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Question 1(Multiple Choice Worth 2 points)
(Linear Functions LC)

Which of the following graphs represents a linear function?

coordinate plane with a graph drawn that passes through the points 2 comma negative 2 and 2 comma negative 1 and 2 comma 0
coordinate plane with a graph drawn that passes through the points negative 1 comma 0 and 0 comma negative 2 and 1 comma negative 4
coordinate plane with a graph that passes through the points negative 2 comma 0 and 0 comma negative 4 and 2 comma 0
coordinate plane with a graph that passes through the points negative 3 comma 0 and 0 comma negative 3 and 3 comma 0 and 0 comma 3
Question 2(Multiple Choice Worth 2 points)
(Linear Functions MC)

Which statement best explains whether the data in the following table represents a linear or nonlinear function?


x y
−4 4
−1 2.5
0 2
4 0
The table represents a nonlinear function because the graph shows a rate of change that is decreasing.
The table represents a linear function because the graph shows a rate of change that is increasing.
The table represents a nonlinear function because the graph does not show a constant rate of change.
The table represents a linear function because the graph shows a constant rate of change.
Question 3(Multiple Choice Worth 2 points)
(Linear Functions MC)

Which of the following tables represents a linear function?


x −2 −1 0 1 2
y 5 2 1 2 5

x −2 −1 0 1 2
y 5 3 1 −1 −3

x 3 3 0 3 3
y −2 −1 0 1 2

x 0 1 2 3 4
y 0 −1 2 −3 4
Question 4(Multiple Choice Worth 2 points)
(Linear Functions MC)

Which statement best explains whether the following graph represents a linear or nonlinear function?

coordinate plane with a graph that passes through the points negative 4 comma 0 and negative 2 comma negative 1 and 0 comma negative 2

The graph represents a linear function because there is a constant rate of change.
The graph represents a linear function because the rate of change is not constant.
The graph represents a nonlinear function because there is a constant rate of change.
The graph represents a nonlinear function because the rate of change is not constant.
Question 5(Multiple Choice Worth 2 points)
(Linear Functions LC)

Which of the following equations represents a linear function?

2x − 4 = 6
x = −2
y equals one half times x squared
y equals two thirds times x plus 4
Question 6(Multiple Choice Worth 2 points)
(Linear Functions MC)

Which statement best explains whether the equation y = 3x2 represents a linear or nonlinear function?

The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a linear function because its graph contains the points (−1, 3), (0, 0), and (1, 3), which are on a straight line.
The equation represents a nonlinear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a nonlinear function because its graph contains the points (−1, 3), (0, 0), and (1, 3), which are not on a straight line.
Question 7(Multiple Choice Worth 2 points)
(Linear Functions MC)

Which statement best explains whether the following table represents a linear or nonlinear function?


x −2 −1 0 1 2
y −4 −2 0 2 4
The table represents a nonlinear function because there is not a constant rate of change in the input values.
The table represents a nonlinear function because there is not a constant rate of change in the output values.
The table represents a linear function because there is a constant rate of change in the input and output values.
The table represents a linear function because there is not a constant rate of change in the input and output values.

The inequality that represents the number of streamers x and balloons y the student council can buy is given as follows:

3.50x + 0.75y ≤ 100.

Each streamer costs $3.50, hence the total cost of purchasing x streamers is given as follows:

3.5x.

Each balloon costs $0.75, hence the total cost of purchasing y balloons is given as follows:

0.75y.

Then the total cost of purchasing x streamers and y balloons is given as follows:

3.50x + 0.75y.

The amount spent can be of at most $100, hence the inequality is given as follows:

3.50x + 0.75y ≤ 100.

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Answer: Rational functions are defined as the ratio of two polynomials. A rational function has the most solutions in common with the function y = 2x + 6 if their graphs intersect at the most points.

If a rational function has the same degree as the polynomial function y = 2x + 6, which is degree 1, and has a leading coefficient that is the same sign as the leading coefficient of y = 2x + 6, then their graphs will intersect at the most points.

One such rational function that has the same degree as y = 2x + 6 and has a leading coefficient that is the same sign is:

y = (2x + 6) / 1

So the rational function y = (2x + 6) / 1 has the most solutions in common with the function y = 2x + 6.

Step-by-step explanation:

Answer:

32.4

Step-by-step explanation:

8% of 30 is 2.4. So, 2.4 + 30 is 32.4.

Answer: 125.4

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The method that can be used to prove that the triangles are congruent is B. AAS.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

There are two angles in the two triangles that are shown to be equal and there is also a side of one triangle that is equal to anther side. These triangles are therefore congruent.

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Product of multiplication of (2+√-25) and (4-√-100) is 58.

Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1).

For example, 6+7i is a complex number, where 6 is a real number and 7i is an imaginary number.

Given complex numbers

(2+√-25) and (4 -√-100)

√-25 = √(5² . -1) = 5√-1

i = √-1

√-25  = 5i

√-100 = √(10² . -1)

√-100 = 10i

Multiplying both numbers

(2+√-25) . (4 -√-100)

then

= (2 + 5i) . (4 - 10i)

Using FOIL method

(a + b)(c + d) = ac + ad + bc + bd

= 8 - 20i + 20i - 50i²

= 8 - 50i²

i² = -1

= 8 + 50

= 58

Hence, 58 is the product of multiplication of (2+√-25)(4-√-100)

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your question is incomplete!

The reflex of angle A is 295 therefore, angle B is 295°

A reflex angle is an angle that is more than 180 degrees and less than 360 degrees. For example, 270 degrees is a reflex angle. In geometry, there are different types of angles such as acute, obtuse and right angles, which are under 180 degrees.

Given that angle B is the reflex angle of angle A, angle is measuring 65°

We need to find the measure of reflex Angle B

We know that,

To find the reflex angle of a given angle, we need to subtract the given measure from 360 degrees.

For example, the reflex angle of 110 degrees = 360 – 110 = 250.

Therefore,

Reflex Angle B = 360° - 65° = 295°

Hence, the reflex of angle A is 295 therefore, angle B is 295°

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Step-by-step explanation:

Nuclear: 6-20 cents per kWh

Coal: 5-17 cents per kWh

Gas: 5-15 cents per kWh

Wind: 2-9 cents per kWh

Hydro: 5-20 cents per kWh

Solar: 10-20 cents per kWh

The simplification process of the expression 6(4y+8)−2y involves distributing '6' to '4y' and '8', and then combining like terms, yielding the simplified expression as 22y+48.

To rewrite the given expression in simplest terms, distribute the 6 to the terms inside the parentheses:

Now subtract 2y:

So, the expression 6(4y+8)−2y can be simplified to 22y + 48.

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Answer:

3x - y - 2 = 0

Step-by-step explanation:

The line-3x - 9y - 12 is given in the general form of the equation of a line, Ax + By + C = 0, where A = -3, B = -9, and C = -12.

To find the equation of the line that passes through the point (2, -8) and is perpendicular to the line-3x - 9y - 12, we need to find the slope of the perpendicular line. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.

The slope of the line-3x - 9y - 12 can be found using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Rearranging the general form equation:

-3x - 9y - 12 = 0

9y = 3x + 12

y = (3/9)x + 4

The slope of the line is m = 3/9. To find the slope of the perpendicular line, we find the negative reciprocal:

m_perpendicular = -1 / (3/9) = -9 / 3

We have the slope of the perpendicular line, now we need to find its equation. To do this, we use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where (x1, y1) is the point through which the line passes and m is the slope of the line. Plugging in the values for the point (2, -8) and the slope -9/3:

y - (-8) = -9/3 (x - 2)

y + 8 = -3x + 6

3x - y - 2 = 0

Answer:

Step-by-step explanation:1/9

The expression (4a³b^4)³ when evaluated is 64a^9b^12

From the question, we have the following parameters that can be used in our computation:

(4a³b^4)³

When expanded, we have

(4a³b^4)³ = 4³ * (a³)³ * (b^4)³

Evaluate the exponents

So, we have the following representation

(4a³b^4)³ = 64a^9b^12

Hence, the solution si 64a^9b^12

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Answer: The original price of the lawn mower was $649

Step-by-step explanation:

If Joaquin bought the lawn mower for $519.20 after a 20% discount, it means that he paid only 80% of the original price. We can use this information to calculate the original price of the mower by setting up the following equation:

0.8x = 519.20

where x is the original price of the lawn mower. To solve for x, we can divide both sides of the equation by 0.8:

x = 519.20 / 0.8

x = $649

To select a sample of 50 students at your school in order to learn something about how many hours per week, on average, students at your school spend engaged in a particular activity, you could use random sampling.

Random sampling involves selecting a sample of individuals from a larger population in a way that ensures each individual has an equal chance of being selected. This helps ensure that the sample is representative of the larger population and can provide accurate results.

Here are the steps you could follow to select a random sample of 50 students at your school:

1. Obtain a list of all the students at your school. This could be a roster or a directory.
2. Assign each student a unique number.
3. Use a random number generator to select 50 numbers from the list of student numbers.
4. Select the students whose numbers were chosen by the random number generator as your sample.

By following these steps, you can ensure that your sample is randomly selected and representative of the larger population of students at your school. This will allow you to accurately estimate how many hours per week, on average, students at your school spend engaged in a particular activity.

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The population of the town after 10 years is expected to be about 12766

We can use the formula for exponential decay to find the population of the town after 10 years.

The formula is:

P = P₀ * (1 - r)^t

Substituting the given values into the formula, we get:

P = 25000 * (1 - 0.065)^10

Simplifying and evaluating using a calculator:

P = 12766

Hence, the population is expected to be about 12766 .

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Answer:

50%

12.5%

1%

10%

37.5%

87%

Answer:

27)50%

28)12.5%

29)1%

30)10%

31)38.4%

32)87%

The relative frequency is the proportion of the total numbers in a data set corresponds to a specific class interval and hence summing over all the relative frequencies must add up to 1, or 100%.

The frequency distribution table is made by building the class intervals of the raw data set, specifically when too many values are occurring many times; we group similar values in the same category, according to a pre-determined range of values. It is a two-column table in which the first column consists of class intervals and the second consists of the frequency corresponding to each interval.

The frequency distribution is made when the raw data is large and when the same number is repeated many times, that is where the concept of frequency comes into play.

Since, the frequency is the count of specific numbers in a data set, the sum of all frequencies corresponding to every class interval has to be the total number of values in the data set.

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The given question is incomplete, complete question is:

What is the sum of all frequencies in a frequency distribution? and why is the sum of all relative frequencies equal to 1?

Answer:

Step-by-step explanation:

To find the surface area of the silo, we need to calculate the areas of the cylinder and hemisphere separately, and then add them together.

The formula for the surface area of a cylinder is:

A_cylinder = 2πrh + 2πr^2

where r is the radius of the base of the cylinder, and h is the height of the cylinder.

In this case, r = 15 feet and h = 30 feet, so we have:

A_cylinder = 2π(15)(30) + 2π(15)^2

A_cylinder = 900π + 450π

A_cylinder = 1350π

The formula for the surface area of a hemisphere is:

A_hemisphere = 2πr^2

where r is the radius of the hemisphere.

In this case, the radius of the hemisphere is also 15 feet, so we have:

A_hemisphere = 2π(15)^2

A_hemisphere = 450π

To find the total surface area of the silo, we add the surface areas of the cylinder and hemisphere:

A_total = A_cylinder + A_hemisphere

A_total = 1350π + 450π

A_total = 1800π

Using 3.14 for π, we can approximate the total surface area as:

A_total ≈ 5652 square feet

Therefore, the farmer will need to cover approximately 5652 square feet of surface area to paint the outside of the silo.

Answer:

21

Step-by-step explanation:

21

Using the secant-secant and tangent-secant formulas, the indicated measures are:

1. x = 1

2. y = 10.

3. SU = 30

4. x = 4

5. x = 1

6. CD = 12

The secant-secant and tangent-secant formulas relates the lengths of the segments formed when two secants or a secant and a tangent intersect outside a circle.

Using the formula, we can solve for the indicated measures as explained below.

1. To find x, apply the secant-secant formula:

(7 + 17) * 7 = (13x + 8x) * 8x

168 = 168x²

168/168 = 168x²/168

1 = x²

x = 1

2. To find y, apply the tangent-secant formula:

20² = y * (y + 30)

400 = y² + 30y

y² + 30y - 400 = 0

Factorize:

(y - 10)(y + 40) = 0

y = 10 or y = -40

y cannot be negative so, y = 10.

3. Apply the secant-secant formula to find the value of x:

(x + 10 + 9) * 9 = (x + 6 + 10) * 10

(x + 19) * 9 = (x + 16) * 10

9x + 171 = 10x + 160

9x - 10x = -171 + 160

-x = -11

x = 11

SU = x + 19 = 11 + 19

SU = 30

4. Apply the tangent-secant formula:

6² = x(x + 5)

36 = x² + 5x

x² + 5x - 36 = 0

Factorize:

(x - 4)(x + 9) = 0

x = 4 or x = -9

x must be positive, therefore, x = 4

5. Apply the secant-secant formula to find x:

18*10 = 20x * 9x

180 = 180x²

1 = x

x = 1

6. Apply the tangent-secant formula:

AB² = (CD + AC) * AC

Substitute the values:

8² = (CD + 4) * 4

64 = 4CD + 16

64 - 16 = 4CD

48 = 4CD

48/4 = CD

12 = CD

CD = 12

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The length of paper he used for wrapping paper is, 702 meters²

Surface area is the sum of the areas of all the faces (or surfaces) of a three-dimensional object. It is a measure of how much area the surfaces of an object take up in two dimensions. The surface area of a solid can be found by adding up the areas of its faces.

To calculate the amount of wrapping paper needed, we need to find the total surface area of the gift box. The surface area of a right rectangular prism is given by the formula:

surface area = 2(lw + wh + lh)

where l, w, and h are the length, width, and height of the prism, respectively.

In this case, the dimensions of the gift box are 9 meters, 9 meters, and 15 meters, so:

surface area = 2(9 x 9 + 9 x 15 + 15 x 9)

                     = 2(81 + 135 + 135)

                     = 2(351)

                     = 702 square meters

Therefore, Lavaughn used 702 square meters of wrapping paper for the gift box.

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The formula for Van 't Hoff's law, which is also known as the law of osmotic pressure, is: П = iMRT, where: Π is the osmotic pressure of the solution,

i is the van 't Hoff factor, which is a measure of the number of particles a solute molecule dissociates into in solution, M is the molar concentration of the solute, R is the gas constant, and T is the absolute temperature. Van 't Hoff is a term used to refer to a Dutch chemist named Jacobus Henricus van 't Hoff, who was known for his work on solutions, chemical equilibrium, and the laws of thermodynamics. To find Van 't Hoff, you can do any of the following: Research: You can learn about Van 't Hoff by doing research on his life and work. There are many online and offline resources available that provide information about his contributions to chemistry and his scientific achievements. Education: If you are a student of chemistry, you are likely to encounter Van 't Hoff's name in your coursework. You can learn about his theories and concepts in your chemistry classes or by consulting your textbooks. Application: You can apply Van 't Hoff's laws and principles in solving problems related to chemical equilibrium, colligative properties of solutions, and other thermodynamic concepts. This may involve using mathematical formulas and equations that are based on his work. In summary, Van 't Hoff refers to a Dutch chemist known for his work in thermodynamics, solutions, and chemical equilibrium. You can learn about his contributions to chemistry through research, education, and application of his principles in problem-solving.

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Answer: You sold 16 bracelets and 21 necklaces

Step-by-step explanation

X# Bracelets        x+y=37     -2(x+y=37)     -2x-2y= -74      x+21=37

Y# Necklaces      2x+3y=95     [tex]\frac{+(2x+3y=95)}{y=21}[/tex]          x=16

              You sold 16 bracelets and 21 Necklaces

The nurse should set the IV pump to deliver 125 mL/hr in order to administer the D5W 750 mL IV over 6 hr.

The nurse should set the IV pump to deliver 125 mL/hr in order to administer the D5W 750 mL IV over 6 hr. To calculate the infusion rate, you can use the formula:

Infusion rate (mL/hr) = Volume to be infused (mL) / Infusion time (hr)

In this case, the volume to be infused is 750 mL and the infusion time is 6 hr. Plugging these values into the formula, we get:

Infusion rate (mL/hr) = 750 mL / 6 hr = 125 mL/hr

Therefore, the nurse should set the IV pump to deliver 125 mL/hr in order to administer the D5W 750 mL IV over 6 hr.

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Answer:

51,300 rupees

Step-by-step explanation:

Surface area of the 2 short walls = 2 x 30 x 2.5 = 150

Surface area of the 2 long walls = 2 x 50 x 2.5 = 250

Surface area of the floor = 50 x 30 = 1500

Total surface area = 150 + 250 + 1500 = 1900 m²

27 rupees/m² x 1900 m² = 51300 rupees

Answer:





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Class 11

>>Applied Mathematics

>>Number theory

>>Complex Numbers

>>The complex number z satisfying the equa

Question



The complex number z satisfying the equations ∣z∣−4=∣z−i∣−∣z+5i∣=0, is

This question has multiple correct options

A

3−i

B

23−2i

C

−23−2i

D

0

Medium

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Updated on : 2022-09-05

Solution



Verified by Toppr

Correct options are B) and C)

We have two equation ∣z∣−4=0 and ∣z−i∣−∣z+5i∣=0

Putting z=x+iy i.e x2+y2=16    ....(1)

and ∣x+iy−i∣=∣x+iy+5i∣

⇒x2+(y−1)2=x2+(y+5)2

⇒y=−2   ...(2)

Putting y=−2 in (1), 

x2+4=16⇒x=±2

Step-by-step explanation:

Hence the complex numbers z satisfying the given equation are 

z1=23−2i and z2=−23−2i