The maximum area of the patio is, 450 feet²
Now, Lets remove the brackets from the function's expression
A(x) = -2x² + 60x
So we got the quadratic function and we have to find the x that corresponds to function's maximum. Let it be X max
As we know ,
X (max) = (X₁ + X₂)/2 ,
where X₁ and X₂ are the roots of the function A(x)
Lets find X₁ and X₂
x (60 - 2x) = 0
Hence, x₁ = 0
And, 60 - 2X₂=0
x₂ = 30
So, X max= (0 + 30)/2 = 15
So A max= A(15) = 15 (60-2 x 15) = 15 (60 - 30) = 15 x 30 = 450 feet²
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Alonzo's gas tank is 1/3 full. After he buys 3 gallons of gas, it is 1/2 full. How many gallons can Alonzo's tank hold?
Answer:
18 gallons
Step-by-step explanation:
18 gallons because 1/3 equals 2/6 and 3/6 equals 1/2 so 3 gallons is 1/6. then just 6×3
Hope this helped
Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average length of time, in months, patients live once starting the treatment. Two researchers each follow a different set of 50 AIDS patients from the start of treatment until their deaths.
a. What is the population of this study?
b. List two reasons why the data may differ.
c. Can you tell if one researcher is correct and the other one is incorrect? Why?
d. Would you expect the data to be identical? Why or why not?
e. If the first researcher collected her data by randomly selecting 40 states, then selecting 1 person from each of those states. What sampling method is that?
f. If the second researcher collected his data by choosing 40 patients he knew. What sampling method would that researcher have used? What concerns would you have about this data set, based upon the data collection method?
The correct answers are:
a. The population of this study is all AIDS patients with revealed symptoms receiving the new AIDS antibody drug.b. Two reasons for potential data differences are variability in patients' health and treatment initiation times.c. Determining correctness between researchers is not possible based solely on data as multiple factors can influence outcomes.d. The data may not be identical due to variations in patients, treatment responses, and data collection methods.e. The first researcher used stratified and simple random sampling by selecting 40 states and one person from each state.f. The second researcher used convenience sampling, which may introduce bias and limit the representativeness of the data set.The explanation for each response can be given as:
a. The population of this study would be all AIDS patients who have revealed symptoms and are receiving the new AIDS antibody drug.
b. Two reasons why the data may differ are:
1. Variability in the patient's overall health and response to the treatment.
2. Differences in the time of diagnosis and initiation of treatment among the patients.
c. It is not possible to determine if one researcher is correct and the other is incorrect solely based on the collected data. Multiple factors, such as the patient's individual characteristics and treatment protocols, could influence the outcomes.
d. The data may not be identical because each researcher is following a different set of patients, and individual patient experiences and outcomes can vary. Additionally, differences in data collection methods or other external factors could contribute to variations.
e. The sampling method used by the first researcher, randomly selecting [tex]40[/tex] states and then selecting one person from each state, is a combination of stratified sampling (based on states) and simple random sampling (within each state).
f. The second researcher used a non-random sampling method by choosing [tex]40[/tex] patients they knew. This method is known as convenience sampling. Concerns regarding this data set include potential bias in patient selection, as the researcher's personal knowledge could introduce subjectivity and may not represent a diverse range of patients receiving the treatment.
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Help please I have to answer these questions using the graph.
The values of the points on the graph of the concentration of the drug in the bloodstream, indicates;
1 a. 24 mg/L
b. Increases; [0, 2]
Decreasing; [2, 20
c. The drug is at the maximum concentration at t = 2 hours
The maximum concentration is 64 mg/L
d. 8 hours
e. The concentration after 1 week is minute
The concentration after 1 month is more reduced than the concentration after 1 week.
f. The concentration of the drug for the first 20 hours increases in the first 2 hours, then decreases and approaches the x-axis as the x-value increases.
What is the graph of a function?A graph is a visual display of the ordered pair of a function on the coordinate plane.
1. The graph in the question specifies the concentration of the drug in the bloodstream after t hours in mg/L
a. The graph indicates that the concentration after 8 hours is 24 mg/L
b. The interval over which the concentration increases is; [0, 2)
The interval over which the concentration decreases is; (2, 20]
c. The graph indicates that the drug is at its maximum concentration when the time t = 2 hours
The maximum concentration, based on the peak of the graph is 64 mg/L
d. The concentration of the drug is 16 mg/L at t = 10 hours, therefore, the time it takes the concentration to decrease to 16 mg/L from the peak therefore is; 10 hours - 2 hours = 8 hours
e. The shape of the graph indicates that the concentration of the drug in the bloodstream continuously decreases after the first two hours, therefore, the concentration after a week will be approximately 0
The concentration after 1 month will trace amounts
f. The concentration of the drug in the bloodstream over the first 20 hours indicates that concentration increases within the first 2 hours, and decreases rapidly in the next 8 hours, such that after 20 hours, the concentration in the blood is less than 4 mg/L
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SOMEONE PLEASE HELP ME ASAP!!!!!!! it will mean a lot
The surface area of the composite solid would be about 576. 05 square feet .
How to find the surface area ?The composite shape is made up of two shapes which are a a cylinder and a pentagonal prism. To find the surface area, you need to find the surface area of these two shapes and then sum these areas.
Area of pentagonal prism :
= 5 a h + 1 / 2 √ ( 5 ( 5 + 2 √ 5 ) ) a ²
a = 4 ft
h = 7 ft
Area of the pentagonal prism is:
= 5 x 4 x 7 + 1 / 2 √ ( 5 ( 5 + 2 √ 5 ) ) 4 ²
= 195.05528 square feet
Area of cylinder:
= 2 π r h + 2 π r ²
= 2 π x 6 x 4 + 2 π x 6 ²
= 376.99112 square feet
The surface area is therefore :
= 195.05528 + 376.99112
= 576. 05 square feet
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A calculator displays 6E6. How do you write 6E6 in standard form
6E6 is a number written in scientific notation, which means that it represents 6 times 10 raised to the power of 6. To write this number in standard form, we need to evaluate the exponent and write the number in expanded form.
6E6 = 6 x 10^6
Evaluating the exponent 6 means multiplying 6 by 10 six times:
6 x 10^6 = 6 x 10 x 10 x 10 x 10 x 10 x 10
Simplifying the expression, we get:
6 x 10^6 = 6,000,000
Therefore, 6E6 in standard form is 6,000,000.
3. Create your own piecewise function with at least two functions. Explain, using complete
sentences, the steps for graphing the function. Graph the function by hand or using a
graphing software of your choice (remember to submit the graph).
The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Answer:
The range of the function is all real numbers less than or equal to 9.
Step-by-step explanation:
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
have a great day and thx for your inquiry :)
Anita has invited her friends to her birthday party. Guess the number of friends she has invited
given the following clues:
•
They are more than the number of days in September.
The sum of their digits is 10.
The difference in their digits is 2.
They are less than 5 dozen.
10. At an exotic food store, a sign states that three pounds of
octopus costs $24. The owner tells you that the pricing of octopus
is a linear function based upon the weight in pounds.
a) Write a linear function to model the relationship between the
cost, c, of octopus and the weight, w, in pounds.
B) Explain the meaning of the slope of your equation as it relates to this problem.
The linear equation is solved and slope is m = (24 - b) / 3 = 8
Given data ,
a)
To write a linear function that models the relationship between the cost, c, of octopus and the weight, w, in pounds, we need to determine the equation of a line in slope-intercept form, y = mx + b, where y represents the cost of octopus (c) and x represents the weight in pounds (w).
We are given that three pounds of octopus costs $24. This gives us a point on the line, which is (3, 24). Using this point, we can find the slope (m) of the line.
Let's use the slope formula:
m = (y2 - y1) / (x2 - x1)
Taking (3, 24) as our first point, and choosing another arbitrary point on the line, let's say (0, b), we can substitute the coordinates into the slope formula:
m = (24 - b) / (3 - 0)
Since the slope is constant for the linear function, we can set this expression equal to m:
m = (24 - b) / 3
Now, we have the slope (m) in terms of b. To find the value of b, we can substitute the coordinates of the known point (3, 24) into the slope-intercept form:
24 = m * 3 + b
Substituting the expression for m:
24 = [(24 - b) / 3] * 3 + b
Simplifying:
24 = 24 - b + b
24 = 24
Since the equation is true for any value of b, we can choose any value for b. Let's choose b = 0 for simplicity.
Plugging in the values of m = (24 - b) / 3 and b = 0, we have:
m = (24 - 0) / 3
m = 24 / 3
m = 8
Therefore, the slope of the linear function is 8
b)
The meaning of the slope in this context is that for each additional pound of octopus purchased, the cost increases by $8. This means that the cost of octopus is increasing at a constant rate of $8 per pound. The positive slope indicates that as the weight of the octopus increases, the cost also increases.
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Mary gave her brother 1/4 of her plums and her sister 1/3. Mary remained with 20 plums. how many plums Mary had before sharing?
Craig has a building block in the shape of a rectangular pyramid. A net of which is shown below.
If a measures 16 cm, b measures 8 cm, and d measures 17 cm, what is the surface area of the rectangular pyramid?
The water usage at a car wash is modeled by the equation W(x) = 3x^3 + 4x^2 − 18x + 4, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x^3 + 2x^2 + 15, where D is the amount of water in cubic feet and x is time in hours.
Write a function, C(x), to model the water used by the car wash on a shorter day.
Answer:
C(x) = 2x^3 + 2x^2 - 18x - 11
Step-by-step explanation:
Step 1: To model the water used by the car wash on a shorter day, we can subtract the amount of water saved from the original water usage function.
Step 2: Therefore, we can define the new function C(x) as: C(x) = W(x) - D(x)
Step 3: Substituting the given functions for W(x) and D(x), we get: C(x) = (3x^3 + 4x^2 - 18x + 4) - (x^3 + 2x^2 + 15)
3x^3 + 4x^2 - 18x + 4 -x^3 - 2x^3 - 15
Step 4: Simplifying by combining like terms, we get:
C(x) = 2x^3 + 2x^2 - 18x - 11
Step 5: Therefore, the function C(x) that models the water used by the car wash on a shorter day is: C(x) = 2x^3 + 2x^2 - 18x - 11
George has opened a new store and he is monitoring its success closely.
He has found that this store’s revenue each month can be modeled by r(x)=x2+6x+10 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars.
He has also found that his expenses each month can be modeled by c(x)=x2−4x+5 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars.
What does (r−c)(4) mean about George's new store?
Responses
The new store will have a profit of $2300 after its fourth month in business.
The new store will have a profit of $2300 after its fourth month in business.
The new store will sell 4500 items in its fourth month in business.
The new store will sell 4500 items in its fourth month in business.
The new store will sell 2300 items in its fourth month in business.
The new store will sell 2300 items in its fourth month in business.
The new store will have a profit of $4500 after its fourth month in business.
Fourth month in business, George's new store will have a profit of $4500. The option "The new store will have a profit of $4500 after its fourth month in business" is the correct response.
To determine the meaning of (r - c)(4) for George's new store, we need to evaluate the expression (r - c) at x = 4.
Given that r(x) represents the store's revenue and c(x) represents the store's expenses, (r - c)(4) represents the difference between the revenue and expenses of the store after four months.
Substituting x = 4 into the expressions for revenue and expenses, we get:
r(4) = (4)^2 + 6(4) + 10 = 16 + 24 + 10 = 50
c(4) = (4)^2 - 4(4) + 5 = 16 - 16 + 5 = 5
Thus, (r - c)(4) = r(4) - c(4) = 50 - 5 = 45.
Therefore, (r - c)(4) means that after its fourth month in business, George's new store will have a profit of $4500 (since r(x) and c(x) are measured in hundreds of dollars).
The option "The new store will have a profit of $4500 after its fourth month in business" is the correct response.
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find the 5th term of the sequence: 2,5,10,17....... pls I need workings
Answer:
37
Step-by-step explanation:
The pattern is
2 (+3 =), 5 (+5 = ), 10 (+7) = , 17 (+9) =, 26 (+11) =, 37
So the difference between terms is +3, +5, +7, +9, +11... adding 2 each time, all odd numbers
Answer:
5th term is 26.
Step-by-step explanation:
5-2 =3. 10 - 5 = 5. 17 - 10 = 7.
notice how the differences are 3, 5, 7?
there's a gap of 2 between each difference.
so, let's call our next term in the sequence a.
a - 17 = (7+2).
a - 17 =9.
a = 26.
so, 5th term is 26.
What is the image of (-8, 6) after a reflection over the line y = -x?
The image of the point after a reflection over the line y = -x is (-6, 8)
Calculating the image of the point after a reflection over the line y = -x?From the question, we have the following parameters that can be used in our computation:
Point = (-8, 6)
Transformation rule
A reflection over the line y = -x
The rule of a reflection over the line y = -x is
(x, y) = (-y, -x)
Using the above as a guide, we have the following:
Image = (-6, 8)
Hence the image of the point after a reflection over the line y = -x is (-6, 8)
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Tianna recently ran a marathon. It took her 4.9 hours to run the 26.2 miles required to complete a marathon.
Find her average speed in miles per hour. Then convert her speed to feet per second. (Hint: 1 mile = 5,280 feet).
(Round your answers to two decimal places)
Number
miles per hour
Number
feet per second
Answer:
8.01 ft/sec
Step-by-step explanation:
Distance = 26.2 miles
Time is taken to run the distance = 4.8hrs
Average speed = ??
Average speed = distance/time
= 26.2miles /4.8hr
= 5.46 miles/hr
Convert 5.46 miles/hr to ft/sec
1 mile = 5280 ft
We have 5.46*5280 = 28828.8 ft/hr
28828.8/3600 = 8.01 ft/sec
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If you roll a 6-sided die 6 times, what is the best prediction possible for the number of times you will roll a six?
How many times?
The best prediction possible for the number of times you will roll a six when rolling a six-sided die six times is one.
The best prediction possible for the number of times you will roll a six in a six-sided die depends on the probability of getting a six in each roll. The probability of getting a six in a single roll of a six-sided die is 1/6 or 16.67%.
Since the rolls are independent events, the probability of rolling a six in any one of the six rolls is still 1/6 or 16.67%. Therefore, the best prediction possible for the number of times you will roll a six is one.
However, it is important to note that probability is not a guarantee, and it is possible to roll a six more than once or not at all. But based on the laws of probability, one is the most likely outcome for the number of times you will roll a six in six rolls of a six-sided die.
In summary, the best prediction possible for the number of times you will roll a six when rolling a six-sided die six times is one.
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Calculate how many 50 cents pieces are in the container if there are 220 pieces of 20 cents
If there are 220 pieces of 20 cents, then there are 380 pieces of 50 cents in the container.
Thabang conserves money by depositing coins in a money box. There are 600 coins in the money box, including 20- and 50-cent pieces.
We proceed as follows to determine how many 50 cent pieces are in the container if there are 220 pieces of 20 cent.
Assume that,
x = number of 20 cents
y = number of 50 cents
So, the total number of cents in the container is 600,so
x + y = 600
Making y the formula's subject, we therefore get that
y = 600 - x
Since x = 220
y = 600 - 220
y= 380
So, there are 380 fifty cents.
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The correct Question is
Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents. So calculate how many 50 cents pieces are in the container if there are 220 pieces of 20 cents
Determine the value of f (2) for the function. Please help!
The value of f (2) for the function is,
⇒ f (2) = undefined
We have to given that;
The function is defined as;
⇒ f (x) = { x³ + 18x² + 99x + 162 ; x ≤ - 3
= { (3x - 6) / (x³ - 7x + 6) ; - 3 < x ≤ 2
= { √(x² - 4) ; x > 2
Hence, We can see that;
At x = 2;
Function is defined as;
⇒ f (x) = (3x - 6) / (x³ - 7x + 6)
Plug x = 2;
⇒ f (2) = (3 × 2 - 6) / (2³ - 7×2 + 6)
⇒ f (2) = (6 - 6) / (8 - 14 + 6)
⇒ f (2) = 0 / 0
⇒ f (2) = undefined
Thus, The value of f (2) for the function is,
⇒ f (2) = undefined
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The slope of the line parallel to the line y = 10 - 8x.
A. 10
B. -8x
C. -8
D. 8
Answer:
The correct answer is C.
Step-by-step explanation:
you use y = mx +b
Zane is in charge of equipment at Putter Around Fun Center. He opens a huge new box of golf
balls that just arrived. The golf balls are assorted colors that are mixed throughout the box.
Zane has no idea how many of each color are in the box, so he randomly picks 30 balls out of
the box. He picks 8 yellow, 3 red, 5 orange, 6 green, and 8 pink golf balls.
Based on the data, what is the probability of choosing a red golf ball?
Write your answer as a fraction.
The probability of choosing a red golf ball as a fraction would be = 1/10.
How to calculate the probability of choosing a red ball at random?To calculate the probability of choosing a red ball at random, the formula that should be used is given below.
That is;
Probability = possible outcome/sample space
Total number of yellow balls= 8
Total number of red ball= 3
Total number of orange balls = 5
Total number of green balls = 6
Total number of pink balls = 8
possible outcome = 3 balls(red)
Sample space = 8+3+5+6+8= 30 balls
Then probability= 3/30 = 1/10
Therefore, when a ball is selected at random the probability that Zane would pick a red ball out of all the golf coloured balls would be= 1/10.
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what is the probability that one of the eggs selected at random was at least 19.75 mm long but less than 22.75 mm long ?
Note that he probability that one of the eggs selected at random was at least 19.75 mm long but less than 22.75 mm long is 0.6%
How did we arrive at this?The percent of eggs total 100.
Based on the frequency, we now that the eggs that are at least 19.75 mm include:
18.75 - 19.75 = 0.8
those that are less than 22.75mm long are:
19.75-20.75 = 4.0
20.75 - 21.75 = 17.3
21.75 - 22.75 = 37.9
Thus, the total of their frequencies are:
0.8 + 4.0 + 17.3 + 37.9 = those that are less than 22.75mm long but at least 19.75 long.
= 60
Thus, the probability that one of the eggs selected at random was at least 19.75 mm long but less than 22.75 mm long is 0.6%
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Full Question:
A biologist measured the lengths of hundreds of cuckoo bird eggs. Use the relative frequency distribution below to answer the questions that follow.
what is the probability that one of the eggs selected at random was at least 19.75 mm long but less than 22.75 mm long ? See attached image.
For ∆RST, RS=3ft, ST=6ft, and m∠R=29°. What are m∠T and m∠S
To find the measures of angles T and S, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
m∠R + m∠S + m∠T = 180°
We know that m∠R = 29°, and we can use the Law of Cosines to find the measure of angle S:
cos(m∠S) = (6^2 + 3^2 - x^2) / (2 * 6 * 3) = 0.9167
m∠S = cos^-1(0.9167) = 23.6°
Now we can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle T:
m∠T = 180° - m∠R - m∠S = 180° - 29° - 23.6° = 127.4°
Therefore, m∠T is 127.4° and m∠S is 23.6°.
mm m mm Answer:
Step-by-step explanation:
mnnmnmn
Write the standard equation of the circle with center (-5,12) that passes through the point (-9,15)
The standard equation of the circle with center (-5,12) that passes through the point (-9,15) is (x + 5 )² + (y - 12)² = 25.
What is the equation of the circle?The standard form equation of a circle with center (h, k) and radius r is:
(x - h)² + (y - k)² = r²
Given that; the center is (-5, 12) and a point on the circle is (-9, 15).
First, we determine the radius, we can use the distance formula between the center and the point on the circle:
[tex]r = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \\\\r = \sqrt{(-9 - (-5))^2+(15 - 12)^2} \\\\r = \sqrt{(-9 + 5)^2+(15 - 12)^2} \\\\r = \sqrt{(-4)^2+(3)^2} \\\\r = \sqrt{16+9} \\\\r = \sqrt{25} \\\\r = 5[/tex]
Now, center: (-5, 12)
h = -5
k = 12
and r = 5
Plug these into the equation above:
(x - h)² + (y - k)² = r²
(x - (-5) )² + (y - 12)² = 5²
Simplify
(x + 5 )² + (y - 12)² = 25
Therefore, the equation of the circle is (x + 5 )² + (y - 12)² = 25.
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A central angle in a circle with a diameter of 9 meters measures radians. 7/18 Find the length
of the arc intercepted by this angle.
To find the length of an arc intercepted by a central angle in a circle, we need to use the formula:
Arc Length = (Angle in radians) * (Radius)
In this case, the circle has a diameter of 9 meters, which means the radius is half of the diameter, so the radius is 4.5 meters.
The central angle measures radians, which we need to convert to radians. To convert a fraction to radians, we divide the numerator by the denominator and multiply by π (pi).
Radians = (7/18) * π
Now we can calculate the length of the arc:
Arc Length = (7/18) * π * 4.5
Simplifying this expression, we can calculate the approximate length of the arc.
It's important to note that the length of the arc is proportional to the measure of the central angle and the radius of the circle. The larger the central angle or the radius, the longer the arc.
In this case, the length of the arc will be determined by the specific value of the central angle in radians and the radius of the circle.
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Find the area of each paralleogram or rhombus
The area of the given parallelogram is 12 yd².
Given that a parallelogram of base 2 yds and height 6 yds,
We need to find the area of the parallelogram,
A parallelogram is a quadrilateral in which the opposite sides are parallel and equal. Parallelograms are classified into three main types: square, rectangle, and rhombus, and each of them has its own unique properties.
A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.
So, the area of a parallelogram = base × height
so the area of the given parallelogram = 6 × 2 = 12 yd²
Hence the area of the given parallelogram is 12 yd².
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Help plssssssss tyyyyyyyy
The solution of measure of angle e is,
⇒ e = 58 degree
We have to given that,
Two lines are intersect each other.
Hence, By definition of linear pair angle, we get;
⇒ e + 122 = 180
Subtract 122 from both sides to isolate e.
This gives us,
⇒ e = 180 - 122
⇒ e = 58
Therefore, The solution of measure of angle e is,
⇒ e = 58 degree
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The total mass of a trolley and some watermelons is 27 kg.
The total mass of the same trolley and some mangoes is 11 kg.
The mass of the watermelons was thrice the mass of the mangoes.
Answer:
Therefore, the mass of the trolley (T) and the mass of the watermelons (W) cannot be determined uniquely based on the given information. We can only express their relationship using Equation (3): 3T + W = 33.
Step-by-step explanation:
Let's assign variables to the masses involved to solve the problem systematically.
Let's say:
Mass of the trolley = T kg
Mass of the mangoes = M kg
Mass of the watermelons = W kg
According to the given information:
The total mass of the trolley and mangoes is 11 kg:
T + M = 11 -- Equation (1)
The mass of the watermelons is three times the mass of the mangoes:
W = 3M -- Equation (2)
Now, we can use these equations to find the values of T, M, and W.
From Equation (2), we can express M in terms of W:
M = W / 3
Substitute this value of M into Equation (1):
T + W / 3 = 11
Multiply through by 3 to eliminate the fraction:
3T + W = 33 -- Equation (3)
Now, we have a system of two equations (Equation 2 and Equation 3) with two unknowns (T and W). We can solve this system to find the values.
Since we don't have a specific value for any variable, we can express the solution in terms of the variables.
Therefore, the mass of the trolley (T) and the mass of the watermelons (W) cannot be determined uniquely based on the given information. We can only express their relationship using Equation (3): 3T + W = 33.
a box is 12cm long and 12cm wide and its 15cm tall what is the surface area of 4 boxes
The surface area of four boxes is 4032cm².
To calculate the surface area of one box, we need to find the area of each of its six faces and then add them up.
The top and bottom faces are both squares with sides of 12cm, so each has an area of 12cm x 12cm = 144cm².
The front and back faces are both rectangles with dimensions of 12cm x 15cm,
So each has an area of 12cm x 15cm = 180cm².
The two side faces are also rectangles with dimensions of 12cm x 15cm, so each has an area of 12cm x 15cm = 180cm².
Adding up the areas of all six faces, we get:
144cm² + 144cm² + 180cm² + 180cm² + 180cm² + 180cm² = 1008cm²
Therefore, the surface area of one box is 1008cm².
To find the surface area of four boxes, we just need to multiply the surface area of one box by 4:
The surface areas of all the faces together:
(144 x 2) + (180 x 2) + (180 x 2) = 504 sq.cm
The surface area of one box is 504 square centimeters.
Since you want the surface area of four boxes, simply multiply this number by 4:
504 sq.cm x 4 = 2016 sq.cm
1008cm² x 4 = 4032cm²
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A terrain in the form of an isosceles trapezoid has the measurements that appear in the figure:
The owner of the land placed a sign in which she wishes to specify the area of the land. Knowing that the height of the trapezoid is 8.7 m, I help complete the sign.
According to the information, we can infer that the sign should read: "Area of land: 178.35 square meters."
How to find the area of the trapezoid?To find the area of the trapezoid, we need to use the formula:
Area = (b1 + b2) / 2 * hwhere,
b1 and b2 = lengths of the parallel basesh = height of the trapezoidFrom the figure, we can see that:
b1 = 25 mb2 = 16 mSubstituting these values into the formula, we get:
Area = (25 + 16) / 2 * 8.7Area = 20.5 * 8.7Area = 178.35 square metersLearn more about figures in: https://brainly.com/question/30740690
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