suppose you want to double the area of the patio shown at the right. find the increase x of both the length and width of the patio

To find the length of a row of bookshelves, we can use the square root function, as the length of a row of bookshelves will be proportional to the square root of the area of the space that Isabel rents.

Mathematically, we can express f(x) as: f(x) = √(x)

Where x represents the area of the space that Isabel rents, and f(x) represents the total length of a row of bookshelves.

The above function takes the square root of the area x, which gives us the length of a row of bookshelves in feet, assuming that the area is in square feet. As x increases, f(x) will also increase, indicating that the length of the row of bookshelves will also increase as Isabel rents a larger area in the warehouse.

To find the length of a row of bookshelves, we can use the square root function, denoted as √(x), where x represents the area of the space that Isabel rents.

For example, if Isabel rents an area of 324 square feet, we can find the length of a row of bookshelves as follows:

x = 324

f(x) = √(x) = √(324) = 18

So, the length of a row of bookshelves would be 18 feet in this case.

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Part 2: Solve a real-world problem using a square root function.

When Isabel began her book-selling business, she stored her inventory in her garage. Now that her business has grown, she wants to rent warehouse space. Lisa owns a large warehouse nearby and can rent space to Isabel. The area of the warehouse is 8,100 square feet. Lisa is willing to rent Isabel as little as 100 square feet of the space or up to as much as the entire warehouse. Her only requirement is that all spaces must be square.

The total length of each row of bookshelves will be of the length of the storage space.

Let x be the area of the space that Isabel rents and f(x) represent the total length of a row of bookshelves. How would you find the length of a row of bookshelves? (3 points)

Write a function that expresses f(x). (10 points)

Danny had the sales of total $16,000.

We have,

He earns a 2.5% commission on his first $4000 in sales.

He earns a 7.5% commission on any amount of sales beyond $4000.

Commission earned = $1000

So, 6.25% of x = 1000

6.25/10 x = 1000

0.0625x = 1000

x= 1000/ 0.0625

x= $16,000

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Danny had the sales of total $16,000.

We have,

He earns a 2.5% commission on his first $4000 in sales.

He earns a 7.5% commission on any amount of sales beyond $4000.

Commission earned = $1000

So, 6.25% of x = 1000

6.25/10 x = 1000

0.0625x = 1000

x= 1000/ 0.0625

x= $16,000

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Therefore, the total volume of the two prisms is 10,404 cubic inches.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically measured in cubic units, such as cubic meters (m³), cubic feet (ft³), or cubic centimeters (cm³). The volume of an object is calculated by multiplying its length, width, and height or by using an appropriate formula for the shape of the object.

Here,

The two prisms have the same dimensions of 17 inches in height, 18 inches in base, and 17 inches in length and width.

To find the volume of a prism, we multiply the area of the base by the height. The base of the prism is a rectangle with length 18 inches and width 17 inches, so the area of the base is:

Area of base = length × width

= 18 in × 17 in

= 306 in²

Therefore, the volume of one prism is:

Volume = area of base × height

= 306 in² × 17 in

= 5202 in³

The volume of the two prisms combined is simply twice the volume of one prism:

Total volume = 2 × 5202 in³

= 10404 in³

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If Scott planted 20% of a garden with roses then the area of

the section of the garden that is planted with roses is 10 square feet

The garder is in rectangle shape

We have to find the area of the garden

The length of the garden is 10 ft and width of garden is 5 ft

Area of garden = 10×5

=50 square feet

Now  Scott planted 20% of a garden with roses

Convert 20% to decimal by dividing 20 by 100

Area of garden which has roses = 50×0.2

=10 square feet

Hence, if Scott planted 20% of a garden with roses then the area of

the section of the garden that is planted with roses is 10 square feet

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The graph of f(x) = (x - 1)/(4(x - 4)) is plotted to represent f(x) = (x - 1)/(4x - 16)

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

f(x) = (x - 1)/(4x - 16)

Factor out 4 from the denominator

So, we have

f(x) = (x - 1)/(4(x - 4))

This means that

f(x) = (x - 1)/(4(x - 4)) is equivalent to f(x) = (x - 1)/(4x - 16)

So, we can plot the graph of f(x) = (x - 1)/(4(x - 4)) to represent f(x) = (x - 1)/(4x - 16)

See attachment for the graph

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The actual distance between the two cities is given as follows:

17 miles.

The actual distance between the two cities is obtained applying the proportions in the context of the problem.

The scale factor is given as follows:

1 inch = 17 miles.

The length of the drawing is given as follows:

1 inch.

Hence the actual distance between the two cities is given as follows:

1 x 17 = 17 miles.

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Answer choice C is correct. That is the total population of wild hogs in that particular area is 100.

Total population in an area refers to the number of individuals of a particular species or group living in a specific geographical region or habitat. This can include both visible and hidden individuals, such as animals that are difficult to spot or track. Total population is an important measure for conservation and management efforts, as it helps determine the size of a population and whether it is growing or declining.

Given that 20 wild hogs were tagged and later they saw 8 tagged wild hogs out of 40 recaptured wild hogs. We need to find the total population of wild hogs in that area.

From the given information we can see,

(Number of hogs tagged) / (Total population) = (Number of tagged hogs recaptured) / (Number of hogs recaptured)

⇒ 20 / x = 8 / 40

⇒ 8x = 20 × 40

⇒ 8x = 800

⇒ x = 100

Therefore, the wildlife group can estimate that the total population of wild hogs in the area is 100.

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Answer:

152 teenagers attended the game.

Step-by-step explanation:

Write the formula:

4% of 3800 people = total teens

Evaluate:

4/100 x 3800

Calculate:

4 x 38

= 152 teens

Answer: yes, the hex of the number 1,000,000 would be 40.

The relative maximum and minimum point as well as the absolute maximum and minimum points based on labeled points on the graph are;

Points 1, 3, and 5 are relative maximum points

Points 2 and 4 are relative minimum points

Point 5 is an absolute maximum point

Point 2 is an absolute minimum point

A relative maximum is a point in which the maximum with regards to the immediate surrounding points.

Therefore, the relative maximum points are;

The points 1, 3, and 5

The relative minimum points are points that are the minimum points, when compared with the surrounding points

The relative minimum are the points 2 and 4

The absolute maximum is the point which is at the highest point on the graph

The absolute maximum on the graph is therefore, the [oint 5

The absolute minimum on the graph is the point which is the minimum point compared to all other points

Therefore, the absolute minimum point is the point 2

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Answer:

Impossible to know, or best guess

Step-by-step explanation:

It is impossible to determine exactly how many bucket loads it would take to empty the world's ocean because the volume of the ocean is constantly changing due to factors such as tides, currents, and sea level rise. However, we can estimate the approximate volume of the ocean and calculate the number of bucket loads needed based on that estimate.

The approximate volume of the world's ocean is 1.332 billion cubic kilometers (km³) or 332.5 million cubic miles (mi³). Assuming that each bucket can hold 10 liters or 0.01 cubic meters (m³) of water, we can calculate the number of bucket loads needed to empty the ocean as follows:

1 km³ = 1,000,000,000 m³

1,332,000,000 km³ = 1.332 x 10¹⁸ m³

1.332 x 10¹⁸ m³ / 0.01 m³ per bucket = 1.332 x 10²⁰ bucket loads

Therefore, it would take approximately 1.332 x 10²⁰ or 133,200,000,000,000,000,000 bucket loads to empty the world's ocean. This number is so large that it is practically impossible to even visualize, let alone accomplish.

Another answer provided by our lord and savior (That one green ai)

The part of a pyramid include the following: E. lateral faces.

In Mathematics and Geometry, the volume of a pyramid can be calculated by using the following formula:

Volume = 1/3 × b × h

Where:

Generally speaking, a pyramid is composed of three main parts and these include the following:

In conclusion, we can reasonably infer and logically deduce that lateral face is a part of any pyramid.

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Okay, let's analyze the two functions based on the options:

Function A:

X f(x)

0 5

1 10

2 20

3 40

4 80

Options:

Neither function A nor function B has an x-intercept. - False, function A has an x-intercept at x=0.

Neither function A nor function B has a y-intercept. - False, function A has a y-intercept at f(x)=5.

The domain and range of both functions contain only positive numbers. - False, function A has values that include 0.

The domain and range of both functions contain only positive numbers and zero. - True, the domain and range of both functions contain only non-negative numbers including 0.

Therefore, the correct choice is:

O The domain and range of both functions contain only positive numbers and zero.

Let me know if you have any other questions!

To solve this equation by combining terms, the answer will be: (c) -4a + 22b.

To solve the equation, we need to combine like terms together. This means that the figures with the suffix, a will come together, while those with the suffix, b will also align themselves. Going by this rule, we will have:

12a -16a + 26b -4b.

= -4a + 22b

When a higher number is to be subtracted from a smaller number, the result will be a negative number as is the case with the terms that have the 'a' initials.

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There were 24 students working in area B in the morning, and 3 times as many, or 72 students, working in area A. The total number of students is then 24 + 72 = 96.

In geometry, an area is the measurement of the amount of space inside a two-dimensional flat surface such as a square, rectangle, triangle, circle, or any other shape. It is usually expressed in square units, such as square centimeters (cm²) or square meters (m²), and is calculated by multiplying the length and width of a rectangular shape or by using specific formulas for different geometric shapes such as the base times the height divided by 2 for a triangle or pi times the radius squared for a circle. The concept of area is fundamental in many branches of mathematics, physics, engineering, and other fields where the measurement of the extent of a surface is important.

Let's assume that the number of students working in area b is x. Then the number of students working in area A is 3x (since there are three times as many students working in area A as in area b in the morning).

Let A be the area of area a, and B be the area of area b. We know that A = 1.5B (since area a is 1 1 2 times the area of area b).

In the morning, the total number of students is x + 3x = 4x.

In the afternoon, 7/12 of the students work in area a, and the rest work in area b. So, the number of students working in area A in the afternoon is 7/12 * 4x = 7x/3, and the number of students working in area b is (1 - 7/12) * 4x = 5x/12.

Since area a was finished at the end of the day, we know that the total area cleaned by the students is A + B = 1.5B + B = 2.5 B. This means that the number of students working in area b is enough to finish 0.5B (since area a was already finished), but 4 more students are needed to finish the remaining 0.5B.

So, we can set up the following equation:

(5x/12) / x = 0.5 / (0.5 + 4/x)

Simplifying this equation, we get:

5x = 6x + 24

x = 24

Therefore, there were 24 students working in area b in the morning, and 3 times as many, or 72 students, working in area A. The total number of students is then 24 + 72 = 96.

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This method can be used to quickly obtain the product of two polynomials.A-6k²+25k²-16k-15.

Expression in math is a combination of numbers, symbols and operators that represent a mathematical quantity or operation. It can be a single number, a single variable, or a combination of numbers, variables and symbols combined together to form a mathematical statement. An expression can also include functions, such as polynomials, exponential functions, or logarithmic functions.


The vertical method involves writing the terms of the two factors side by side and multiplying them together to get the product.

(3k+5)  (2k²-5k-3)

6k³  +   0k²  +   0k   +  -15
0k³  +  10k²  + -15k   +   0
0k³  +   5k²   + -15k   +   0
0k³ +   0k²  +  15k   +   0

Adding the terms in each column yields the product:

A-6k³+25k²-16k-15

Therefore, the correct answer is A-6k³+25k²-16k-15.

In conclusion, using the vertical method can simplify algebraic multiplication problems by breaking them down into columns and adding the terms in each column. This method can be used to quickly obtain the product of two polynomials.

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Answer:

161

Step-by-step explanation:

angle 5 is supplementary to the given angle 180-1

Thus, the dimensions of the rectangle are - length 22 inches and width 13 inches.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). The opposite sides of a rectangular are equal and parallel. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.

Let the length of rectangle be 'l'

Let the width be 'w'.

Then,

Perimeter = 2(l + w)

70 = 2(l + w)

35 = l + w

l = 35 - w ...eq 1

Now,

Area = length * width

286 = l*w ...eq 2

Put eq 1 in eq 2

286 = (35 - w)*w

286 = 35w - w²

w² - 35w + 286 = 0

Solving the quadratic equation:

w² - 22w - 13w + 22*13 = 0

w(w - 22) - 13(w - 22)= 0

(w - 22)(w - 13) = 0

w = 22 and w = 13

As, length is greater than width-

width w = 13 inch

Length l = 35 - 13 = 22 inches.

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1. If the gross domestic product of a country is significantly higher in one year than in another, the factor that might account for the difference is d. all of these.

2. The Lorenz Curve for the United States indicates that the richest 20 percent of households have d. 46.8 percent of the nation's income.

3. The economic condition most likely to be caused by a war affecting oil production in the Mid East would be a. demand-pull inflation.

The gross domestic product or GDP refers to the total monetary value of goods produced and services provided in a country during one specific period.

The Lorenz Curve, developed by Max Lorenz measures income inequality or wealth inequality using a graphical representation.

When there is a shortage in supply, pressure is mounted on the available quantity of an item, causing its price to increase.

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Answer:

Step-by-step explanation:

(a) π/4

(b) 0

(c) 1

(d) 1

(e) 2/3

(f) 1/2

Answer:

1/16

Step-by-step explanation:

(1/4)x(1/4)= 1/16

Answer:

12[tex]x^{2}[/tex]+4x

Step-by-step explanation:

area = width * height

substitution: area = (3x+1)*4x

distributive property: area = (4x*3x)+(4x*1)

simplify: area = 12[tex]x^{2}[/tex]+4x

Where the above conditions existing, the probability that a randomly selected site will have a    snow depth between 2.25 and 2.7 inches is 68.3 %.

t the value The value one standard deviation below the mean is 2.25 inches.

The  value one standard deviation above the  mean is 2.75 in.

To find the probability , calculate the z-scores for these values

z1 = (2.25  - 2.5 ) /0.25 = -1

z2= ( 2.7 -2.5 )   / 0.25 = 0.8

Using a standard normal distribution table ....

we can see that the probability of a z-  score between -1 and 0.8 is approximately 0.683, or 68.3%.

Hence,  the probability that a randomly chosen location will have a snow depth between 2.25 and 2.7 inches is 68.3%.

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Answer: A is 36 cm^2

Step-by-step explanation:

The missing sides of the triangle are

10). ∠ ABD = 60 degrees

11). ∠ ADB = 90 degrees

12). ∠ BAD = 30 degrees

13). ∠ CAD = 30 degrees

14. BD is half of the length = BC / 2 = 6/2 = 3

15. AD is the height this is solved using Pythagoras theorem as below

AD^2 = AB^2 - BD^2

AD^2 = 6^2 - 3^2

AD^2 = 36 - 9

AD = sqrt (27)

16. Area of Δ ABC

= 1/2 * base * height

= 1/2 * 6 * sqrt (27)

= 9 sqrt (3)

= 15.59 square units

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Step-by-step explanation:

y=mx+b

y= -5 x= 10

-5 = 2/5 (10) + b

-5 = 4 + b

b= -9

the equation of aline is y = 2/5(x) -9

or 2x = 5y + 45

Answer:

(-6,3)

Step-by-step explanation:

reflect over x=2, so you. move Y up by 2. 1+2 =3