remaining problems are done in a similar way.

_____

* DNE = does not exist. There is no matching solution set for the complex numbers that are the solutions to this.

---------------------

Hope this helps!

Brainliest would be great!

---------------------

With all care,

07x12!

Answer:

251 inches

Step-by-step explanation:

c = 2πr

c = 2(3.14)(5) = 31.4

31.4 x 8 rev. = 251 inches

Answer:

I think D

Step-by-step explanation:

Verticle or horizontal line test, it would be a function either way

Answer:

IT IS (M-4)(M+1)

Step-by-step explanation:

BECAUSE ALL THE OTHER QUESTION HAVE THE VARIABLE AS X

AND THIS ONE IS M

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

    ✌          -ZYLYNN JADE ARDENNE

Answer: The answer is (D)  t  =  √2d/₅

Step-by-step explanation:

Since a = 2d/t²

Now making t the subject of the formula

at²  = 2d

t²   = 2d/a, to find t , take the square root of both sides

t    =  √2d/₅ since a = 5m⁻².

The answer is d

Answer:

No the evidence is not sufficient

Step-by-step explanation:

From the question we are told that

    The  sample  size is  [tex]n = 900[/tex]

   The  sample  proportion is  [tex]\r p = 0.75[/tex]

    The  population proportion is  [tex]p = 0.72[/tex]

The  Null hypothesis is

   [tex]H_o : p = 0.72[/tex]

The  Alternative  hypothesis is

   [tex]H_a : p > 0.72[/tex]

The level of significance is given as  [tex]\alpha = 0.05[/tex]

The critical value for the level of significance is  [tex]t_{\alpha } = 1.645[/tex]

 Now the test statistic is mathematically evaluated as

          [tex]t = \frac{\r p - p }{ \sqrt{\frac{p(1-p)}{\sqrt{n} } } }[/tex]

substituting values

        [tex]t = \frac{ 0.75 - 0.72 }{ \sqrt{\frac{0.72 (1-0.72)}{\sqrt{900} } } }[/tex]

        [tex]t = 0.366[/tex]

Since the critical value is  greater than the test statistics then the Null hypothesis is rejected which there is no sufficient evidence to support the claim