Let z = 3 + 2i and w = 4 + i. What best describes the geometric construction of the product z times w on the complex plane?

z is stretched by a factor of StartRoot 17 EndRoot and rotated 14° counterclockwise
z is stretched by a factor of StartRoot 17 EndRoot and rotated 76° counterclockwise
z is stretched by a factor of 5 and rotated 14° counterclockwise
z is stretched by a factor of 5 and rotated 76° counterclockwise

Answer:

Step-by-step explanation:

You want to know the number of dogs and chickens a farmer has if there are 60 total, having a total of 148 legs.

Let d represent the number of dogs. Then 60-d is the number of chickens, and the total number of legs is ...

  4d + 2(60 -d) = 148

Simplifying gives ...

  2d +120 = 148

  d +60 = 74 . . . . divide by 2

  d = 14 . . . . . . . subtract 60

  60 -d = 46 . . . . the number of chickens

The farmer has 14 dogs and 46 chickens.

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Answer:

uhhhhh 3

Step-by-step explanation:

Step-by-step explanation: I know, hardest question known to man.

Answer:

M = 1

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

If he is doing 2 short runs and one long run, and his 2 short runs equal 2.25 miles, you'd need to subtract them from the total to find out the long run.

The number of pounds of strawberries sold and the number of pounds of grapes sold is 32 and 20 respectively.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given that the selling price of strawberries each pound = $2.50,

The selling price of grapes each pound = $2

The total earning = $160

Let x is the no of a pound of strawberries and y is the no of a pound of grapes sold, then equation will be,

x = y + 12 and 2.50x + 2y= 160

Solve the equation by substitution method;

x = 32 and  y = 20

Therefore, the number of pounds of strawberries sold is 32

the number of pounds of grapes sold is 20.

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Answer:

x1=2. y1=0. x2=2. y2=6. please mark brainliest!

Answer:

So the question is

(2,0) (2,6)

Generallyit is (x1,y1) (x2,y2)

Hence

x1 = 2

x2 = 2

y1=0

y2=6

Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-3,5) and (7,1)

The distance between them is

We have the final answer as

Hope this helps you

Answer:

The wood was cut approximately 8679 years ago.

Step-by-step explanation:

At first we assume that examination occured in 2020. The decay of radioactive isotopes are represented by the following ordinary differential equation:

\(\frac{dm}{dt} = -\frac{m}{\tau}\) (Eq. 1)

Where:

\(\frac{dm}{dt}\) - First derivative of mass in time, measured in miligrams per year.

\(\tau\) - Time constant, measured in years.

\(m\) - Mass of the radioactive isotope, measured in miligrams.

Now we obtain the solution of this differential equation:

\(\int {\frac{dm}{m} } = -\frac{1}{\tau}\int dt\)

\(\ln m = -\frac{1}{\tau} + C\)

\(m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }\) (Eq. 2)

Where:

\(m_{o}\) - Initial mass of isotope, measured in miligrams.

\(t\) - Time, measured in years.

And time is cleared within the equation:

\(t = -\tau \cdot \ln \left[\frac{m(t)}{m_{o}} \right]\)

Then, time constant can be found as a function of half-life:

\(\tau = \frac{t_{1/2}}{\ln 2}\) (Eq. 3)

If we know that \(t_{1/2} = 5730\,yr\) and \(\frac{m(t)}{m_{o}} = 0.35\), then:

\(\tau = \frac{5730\,yr}{\ln 2}\)

\(\tau \approx 8266.643\,yr\)

\(t = -(8266.643\,yr)\cdot \ln 0.35\)

\(t \approx 8678.505\,yr\)

The wood was cut approximately 8679 years ago.

Answer:

D

Step-by-step explanation:

Yes, it does because it passes the vertical line test. We don't have to worry about the horizontal line test because it isn't a valid test. For example, let's imagine a parabola. That doesn't pass the horizontal line test, but it's still a function. This means that we can eliminate option B. We can do the same to C because a function doesn't necessarily have to be a straight line (like the parabola). That leaves us with options A and D. These both have to do with the vertical line test, so let's do it! If we place a vertical line anywhere on this graph, we will see that there are no vertical lines that intersect at 2 places with the graph. Therefore, it passes the vertical line test, and is a function. Hope this helps!

The answer is:

g(x + 1) = 6x + 1

g(4x) = 24x -5

Work/explanation:

To evaluate, I plug in x + 1 into the function:

\(\sf{g(x)=6x-5}\)

\(\sf{g(x+1)=6(x+1)-5}\)

Simplify

\(\sf{g(x+1)=6x+6-5}\)

\(\sf{g(x+1)=6x+1}\)

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

Do the same thing with g(4x)

\(\sf{g(4x)=6(4x)-5}\)

\(\sf{g(4x)=24x-5}\)

Hence, these are the answers.

The expression which shows how many grams of raisins are in the bowl will be

(0.01x) * 150 + (0.01y) * 250

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The expression which shows how many grams of raisins are in the bowl will be:

= (x% × 150) + (y% × 250)

= (0.01x) * 150 + (0.01y) * 250

This equation represents the total grams of raisins in the bowl by multiplying the weight of the Oreana's bag by the percentage of raisins in it, and adding that to the product of the weight of Brandon's bag and the percentage of raisins in it. The "0.01" is used to convert the percentages from x and y to decimal form.

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Answer: 12 each

Step-by-step explanation: 72 divided by 6 = 12

Domain of f is ( -4 ,1 ) and Range of f is (4 , -5)

The domain refers to the set of possible input values.

The domain of a graph consists of all the input values shown on the x-axis.

The range is the set of possible output values, which are shown on the y-axis.

According to the graph ,

The horizontal extent of the graph is starting from -4 and ending on 1

Therefore , the domain of graph is (-4 , 1)

These points are not included in the domain , you can observe the end points of curves is not filled

The vertical extent of graph is starting from 4 and going downwards till -5

so, Range of graph is (4 , -5)

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Answer:

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

Step-by-step explanation:

Vertex form:

y=a(x-h)^2+k

h=-3, k=-8

y=a(x+3)^2-8

sub (-4,-5)

-5=a(-4+3)^2-8

a=3

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

The alternative hypothesis is Ha : μa ≠ μb Ha : μa - μb ≠ 0

Since they want to find out if the difference in the mean times spent studying by the students of the two schools is statistically significant, it means that it is a two directional test. Also called a two tailed test. The hypothesis would be as follows:

Null Hypothesis: There is no difference in the mean times spent by the schools' students.

Alternative Hypothesis: There is at least some difference in the mean times spent by the schools' students.

By using the appropriate symbols, it becomes

The null hypothesis is

H0 : μa = μb H0 : μa - μb = 0

The alternative hypothesis is

Ha : μa ≠ μb Ha : μa - μb ≠ 0

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As he rolls the dough, if length is increasing at a rate of 0.5 cm/sec, the rate at which the radius is changing when the radius is 1cm and the length is 5cm will be -0.05 cm/sec using the concept of increasing or decreasing functions.

As per the question statement, if dough is in form of a cylinder and its length is increasing at a rate of 0.5 cm/sec, we have to find the rate at which the radius is changing when the radius is 1cm and the length is 5cm.

Volume V = πr^2h, where 'r' is the radius and 'h' is the length

dV/dt = πr^2*(dh/dt) + h*2πr*(dr/dt) [Derivation wrt 't']

dV/dt = 0, as quantity of dough is same.

so at r = 1cm and h = 5cm

0 = π(1^2)*(0.5) + 5*2π*1(dr/dt)

5*2π*1(dr/dt) = -π(1^2)*(0.5)

10π*(dr/dt) = -π*0.5

(dr/dt) =  -0.05 cm/sec

Hence, as he rolls the dough, if length is increasing at a rate of 0.5 cm/sec, the rate at which the radius is changing when the radius is 1cm and the length is 5cm will be -0.05 cm/sec using the concept of increasing or decreasing functions.

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Answer:

10.7

Step-by-step explanation:

Since this is a right triangle, we can use trig functions to calculate the hypotenuse.

We know the opposite side from the angle labeled 59 degrees.

sin 59 = opp side / hypotenuse

sin 59 = 9.2/x

x = 9.2/ sin 59

x = 10.733

Answer:

$3.79x ≤ $15

Step-by-step explanation:

Answer:

x≤ 3

Step-by-step explanation:

x- number of bags

x*$3.79 ≤  $15 ⇒ x ≤ 15/3.79 ⇒ x≤ 3

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

The recursive relation of the data distribution a(n) = a ( n - 1 ) x n - ( n - 1 ).

A sequence of values is defined by a mathematical equation termed as a recursive relation, also known as recursive relation. It derives current value(s) through specified initial value(s) and previous value dependent rule(s). In essence, it generates numeric sequences.

Note that every individual unit can be derived by multiplying the preceding one with a rising integer, and subsequently subtracting a descending integer:

1 x 1 - 0 = 1

1 x 2 - 1 = 1

1 x 3 - 2 = 5

5 x 4 - 3 = 17

17 x  5 - 4 = 71

71 x 6 - 5 = 247

We can deduce the relation of a(n) = a ( n - 1 ) x n - ( n - 1 ).

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The two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. We denote the similarity of triangles here by ‘~’ symbol.

It is given that two triangles that are JKL and MNP are considered in which:

Now, from ΔJKL and ΔMNP, we have

∠K = ∠N (Given in the question)

∠L = ∠P(Given in the question)

Thus, by AA rule of similarity,

ΔJKL is similar to ΔMNP.

Therefore, the two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

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It will take 15 days for the hair to grow from 12mm to 16.5mm

By "average rate" in this context, we mean the typical or usual amount of hair growth per unit of time, which is often measured in millimeters per day. This rate can vary slightly depending on factors such as age, gender, genetics, diet, and overall health.

Let's first find out how much the hair needs to grow by subtracting its initial length (12mm) from its target length (16.5mm):

16.5mm - 12mm = 4.5mm

Now we can divide this growth by the average rate of hair growth to find the number of days it will take to grow this much:

4.5mm ÷ 0.3mm/day = 15 days

Therefore, it will take 15 days for the hair to grow from 12mm to 16.5mm.

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Answer:

32

Step-by-step explanation:

Step 1:

24 : 45 = x : 60

Step 2:

45x = 1440

Answer:

x = 32

Hope This Helps :)

The number of the cabinet doors machine will paint is 32.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that machine can paint 24 cabinet doors in 45 minutes. The number of cabinets painted in 1 hour will be calculated as below:-

24 : 45 = x : 60

45x = 1440

x = 32

Therefore, the number of the cabinet doors machine will paint is 32.

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Answer:

minium:-2................

The function f(x) = 4x² – 16x + 6 has a minimum value is –10 when the value of x is 2. Then the correct option is B.

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

The function is given below.

\(f(x) = 4x^2 -16x + 6\)

Differentiate the function, then we have

\(\dfrac{d }{dx} f(x) =\dfrac{d}{dx}(4x^2 -16x + 6) \\\\ \dfrac{d }{dx} f(x) =8x - 16 \\\)

The value of x will be

\(8x - 16 = 0\\x = 2\)

Then again differentiate the function, if the value comes negative then maxima and if the value is positive then minima.

\(f''(x) = \dfrac{d }{dx} f'(x) \\\\f''(x)=8x - 16 \\\\f''(x) = 8\\\\ f''(x) > 0\)

Then the function is minimum at 2.

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Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

Answer: 14π

Step-by-step explanation: The formula for circumference is 2 * pi * the radius. However, we are looking for the terms of pi, so we will multiply 2 times pi to get 2 pi. then we get 2 pi x 7 which gives us 14pi, the answer.

Answer:

\(\sqrt{(-\frac{806}{94}+8)^2+(-\frac{215}{94}-9)^2+ (-\frac{251}{94}-8)^2}\) Whatever this number may be

Step-by-step explanation:

The distance will be on the plane containing the point, and perpendicular to the line - which exists as long as the point doesn't sit on the line, but in that case our distance will simply be zero. Good news, since the line is given in parametric equation, the equation of the plane is easy to write by simply computing the dot product between the vector generating the line - or any multiple of it! - and the vector joining a random point x y z of the space with our given point, and setting it equal to zero. The equation of our plane is thus

\(6(x-(-8)) + 3(y-9) -7(z-8) = 0\\6(x+8)+3(y-9)-7(z-8)=0\)

We could multiply now or later, doesn't matter, so let's wait. Now, we need to know when the line passes through the plane, so let's plug the (parametric) coordinate of the line and let's see for which value of t that happens:

\(6(-2-6t+8) +3(1-3t -9) -7(-5+7t-8) =0\\6(6-6t) -3(8+3t)+7(13-7t)=0\\36-36t-24-9t+91-49t = 0\\t=103/94\)

Found this value of t, we can use it to find the coordinate of the point in common between the line and the plane:

\((-2-6\frac {103}{94};1-3\frac {103}{94}; -5+7\frac {103}{94}) = (-\frac{806}{94};-\frac{215}{94};-\frac{251}{94})\)

At this point it's simply a matter of calculating the distance between two points in 3D space, given by the usual \(\sqrt{\Delta x^2+\Delta y^2+\Delta z^2}\), whatever abomination of a number it might become:

\(\sqrt{(-\frac{806}{94}+8)^2+(-\frac{215}{94}-9)^2+ (-\frac{251}{94}-8)^2}\)

At this point is a simple exercise in number crunching which I refuse to entertain more - but please double check all calculation above in case I didn't notice something.

Answer:3 is nonlinear ,1 is function ,domain is the input and the range is the output, mx is the slope and the b is the y intercept

Step-by-step explanation: