A rectangle has perimeter 70 inches, and its area is 286 sq-inches. Find the dimensions of this
rectangle. (For purposes of this problem only, the width is shorter than the length.)
length =
width=
inches
inches
Enter your answers as numbers. If necessary, round to the nearest hundredths.
Thus, the dimensions of the rectangle are - length 22 inches and width 13 inches.
Explain about the rectangle: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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Two different functions are represented.
Function A:
X
0
1
2
3
4
f(x)
5
10
20
40
80
Function B:
Which statement best compares the two functions?
Neither function A nor function B has an x-intercept.
Neither function A nor function B has a y-intercept.
The domain and range of both functions contain only
positive numbers.
O The domain and range of both functions contain only
positive numbers and zero.
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!
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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Simplify using the vertical method
This method can be used to quickly obtain the product of two polynomials.A-6k²+25k²-16k-15.
What is expression?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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Hi can i convert the binary number 1000000 to a hexadecimal number?
Answer: yes, the hex of the number 1,000,000 would be 40.
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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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
ANSWER THIS FIRST GET BRAINLESS W EXPLANATION!
3. Combine terms: 12a + 26b -4b – 16a.
(a) 4a + 22b,
(b) -28a + 30b,
(c) -4a + 22b,
(d) 28a + 30b.
To solve this equation by combining terms, the answer will be: (c) -4a + 22b.
How to solve the equationTo 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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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)
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
Miller Toy Company manufactures a plastic swimming pool at its Westwood Plant. The plant has been experiencing problems as shown by its June contribution format income statement below:
Flexible
Budge
Actual
Sales (7,000 pools)
$265,000 $265,000
Variable expenses:
Variable cost of goods sold*
79,240
97,525
Variable selling expenses
19,000
19,000
Total variable expenses
98,240
116,525
Contribution margin
166,760
148,475
Fixed expenses:
Manufacturing overhead
Selling and administrative
Total fixed expenses
Net operating income (loss)
67,000
67,000
85,000
85,000
152,000
152,000
$ 14,760 $ (3,525)
Janet Dunn, who has just been appointed general manager of the Westwood Plant, has been given instructions to "get things under control. Upon reviewing the plant's income statement, Ms. Dunn has concluded that the major problem lies in the variable cost of goods sold. She has been provided with the following standard cost per swimming pool:
Direct materials
Direct labor
Variable manufacturing overhead
Total standard cost per unit
Standard
Quantity or
Hours
3.5 pounds
0.4 hours
0.3 hours
Standard Price or Rate
§ 2.10 per pound
$ 7.60 per hour
$ 3.10 per hour
Standard
Cost
$ 7.35
3.04
0.93
$ 11.32
During June, the plant produced 7,000 pools and incurred the following costs:
a. Purchased 29,500 pounds of materials at a cost of $2.55 per pound.
b. Used 24,300 pounds of materials in production. (Finished goods and work in process inventories are insignificant and can be ignored.)
c. Worked 3,400 direct labor-hours at a cost of $7.30 per hour.
d. Incurred variable manufacturing overhead cost totaling $8,400 for the month. A total of 2,400 machine-hours was recorded.
It is the company's policy to close all variances to cost of goods sold on a monthly basis
Required:
1. Compute the following variances for June:
a. Materials price and quantity variances
b. Labor rate and efficiency variances.
c. Variable overhead rate and efficiency variances.
2. Summarize the variances that you computed in (1) above by showing the net overall favorable or unfavorable variance for the month.
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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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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A rectangle has a height of 4x and a width of 3x +1. Express the area of the entire rectangle. Expression should be expanded. Area =
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
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
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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1. a gallon of water weighs 8 1/3 lbs.
a. what is the weight of 25
gallons of water?
b. If the weight of an empty 25 gallon tank is 1/10 of the water it can hold, what is the weight of the tank?
c. what is the weight of a 25 gallon tank filled with water?
Find the area of shaded region.
Answer: A is 36 cm^2
Step-by-step explanation:
1. If the gross domestic product of a country is significantly higher in one year than in another, what
might account for the difference
a. population growth
b. greater available resources and technological advances
Oc. inflation
C.
d. all of these
2. The Lorenz Curve for the United States indicates that the richest 20 percent of households have
what percentage of the nation's income
a. 20 percent
b. 3.8 percent
c. 90 percent
d. 46.8 percent
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
b. cost-push inflation
c. deflation
d. cost of living inflation
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.
What is the gross domestic product?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.
What is the Lorenz Curve?The Lorenz Curve, developed by Max Lorenz measures income inequality or wealth inequality using a graphical representation.
What is demand-pull inflation?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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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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help with calculus. determine wheter each labeled point is an absolute maximum or minumum OR a relative maximum or minimum or neither
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
What is a relative maximum 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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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)
In the diagram shown, Δ ABC is equilateral. AD is an altitude.
10). ∠ ABD = ______.
11). ∠ ADB = ______.
12). ∠ BAD = _____.
13). ∠ CAD = _____.
Suppose AB = 6. Find:
14). BD
15). AD
16). Area of Δ ABC
The missing sides of the triangle are
10). ∠ ABD = 60 degrees
11). ∠ ADB = 90 degrees
12). ∠ BAD = 30 degrees
13). ∠ CAD = 30 degrees
How to find the missing sides in the triangle14. 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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What is (1/4) to the second power
Answer:
1/16
Step-by-step explanation:
(1/4)x(1/4)= 1/16
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
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 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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Are the functions f(x) and g(x) inverses of each other? Use composition of functions to determine your answer.
f(x) = 7x-1
x+1
g(x)
O Yes
O No
Fill in the blanks.
The depth of the snow in my yard is normally distributed, with a mean of 2.5 inches and a standard
deviation of 0.25 inches.
What value is one standard deviation below the mean?
Hint: Read the section on the empirical rule.
inches
What value is one standard deviation above the mean?
I
What is the probability that a randomly chosen location will have a snow depth between 2.25 and 2.7
inches? 68
percent
Submit Question
inches
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 %.
What is the explanation for this ?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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Approximately 8% of all people have blue eyes. A random sample of 20 people is selected, find μ. Round to one decimal place. Answer
Answer:
The mean of a binomial distribution is μ = np, where n is the sample size and p is the probability of success (having blue eyes).
μ = 20 x 0.08
μ = 1.6
Rounded to one decimal place, μ is 1.6.