A function f is defined on the complex numbers by f(z) = (a+bi)z, where a and b are positive real numbers. Each point in the image of f is equidistant from the point z and the origin. Given that |a+bi| = 8, find a and b.

Enter your answer as an ordered pair: (a,b)

I tried this question 3 times but I'm a little stuck on where to go after a couple steps.. can someone help please??

The weight of an object is the amount of gravitational force applied on the object by the earth. The weight of the oranges to be used is 6.25 pounds.

The level of influence of the earth's gravitational pull on an object determines its weight. This depends also on the size of the mass of the object.

Given that Bella bought 15.625 pounds of oranges.

Let the weight of the oranges required to prepare fruit salad be represented by W. Then the weight of the oranges required is 0.4 of the weight of oranges bought, so that;

W = 0.4 * 15.625

   = 6.25

W = 6.25

Thus, the weight of the oranges required to be used for fruit salad is 6.25 pounds.

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By using the concept of Linear Transformation, the value of T(W) obtained is T(W) = (2, 6)

What is Linear Transformation?

A function through one vector space to the next that respects this same underlying (linear) structure of the each vector space is called a linear transformation. A linear operator, or map, is another name for a linear transformation. The transformation is known as just an endomorphism as well as, if invertible, an automorphism when the range of a transformation matches the domain. The underlying field of the two vector spaces must be identical.

Let u, v be two element of a vector space V and let c be a scalar

T is said to be a Linear Transformation if

i) T(u + v) = T(u) + T(v)

ii) T(cu) = cT(u)

T: [tex]\mathbb{R}^{3} \rightarrow \mathbb{R}^2[/tex] is a linear transformation

U = (1, -3, 3), V = (−1,3,−2)

W = [tex]c_1[/tex] U + [tex]c_2[/tex] V

(-3, 9, -7) = [tex]c_1[/tex](1, -3, 3) + [tex]c_2[/tex](-1, 3, -2)

[tex]c_1 - c_2 = -3[/tex] ...... (1)

[tex]3c_1 - 2c_2 = -7[/tex] ..... (2)

Multiplying (1) by 2

[tex]2c_1 - 2c_2 = -6[/tex] .... (3)

Subtracting  (2) from (3),

[tex]c_1 = 1[/tex]

Putting the value of [tex]c_1[/tex] in (1)

1 - [tex]c_2[/tex] = -3

[tex]c_2 = 3 + 1\\c_2 = 4[/tex]

T(W) =  T(U) +  4T(V)

T(W) = (2, 2) + 4(0, 1)

T(W) = (2, 6)

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The three ordered pairs for the equation y = -4x+3 are (0,3), (1,-1) and (2,-5).

According to the question,

We have the following equation:

y = -4x+3

We have to find the three ordered pairs when the values of x are given in the table.

When x = 0, we have the following value of y:

y = -4*0+3

y = 3

When x = 1:

y = -4*1+3

y = -4+3

y = -1

When x = 2:

y = -4*2+3

y = -8+3

y = -5

Hence, the three ordered pairs for the equation y = -4x+3 are (0,3), (1,-1) and (2,-5).

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The equation of the linear function in slope-intercept form is [tex]y=-5x+5[/tex]

When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope-intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.

Different values of x and y  are given.

Find the slope using any two points from the given points.

[tex]m=\frac{-5-0}{2-1}\\ =-5[/tex]

Use the point-slope form of line to obtain the equation.

[tex]y-0=-5(x-1)\\[/tex]

Arrange the equation in slope- intercept form.

[tex]y=-5x+5[/tex]

So, the equation of the linear function in slope-intercept form is [tex]y=-5x+5[/tex].

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Answer:

49.57

Step-by-step explanation:

0.7 can go into 34.7 49 times. 0.7*49=37.3

34.7-34.3=0.4 and 0.4/0.7 is 4/7 or 0.57...

So 49+.57=49.57

Answer:

The second period from 1669 to 1687 was the highly productive period in which he was Lucasian professor at Cambridge. The third period (nearly as long as the other two combined) saw Newton as a highly paid government official in London with little further interest in mathematical research.

Step-by-step explanation:

The number of hours that it takes for Paul to do the job alone is of:

6 hours.

The time that it takes for Paul to do the job alone is given by the together rate, which is obtained as the sum of the separate rates.

The rates in the context of this problem are given as follows:

Hence the value of x is obtained applying the together rate, and it gives the number of hours that it takes for Paul to do the job alone.

Hence:

1/(x - 2) = 1/x + 1/12

1/(x - 2) = (12 + x)/(12x)

Applying cross multiplication, we have that:

(12 + x)(x - 2) = 12x

x² + 10x - 24 = 12x

x² - 2x - 24 = 0

(x + 4)(x - 6).

Applying the Factor Theorem, the solutions are given as follows:

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Answer:

2(x+5) I believe

Step-by-step explanation:

(x-2)9

9x-18

good luck <33

The value of h in a regular polygon of 16 sides is 37.3.

According to the question,

We have the following information:

A regular polygon has 16 sides. And one of its angles measures (5h − 29)°.

We know that following formula is used to find the sum of interior angles of a polygon:

(n-2)*180 where n is the number of sides of a polygon

(16-2)180

14*180

2520°

Now, in this polygon, there are 16 sides. So, there will be 16 angles.

Now, to find the measurement of one angle, we will divide total sum by number of angles.

One angle = 2520/16

One angle = 157.5°

Now, we have the following expression:

5h-29 = 157.5

5h = 157.5+29

5h = 186.5

h = 186.5/5

h = 37.3

Hence, the correct option is B (the second one).

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Answer: 42 km of 120km is 35%

Step-by-step explanation: 42 ÷ 120 is 0.35 then you move decimal 2 places right to get percent.

The value of x is a counter example to the student's conjecture (x = 2).

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that x is a non-negative number, a student conjectured that x + 4 < x².

Since x is a non-negative number, A and B are eliminated.

This leaves C and D at the value of x = 2,

2 + 4 < 2²

6 < 4 is false.

Therefore, the value of x is a counterexample to the student's conjecture (x = 2).

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Graph (B) represents the base function f (x)=√x and the stretched function [tex]g (x) = \frac{-3}{2} \sqrt{x}[/tex].

Graphs are used to map functions of two variables on a Cartesian coordinate system, which is composed of a horizontal x-axis, vertical y-axis.

The graph of this function can be obtained by putting different values of x.

x = 0 gives f (x) = 0

x = 1 gives f (x) = 1

x = 2 gives f (x) = 1.414

x = 3 gives f (x) = 1.732

Drawing these points in the graph and connecting we get a curve(black) which can be seen in all  given diagram (A), (B), (C), (D).

Now, we have stretched function  [tex]g (x) = \frac{-3}{2} \sqrt{x}[/tex]

The graph of this function can be obtained by putting different values of x.

x = 0 gives g (x) = 0

x = 1 gives g (x) = -1.5

x = 2 gives g (x) = -2.121

x = 3 gives g (x) = -2.598

Drawing these points in the graph and connecting we get a curve(red) which can be seen in diagram (D).

By combining these two graphs we get the graph of diagram (D).

Therefore, the base function f (x) and the stretched function g (x) together represents the diagram (D).

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The product of the algebraic expression as the product of (2p + q) and (-3q - 6p + 1) is; - 12p² - 12pq + 2p - 3q²+ q

We want to find the product of (2p + q) and (-3q - 6p + 1) and this gives;

(2p + q) * (-3q - 6p + 1)

Now, this can be broken down further using distributive property of algebra into;

2p(-3q - 6p + 1) + q(-3q - 6p + 1)

= -6pq - 12p² + 2p - 3q² - 6pq + q

= - 12p² - 3q² - 12pq + 2p + q

Rearranging gives us;

- 12p² - 12pq + 2p - 3q²+ q

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The probability of selecting four cards of the same suit is 0.0106.

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Given that, four cards are selected at random without replacement from a well-shuffled deck of 52 playing cards

No. of cards for each suit = 13

Total types of four suits = 4(hearts, spades, diamond, clubs)

Probability = (conditional case)/(total case)

So, total number of conditional case = No. of case of selecting all 4 cards of hearts suit + no. of case of selecting all 4 cards of spades suit + no. of case of selecting all 4 cards of clubs suit + no. of case of selecting all 4 cards of diamonds suit

= 13C4 + 13C4 + 13C4 + 13C4

= 4*13C4 = 4*13!/9!4! = 4*13*12*11*10*9!/9!*4*3*2*1 = 2860

Total number of cases = 52C4 = 52!/48!4! = 270725

So, probability of getting all 4 cards of the same suit =

2860/270725

​= 0.0106.

Hence, The probability of selecting four cards of the same suit is 0.0106.

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As per the concept of direct variation, y = 80 when x = 5, then the direct variation equation shows the relationship between x and y will be y = 16x

Equation

Basically, the equation is a statement that two expressions, which include variables and/or numbers, are equal. And in essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

Given,

In a direct variation, y=80 when x=5.

Here we have to write a direct variation equation that shows the relationship between x and y.

Here we have given that,

The value of y = 80 when x = 5

Therefore, there are often two different sorts of variables in analytics.

And we have obtained that independent variables will have an impact on dependent variables.

Now, what occurs as a result of the independent variable is referred to as a dependent variable.

Here we have given equation x is the independent variable while y is the dependent variable.

So, it can be written as,

=> 80 = 16(5)

Therefore, the resulting equation is y = 16x

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The perimeter of the triangle is, 8x + 3y +1.

What is perimeter?

A perimeter is a closed path that encloses, surrounds, or delimits a one-dimensional length, a two-dimensional shape, or both. The circumference of a circle or an ellipse is its perimeter. There are numerous practical uses for calculating the perimeter.

Let, the side lengths of the triangle are (7x - 4), (x + 3) and (3y + 2).

Since the perimeter is the sum of all side lengths.

So,

Perimeter = (7x - 4) + (x + 3) + (3y + 2)

                 = 7x - 4 + x + 3 + 3y + 2

Perimeter = 8x + 3y + 1

Hence, the perimeter of the triangle is, 8x + 3y + 1.

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The distance between the points (-4, -5) and (8, 0) is 13 units

The coordinates of the first point = (-4, -5)

The coordinates of the second point = (8, 0)

The distance between the two points d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Where d is the distance between two points

[tex](x_1,y_1)[/tex] is the coordinates of the first point

[tex](x_2,y_2)[/tex] is the coordinates of the second point

Substitute the values in the equation

The distance between the two points = [tex]\sqrt{(8--4)^2+(0--5)^2}[/tex]

= [tex]\sqrt{12^2+5^2}[/tex]

Find the square of each term

= [tex]\sqrt{144+25}[/tex]

Add the terms together

= [tex]\sqrt{169}[/tex]

Find the square root of the number

= 13 units

Hence, the distance between the points (-4, -5) and (8, 0) is 13 units

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Answer:

  c ≈ 14.76

Step-by-step explanation:

In right triangle ABC, you have short sides a=7 and b=13. You want the length of the hypotenuse, 'c'.

The Pythagorean theorem tells you the relationship between the sides of a right triangle is ...

  c² = a² +b²

Filling in the given values, we have ...

  c² = 7² +13² = 49 +169 = 218

  c = √218 ≈ 14.7648

Rounding to hundredths, we have ...

  c ≈ 14.76

__

Additional comment

Your posted question asks for the value of C (capitalized). That refers to the right angle, so its value is C = 90°. It is always helpful if you ask for what you really want to know.

To meet the given requirements 3 ounces of Brand A and 4 ounces of Brand B should be served , the minimum cost is $43 .

In the question ,

it is given that ,

the each serving should not be larger than  8oz .

let the number of Ounces of Brand A food = x , and

let the number of ounces of brand B = y ,

So , x + y ≤ 8

Brand A has 3 units of Nutrient 1 and 4 units of Nutrient 2 , and

Brand B has 5 units of Nutrient 1 and 2 units of Nutrient 2 ,

So , 3x + 5y ≥ 29 ,

and 4x + 2y ≥ 20,

and x , y ≥ 0  .

given, that

cost of Brand A = 5 cents/ounce

cost of Brand B = 7 cents/ounce

So , the cost equation is c(x) = 5x + 7y ,

drawing the given inequalities on the graph ,

From the graph given below , we find that the vertices of the feasible region are ,

(2,6) , (5.5,2.5) , (3,4)

Substituting the points in the cost equation , we get

For point (2,6) , C = 5(2) + 7(6) = 10 + 42 = 52

For point (3,4), C = 5(3) + 7(4) = 15 + 28 = 43

For point (5.5,2.5) , C = 5(5.5) + 7(2.5) = 45 ,

the minimum cost is at point (3,4) ,

So , 3 ounces of Brand A and 4 ounces of Brand B should be used .

Therefore , To meet the given requirements 3 ounces of Brand A and 4 ounces of Brand B should be served , the minimum cost is $43 .

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The values of x and y are 23.3 and 106 as per given diagram.

What is Alternate Interior Angles?

Hence, (3x + 4)° = 74°

3x = 74° - 4°°

x = 70° / 3

x = 23.3

What is Interior Angles on the Same Side of the Transversal?

Hence, (3x+4)° + y° = 180°

74° + y° = 180°

y = 106°

Hence, the values of x and y are 23.3 and 106 as per given diagram.

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Maya is playing a trivia game with multiple choice questions. Each question has 222 correct answers among 555 answer choices. Maya has no idea what the answers to a certain question are, so she needs to choose two different answers at random.

The probability that maya's first guess is correct and her second guess is incorrect is 0.24.

From the question given above, the following data were obtained:

Correct answer (C) = 222

Total answer = 555

Incorrect answer (I) = 555 – 222 = 333

Next, we shall determine the probability that her 1st guess is correct.

Correct answer, nC = 222

Total answer, nS= 555

Probability of correct answer, P(C) =?

P(C) = nC / nS

P(C) = 222 / 555

Next, we shall determine the probability that her 2nd guess is incorrect

Incorrect answer, nI = 333

Total answer, nS = 554

Probability of incorrect answer, P(I) =?

P(I) = nI / nS

P(I) = 333 / 554

Finally, we shall determine the probability that her first guess is correct and her second guess is incorrect.

Probability of correct answer, P(C) = 222 / 555

Probability of incorrect answer, P(I) = 333 / 554

Probability of 1st correct and 2nd incorrect, P(C n I) =?

P(C n I) = P(C) × P(I)

P(C n I) = (222 / 555) × (333 / 554)

P(C n I) = 0.24

Hence the answer is, The probability that maya's first guess is correct and her second guess is incorrect is 0.24.

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Answer:

0.3

Step-by-step explanation:

Khan Academy ;)

y = -1/3 x + 5 this equation represents the given graph.

How do you plot points on graph ?

Proof :

(0, 5) and ( 15, 0) these are the points where the graph is plotted.

y = -1/3 x + 5

put x= 0 and find y

y = 0 + 5

y = 5

put y = 0 and find x

0 = -1/3 x + 5

-5 = -1/3 x

x = 15

So, now we get the same points i.e, (0, 5) and ( 15, 0) as plotted in the given graph.

Hence, we can say that  y = -1/3 x + 5 this equation represents the given graph.

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Answer:

2m Wide

Step-by-step explanation:

Answer:

25% red and 28% blue.

Step-by-step explanation:

By evaluating the exponential equation, we will see that the amount owed after 6 years is $8551.56

The formula we need to use is the exponential equation:

A = P*(1 + r/n)^(n*t)

Where:

P is the initial amount, here we know that it is $5,300

r is the rate, in this case is 8%, but it needs to be written as a decimal, so we have r = 0.08

t is the variable, this time is the time in years, we want to find the amount owed after 6 years, so t = 6

n is how many the the rate applies on one unit of t, in this case the rate is monthly, and there are 12 months on a year, so n = 12.

Replacing all that in the given formula we will get:

A = $5,300*(1 + 0.08/12)^(12*6) = $8551.56

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The x- and y- intercepts of then graph of; -2x + y = 22 as required in the task content are; -11 and 22 respectively.

It follows from the task content that the x- and y-intercepts of the graph of the equation; -2x + y = 22 are to be determined.

Recall that the y-intercept of a graph refers to the value of y when x = 0.

Therefore; we have;

-2(0) + y = 22;

y = 22.

Recall that the x-intercept of a graph refers to the value of x when y = 0;

-2x + 0 = 22

x = 22/-2

x = -11.

On this note, it follows that the x-intercept of the graph is at x = -11 while the y-intercept is at; y = 22.

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Answer:

Its 12.5 miles per hour.

Step-by-step explanation:

Distance covered by cyclist=3.75 miles. Time =0.3 hours. Speed =3.75÷0.3=12.5

hope this helps

Answer:

0.4 miles per hour

Step-by-step explanation:

Distance covered= 5.83 miles

Time taken to cover the distance =0.4 hours

[tex] speed \: = \frac{distance}{time} [/tex]

[tex] = \frac{5.83}{0.4} [/tex]

=14.575 ~=14.5 miles per hour

If the rate (speed) = 14.575 miles per hour

Distance = 5.5 miles

[tex]time = \frac{distance}{speed} [/tex]

[tex] = \frac{5.5}{14.575} [/tex]

=0.337 ~= 0.4 hours

Carlos harvests cassavas at a constant rate. He needs 353535 minutes to harvest a total of 151515 cassavas.

The ratio of the change in dependent values or outputs to the change in independent values or inputs is known as the rate of change. The change, which also refers to the function's slope, represents the shift in values between two points on a coordinate plane. The formula for the rate of change is (y2 - y1)/, where y stands for the dependent variable and x for the independent variable (x2 - x1).

Given:

Carlos gives  353535 minutes to harvest a total of 151515 cassavas.

Find:

We have to find the total number of cassavas.

Solution:

Carlos harvests cassava at constant rate is 353535 minutes per 151515 cassavas

= 151515/353535

= 0.429

A formula for the quantity of cassava (C) that Carlos harvests each time (T).

This means that after 353535 minutes, 151515 cassavas have been harvested, after 700000 minutes, 300000 cassavas, and so on.

Hence, the required constant rate is 0.429T.

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