Use the trapezoidal rule to approximate the value of
∫ ^4√xdx for n = 4
Answers
using the trapezoidal rule with n = 4, we can approximate the value of the integral ∫ ²4√xdx as 4.5417.
To approximate the value of the integral ∫ ²4√xdx using the trapezoidal rule with n = 4, we will first divide the interval [1,4] into 4 equal subintervals:
Δx = (4-1)/4 = 0.75
The 5 points at which we will evaluate the integrand are:
x0 = 1
x1 = 1.75
x2 = 2.5
x3 = 3.25
x4 = 4
Using the trapezoidal rule formula, we have:
∫ ²4√xdx ≈ Δx/2 [f(x0) + 2f(x1) + 2f(x2) + 2f(x3) + f(x4)]
where f(x) = x²(1/4)
Plugging in the values, we get:
∫ ²4√xdx ≈ 0.75/2 [f(1) + 2f(1.75) + 2f(2.5) + 2f(3.25) + f(4)]
≈ 0.375 [1 + 2(1.3161) + 2(1.4953) + 2(1.6746) + 2]
≈ 4.5417
Therefore, using the trapezoidal rule with n = 4, we can approximate the value of the integral ∫ ²4√xdx as 4.5417.
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Related Questions
the design of a square rug for your living room is shown. you want the area of the inner square to be 25% of the total area of the rug. find the side length x of the inner square
Answers
If the area of the inner square to be 25% of the total area of the rug, the side length of the inner square is 3 ft.
The first step to solve this problem is to find the area of the entire rug. Since one side of the rug is given as 6 ft, the area of the entire rug is:
Area of rug = (side length)² = 6² = 36 ft²
Next, we need to find the area of the inner square, which is 25% of the total area of the rug. We can write this as:
Area of inner square = 0.25 * Area of rug
Substituting the value of the area of the rug, we get:
Area of inner square = 0.25 * 36 = 9 ft²
The formula for the area of a square is A = side², so we can solve for the side length of the inner square as follows:
9 = x²
x = √(9)
x = 3 ft
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Complete question is:
The design of a square rug for your living room has one side of the rug is 6 ft. you want the area of the inner square to be 25% of the total area of the rug. find the side length x of the inner square.
Mr. Johns gave a test last week and Ginny missed one question. She answered that 14.5 people would ride on each bus rather than 15. Her parents would like a conference because she did the math problem correctly and should receive credit even though her answer was not reasonable. How should Mr. Johns handle this situation
Answers
Mr. Johns handle this situation to Agree to meet, listen to their concerns, and then explaining that one component of math is understanding reasonable answers.
Mr. Johns gave a test last week and Ginny missed one question. She answered that 14.5 people would ride on each bus rather than 15. Her parents would like a conference because she did the math problem correctly and should receive credit even though her answer was not reasonable.
Mr. Johns handle this situation to Agree to meet, listen to their concerns, and then explain that one component of math is understanding reasonable answers.
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What is the compliment of a 45 degree angle
Answers
The complement of 45° is the angle that when added to 45° forms a right angle (90° ).
in exercises 39–66, use the appropriate limit laws and theorems to determine the limit of the sequence or show that it diverges. an = 10 + (–1/9)^n
Answers
The given sequence is defined as a_n = 10 + (-1/9)^n. By applying the limit laws and theorems, we can determine the limit of the sequence or show that it diverges.
The sequence a_n = 10 + (-1/9)^n does not converge to a specific limit. The term \((-1/9)^n\) oscillates between positive and negative values as n approaches infinity.
As n increases, the exponent n alternates between even and odd values, causing the term (-1/9)^n to alternate between positive and negative. Consequently, the sequence does not approach a single value, indicating that it diverges.
To further understand this, let's analyze the terms of the sequence. When n is even, the term (-1/9)^n becomes positive, and as n increases, its value approaches zero.
Conversely, when n is odd, the term (-1/9)^n becomes negative, and as n increases, its absolute value also approaches zero. Therefore, the sequence oscillates indefinitely between values close to 10 and values close to 9.
Since there is no ultimate value approached by the sequence, we can conclude that it diverges.
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Two congruent ellipses are perpendicular to each other. Squares fill the gaps between the two ellipses as shown. Show that the side of the square equals half the minor axis of the ellipse.
Answers
The side of the square equals half the minor axis of the ellipse.
To show that the side of the square is half the minor axis of the ellipse, we must prove that the angles of the ellipses and the squares are congruent. To do this, we must first draw in the diagonals of the square, which will form two additional isosceles triangles.
Since the ellipses are perpendicular, the angles of the ellipses and the squares will be the same. Since the angles of the isosceles triangles are equal, the side of the square must be equal to half of the minor axis of the ellipse. Therefore, the side of the square is equal to half of the minor axis of the ellipse.
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show us a parallelogram ABCD is given.If the diagonals AC and BC interest at O and AO = 4cm, find the length of AC.
plssssssss write the real answer.
Answers
Answer:
8 cmStep-by-step explanation:
We know the diagonals of a parallelogram bisect each other.
If O is the point of intersection of diagonals, AC is split into AO and OC.
AC = AO + OCSince AO = OC, the length of AC is:
AC = 2*AO = 2*4 cm = 8 cmWhen Bruce got his first job, he put $6,225 of his earnings into an investment account to save for retirement. The value of the account is predicted to double each decade.
If Bruce makes no other deposits or withdrawals, what can he predict the value of his investment account to be after 3 decades?
Answers
Answer: Bruce can predict the value of his investment account to be $49,800 after 3 decades
Step-by-step explanation:
If the value of the investment account doubles every decade, then after one decade (10 years), it will be worth $6,225 x 2 = $12,450.
After two decades (20 years) it will be worth $12,450 x 2 = $24,900.
Finally, after three decades (30 years), it will be worth $24,900 x 2 = $49,800.
Therefore, Bruce can predict the value of his investment account to be $49,800 after 3 decades if he makes no other deposits or withdrawals.
jesse is putting a ribbon around a square frame. He uses 24 inches of ribbon. How long is each side of the frame
Answers
24÷4=6
So six
you roll a 6-sided dice.
what is p(1)?
write your answer as a fraction or whole number.
how would I go about solving this?
Answers
Answer:
\(\frac{1}{6}\)
Step-by-step explanation:
ok so the probabilty of getting something on a six sided die is \(\frac{1}{6}\), since there was 6 possible outcomes. so the probabolity of getting 1 would be 1 out of 6
i hope this helps :)
A survey asked 80 students if they watch football and if they like to watch basketball. The results are given in the following two-way table
Answers
Answer:
It will be 53
Step-by-step explanation:
add all of them up together
A flagpole 12 meters tall casts a 24-meter shadow. Nearby, luke stands and is 4 meters tall. Determine the length of luka's shadow. Include all labels.
Answers
Answer:
8 meters
Step-by-step explanation:
This is a question that deals with Proportion
Height of flagpole/Shadow of flagpole = Height of Luke/Shadow of Luke
Length of the shadow of Luke = x
= 12/24 = 4/x
We cross Multiply
12 × x = 24 × 4
x = 24 × 4/12
x = 8 meters
Hence, the length of the shadow of Luke = 8 meters
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
Question 2
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
Question 3
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20
A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.
Question 4
The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can we draw from the circle graph?
Together, Streetcar and Cable Car are the preferred transportation for 168 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
Bus is the preferred transportation for 45 residents.
Bicycle is the preferred transportation for 50 residents.
Question 5
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
Question 7
At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer mustard on a hot dog?
900
2,000
2,100
4,000
Question 8
The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
Answers
Burger Quick, because it has a larger median.
How to explain the informationBurger Quick typically has more wait time because it has a larger range (30-2=28) compared to Super Fast Food (27-3=24) and also has a larger interquartile range (IQR) (24-9.5=14.5) compared to Super Fast Food (15.5-8.5=7), indicating more variability in the wait times. The fact that Burger Quick's median (15.5) is larger than Super Fast Food's median (12) reinforces this conclusion.
Therefore, the correct answer is: Burger Quick, because it has a larger median.
Answer 2: The appropriate measure of center for this data is the median, which is represented by the line in the box at 19. This is because the data is skewed, with a longer tail to the right, and the median is less sensitive to extreme values compared to the mean. Therefore, the correct answer is: The median is the best measure of center, and it equals 19.
Answer 3: The measure of variability that the charity should use to accurately represent the data is the IQR (Interquartile Range), which is the range of the middle 50% of the data. The reason for this is that the data is skewed to the right, with many values concentrated in the upper range of the data, and the IQR is less sensitive to outliers compared to the range.
The IQR for this data is 20-10=10, which represents the spread of the middle 50% of the data. Therefore, the correct answer is: The IQR of 20 is the most accurate to use, since the data is skewed.
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Shiloh is starting a new workout regimen. Her trainer recommends that she increase the number squats she does by 35% every week. If in the second week Shiloh is doing 108 squats, how many squats did she do during her first week?
Answers
Shiloh has done 80 squats during her first week.
Shiloh was recommended by the trainer to increase the number of squads she does by 35% every week, so she does 108 squats in the second week. We have to find how many squats she did during her first week.
This is the percentage increase in value that something obtains that is greater than 100.
Let the number of squats in the first week be x.
After increasing by 35% she does 108 squats.
x+35/100*x=108
x+0.35*x=108
1.35x=108
x=108/1.35
x=80 squats.
Therefore, the number of squats she did in first week is 80 squats before increasing the squats by 35 percentage.
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Find the equation of the line through (−1,−2) which is perpendicular to the line y=x^2−9.
Give your answer in the form y=mx+b.
Answers
The equation of the line through (−1,−2) which is perpendicular to y = 2x - 9 is y = -(1/2)x - 5/2
What is an equation?
An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents
The standard form of a linear function is:
y = mx + b
where m is the rate of change (slope) and b is the y intercept
Two lines are perpendicular if the product of their slope is -1.
Given the line y = 2x - 9. The line perpendicular to y = 2x - 9 would have a slope of -1/2.
The line perpendicular to y = 2x - 9 that includes the point (-1, -2), is:
y - y₁ = m(x - x₁)
substituting:
y - (-2) = (-1/2)(x - (-1))
y = -(1/2)x - 5/2
The equation of the line is y = -(1/2)x - 5/2
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I only need help with 10
Answers
Answer:
im pretty sure its a,e and i,d
Step-by-step explanation:
i need help with this question!
Answers
Answer:
c¹⁵
Step-by-step explanation:
When there are parenthesis like that you multiply the exponents.
Find the first 4 terms of the sequence defined by f(1) = 8 and f(n) = f(n-1)- 7
8, 1, -6, -13
8, 15, 22, 29
1, 8, 15, 22
-7, 1, 9, 17
Answers
Answer:
16
Step-by-step explanation:
2 times 1 is 2
7) in ΔFGH, FH= 8ft, FG= 13ft, and m∠F = 72°. Find the length of HG. Label the diagram to help you. round your number to the nearest whole number.
8) What is the measure of x in the triangle below? Round to the nearest degree. the figure is not drawn to scale.
Answers
7) Required value of HG is 13 ft.
8) The measure of x in the triangle below is 13 ft.
What is value of cosine formula ?
let say there is AABC,and opposite side of ZA is a, opposite side of <B is b, opposite side of C is c.
then cos(A) = (b² × c² - a²)/(2bc)
given that AFGH . FH = 8ft , FG = 13ft ,and m angle F = 72 deg
by law of cosines to find the HG, since
we know the lengths of FH and FG and
the measure of angle F.
Let's say length of HG be "x".
Then by law of cosines:
x² = 8² + 13²- 2(8)(13) × cos(72°)
x²= 64 + 169 - 208cos(72°)
cos(72°) , which is approximately 0.309., we get:
x²= 233 - 208(0.309)
x² = 169.072
x² = 64+169-208cos(72°)
cos(72°), which is approximately 0.309., we get:
x² = 233-208(0.309)
x²= 169.072
Taking the square root of both sides, we get:
x = 13 (approx)
So the length of HG is approximately 13 feet.
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which terms are used to describe events that have NO outcomes in COMMON?
Answers
Events that have no outcomes in common are said to be disjoint or mutually exclusive.
Two sets are known to be mutually exclusive when they have no common elements. Mutually exclusive events are those that cannot take place at the same moment.
If two events are considered disjoint events, then the probability of both events occurring at the same time will be zero.
Set A = {2, 4, 6, 8, 10, 12, 14, 16}
Set B = {1, 3, 5, 7, 9, 11, 13, 15}
A and B do not have any numbers in common, so P (A ∩ B) = 0. Therefore, A and B are mutually exclusive.
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Wes wanted to bake cookies so he preheated the oven, the graph below shows the temperature of the oven over different periods of time
Answers
the temperature will be 2.5 degrees per second.
We are given the data:
Seconds Temperature (°F)
0 75
10 100
20 125
30 150
We need to find the temperature in degrees per second.
So, we get that:
Seconds Temperature (°F) degrees / sec
0 75 Nil
10 100 (100 - 75) / (10 - 0) = 2.5
20 125 (125 - 100) / (20 - 10) = 2.5
30 150 (150 - 125) / (30 - 20) = 2.5
Therefore, the temperature will be 2.5 degrees per second.
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Amelia is standing next to a lighthouse on the edge of a cliff overlooking the ocean. The cliff is 30 meters above sea level, and the lighthouse has a height of 15 meters. There is a man fishing in a boat directly below Amelia who has hooked a fish that is 10 meters below the surface of the water. Use a positive or negative number to represent the location in relation to sea level. Amelia= Top of the Light house= The Boat= The Fish= How many meters is Amelia from the fish?
Answers
Answer:
Amedia = 30 m
Top of the Lighthouse = +45 m
Boat = 0
Fish = - 10 m
The distance between Amelia and the fish is 40 meter
Step-by-step explanation:
Amelia = 30 m ( height of the cliff) since Amelia is standing on it's edge
-Top of lighthouse = lighthouse is located on top of the cliff ;
mean height of cliff + height of light house = (30 + 15) = 45 m
-The boat = 0 (on the surface of water) ; this is the sea level surface or point
-The fish = - 10 m (10 meters below the water surface).
Distance between Amelia and fish :
30 m - ( - 10 m) = 30 m + 10 m = 40 m
Find the sum of the squares of 3, 2, 1, and -1
Answers
Answer:
15
Step-by-step explanation:
3 x 3=9
2 x 2=4
1x1=1
-1x-1=1
9+4+1+1=15
Answer:
15
Step-by-step explanation:
The square of 3 is 3 times 3, so 9.
2 times 2 is 4.
1 times 1 is 1.
-1 times -1 is 1, because the negative cancels out.
So, it's 9 plus 4 plus 1 plus 1, so the answer is 15.
a gambler is betting on a coin-flip game. if it is head he wins $1 but if it is tail he loses $1. suppose the coin is fair, that is, the probability of head or tail is 1/2, what is the standard deviation of his payoff?
Answers
The gambler's payoff has a standard deviation of $1. The gambler can expect to win or lose $1 on average for each coin flip, and there is a high degree of variability in the possible outcomes of the game.
The standard deviation of the gambler's payoff can be calculated using the following formula:
σ = √(Σ(xi - μ)^2 * P(xi))
where σ is the standard deviation, xi is the possible outcome of the game, μ is the expected value of the game, and P(xi) is the probability of each outcome.
In this case, there are two possible outcomes: winning $1 with probability 1/2 and losing $1 with probability 1/2. The expected value of the game is:
μ = (1/2 * $1) + (1/2 * -$1) = $0
To calculate the standard deviation, we need to determine the variance first. The variance can be calculated as:
σ^2 = Σ(xi - μ)^2 * P(xi)
= (1 - 0)^2 * 1/2 + (-1 - 0)^2 * 1/2
= 1
Therefore, the standard deviation is:
σ = √1 = 1
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Add.
-1 3/4 + (-3/5) + (-1/4)
Enter your answer as a simplified mixed number in the box.
Answers
Answer:
-2 3/5
Step-by-step explanation:
that is the answer yep
Patrick is excited to attend his son’s soccer game tomorrow
evening, but he also needs to ensure his daughter arrives at her
coding class on time. Patrick is debating whether taking the train
or his
Answers
Personal car would be the best option to manage both tasks efficiently. While the train is a reliable mode of transportation, it may have fixed schedules that might not align perfectly with Patrick's needs.
On the other hand, using his personal car provides more flexibility and allows him to tailor the departure time according to his daughter's coding class schedule.
If Patrick decides to take the train, he would need to check the train schedule to see if there are convenient departure and arrival times for both the soccer game and the coding class. This option would require planning and coordination to ensure he arrives at the game on time and can pick up his daughter afterward.
Using his personal car gives Patrick the freedom to leave at a time that accommodates both the soccer game and the coding class. He can drop off his daughter at her coding class, attend the soccer game, and then pick her up afterward without being restricted by train schedules.
Considering the circumstances, Patrick might find it more convenient to use his personal car to manage both tasks effectively and ensure he can attend his son's soccer game while also ensuring his daughter arrives at her coding class on time.
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Assume that a country is endowed with 5 units of oil reserve. There is no oil substitute available. How long the oil reserve will last if (a) the marginal willingness to pay for oil in each period is given by P = 7 - 0.40q, (b) the marginal cost of extraction of oil is constant at $4 per unit, and (c) discount rate is 1%?
Answers
Given the marginal willingness to pay for oil, the constant marginal cost of extraction, and a discount rate of 1%, the oil reserve will last for approximately 10.8 periods.
To determine how long the oil reserve will last, we need to find the point at which the marginal cost of extraction equals the marginal willingness to pay for oil. In this case, the marginal cost is constant at $4 per unit. The marginal willingness to pay is given by the equation P = 7 - 0.40q, where q represents the quantity of oil extracted.
Setting the marginal cost equal to the marginal willingness to pay, we have:4 = 7 - 0.40q
Simplifying the equation, we get:0.40q = 3
q = 3 / 0.40
q ≈ 7.5So, at q ≈ 7.5, the marginal cost and marginal willingness to pay are equal. We can interpret this as the point at which the country would extract the oil until the quantity reaches 7.5 units. To determine how long this would last, we need to divide the total oil reserve (5 units) by the extraction rate (7.5 units per period):5 / 7.5 ≈ 0.67
Since the extraction rate is less than 1 unit per period, it means that the oil reserve will last for approximately 0.67 periods. However, the discount rate of 1% needs to be taken into account. To calculate the present value of the oil reserve, we discount each period's value. Using the formula for present value, we find that the oil reserve will last for approximately 10.8 periods.
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Sabrina is going to rent a bicycle while in vacation. There are two rental companies she can choose from. The first company charged $10 plus a rate of $2 per hour until the bicycle is returned. The second company’s rental charges can be represented by the equation c=3h+6 where c represents the rental cost and h represents the number of hours the bicycle is rented. If Sabrina plants to bicycle for 3 hours, what is the least amount she could pay in rental fees?
Answers
Answer:
pretty sure its 16 but im not sure.
Step-by-step explanation:
Use estimation to evaluate 8,627.5 ÷ 35
Answers
Answer:
246.5
Step-by-step explanation:
86275÷35
= 246.5
approximately 247
What is the following product? Assume y greater-than-or-equal-to 0 3 StartRoot 10 EndRoot (y squared StartRoot 4 EndRoot StartRoot 8 y EndRoot).
Answers
The product is given as 6y²√10 +12√5y. Option A
How to determine the productIt is important to know that algebraic expressions are defined as expressions that are made up of terms, variables, constants and factors.
From the information given, we have that;
3√10 (y²√4 + √8y)
Substitute the value√4 with 2
3√10(y²×2 +√8y)
Substitute √8y with 2√2y
3√10(2y²+2√2y)
Expand the bracket, we get;
3×2y²√10 + 3×2×√10×√2y
Multiply the value, we get;
6y²√10 + 6√20y
simplify √20y to 2√5y
6y²√10 + 6 × 2√5y
Multiply the values, then add the product of the separate expressions, we get;
6y²√10 +12√5y
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The complete question:
What is the following product? Assume y greater-than-or-equal-to 0
3 StartRoot 10 EndRoot (y squared StartRoot 4 EndRoot + StartRoot 8 y EndRoot)
A. 6 y squared StartRoot 10 EndRoot + 12 StartRoot 5 y EndRoot
B. 6 StartRoot 10 EndRoot + 12 StartRoot 5 y EndRoot
C. 6 y squared StartRoot 10 EndRoot + 4 StartRoot 5 y EndRoot
D. 3 y squared StartRoot 10 EndRoot + 12 StartRoot 5 y EndRoot
Please answer correctly !!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!
Answers
SBSE: Remember, that whole line is 180 degrees, and the right angle would be 90 degrees.
If there are one variable, then there is only one equation.
The equation would be 54+90+8p+4=180
Let’s solve that!
54+90+4 is 148.
Then move that back to the main equation: 148+8p=180
8p=180-148
8p=32
p=32/8
p=4
p would be 4!