Create the polynomial which has roots 3and 2

Answer:

BD - HF

CD - GH

AC - EG

The equation in slope-intercept form of line k is y = - x + 5.

What is the equation of the line?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

The equation of a line in slope- intercept form is

y = mx + c

where,

   m is the slope and c the y- intercept.

We have,

y = x - 3

∴  It is in the slope intercept form.

with slope m = 1

Given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular} = -\frac{1}{m} = -\frac{1}{1} = -1\) ,

The partial equation of line j is,

y = - x + c

By substituting (2, 0) into the partial equation we get, c

0 = - 2 + c

c = 0 + 2 = 2

∴ c = 2

The equation of line j is y = - x + 2.

Similarly,

The slopes of parallel lines are the same.

The partial equation of line k is,

∴ y = - x + c

By substituting (- 1, 6) into the partial equation we get, c

6 = 1 + c

c = 6 - 1 = 5

∴ c = 5

The equation of line k is y = - x + 5.

Therefore, the equation in slope-intercept form of line k is y = - x + 5.

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The geometric mean is used to determine the average annual percent increase, as it accurately accounts for compounding growth over multiple periods. The correct option is E.

The measure of central tendency that is typically used to determine the average annual percent increase is the arithmetic mean. This measure takes the sum of all the values and divides it by the total number of values.

It is important to note that other measures, such as the geometric mean, can also be used in certain situations. But for most cases, the arithmetic mean is the go-to measure for determining the average annual percent increase.

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Answer:

The median of the data set is 18.5

Step-by-step explanation:

To find the median of this set of data values, we need to first arrange them in numerical order:

10, 14, 15, 17, 20, 21, 22, 25

The middle value is the median. If there is an odd number of values, there will be exactly one middle value, and if there is an even number of values, the median will be the average of the two middle values.

In this case, there are 8 values, which is an even number. So, we take the average of the sum of the 2 middle numbers:

Median of Data Set = (17 + 20)/2 = 18.5

Therefore, the median of the data set is 18.5.

The research reveals that emotional people tend to be more satisfied with their jobs, committed to their employer, and produce more work than conscientious individuals is False.

Emotional intellect is the capacity to recognize and regulate a person's emotions and comprehend the emotions the others. A high EQ helps you to build connections, lower team stress, defuse battles and improve job fulfillment.

It can help a graduate evolve the best at what they do, be the best coworker possible, and achieve professional victory. Communication, partnership, and relationship-building skills are enhanced by higher levels of emotional intelligence. It also enables best focus on the work.

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The complete question is-

research reveals that emotional people tend to be more satisfied with their jobs, committed to their employer, and produce more work than conscientious individuals.

a. True

b. False

EXPLANATION:

We are given the following details for a triangular prism;

Note that for the rectangular base, one side is 3 times the other. Hence, if the width is w, then the length would be 3 times w.

The surface area of a rectangular prism is;

With the side lengths given we can now substitute and we'll have;

Divide both sides by 2;

We shall now move all terms to one side of the equation;

We can now solve this quadratic equationwith the quadratic equation formula;

Where the variables are;

We now have two solutions. We shall take the positive one since our side lengths cannot be a negative value.

Therefore having the width as 3, the length which is 3 times the width is 3 times 3 and that gives 9.

Therefore;

ANSWER:

Answer:

point U

Step-by-step explanation:

I learned this before

Hope this helps

A 50 percent increase in Earth's albedo, which refers to the reflectivity of its surface, would lead to a decrease in average surface temperatures.

Albedo plays a crucial role in determining how much of the sun's energy is absorbed or reflected by the Earth. The given information states that approximately 30 percent of the sun's energy is currently reflected back into space. If Earth's albedo increases by 50 percent, meaning more energy is reflected, it would result in less energy being absorbed by the Earth's surface and atmosphere.

The increased albedo would cause a higher percentage of the incoming solar radiation to be reflected and scattered back into space. With less energy being absorbed, the average surface temperatures would decrease. This is because less solar energy would be available to warm the Earth's surface and drive atmospheric processes that contribute to temperature regulation. Therefore, a 50 percent increase in Earth's albedo would likely lead to a cooling effect and lower average surface temperatures on our planet.

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Answer:

I believe it's C

Step-by-step explanation:

The surface area of the bottom is 64 because it's 8 times 8.

All of the sides are 8 times 12.

8 times 12 is 96.

96 times 4 (for all four sides) is 384.

So the sides (384) plus the bottom (64) is 448, or C

True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

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When converting degrees to radians, we use the formula:Radians = degrees x (π/180)Let's now use the formula to convert -300 degrees to radians:-300 x (π/180) = -5π/3So, the radian measure of -300° is -5π/3.
To convert -300° to radians, follow these steps:

Step 1: Recall the conversion factor between degrees and radians: 1° = π/180 radians.

Step 2: Multiply the given degree measure by the conversion factor: -300° * (π/180 radians).

Step 3: Simplify the expression: -300π/180.

Step 4: Reduce the fraction: -5π/3.

So, the radian measure of -300° is -5π/3.

The one-sample Z test is used when we want to know whether our sample comes from a particular population. The name of the one-sample Z test tells us the general research design of studies in which this statistic is selected to test hypotheses.

For instance, we are doing research on data collected from successive cohorts of students taking the Elementary Statistics class. We may want to know if this particular sample of college students is similar to or different from college students in general. The one-sample Z test is used only for tests of the sample mean. Thus, our hypothesis tests whether the average of our sample (M) suggests that our students come from a population with a know mean (m) or whether it comes from a different population.

The statistical hypotheses for one-sample Z tests take one of the following forms, depending on whether your research hypothesis is directional or nondirectional. In the equations below m1 refers to the population from which the study sample was drawn; m is replaced by the actual value of the population mean.

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Answer:

Mary bought 6 pounds of coffee

Step-by-step explanation:

80 - 30.74 = 49.26

49.26 divided by 8.21 =6

Answer:

5/8

Step-by-step explanation:

The number of possible outcomes after flipping 3 coins is $2 \times 2 \times 2 = 8$. If the dime isn't heads, we need both the penny and nickel to be heads. If the dime is heads, the other two could be anything. So there are a total of $1+(2 \times 2)=5$ ways for us to get at least 6 cents. The answer is $\boxed{\dfrac58}.$

Answer:yes

Step-by-step explanation:because it make sense that way

Answer:

26.69

Step-by-step explanation:

The question lacks the required diagram. Find the diagram attached

The missing side is x;

From the triangle we are given;

Opposite = x

Hypotenuse = 29

Angle of elevation = 67 degrees

Using the SOH CAH TOA identity;

Sin theta = opposite/hypotenuse;

sin 67 = x/29

x = 29sin67

x = 29(0.9205)

x = 26.69

Hence the length of the missing side is 26.69

All trigonometric ratios of triangle PQR were calculated.

In the given right triangle PQR

PR = 14

QR = 50

So, using Pythagoras' theorem

PQ = 48

Sine of an angle = Opposite side / Hypotenuse

cosine of an angle = Adjacent side/ Hypotenuse

Tangent of an angle = Opposite side/ Adjacent side

So, SinQ = 14/50 =7/25      

CosecQ = 1/SinQ = 25/7

CosQ= 48/50 = 24/25

SecQ = 1/CosQ = 25/24

TanQ = 14/48 = 7/24

CotQ = 1/tanQ = 24/7

SinR=24/25

CosecR = 1/SinR= 25/24

CosR=7/25

SecR = 1/Cosr = 25/7

TanR =24/7

CotR = 1/tanR = 7/24

Thus, All trigonometric ratios of triangle PQR were calculated.

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Answer:

1) n + 12

2) n + 7

3) 15x

4) 2y - 20

5) \( \dfrac{x}{-2} + 7 \)

6) 2n - 3

7) 3(12 + x)

First, we need to determine an equation for both Arcade X and Arcade Y.

Arcade X: 0.65t + 5 = P

Arcade Y: 0.45t + 10 = P

If you graph both lines, we will find the solution to be (25, 21.25), which means that D. 25 tokens will need to be bought in order for the total cost in both arcades to be the same.

I have included the graph here.

Answer:

Step-by-step explanation:

Given  g (x) = \(\frac{x+1}{x-2}\) and \(h(x) = 4-x\), we are to find \((goh)(-3)\)

First we need to get \((goh)(x)\)

\((goh)(x) = g(h(x))\\g(h(x))= g(4-x)\\g(4-x) = \frac{(4-x)+1}{(4-x)-2}\\ g(4-x) = \frac{5-x}{2-x}\\substitute \ x = -3 \ into \ resulting \ function\\ g(4-x) = \frac{5-x}{2-x}\\(goh)(-3) = \frac{5-(-3)}{2-(-3)}\\\\(goh)(-3) = \frac{8}{5}\\\)

Hence \((goh)(x)\ is \ Eight-fifths\)

Also given f(x) = x and g(x) = 1/x, we are to find \((fog)(x)\)

\((fog)(x) = f(g(x))\\f(g(x)) = f(\frac{1}{x} )\\ since \ f(x) = x^2, we\ will \ repalce\ x \ with \ \frac{1}{x} \ to \ have;\\ f(\frac{1}{x} ) =( \frac{1}{x})^2\\\\\)

\(f(\frac{1}{x} ) = \frac{1}{x^2}\)

For the pair of function f(x) = 2/x and g(x) = 2/x

f(g(x)) = f(2/x)

f(2/x) = 2/(2/x)

f(2/x) = 2*x/2

f(2/x) = x

Hence f(g(x)) = x

For the pair of function f(x) = x-2/3 and g(x) = 2-3x

f(g(x)) = f(2-3x)

f(2-3x) = (2-3x-2)/3

f(2-3x) = -3x/3

f(2-3x) = -x

f(g(x)) = -x for the pair of function

For the pair of function f(x) = x/2 - 2 and g(x) = x/2 + 2

f(g(x)) = f(x/2 + 2)

f(x/2 + 2) = f((x+4)/2)

f((x+4)/2) =  [(x+4)/2]/2 - 2

f((x+4)/2) =  (x+4)/4 - 2

find the LCM

f((x+4)/2) =  [(x+4)-8]/4

f((x+4)/2) =  (x-4)/4

Hence f(g(x)) for the pair of function is (x-4)/4

Answer:

The range of g(x) is y > 0

The ranges of f(x) and h(x) are different from the range of g(x)

We will have the following:

From the polynomial we will have that:

*It falls to the left and rises to the right.

This can be seeing as follows:

FMECA is a bottom-up hardware approach to risk assessment. It is an inductive, or data-driven, linking elements of a failure chain as follows: Effect of Failure, Failure Mode, and Causes/Mechanisms. To estimate the reliability of software, most software prediction models use the probability density function to predict "Mean Time To Failure."

FMECA is a systematic and structured analytical methodology used to identify potential failures in a system, equipment, process, or product, and to assess the effect and probability of those failures. FMECA stands for Failure Modes, Effects, and Criticality Analysis. FMECA is similar to FMEA (Failure Modes and Effects Analysis) in that it is used to identify failure modes and assess their risk.

However, FMECA goes beyond FMEA by analyzing the criticality of each failure mode. This makes it an effective tool for identifying the most significant failure modes and prioritizing them for corrective action. A Probability Density Function (PDF) is a function that describes the likelihood of a random variable taking on a particular value.

PDF is used in software prediction models to estimate the reliability of software by predicting "Mean Time To Failure" (MTTF). MTTF is the average time between failures of a system, equipment, process, or product.

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Answer:

V = x³ - 3x² + 3x - 1

Step-by-step explanation:

The volume (V) of a cube is calculated as

V = s³ ( s is the measure of the side )

Here s = x - 1 , thus

V = (x - 1)³

   = (x - 1)(x - 1)(x - 1) ← expand the second pair using FOIL

   = (x - 1)(x² - 2x + 1) ← distribute

   = x³ - 2x² + x - x² + 2x - 1 ← collect like terms

   = x³ - 3x² + 3x - 1

The correct choice is within your skills and abilities.

Once you get to determine things you are capable of and things you are not capable of, you will be able to concentrate on your strengths more. This will in turn produce big results as compared to if you opted to concentrate on your weaknesses.

It will also result in no or less time wasted in doing what you are less capable of.

Its almost close to impossible to be able to do everything. Each person is gifted in a certain area or skill or capability. We are all different and that's okay.

Its so important to concentrate in the areas you are more comfortable with. This will help you much with improving your skills and abilities.

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Answer:

Step-by-step explanation:

a you just had to say a

The correct answers are :

(5x)² ≥ 46

x² + 5x ≤ 46

5x² > 46

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Here, Suppose number is x

1)  The square of the product of 5 and a number is not less than 46.

Step 1

Product of 5

5x

Step 2

Square of product of 5

(5x)²

Step 3

A number is not less than 46

(5x)² ≥ 46

2)  The sum of square of a number and five times that number is not more than 46

Step 1

Square of a number

x²

Step 2

Five times that number

5x

Step 3

The sum = x² + 5x

Step 4

Is not more than 46

x² + 5x ≤ 46

3)  The product of 5 and the square of a number is greater than 46

Step 1

The square of a number

x²

Step 2

The product of 5

5x²

Step 3

Is greater than 46

5x² > 46

Thus, The correct answers are :

(5x)² ≥ 46

x² + 5x ≤ 46

5x² > 46

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The required value of  polynomial is f(x) = x² - 35x + 219.

To find the smallest possible value of the polynomial f(x), we need to consider the smallest possible values for x. Given that f(7) = 23 and f(8) = 3, we can use these equations to form a system of equations.

Let's write the system of equations:
f(7) = 23, which means a(7²) + b(7) + c = 23
f(8) = 3, which means a(8²) + b(8) + c = 3

Simplifying these equations, we get:
49a + 7b + c = 23
64a + 8b + c = 3

To solve this system of equations, we can subtract the second equation from the first:
(49a + 7b + c) - (64a + 8b + c) = 23 - 3
49a - 64a + 7b - 8b = 20
-15a - b = 20

Now, we need to find the smallest possible value for a. Since a is an integer, we want the coefficient of a to be as small as possible. If we let a = 1, the coefficient becomes -15. This means that the absolute value of b will be minimized, resulting in the smallest possible value of the polynomial.

Plugging in a = 1 into the equation, we have:
-15(1) - b = 20
-15 - b = 20
-b = 20 + 15
-b = 35
b = -35

Now, we can substitute the values of a and b back into one of the original equations to find c:
a(7²) + b(7) + c = 23
(1)(49) + (-35)(7) + c = 23
49 - 245 + c = 23
-196 + c = 23
c = 23 + 196
c = 219

Therefore, the polynomial is f(x) = x²- 35x + 219.

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The inverse of (- 2 . 3 ) is (1 / - 2.3 ).

In mathematics, the inverse of a number refers to the concept of taking its reciprocal; for instance (2 . w ) results in its reciprocal as ( 1/ 2. w ). When a number is multiplied by its inverse the result yields 1, meaning that the product of the number and its inverse, i.e. reciprocal always equals 1.

As per the given number which is (-2.3) and its inverse is ( 1 / -2.3 ), when these two numbers are multiplied together they result in 1. Such as:

(-2.3) x ( 1 / -2.3 ) = 1

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Answer:

-250

Step-by-step explanation:

Answer:

x=30°

Step-by-step explanation:

Find angles of the triangles:

Angles on a straight line:

180°-120°=60°

Opposite angles(intersection property):

55°= 55°

Sum of angles in a triangle = 180°

So:

------>60°+55°+2x+5=180°

------>120°+2x=180°

------>2x=180°-120°

------>2x=60°

------>x=60/2°

------>x=30°

let an agle be 'a' and 'b' ,

120°+a=180° ( linear pair )

a=120°-180°

a=60°

b=55°(opposite angle )

a+b+2x+5=180°(angle sum property)

60°+55°+2x+5=180°

120°+2x=180°

2x=180-120

2x=60

x=60/2

x=30

hence, the value of x is 30

The probability that the next buyer of this automobile will desire an automatic gearbox or built-in GPS is 0.95, or 95%.

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

Event A: Requesting automatic transmission

Event B: Requesting built-in GPS

90% of all buyers request automatic transmission

\(P (A) 0.9\)

82% of all buyers request built-in GPS

\(P (B) 0.82\)

77% of all buyers request both automatic transmission and built-in GPS.

\(P (A n B) 0.77\)

This is P(AU B), which is given by:

\(u B) P(A) + P(B) - n B)\\so U B) 0.9 + 0.82 — 0.77 0.95\\\)

The probability that the next buyer of this automobile will desire an automatic gearbox or built-in GPS is 0.95, or 95%.

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Answer:

60 square foot

Step-by-step explanation:

Perimeter of a rectangular garden = 58 foot

Let x and y denote length and width of the rectangular garden.

2 (Length + Width) = Perimeter of the rectangular garden

\(2(x+y)=58\\x+y=\frac{58}{2}\\ x+y=29\)

So,

length = x

width = y = \(29-x\)

The length is reduced by 7 feet and the width becomes half.

New length = \(x-7\)

New width = \(\frac{1}{2}(29-x)\)

New perimeter = 34 foot

\(2[(x-7)+\frac{1}{2}(29-x)]=34\\ 2[2(x-7)+(29-x)]=2(34)\\2(x-7)+(29-x)=34\\2x-14+29-x=34\\2x-x-14+29=34\\x+15=34\\x=34-15\\x=19\)

So,

New length \(=x-7=19-7=12\,\,foot\)

New width = \(\frac{1}{2}(29-19)=\frac{1}{2}(10)=5\,\,foot\)

Area of the new smaller garden = New length × New Width

= 12 × 5

= 60 square foot