Your cousin is building a new house. The layout of the first floor is shown in the diagram above. Using the
diagram and knowledge of polynomials find the following:
1. Write a polynomial that represents the length of the north side of the house. Then simplify the
expression.
2. Write a polynomial expression that represents the area of the kitchen. Then multiply to put the
polynomial in standard form.
3. Write a polynomial expression that represents the area of the bedroom. Then multiply to put the
polynomial in standard form.
4. Find the dimensions of the bathroom in terms of x. (Hint the west and east side of the house
should be equal.)

The height of the room is 5 m.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Length = 7 m

Width = 2 m

Height = x

Four walls of a room will have,

Two walls of length x height.

Two walls of Width x height.

Now,

Area four walls of the room = 90 m

2 (length x height) + 2 (Width x height) = 90

2 (7x) + 2 (2x) = 90

14x + 4x = 90

18x = 90

x = 5

Thus,

Height of the room = 5 m.

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Step-by-step explanation:

The area of a rectangle is given by the formula:

Area = length * width

In this case, the length of the rectangle is given by x + 3 and the width is given by x - 4.

Therefore, the area of the rectangle is:

Area = (x + 3) * (x - 4)

The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (length + width)

In this case, the length of the rectangle is given by x + 3 and the width is given by x - 4.

Therefore, the perimeter of the rectangle is:

Perimeter = 2 * ((x + 3) + (x - 4)) = 2x - 2

So the area of the rectangle is (x + 3)(x - 4) and the perimeter is 2x - 2.

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Answer: Area= x^2-x-12  ,  Perimeter = 4x-2

Step-by-step explanation: According to the question,

Length = x+3

Breadth = x-4

Area of a rectangle = Length * breadth

Area = (x+3)(x-4)

Area = x^2-x-12

Perimeter of rectangle = 2*(length+ breadth)

Perimeter = 2* (x+3+x-4)

                 = 2*(2x-1)

                 = 4x-2

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The linear specific solution of the form [tex]y= mx + b[/tex] where [tex]m + b = 4- 2 = 2[/tex]

Differential equation that cannot be separated:

Non-separable differential equations are those that are incapable of being written as-  [tex]\frac{dy}{dx} = f(x) g(y)[/tex]

In other words, the differential equations that cannot be separated are referred to as non-separable differential equations.Differential equations with non-separable variables are those in which the variables cannot be separated. These equations are difficult to solve and call for techniques that will be covered in upcoming courses, such as numerical or analytical approaches.

Given is the equation,

[tex]\frac{dy}{dx} = 8x - 2y[/tex]

[tex]y = 4x - 2 + ex^{-2x}[/tex]

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The speed at which Shola climbed is 5 m/s and the time taken by Shola to reach the edge is 6 seconds.

According to the question

Given:

The total distance traveled by Shola = 30 meters

He covered a total distance of 22.5 meters  (i.e. 30 meters - 7.5 meters) in 4.5 seconds.

His speed is thus 5 m/s since speed is equal to both distance and time.

Since he has 7.5 meters to cover, the remaining distance,

Therefore, the time it took him to travel the distance was 7.5/5, or 1.5 seconds.

Consequently, the total amount of time needed to go 30 meters,

T=4.5+1.5=6, or one second.

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Answer:

Step-by-step explanation:

Just use a calculator

The perimeter of the rectangle is (29.5t+7)feet

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference.

To find the perimeter of the rectangle we add a the sides together i.e

p = l+l+w+w

p = 2(l+w)

p =2 ( 8.25t - 6.5+ 6.5t + 10)

p = 2( 14.75t + 3.5)

p = (29.5t + 7) feet

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The trigonometric equation 7cos(9x) - 1 = 17 has an undefined solution.

The trigonometric equation for this problem is defined as follows:

7cos(9x) - 1 = 17

Isolating the cosine, we have that:

7cos(9x) = 18

cos(9x) = 18/7

Now we isolate x applying the arc cosine, which is the inverse of the cosine, as follows:

9x = arccos(18/7)

9x = undefined.

The solution is undefined because the arccosine only exists for values between -1 and 1, as the cosine of an angle is always going to assume a value between -1 and 1.

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Answer:

where's the graph?

Step-by-step explanation:

The value of x is 15 and the angles in the pentagon are 105,49,90,33,83

What is interior angles in a pentagon ?

The interior angles in a pentagon are the angles which are inside the pentagon and sum of the interior angles in a pentagon is 540 degrees.

Given ,

From the figure we can say that it is pentagon.

And the sum of exterior angles in a pentagon is always 360 degrees.

SO,

7x+49+6x+33+83 = 360

13x + 165 = 360

13x = 360 - 165

13x = 195

x = 195 / 13

x = 15

So, the angles could be 7x = 7*15 = 105  and 6x = 6*15 = 90

Therefore, The value of x is 15 and the angles in the pentagon are 105,49,90,33,83 .

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The solution is, A. About 257 jars, the employee can complete in 1 hour.

Here, we have,

given that,

Given that it takes an employee about 14 seconds to lift, close, fill, and shelve a jar of peanut butter,

To calculate this, you would take the number of seconds in an hour

(60 seconds/minute * 60 minutes/hour = 3600 seconds)

and divide it by the number of seconds it takes to complete one jar

(14 seconds/jar).

3600 seconds / 14 seconds/jar

= 257 jars/hour.

so, About 257 jars, the employee can complete in 1 hour.

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Answer:

The constant of a polynomial function is the coefficient of the term with the highest degree (the term with the highest power of x), which in this case is 0. Therefore, the constant of the polynomial function f(x)=-(x+3(x+7)²(x-1)⁵(x+1)⁷(x-4) is 0.

A statement which best compares the heights of the bars of the bar chart include the following: B. There are 3 times as many people in the Burgers group as in the Pasta group.

In order to better understand and compare number of people who attended her food festival and their favorite food items, we would take note of the following important information;

Based on the information provided above, we can reasonably and logically deduce that the rectangular bar representing Burgers bar with a numerical value of 60 is three times as tall as the rectangular bar representing Pasta bar with a numerical value of 20.

Burgers bar = 20 × 3

Burgers bar = 60 people.

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Answer:  B. There are 3 times as many people in the Burgers group as in the Pasta group.

Step-by-step explanation: <3

The standard error of the mean for these data is 13.14 pounds..

The standard error of the mean (SEM) is a measure of the variability of the sample mean. It is calculated as the standard deviation of the sample divided by the square root of the sample size.

To find the SEM for the given data, we first need to calculate the sample mean:

(160 + 215 + 195) / 3 = 190

Then we need to calculate the deviation of each value from the mean:

160 - 190 = -30

215 - 190 = 25

195 - 190= 5

Next, we need to square these deviations:

(-30)² = 900

25² = 625

5² = 25

Next, we need to calculate the variance:

(900 + 625 + 25) / 3 = 516 2/3

Then we need to calculate the standard deviation:

√(516 2/3) = 22.73

Finally, we can calculate the standard error of the mean:

22.73 / √(3) = 13.14

So, the standard error of the mean for these data is 13.14 pounds.

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The choices that describe an exact number are option b, option c, option d, and option e because they show a definite countable quantity with 100% accuracy.

The following options describe an exact number:

b. The house has four bedrooms.

c. There is one gram of salt in this beaker.

d. You drank one liter of water.

e. The little dog weighs 10 kilograms.

These numbers are exact because they are specific measurements that are not subject to uncertainty. They are countable and defined. While "you ran two miles" or "you drank one liter of water" could be approximate measurements.

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Upon factorization, The factors of the equation be x = 1, x = -2 + 3i, x = -2 - 3i and x = 1.

In mathematics, factorization or factoring is the process of breaking down one entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication produces the original number, matrix, etc.

Factorization is the process of shrinking the bracket of a quadratic equation, as opposed to widening the bracket and turning the equation into a product of factors that cannot be further reduced.

To solve a quadratic equation by factoring, factor the expression, set each factor equal to 0, and then solve each equation. To accomplish this, set up the terms in the equation so that the other side equals 0.

Let the given equation be f(x) = 2x³ + 6x² + 18 x - 26 and x - 1 then

2x³ + 6x² + 18x - 26 = 0

Factor 2x³ +6x² +18x-26: 2(x-1) (x²+4x+13)

2(x-1) (x²+4x+13) = 0

Using the Zero Factor Principle: If ab=0 then a=0 or b=0, x-1=0 or

Solve - 1=0:

x = 1

Solve x² + 4x + 13 = 0: x² + 3i, x = - 2 - 3i

The solutions are

x = 1, x = -2+31, x = -2 - 31

The given equation be x - 1,

x-1= 0 then x = 1.

Therefore, the factors of the equation be x = 1, x = -2 + 3i, x = -2 - 3i and x = 1.

The complete question is:

If f(x) = 2x²+6x²+18x-26 and x-1 is a factor of f(x), then find all of the zeros of f(x) algebraically.

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Answer:

1935

Step-by-step explanation:

Step 1: If 4% of a number is 77, then what is 100% of that number? Setup the equation.

77

4% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

4Y = 77 x 100

4Y = 7700

Y = 7700

100 = 1,925

Answer:

[D] -45 + 54x

Step-by-step explanation:

Base on the given we can use the distributive property to solve this:

Distributive property ⇒ Multiply outside numbers with each term inside the parenthesis.

-9 (5 - 6 x )  → {-9 × 5 = -45 } {-9 × -6x = 54x}

Now let's put it together;

-45 + 54x

Hence, [D] -45 + 54x is the correct answer.

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Answer:

a. The population is 100 college students.

b. The population is finite.

c. Two parameters and their values:

The total population size: 100

The sample size: 10

d. The sample is a group of 10 college students chosen from the population of 100.

e. Two corresponding statistics and their values:

The sample proportion: This is the proportion of individuals in the sample who have a certain characteristic (e.g. majoring in a certain subject). It is calculated by taking the number of individuals with the characteristic and dividing by the sample size. Its value would be different for each sample of size 10 taken.

The sample mean: This is the average of the measurements for the individuals in the sample. It is calculated by summing up the measurements and dividing by the sample size. Its value would be different for each sample of size 10 taken.

f. When another sample of size 10 is taken, the population and its size remains fixed but sample proportion and sample mean would change.

Step-by-step explanation:

Answer: 23,600

Step-by-step explanation: 120x2 = 240, 240x15 = 3600. 20,000 + 3600 = 23,600

B

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As per the triangles ABC and SDC are similar triangles then Gilligan can conclude that triangles ABC and SDC are similar and Gilligan can conclude that the distance of the ship from the shore is 509 feet.

The term called triangle in math is defined as a three-sided polygon, which has three vertices

Here from the question we understand points S, C and A are collinear, here we have know that line AB and SD are vertical and parallel lines at the either sides of point C.

So we can conclude that triangles ABC and SDC are similar.

The distance from the ship is calculated as,

=> SD: 130 = AB: 23

Here we have to substitute 90 for AB, then we get,

=> SD: 130 = 90: 23

When write it as,

=>SD/130 = 90/23

When we simplify this then we get  Gilligan can conclude that the distance of the ship from the shore is 509 ft

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Answer:

[tex] \frac{3}{4} + \frac{1}{3} \\ \frac{ \: \: 9 \: \: + \: \: 4 \: \: }{12} \\ \frac{13}{12} [/tex]

The area in square meters will the oil slick cover is 9.5×10⁶ m².

15 barrels of diesel spilt into the ocean, where each barrel contains 42 gallons. Thereby the total volume of the oil spilt by 15 barrels is calculated as follows:

The total volume of the oil spilt by 15 barrels = 15× 42 gallons.

=630 gallons

1 gallon = 3.78541 liters

Volume in L = 630 gallons × 3.78541 liters/ 1 gallon

= 2384.8083 L

1 L = 10⁻³ m³

2384.8083  L = 2384.8083 × 10⁻³ m³

= 2.3848083 m³

The area covered by the oil spill has to be determined, where the thickness of the oil spill is given to be 2.5×10² nm.

1 nm = 10⁻⁹ m

Thereby, 2.5×10² nm = 2.5×10²×10⁻⁹ m

= 2.5×10⁻⁷ m

Area (m²) = volume (m³)/thickness (m)

= 2.3848083 m³/ 2.5×10⁻⁷ m

= 0.95392×10⁷ m²

= 9.5×10⁶ m²

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Answer:

Using a standard normal distribution table, we can find that the percentage of homes that have a monthly utility bill of more than $83 is approximately 13.6%.

Step-by-step explanation:

If the distribution of the monthly utility bill for gas or electric energy can be considered mound-shaped and symmetric, we can use the standard normal distribution table to find the percentage of homes that have a monthly utility bill of more than $83.

To use the standard normal distribution table, we need to standardize the variable by subtracting the mean and dividing by the standard deviation:

(83 - 91) / 8 = -0.875

This means that a monthly utility bill of $83 is 0.875 standard deviations below the mean.

Using a standard normal distribution table, we can find that the percentage of homes that have a monthly utility bill of more than $83 is approximately 13.6%.

After finding the ratio, the population of Illinois than Alaska is 20 times greater.

The population of Alaska is approximately 6.5 x [tex]10^5[/tex] people.

The population of Illinois is about 1.3 x [tex]10^7[/tex] people.

We have to find how many times greater is the population of Illinois than Alaska.

We will use their population ratio to determine how many times the population of Illinois is greater than the population of Alaska.

Ratio = Population of Illinois's /Population of Alaska

Ratio = 1.3 x [tex]10^7[/tex]/6.5 x [tex]10^5[/tex]

Now simplifying.

Ratio = 0.2 x [tex]10^2[/tex]

Ratio = 20

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Answer:

3 + n = 2n - 5

Step-by-step explanation:

let 'n' equal 'a number'

'more than' implies 'addition', so 3 + n

'is' in math implies 'equals', so 3 + n =

'double the number' means to multiply it by 2

'less than' implies 'subtraction'

So final result is:

3 + n = 2n - 5

Palisade Bakery is a better buy than Union City Bakery.

To determine which bakery has the better buy, we need to calculate the cost per muffin at each bakery. It is determined by dividing the total cost by total number of muffins. Assuming one batch has ten muffin as not mentioned.

Union City Bakery: $10.00 / 3 batches = $3.33 per batch (approx)

= $3.33/ 10

= $0.33 per muffin

Palisade Bakery: $6.25 / 20 muffins = $0.31 per muffin

Based on this calculation, Palisade Bakery has the better buy as each muffin costs $0.31, which is cheaper than the cost per muffin at Union City Bakery, which is approximately $0.33 per muffin.

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For the given stem and leaf plot, the range of data is option C: 25.

What is stem and leaf plot?

A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

The stem and leaf plot for data is given.

The range of data is defined as a measure of the difference between the maximum value of data and the minimum value of data.

From the stem and leaf plot the maximum value obtained is = 35

From the stem and leaf plot the minimum value obtained is = 10

The range is then calculated as -

Range = Maximum value - Minimum value

Range = 35 - 10

Range = 25

Therefore, the range is 25.

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Probability that 2 or more of the statistics courses are in same slot is 0.28.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

probability that 2 or more of the statistics courses are in same slot

=1-P(all 3 are in different slots)

=1-P(select 3 from 10 slots and arrange them)

=1-(10*9*8)/10^3

=0.28

Therefore, probability that 2 or more of the statistics courses are in same slot is 0.28.

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The given scatter plot depicts the exponential function. Therefore, option 1 f(x) = 2ˣ is the correct one.

A scatter plot is a particular kind of graphic diagram that uses Cartesian coordinates to show the values of two variables for a collection of data.

We write y as the function of x as y=f(x). Here, f is considered the name of the function and x is the value of the function. To check which function depicts the given scatter plot, we have to substitute the values for x and find the function. Then, plot the graph.

By doing we get, the plot for f(x) = 2ˣ is equivalent to the given scatter plot. Because this graph depicts the exponential function where the graph passes through the point (0,1). Therefore, option 1 correctly depicts the given plot. Option 2 depicts the identity function and 4 depicts squaring or quadratic function.

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To add or subtract mixed numbers, first add or subtract the integer (whole number) portions of the mixed numbers, then add or subtract the fractional portions of the mixed numbers. Reduce the fractional portion of the answer to its lowest terms and combine it with the integer portion of the answer to get the final answer.

1. To add mixed numbers, first add the integer (whole number) portions of the two mixed numbers together. The result is the integer portion of your answer.

2. Next, add the fractional portions of the two mixed numbers together. If the fractional parts of the two mixed numbers have different denominators, you'll need to convert them to have the same denominator.

3. Reduce the fractional portion of your answer to its lowest terms. This is the fractional portion of your answer.

4. Combine the integer portion of your answer with the fractional portion of your answer to get the final answer.

5. To subtract mixed numbers, first convert the fractional portion of the subtrahend (the number being subtracted) to an equivalent fraction with the same denominator as the minuend (the number being subtracted from).

6. Subtract the integer portions of the two mixed numbers. The result is the integer portion of your answer.

7. Subtract the fractional portions of the two mixed numbers. Reduce the fractional portion of your answer to its lowest terms. This is the fractional portion of your answer.

8. Combine the integer portion of your answer with the fractional portion of your answer to get the final answer.

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