Answer:
Step-by-step explanation:
To find the next two terms in the sequence, we need to look for a pattern or rule that generates the sequence.
Looking at the differences between successive terms, we can see that they are increasing by 1, 2, and 3 respectively:
7 - 4 = 3
12 - 7 = 5
19 - 12 = 7
So, the next difference should be 9, and we can add it to the last term in the sequence to get the next term:
19 + 9 = 28
Similarly, we can add the next difference of 11 to get the term after that:
28 + 11 = 39
Therefore, the next two terms in the sequence are 28 and 39.
So, the complete sequence is: 4, 7, 12, 19, 28, 39.
A wildlife group is trying to determine how many wild hogs are in a certain area. They trapped, tagged, and released 20 wild hogs. Later, they counted 8 wild hogs out of the 40 they saw.
What can the wildlife group estimate is the total population of wild hogs in that area?
A. 80
B. 90
C. 100
D. 16
Answer choice C is correct. That is the total population of wild hogs in that particular area is 100.
What do you mean by total population in a area?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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A normal distribution has a mean of 33 and a standard deviation of 4. Find the probability that a randomly selected x-value from the distribution is in the given interval. a. between 29 and 37 b. between 33 and 45 c. at least 29 d. at most 21
Step-by-step explanation:
We can use the standard normal distribution to calculate probabilities for a normal distribution with mean 33 and standard deviation 4. We just need to standardize the intervals using the formula:
z = (x - mu) / sigma
where x is the specific value in the interval, mu is the mean, sigma is the standard deviation, and z is the corresponding z-score.
a. Between 29 and 37:
z1 = (29 - 33) / 4 = -1
z2 = (37 - 33) / 4 = 1
Using a standard normal distribution table, the cumulative probability of z being between -1 and 1 is approximately 0.6827.
So the probability that a randomly selected x-value from the distribution is between 29 and 37 is approximately 0.6827.
b. Between 33 and 45:
z1 = (33 - 33) / 4 = 0
z2 = (45 - 33) / 4 = 3
The cumulative probability of z being between 0 and 3 is approximately 0.4987.
So the probability that a randomly selected x-value from the distribution is between 33 and 45 is approximately 0.4987.
c. At least 29:
z = (29 - 33) / 4 = -1
The cumulative probability of z being less than -1 is approximately 0.1587. So the probability that a randomly selected x-value from the distribution is at least 29 is approximately 1 - 0.1587 = 0.8413.
d. At most 21:
z = (21 - 33) / 4 = -3
The cumulative probability of z being less than -3 is very close to 0. So the probability that a randomly selected x-value from the distribution is at most 21 is approximately 0.
A group of students was to clean up to two areas in their school. area a was 1 1 2 times of area b. in the morning (half of a day), the number of students cleaning area a was 3 times that of the number of students in area b. in the afternoon (another half of a day), 7/12 of the students worked in area a while the rest of them in area b. at the end of the day, area a was done, but area b still needed 4 students to work one more day before it was done. how many were there in this group of students?
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.
What is an area?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.
According to the given equationLet'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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Danny works at the hunting and fishing supply store. At the end of each month he earns a commission on all of his sales for that month.
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. Lastmonthheworkedhardandearned$1000commission. How much,in dollars,did he have in sales last month?
(The answer is 16,000 I just need to figure out how to do it)
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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line with slope m
below:
2|5
and containing the point (10,-5). Type your answer is slope-inte
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
33.3/11=_____ (round to the nearest hundredth)
33.3/11 = 3.02727272727...
Then, rounding to the nearest hundredth means keeping only two decimal places. The third decimal place is 7, which is greater than or equal to 5, so we round the second decimal place up:
3.03
Therefore, 33.3/11 rounded to the nearest hundredth is 3.03.
Using the following conversions between the metric and U.S. systems, convert the measurement.
Round your answer to 6 decimal places as needed
1 meter≈ 3.28 feet
1 Lite≈ 0.26 gallons
1 kilogram≈ 2.20 pounds
15.048 dL≈ qt
15.048 deciliters is equivalent to 1 quart.
What is conversion?Conversion is the process of changing a quantity from one unit of measure to another unit of measure using a conversion factor or a formula.
We have:
To convert meters to feet, multiply by 3.28.
To convert liters to gallons, multiply by 0.26.
To convert kilograms to pounds, multiply by 2.20.
To convert deciliters to quarts, divide by 15.048.
Let's use these conversions to convert the given measurement:
15.048 dL = qt
Dividing both sides by 15.048, we get:
1 dL = qt/15.048
Multiplying both sides by 0.946353, which is the number of quarts in a liter, we get:
0.946353 dL = qt/15.048 * 0.946353
Simplifying the right-hand side, we get:
0.946353 dL = qt/15.961
Multiplying both sides by 3.78541, which is the number of liters in a gallon, we get:
3.78541 * 0.946353 dL = 3.78541 * qt/15.961
Simplifying the left-hand side, we get:
3.58702 L = qt/4.22676
Multiplying both sides by 4.22676, we get:
15.1485 L = qt
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What is the image of point (-6,1) after the reflection over the line x=2
Answer:
(-6,3)
Step-by-step explanation:
reflect over x=2, so you. move Y up by 2. 1+2 =3
Find the value of x in the triangle shown below.
X=
4.5
56°
4
4
X°
Answer:
68.9 degrees
Step-by-step explanation:
To find this we can use the rule of sines.
It states [tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]
We will use 56 degrees and its complementary measurement, which is discovered by observing the opposite side from the angle, which is 4. Then, we will find the side that compliments x, which is 4.5. Then we can plug those values into the rule of sines.
[tex]\frac{sin56}{4}=\frac{Sinx}{4.5}[/tex]
Then, we want to get Sin x by itself.
[tex]\frac{sin56}{4}*4.5=sinx[/tex]
Then, we can solve for sin x.
[tex]0.932667269124=sinx[/tex]
finally, we need to take the inverse of sin to find our solution.
[tex]sin^{-1} (0.932667269124)=sin^-^1(sinx)\\x=68.85\\[/tex]
Which can be rounded to 68.9.
Help me solve this for class please
Answer:
Step-by-step explanation:
(a) π/4
(b) 0
(c) 1
(d) 1
(e) 2/3
(f) 1/2
Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 4; zeros: 6 (Multiplicity 2); 3i
Enter the expanded polynomial. Let a represent the leading coefficient.
f(x) = a( )
Answer:
Step-by-step explanation:
The polynomial f(x) with real coefficients, degree 4, and zeros 6 (multiplicity 2), 3i can be formed as follows:
Since the zero 6 has a multiplicity of 2, it appears twice in the factored form of f(x), i.e., (x-6)(x-6) = (x-6)^2.
The other zero is 3i, which means its complex conjugate, -3i, is also a zero. Therefore, the factored form of f(x) can be written as:
(x-6)^2(x-3i)(x+3i)
Expanding this expression, we get:
f(x) = (x-6)^2(x^2 + 9)
Multiplying this out, we get:
f(x) = x^4 - 12x^3 + 81x^2 - 216x + 324
Therefore, the polynomial f(x) with real coefficients, degree 4, and zeros 6 (multiplicity 2), 3i can be written as:
f(x) = x^4 - 12x^3 + 81x^2 - 216x + 324.
3800 people attended a football game. If 4% of the people who attended were
teenagers, how many teenagers attended the game?
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
The figure shows two parallel lines intersected by a transversal. One of the
angle measures is given. Find the measure of the indicated angle.
Find the measure of angle 5.
6
5
19°
4
3
2
Answer:
161
Step-by-step explanation:
angle 5 is supplementary to the given angle 180-1
Find inverse of the following f(x)=x^3+9
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]\stackrel{f(x)}{y}~~ = ~~x^3+9\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~y^3+9} \\\\\\ x-9=y^3\implies \sqrt[3]{x-9}=y=f^{-1}(x)[/tex]
Paul bakes raisin bars in a pan shaped like a rectangular prism. The volume of the pan is 252 cubic inches. The length of the pan is 12 inches, and its width is 10-1/2 inches. What is the height of the pan? Enter your answer in the box
Answer:
The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height of the prism, respectively. We are given that the volume of the pan is 252 cubic inches, the length is 12 inches, and the width is 10-1/2 inches.
So, 252 = 12 x 10.5 x h
Simplifying the right side of the equation, we get:
252 = 126h
Dividing both sides by 126, we get:
h = 2
Therefore, the height of the pan is 2 inches.
An island is located 48 miles N23°38'W of a city. A
freighter in distress radios its position as N11°26'E of the
island and N12° 16'W of the city. How far is the freighter
from the city?
The freighter is approximately 164.33 miles from the city.
How to determine how far is the freighter from the city?We can use the Law of Cosines to solve this problem. Let's label the distances as follows:
d: distance between the city and the freighter
x: distance between the city and the island
y: distance between the island and the freighter
First, we need to find x using the given coordinates:
N23°38'W is equivalent to S23°38'E, so we have:
cos(23°38') = x/48
x = 48cos(23°38') ≈ 42.67 miles
Next, we can use the coordinates of the freighter to find y:
N11°26'E is equivalent to E11°26'N, and N12°16'W is equivalent to S12°16'E. This means that the angle between the island and the freighter is:
23°38' + 11°26' + 12°16' = 47°20'
cos(47°20') = y/d
We can rearrange this equation to solve for y:
y = dcos(47°20')
Now we can use the Law of Cosines to solve for d:
d² = x² + y² - 2xy cos(90° - 47°20')
d² = 42.67² + (d cos(47°20'))² - 2(42.67)(d cos(47°20')) sin(47°20')
d² = 1822.44 + d² cos²(47°20') - 2(42.67)(d cos(47°20')) sin(47°20')
d² - d² cos²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')
d² (1 - cos²(47°20')) = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')
d² sin²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')
d² = (1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')) / sin²(47°20')
d ≈ 164.33 miles
Therefore, the freighter is approximately 164.33 miles from the city.
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How many bucket loads would it take to bucket out the world’s ocean
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)
What is the length of the unknown leg
of the right triangle?
2 ft
3 ft
(The figure is not drawn to scale.)
The length of the unknown leg of the right triangle is ft.
(Round to one decimal place as needed.)
Thus, the unknown leg x of the right angled triangle is found as 2.2 ft.
Explain about the right triangle:A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.
What a Right Triangle Looks Like
In a right triangle, the right angle is often the biggest angle.The longest side is the hypotenuse, which is the side that faces the right angle.A right triangle cannot include any obtuse angles.For the given right triangle:
Let the unknown length be 'x'.
Using the Pythagorean theorem:
3² = 2² + x²
x² = 3² - 2²
x² = 9 - 4
x² = 5
x = 2.2
Thus, the unknown leg x of the right angled triangle is found as 2.2 ft.
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Find the volume of the two prisms.
someone pls help me I need to ace this test
Therefore, the total volume of the two prisms is 10,404 cubic inches.
What is volume?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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Help with this math please.
The actual distance between the two cities is given as follows:
17 miles.
How to obtain the actual distance?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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The average daily balance of a credit card for the month of March was $1900 and the unpaid balance at the end of the month was $1700. If the annual percentage rate is 32.4% of the average daily balance, what is the total balance on the next billing date, April 1?
Round your answer to the nearest cent.
Using the average daily balance, the total balance on the next billing date, April 1 is $5,059.73.
What is the average daily balance?The average daily balance is a credit card method of computing finance charges.
To determine the average daily balance, the sum of the daily balances over your billing cycle is divided by the number of days in the billing cycle.
The finance charge is then the product of the average daily balance multiplied by the APR and the number of days involved, divided by 365 days.
Average daily balance = $1,900
Unpaid balance at month-end = $1,700
APR = 32.4%
The finance charge for the month = $9.73 ($1900 x 32.4% x 30/365)
The total balance on the next billing date, April 1 = $5,059.73 ($5,050 + $9.73)
Thus, on April 1, the next billing cycle, the balance on the card is $5,059.73.
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Help Please Be Fast
The maximum value of the objective functions are 2600, 27 and 1980
Solving the objective function graphicallyGiven that
Max Z = 8x + 16y
Where the constraints are
3x + 6y ≤ 900
x + y ≤ 200
y ≤ 125
x, y ≥ 0
Plotting the constraints 3x + 6y ≤ 900, x + y ≤ 200 and y ≤ 125 on the same graph, the coordinates of the feasible region are:
(x, y) = (100, 100), (75, 125) and (50, 125)
So, we have
Z = 8(100) + 16(100) = 2400
Z = 8(75) + 16(125) = 2600
Z = 8(50) + 16(125) = 2400
Hence, the maximum value is 2600
Solving the objective function graphicallyGiven that
Max Z = 6x + 3y
Where the constraints are
2x + y ≤ 8
3x + 3y ≤ 18
y ≤ 3
x, y ≥ 0
Plotting the constraints 2x + y ≤ 8, 3x + 3y ≤ 18 and y ≤ 3 on the same graph, the coordinates of the feasible region are:
(x, y) = (3, 3), (2.5, 3) and (2, 4)
So, we have
Z = 6(3) + 3(3) = 27
Z = 6(2.5) + 3(3) = 24
Z = 6(2) + 3(4) = 24
Hence, the maximum value is 27
Solving the objective function by simplexGiven the objective function, the constraints and the final simplex tableau
We have the final values to be
Z = 1980
This means that the maximum value is 1980
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What is (1/4) to the second power
Answer:
1/16
Step-by-step explanation:
(1/4)x(1/4)= 1/16
This year's property taxes on a parcel are $1,743.25. If a sale of the property is to be closed on
August 12, what is the approximate tax proration that will be charged to the seller based on a 360-day
year?
Answer:
$1070.16
Step-by-step explanation:
You want the prorated amount of taxes if the annual amount is $1743.25 and the sale closes August 12, based on a 360 day year.
Months and daysA 360-day year assumes months are 30 days. The tax charged to the seller will be that for 7 months plus 11 days:
(7·30 +11)/360 × $1743.25 = $1070.16
The seller will pay $1070.16 of the tax bill.
__
Additional comment
We have presumed the buyer pays the taxes for August 12, the first day they own the property.
5. Scott planted 20% of a garden with roses. What is the area of
the section of the garden that is planted with roses?
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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HELP FAST PLEASE!!
Which of the following are parts of a pyramid?
altitude
vertex
lateral edges
sides
lateral faces
The part of a pyramid include the following: E. lateral faces.
How to calculate the volume of a pyramid?In Mathematics and Geometry, the volume of a pyramid can be calculated by using the following formula:
Volume = 1/3 × b × h
Where:
h represent the height of a pyramid.b represent the base area of a pyramid.Generally speaking, a pyramid is composed of three main parts and these include the following:
ApexLateral faceBaseIn conclusion, we can reasonably infer and logically deduce that lateral face is a part of any pyramid.
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Find the area of shaded region.
Answer: A is 36 cm^2
Step-by-step explanation:
How do I write this in a function?? And then also how do I graph this function?? Thank you.
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.
What is the square root function?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.
Determine the area of the space that Isabel rents, denoted as x. This could be obtained from the rental agreement or by measuring the area of the space using appropriate units (e.g., square feet).Take the square root of x using a calculator or by using a mathematical formula. The square root of x, denoted as √(x), represents the positive value which, when multiplied by itself, gives x.The resulting value of √(x) represents the total length of a row of bookshelves in feet (assuming that the area is in square feet), as per the requirement given in the problem statement.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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See full text below
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)
PLEASE HELP IT'S FOR MY TEST
Use long division to rewrite this rational function in transformation form, then graph.
[tex]f(x) = \frac{x-1}{4x-16} \\[/tex]
The graph of f(x) = (x - 1)/(4(x - 4)) is plotted to represent f(x) = (x - 1)/(4x - 16)
Rewriting the rational functionFrom 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 expression (cscx + cotx)? is the same as____.
The expression (cscx + cotx)² is the same as csc²x + 2(cscx)(cotx) + cot²x. (option a).
The given expression is (cscx + cotx)². To simplify this expression, we can use the formula for squaring a binomial, which is (a + b)² = a² + 2ab + b². In this case, a = cscx and b = cotx. Therefore, we can substitute these values into the formula to get:
(cscx + cotx)² = csc²x + 2(cscx)(cotx) + cot²x
So the expression (cscx + cotx)² is the same as csc²x + 2(cscx)(cotx) + cot²x.
Hence the correct option is (a).
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