Factoriser A(x)=(x+2)^2

Answer:

Jennifer will choose office 3, as it has a area of 98ft

Step-by-step explanation:

1. Has a area of 96ft  ( 12 x 8 = 96 )

2. Has a area of 90ft ( 9 x 10 = 90 )

3. Has a area of 98ft ( 14 x 7 = 98 )

4. Has a area of 90ft ( 15 x 6 = 90 )

On graphing the given models we got a parabola as shown below

To graph the given equation, find the coordinate points using the given variables. In this problem, we have taken the values of t as 0, 1, and -1 from that find the values of 'h' and form the coordinate points. Now plot the resultant points as a graph.

Here we have

h = - 16t² + 12 represents the height that corn from the ground

Where t represents the time in sec

From given equation,

at t = 0 => h = 12

at t = 1 => h = - 4

at t = -1 => h = -4

Now take h = y and t = x

The coordinates we got are (0, 12) (1, -4) and (-1, -4)

Now use the above points to draw the graph as shown below  

Therefore,

On graphing the given models we got a parabola as shown below

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The mass of the yogurt is 99 grams.

A ratio is a numerical relationship showing how often one value includes or is included inside another. It is used to compare two numbers.

Given:

A dessert contains yogurt and fruit inside.

The total mass of the dessert = 165 grams.

And the ratio of the mass of fruit to the mass of yogurt is 2 : 3.

Let the mass of the fruit is 2x and the mass of the yogurt is 3x.

So, 2x + 3x = 165

5x = 165

x = 165/5

x = 33

The mass of the yogurt is 33(3) = 99 grams.

Therefore, the required mass is 99 grams.

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The prepositional phrase would be B. of the bees.

The prepositional phrase would be C. he took shelter.

A prepositional phrase is a group of words that includes a preposition (such as "in," "on," "at," "by," "with," etc.) and a noun or pronoun object, along with any associated modifiers.

Prepositional phrases can be used in a variety of ways, including to describe location, time, possession, and other relationships between words in a sentence. In the given statements, the prepositional phrases would be "of the bees" and " he took shelter. "

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Answer:whitch one are they talking about I think it might be answer 3

Step-by-step explanation:

The time it takes to evaluate 27 + 72 is not a random variable, because it is a deterministic quantity that does not involve any uncertainty or probability.

The exact time it takes to evaluate 27 + 72 is not a random variable, because it is a deterministic quantity that does not involve any element of chance or uncertainty. The result of the addition is always the same and can be calculated precisely in a finite amount of time.

Random variables, on the other hand, are variables that can take on different values with certain probabilities, and are used to model phenomena that involve uncertainty or randomness. Discrete random variables take on a countable set of values, while continuous random variables take on an uncountably infinite range of values.

In summary, the time it takes to evaluate 27 + 72 is not a random variable, because it is a deterministic quantity that does not involve any uncertainty or probability.

In mathematics, a variable is a symbol or letter that represents a value or quantity that can change or vary. Variables are used to express relationships between different quantities and to solve equations.

For example, in the equation y = 2x + 3, x and y are variables. The value of y depends on the value of x, which can vary. We can solve for the value of y for different values of x, and the solution will be a set of ordered pairs (x, y) that form a straight line when plotted on a graph.

Variables can be used to represent a wide range of quantities, including numbers, vectors, functions, and more. They are an essential tool in many branches of mathematics, including algebra, calculus, and statistics.

In addition to mathematics, variables are also used in many other fields, including science, engineering, and computer programming, to represent quantities that can change or be controlled. In these fields, variables are often used to model complex systems or to simulate experiments, and are a fundamental concept in data analysis and computational thinking.

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The solution is, Loan origination fee = $696

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

Given:

Home value = $58,000

Loan-to-value loan = 80%

Loan origination fee = 1.5 points = 1.5%

Find:

Loan origination fee = ?

Computation:

Total loan amount = Home value × Loan-to-value loan

Total loan amount = $58,000 × 80%

Total loan amount = $46,400

Loan origination fee = Total loan amount × 1.5%

Loan origination fee = $46,400 × 1.5%

Loan origination fee = $696

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By applying formula, we were able to convert 51cm to inches, which is 20.08 inches.

First, we need to understand the conversion factor between centimeters and inches. One inch is equal to 2.54 centimeters. This means that we can convert centimeters to inches by dividing the measurement in centimeters by 2.54.

To convert 51cm to inches, we will use the formula:

Measurement in inches = Measurement in centimeters / 2.54

So, to convert 51cm to inches, we will divide 51 by 2.54:

Measurement in inches = 51 / 2.54

Measurement in inches = 20.08 inches (rounded to two decimal places)

Therefore, 51cm is equivalent to 20.08 inches.

In conclusion, knowing measurement conversions is an essential skill to have, especially when dealing with different systems of measurement. To convert centimeters to inches, we divide the measurement in centimeters by 2.54.

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Answer:

52.75

i hope it helps

The given sequence is an arithmetic sequence.

An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a fixed constant called the common difference to the previous term. A geometric sequence is a sequence of numbers in which each term after the first is obtained by multiplying the previous term by a fixed constant called the common ratio.

In the given sequence

103.8 - 111 = -7.2

96.6 - 103.8 = -7.2

Similarly we can observe that each term is obtained by subtracting 7.2 from the previous term. Therefore, the common difference is -7.2, and the sequence is an arithmetic sequence.

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The north campus had 600 students and the south campus had 600 students.Using this ratio, we can solve for the total number of students at the north campus, which is 600 students (10 women x 60 = 600 students).

Before the merger, the north campus had 10% of the students as women, which is the same as saying 10 out of every 100 students were women. This means that 100 students would have been 10 women. Using this ratio, we can solve for the total number of students at the north campus, which is 600 students (10 women x 60 = 600 students). The same process can be done for the south campus, which had 50% of its students as women. This means that 50 out of every 100 students were women, which means that the total number of students at the south campus would have been 600 (50 women x 60 = 600 students). Therefore, the north and south campuses had 600 students each before the merger, for a total of 1200 students between the two campuses.

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Answer:

The x-intercept is the point where a line crosses the x-axis

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

tan x  = 110 /11

Arctan( tan x) = arctan(110/11)

   x     =   84.3°

The variable x has no true value in the similar shapes

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

The figure

Using the figure, we have the following ratio

3x : 4x - 1 = 4x - 1 : x² - x - 2

Factorize

3x : 4x - 1 = 4x - 1 : x² + x - 2x - 2

So, we have

3x : 4x - 1 = 4x - 1 : x(x + 1) - 2(x + 1)

This gives

3x : 4x - 1 = 4x - 1 : (x - 2)(x + 1)

Express as fraction

3x/(4x - 1) = (4x - 1)/(x - 2)(x + 1)

So, we have

3x(x - 2)(x + 1) = (4x - 1)(4x - 1)

Using a graphing tool, we have

x = undefined

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In an experimental study, the variable of interest is a changing quantity that would be measured. A number of these different factors, known as the original study factors, are monitored so that information on how the factors impact some other interesting as the predictor variables, or merely the response, can be obtained.

Is the variable under consideration an independent variable?

Interesting outcome variable

This is also referred to as a regression model or an interest component. It is a "input" variable that serves as a factor that what a researcher is able within a contained way to test this same impact of changing the amounts of the predictor variables on the overall result measured. An observation falls under the category of data collection case.

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63 inches is nearly equal to 160.02 cm, rounded to two decimal places.

The Imperial and US Customary measuring systems both utilise the inch as their unit of measurement.

It is the unit of length.

Furthermore, length is measured in centimetres,

Used in the International System of Units,

This is the metric system's present configuration.

52 centimetres equal 20.47 inches (centimeters).

63 inches are equal to 160.02 centimetres.

To convert inches to centimeters,

We can use the following conversion:

1 inch = 2.54 cm

Therefore,

To convert 63 inches to centimeters,

You can multiply 63 by 2.54:

63 inches × 2.54 cm/inch

= 160.02 cm

So 63 inches is nearly equal to 160.02 cm, rounded to two decimal places.

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25 kilometers is approximately equal to 15.5343 miles ( rounded to four decimal places )

The conversion factor from kilometers to miles is 0.621371.

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

So, to convert kilometers to miles you can multiply the number of kilometers by 0.621371.

The distance in kilometer = 25 kilometers

The distance in miles = conversion factor × The distance in kilometer

Substitute the values in the equation

The distance in miles = 25 × 0.621371

Multiply the numbers

=  15.5343 miles (to three decimal places).

Therefore, 25 km is 15.5343 miles

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Answer:

55%

Step-by-step explanation:

To get 55 I just divided 33/60 and multiplied it buy 100

To convert 1 cubic centimeter (cc) to ounces (oz), apply conversion factor between the two units. The conversion factor is:

1 cc = 0.033814 oz

This means that one cubic centimeter is equivalent to 0.033814 ounces.

Therefore, the mathematical expression to convert 1 cc to oz is:

1 cc * (0.033814 oz/cc) = 0.033814 oz

So, 1 cc is equal to 0.033814 ounces.

A conversion factor is a mathematical expression that expresses the relationship between two units of measurement. It is used to convert measurements between units.

Conversion factors are commonly used to convert measurements between different units of measurement in math, science, and engineering. They are a useful tool for performing calculations and comparing data in various units.

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15) The set is a basis for R² because it is linearly independent and spans R². 16) The set is not a basis for R² because it is linearly dependent. 17) The set is a basis for R³ because it is linearly independent and spans R³. 18) The set is a basis for R³ because it is linearly independent and spans R³.

Exercise 15:

To determine if the set {[5,-2],[10,-3]} is a basis for R², we need to check if the set is linearly independent and spans R².

To check for linear independence, we set the linear combination of the vectors to zero and solve for the coefficients:

c₁[5,-2] + c₂[10,-3] = [0,0]

This leads to the system of linear equations:

5c₁ + 10c₂ = 0

-2c₁ - 3c₂ = 0

Solving for c₁ and c₂ gives us c₁ = 0 and c₂ = 0, which means that the set is linearly independent.

To check for spanning, we need to determine if any vector in R² can be expressed as a linear combination of {[5,-2],[10,-3]}. Let [x,y] be an arbitrary vector in R². We can solve for c₁ and c₂ in the equation c₁[5,-2] + c₂[10,-3] = [x,y] to get c₁ = (3y - 2x)/(-20) and c₂ = (x - 5y)/(-20). Since we were able to express any vector in R² as a linear combination of {[5,-2],[10,-3]}, the set {[5,-2],[10,-3]} is a basis for R².

Exercise 16:

To determine if the set {[-4,6],[2,-3]} is a basis for R², we again need to check for linear independence and spanning.

Setting the linear combination of the vectors to zero and solving for the coefficients gives:

c₁[-4,6] + c₂[2,-3] = [0,0]

which leads to the system of linear equations:

-4c₁ + 2c₂ = 0

6c₁ - 3c₂ = 0

Solving for c₁ and c₂ gives us c₁ = c₂ = 0, which means that the set is linearly independent.

To check for spanning, we again need to determine if any vector in R² can be expressed as a linear combination of {[-4,6],[2,-3]}. Let [x,y] be an arbitrary vector in R². Solving for c₁ and c₂ in the equation c₁[-4,6] + c₂[2,-3] = [x,y] gives us c₁ = (-3y + 2x)/(-20) and c₂ = (6y - 4x)/(-20). However, we notice that the determinant of the matrix formed by the two vectors is zero, which means that the vectors are linearly dependent and cannot form a basis for R².

Exercise 17:

To determine if the set {[0,1,-2],[5,-7,4],[6,3,5]} is a basis for R³, we need to check for linear independence and spanning.

Setting the linear combination of the vectors to zero and solving for the coefficients gives:

c₁[0,1,-2] + c₂[5,-7,4] + c₃[6,3,5] = [0,0,0]

which leads to the system of linear equations:

5c₂ + 6c₃ = 0

c₁ - 7c₂ + 3c₃ = 0

-2c₁ + 4c₂ + 5c₃ = 0

Solving for c₁, c₂, and c₃ gives us c₁ = c₂ = c₃ = 0, which means that the set is linearly independent.

To check for spanning, we need to determine if any vector in R³ can be expressed as a linear combination of {[0,1,-2],[5,-7,4],[6,3,5]}. Let [x,y,z] be an arbitrary vector in R³. We can solve for c₁, c₂, and c₃ in the equation c₁[0,1,-2] + c₂[5,-7,4] + c₃[6,3,5] = [x,y,z] to get c₁ = (-5y - 6z)/(-47), c₂ = (-2x - 3z)/(-47), and c₃ = (x + y)/47. Since we were able to express any vector in R³ as a linear combination of {[0,1,-2],[5,-7,4],[6,3,5]}, the set {[0,1,-2],[5,-7,4],[6,3,5]} is a basis for R³.

Exercise 18:

To determine if the set {[1,1,-2],[-5,-1,2],[7,0,-5]} is a basis for R³, we need to check for linear independence and spanning.

Setting the linear combination of the vectors to zero and solving for the coefficients gives:

c₁[1,1,-2] + c₂[-5,-1,2] + c₃[7,0,-5] = [0,0,0]

which leads to the system of linear equations:

c₁ - 5c₂ + 7c₃ = 0

c₁ - c₂ = 0

-2c₁ + 2c₂ - 5c₃ = 0

Solving for c₁, c₂, and c₃ gives us c₁ = c₂ = c₃ = 0, which means that the set is linearly independent.

To check for spanning, we need to determine if any vector in R³ can be expressed as a linear combination of {[1,1,-2],[-5,-1,2],[7,0,-5]}. Let [x,y,z] be an arbitrary vector in R³. We can solve for c₁, c₂, and c₃ in the equation c₁[1,1,-2] + c₂[-5,-1,2] + c₃[7,0,-5] = [x,y,z] to get c₁ = (y - 7z - 1)/(-10), c₂ = (-x + z + 1)/10, and c₃ = (2x - 2y + 5z)/10. Since we were able to express any vector in R³ as a linear combination of {[1,1,-2],[-5,-1,2],[7,0,-5]}, the set {[1,1,-2],[-5,-1,2],[7,0,-5]} is a basis for R³.

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Complete question:

Determine which sets in exercises 15–18 are bases for R² or R³. justify each answer!

15. {[5,-2],[10,-3]}

16. {[-4,6],[2,-3]}

17. {[0,1,-2],[5,-7,4],[6,3,5]}

18. {[1,1,-2],[-5,-1,2],[7,0,-5]}

200 pounds is approximately equal to 90.7185 kg ( rounded to four decimal places )

To convert 200 pounds to kg, we can use the following formula:

1 pound = 0.453592 kg

The conversion factor is 0.453592

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The mass in kg = conversion factor × The mass in pounds

Substitute the values in the equation

The mass in kg = 0.453592 × 200

Multiply the numbers

= 90.7185 kg  ( rounded to four decimal places )

Therefore, 200 pounds is 90.7185 kg

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Answer:

Step-by-step explanation:

792!

Answer:

792

Step-by-step explanation:

First she increases 800 by 10 percent

Since 10 percent of 800 is 80, it becomes 880

then she decreases this result by 10 percent

since 10 percent of 880 is 88, the result becomes 880-88=792

Therefore 792 is the final number

Answer: We can use the formula for the price elasticity of demand to solve this problem:

Price elasticity of demand = percent change in quantity demanded / percent change in price

We are given that the price of chicken breast rises from $3.00 to $3.60 per pound, which is a 20% increase:

percent change in price = (3.60 - 3.00) / 3.00 = 0.20 = 20%

We are also given that the demand for chicken breast falls by 25%, which is a 25% decrease:

percent change in quantity demanded = -25%

Using these values in the formula, we get:

Price elasticity of demand = (-25%) / (20%) = -1.25

Since we are interested in the absolute value of the price elasticity of demand, we have:

|Price elasticity of demand| = |-1.25| = 1.25

A price elasticity of demand greater than 1 is considered elastic, and a price elasticity of demand less than 1 is considered inelastic. Therefore, the answer is (d) 1.25; elastic.

Step-by-step explanation:

Volume of a cone

1/4π ft³

To find the volume of the cone, we use the formula

volume = (1/3) × π × r² × h

From the question, we are given its height and radius

we substitute for these in the equation above. these will give us the answer. (note in terms of pi)

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Answer:

As x --> ∞, then y --> - ∞

Step-by-step explanation:

As the value of x increases(as the graph goes right), the graph seems to go down, meaning the y-values are getting more an more negative. This means that as x approached infinity, the y values approach negative infinity ( x --> ∞, y --> - ∞ ).

As the value of x decreases(going to the left), the graph seems to go higher and higher. Therefore, as x approaches negative infinity, the y-value approach infinity. ( x --> - ∞, y --> ∞ )

Out of the options given, the one As x --> ∞, then y --> - ∞ is true.

The steps to calculate the retirement bank rate are

1) Calculate your current retirement savings

2) Estimate your future retirement savings

3) Calculate your retirement savings rate

4) Adjust your savings rate as needed

Calculating your retirement savings rate can be a helpful way to ensure you're saving enough money to support your retirement. Here are the steps to calculate your bank rate retirement online:

Calculate your current retirement savings: You'll need to calculate the total amount of money you've saved for retirement so far,

Estimate your future retirement savings: You can use an online retirement calculator to estimate the amount of money you'll have saved by the time you retire based on your current savings rate,

Calculate your retirement savings rate: To calculate your retirement savings rate, divide your total retirement savings by your retirement savings goal.

Adjust your savings rate as needed: If your retirement savings rate is lower than you'd like, consider increasing your savings rate by contributing more money to your retirement accounts or exploring other investment options.

It's important to keep in mind that retirement planning is a complex process, and there are many factors that can impact your retirement savings rate, such as inflation, unexpected expenses, and changes in the stock market.

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The value which is converted from Celsius to Fahrenheit is given by 38 Celsius is equal to 89.6 Fahrenheit.

Units which represents the measurement of the temperature in standard form Celsius and Fahrenheit .

Formula which relates the Celsius and Fahrenheit are given by

(°C × 9/5) + 32 =°F

Now Substitute the value 32 Celsius which needs to convert  into Fahrenheit we get,

(32°C × 9/5) + 32

= ( 288 / 5 ) + 32

= ( 57.6 ) + 32

= 89.6°F

Therefore, the converted value from Celsius to Fahrenheit for the given 32 Celsius is given by 89.6 Fahrenheit.

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The above question is incomplete , the complete question is:

What is the conversion of 32°C to °F ?

To verify equivalent expressions, you need to evaluate the expressions for different values of x and compare the results. For the given list of x values (0, 1, 2), you can plug them into the two equations one at a time and compare the results.

For x=0:

Equation 1: 0

Equation 2: 0

For x=1:

Equation 1: 1

Equation 2: 1

For x=2:

Equation 1: 4

Equation 2: 8

Since the results of the equations do not match for x=2, the expressions are not equivalent.

To verify equivalent expressions, you can plug in the given values of x into the equations and see if they produce the same result. Here are the steps to do this:

1. Take the first equation and plug in the value of x. For example, if the equation is y = 2x + 1 and x = 0, then y = 2(0) + 1 = 1.

2. Do the same for the second equation with the same value of x. For example, if the second equation is y = x + 1 and x = 0, then y = 0 + 1 = 1.

3. Compare the results of the two equations. If they are the same, then the expressions are equivalent for that value of x.

4. Repeat these steps for the other values of x (1 and 2) and fill out the rest of the table with the results.

5. If the expressions produce the same result for all values of x, then they are equivalent expressions.

I hope this helps! Let me know if you have any further questions.

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The vertex form of the quadratic equation is:

h(t) = -42*(x - 3)² + 378

And the maximum height is 378 ft.

We know that the height of the projectile is defined by the quadratic equation:

h(t) = -42t² + 252t

Remember that for any quadratic equation:

y = a*x² + b*x + c

The vertex is at:

x = -b/2a

So in this case, the vertex is at:

t = -252/(2*-42)

t = 3

So the maximum height of the projectile is:

h(3) = -42*3² + 252*3 = 378

And thus, the vertex is (3, 378), then the vertex form is:

h(t) = -42*(x - 3)² + 378

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