1) The lines AC and BO are parallel (by alternate interior angles), so BMED is a trapezoid.
2) CD = 2AD.
Trapezoid and mid point1) To prove that BMED is a trapezoid, we need to show that BM || ED.
Since O is the midpoint of AM, we have OB || MD (as OB and MD are both perpendicular to AM).
Also, since E is the midpoint of DC, we have DE || AC (as DE and AC are both perpendicular to BC).
Therefore, to show that BM || ED, it is enough to show that AC || OB.
We know that OB is a transversal to the parallel lines BM and AM, so we have:
∠OBD = ∠MBC (corresponding angles)
Similarly, we have:
∠OAD = ∠ABC (corresponding angles)
Since ∠MBC = ∠ABC (because [AM] is the median), we have:
∠OBD = ∠OAD
Therefore, the lines AC and BO are parallel (by alternate interior angles), so BMED is a trapezoid.
2) To prove that D is the midpoint of [AE], we need to show that AD = DE.
Since [AM] is the median, we have:
AD = MC
Also, since E is the midpoint of DC, we have:
DE = EC
So it is enough to show that MC = EC.
Since O is the midpoint of AM, we have:
OM = MA/2
But MA = MC + AC/2 (because [AM] is the median), so we have:
OM = (MC + AC/2)/2
= MC/2 + AC/4
Also, since E is the midpoint of DC, we have:
OE = EC/2
But AC = 2DC (because [AM] is the median), so we have:
OE = EC/2 = AC/4
Therefore, we have:
OM = OE
So triangle OME is isosceles, and we have:
∠OEM = ∠OME
But ∠OED = ∠OEM (because DE || AC), so we have:
∠OED = ∠OME
Therefore, triangles ODE and OME are similar, so we have:
OD/OM = OE/OE
= 1
Therefore, OD = OM.
But we also have:
OM = MA/2 = MC/2 + AC/4
= AD/2 + AC/4 (because [AM] is the median)
So we have:
OD = OM = AD/2 + AC/4
= AD/2 + DC/2 (because AC = 2DC)
= (AD + DC)/2
= AE/2 (because E is the midpoint of DC)
Therefore, we have shown that D is the midpoint of [AE].
Moreover, we have:
CD = AE/2 = AD + DC/2 = AD + AC/4 (because AC = 2DC)
= AD + MC/2 (because [AM] is the median)
= AD + AD/2 (because AD = MC)
= 3AD/2
So we have CD = 2AD.
3) To prove that OD = 4BD, we need to show that BD = (1/4)OM.
Since [AM] is the median, we have:
BM = MC
Also, since O is the midpoint of AM, we have:
OM = BM/2 + AM/2
= BM/2 + 2BM/2 (because [AM] is the median)
= 3BM/2
Therefore, we have:
BD = BM - MD
= MC - MD
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I WILL GIVE 10 POINTS
Divide 15x5 − 3x3 − 9x2 by −3x2.
12x3 − 6x − 12
−5x3 − 6x + 3
−5x3 + x + 3
−5x3 + x − 3
The option (3) is correct the quotient is −5x³ + x + 3.
What is factorization method in quadratic equation ?To solve quadratic equations by factoring, we first express the quadratic polynomial into a product of factors by using middle term splitting or different identities and then set each factor equal to 0. The equation a x 2 + b x + c = 0 ( a ≠ 0 ) can be written as.
According to given question
To divide[tex]15x^5[/tex] − 3x³ − 9x² by −3x² using the factorization method, we can factor out −3x² from the expression and simplify to get:
[tex]15x^5[/tex]− 3x³ − 9x²= −3x²(−5x³ + x + 3)
Therefore, the quotient is −5x³ + x + 3.
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Use the form |x – b| < c or |x – b| > c to write an absolute value inequality that has the solution set x= < –9 or x>=-5.
Answer: |x + 9| > 0 or |x + 5| < 4
Step-by-step explanation: To begin with, ready to utilize the frame |x - b| > c to speak to the arrangement x < -9:
|x - (-9)| >
Rearranging this gives:
|x + 9| >
Another, we are able utilize the frame |x - b| < c to speak to the arrangement x ≥ -5. Ready to select a esteem of c that's more noteworthy than the remove from -5 to the closest endpoint of the arrangement set (which is -9):
|x - (-5)| < 4
Rearranging this gives:
|x + 5| < 4
Joining these two supreme esteem disparities with an "or" explanation gives:
|x + 9| > or |x + 5| < 4
Rearranging this gives:
x < -9 or -9 < x < -1
We will see that the primary portion of the arrangement set (x < -9) is as of now spoken to within the to begin with supreme esteem imbalance, and the moment portion (x ≥ -5) is spoken to by the moment supreme esteem imbalance.
Pre-Caclus 75 points + [tex]Brainliest[/tex]
Question shown in picture.
Options:
[tex]\frac{x - 28}{x-46}[/tex]
[tex]\frac{x - 13}{x-28}[/tex]
[tex]\frac{x - 7}{x-13}[/tex]
[tex]\frac{x - 13}{x-46}[/tex]
Expectations:
Correct
Explantion
Reasonable
Must not:
Incorrect
No explanation
Spam
Gibberish
Question:
Answer:
Factoring the polynomials and then simplifying:
[tex] \frac{ {x}^{2} - 20x + 91}{ {x}^{2} - 35x + 196} \times \frac{ {x}^{2} - 74x + 1288}{ {x}^{2} - 92x + 2116 } [/tex]
[tex] \frac{(x - 7)(x - 13)}{(x - 7)(x - 28)} \times \frac{(x - 28)(x - 46)}{(x - 46)(x - 46)} [/tex]
[tex] \frac{x - 13}{x - 46} [/tex]
Answer:
x−46
x−13
Step-by-step explanation:
Explanation in picture :)
A two-digit number is such that the sum of the digits is 13 and the product of the digits is 40. Find the number.
Answer: Either 58 or 85
Step-by-step explanation:
5 + 8 = 13
8 + 5 = 13
5 x 8 = 40
8 x 5 = 40
May you please go over step by step of how to do this
The missing lengths of a geometric system are listed below: AC = 114, BC = 96, BE = 3
How to determine missing lengths of two similar triangles
In this problem we find a geometric system formed by two similar triangles. Two triangles are similar if every pair of corresponding sides have the same proportion. Then, the system is described by this proportion formula:
AB / AC = AE / AD = BE / CD
18 / AC = 15 / 95 = BE / 19
Then,
18 / AC = 15 / 95
AC = 18 × (95 / 15)
AC = 114
15 / 95 = BE / 19
BE = 19 × (15 / 95)
BE = 3
Now, we determine the length of side BC:
BC = AC - AB
BC = 114 - 18
BC = 96
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Kyle who is a lifeguard is roping off a rectangular swimming area of 70 m. He uses the beach as one side.
Determine the minimum length, to 2 decimal places, of rope needed.
If he uses the beach as one side. the minimum length, to 2 decimal places, of rope needed is: 70 meters of rope.
What is the minimum length?Let's assume that the length of the swimming area is L and the width is W. The perimeter of the swimming area will be the length of the rope that Kyle needs to rope off the area.
From the problem, we know that one side of the swimming area is the beach, so we have:
L + W + L = 70
Simplifying this equation, we get:
2L + W = 70
To find the minimum length of rope needed, we need to minimize the perimeter of the swimming area. We can use the above equation to express W in terms of L:
W = 70 - 2L
Substituting this expression for W into the formula for the perimeter, we get:
P = L + W + L
= 2L + (70 - 2L)
= 70
So the perimeter of the swimming area is fixed at 70 m, regardless of the values of L and W. Therefore, the minimum length of rope needed to rope off the area is simply the perimeter of the swimming area, which is 70 meters.
Therefore, Kyle needs a minimum of 70 meters of rope.
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retail price $24.50; discount rate 15%
system of equations find the cost each treat please
The costs of each treat are
cookies = 6.48, ice cream 1 = 8.98 and ice cream 2 = 10.25cookies = 1.19, ice cream 1 = 2.99 and ice cream 2 = 4.99Finding the cost of each treat using system of equationsTo solve this, we use the followign representations
x = cookies
y = ice cream 1
z = ice cream 2
Treat 1
Using the columns to generate the system of equations, we have
x + y + z = 25.71
z + 2x = 23.21
3y = 26.94
So, we have
y = 8.98
The other equations become:
x + 8.98 + z = 25.71
z + 2x = 23.21
When solved, we have
x = 6.48
z = 10.25
Treat 2
Using the rows to generate the system of equations, we have
x + 2y = 7.17
y + 2x = 5.37
3z = 14.97
So, we have
z = 4.99
The other equations when solved, we have
x = 1.19
y = 2.99
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What do all products of the square of binomial have in common?
The square of binomial have in common is x² - 14x + 49
The first two products you have given, (x + 9)(x + 9) and (x - 7)(x - 7), are examples of the square of a binomial. To find the product of two binomials, we use what's called the FOIL method. FOIL stands for First, Outer, Inner, Last, and it's a way to remember the steps involved in multiplying two binomials.
When we multiply (x + 9)(x + 9), we first multiply the first terms in each binomial: x * x = x². Then we multiply the outer terms: x * 9 = 9x. Next, we multiply the inner terms: 9 * x = 9x. Finally, we multiply the last terms in each binomial: 9 * 9 = 81. So, putting it all together, we get:
(x + 9)(x + 9) = x² + 9x + 9x + 81
= x² + 18x + 81
Similarly, when we multiply (x - 7)(x - 7), we get:
(x - 7)(x - 7) = x² - 7x - 7x + 49
= x² - 14x + 49
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Complete Question:
Find each product. (x + 9) (x + 9) , (x - 7)(x - 7) (2x - 1 )²
a. What do all products of the square of a binomial have in common?
A campground allows a maximum of 6 campers in a camp site. How many camp sites does a group of 237 campers need?
a group of 237 campers would require 40 campsites (since we cannot have half of a campsite).
How to solve the question?
To determine the number of camp sites required for a group of 237 campers, we can divide the total number of campers by the maximum number of campers allowed per site.
237 campers ÷ 6 campers per site = 39.5
Since we cannot have a fraction of a campsite, we need to round up to the nearest whole number. This is because we need to ensure that there is enough space for all of the campers, and rounding up will ensure that we have enough sites to accommodate them.
Therefore, a group of 237 campers would require 40 campsites (since we cannot have half of a campsite).
It is important to note that while this calculation is a good starting point, it is always a good idea to check with the campground to ensure that they can accommodate a group of this size. Additionally, the campground may have specific policies or procedures in place for reserving campsites for large groups.
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help please
A family is filling up a circular pool. The pool has a depth of 6 feet and a diameter of 8 feet. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water will it take to fill up the pool completely? Use π = 3.14 and round to the nearest gallon.
2,255 gallons
1,127 gallons
301 gallons
40 gallons
To fill the entire pool we will 2,255 need gallons of water.
What is volume?Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.
Given, A family is filling up a circular pool. The pool has a depth of 6 feet and a diameter of 8 feet.
From the general formula of the volume of a cylinder,
Volume = pi × radius² × height
In our case,
radius = 8/2 = 4
Height = 6
Thus, Volume = 3.14 × 4 × 4 × 6
The volume of the Pool = 301.44 Cubic foot
Since there are 7.48 gallons of water in a cubic foot
Thus,
The volume of the pool in gallons = 301.44 × 7.48
The volume of the pool in gallons = 2,254.77
Therefore, to fill the entire pool we will 2,255 need gallons of water.
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Answer:
To fill the entire pool we will 2,255 need gallons of water.
Step-by-step explanation:
a continuous random variable x has a uniform distribution between 5 and 25 (inclusive), then p(x = 15) = 0.05. a. true b. false
Answer:
Step-by-step explanation:
The probability of a continuous random variable taking any specific value is always zero, so the statement p(x = 15) = 0.05 is false.
3-9 On a 1500 square foot gable roof, there will be approximately 11% waste. (True or False)
Given statement: On a 1500 square foot gable roof, there will be approximately 11% waste.
The given statement is False.
The statement provides information on the amount of waste but does not provide sufficient information to determine the total area of roofing material required for the gable roof.
Therefore, it is impossible to determine whether the waste percentage is accurate or not.
The statement "On a 1500 square foot gable roof, there will be approximately 11% waste" can be either True or False depending on the specific roofing materials and project details.
However, it's not uncommon for roofing projects to have waste percentages in that range (around 10-15%), especially for complex designs or when using materials like shingles.
Keep in mind that waste factors may vary depending on the type of roof, materials used, and installation methods. Always consult with a professional to get accurate waste estimates for your specific project.
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Special right triangles
The measure of angle FCD is 130 degrees.
What is an angle?
In planar geometry, an angle is a shape made up of two rays or lines that share an endpoint. The Latin word "angulus" (which means "corner") is where the word "angle" first arose.
The pair of alternative internal angles that are congruent must first be found. The angles formed on the opposing sides of the transversal EF are known as alternate internal angles since AB and CD are parallel lines. We possess
Angle AGE and angle FCD are alternate interior angles.
Angle AGE measures 130 degrees.
Therefore, we can conclude that angle FCD also measures 130 degrees. So, the measure of angle FCD is 130 degrees.
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what is the maximum number of mail swaps bagelbot can perform between officials from a and officials from b? assume every official regularly receives a lot of mail, and bagelbot can redirect any of it anywhere at any time. (i.e., what is the maximum number of edges possible for a bipartite graph between a and b?)
The maximum number of mail swaps that Bagelbot can perform between officials from A and officials from B can be 150 .
It can be determined by calculating the maximum number of edges possible for a bipartite graph between A and B. A bipartite graph is a graph in which the vertices can be divided into two disjoint sets such that every edge connects a vertex in one set to a vertex in the other set.
In this case, the officials from A and officials from B represent the two disjoint sets.
The maximum number of edges in a bipartite graph between A and B can be calculated as the product of the number of officials in A and the number of officials in B. Therefore, if there are n officials in A and m officials in B, the maximum number of mail swaps that Bagelbot can perform is n x m.
For example, if there are 10 officials in A and 15 officials in B, the maximum number of mail swaps that Bagelbot can perform is 10 x 15 = 150.
This means that Bagelbot can potentially redirect up to 150 pieces of mail between officials from A and officials from B.
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barron's reported that the average number of weeks an individual is unemployed is 18.5 weeks. assume that for the population of all unemployed individuals the population mean length of unemployment is 18.5 weeks and that the population standard deviation is 4 weeks. suppose you would like to select a sample of 40 unemployed individuals for a follow-up study. what is the probability that a simple random sample of 40 unemployed individuals will provide a sample mean within 1 week of the population mean? (round your answer to four decimal places.)
The probability that a sample mean of 40 unemployed individuals will be within 1 week of the population mean of 18.5 weeks with a population standard deviation of 4 weeks is 0.6827, rounded to four decimal places.
Given that the population mean length of unemployment is 18.5 weeks and the population standard deviation is 4 weeks, we want to find the probability that a simple random sample of 40 unemployed individuals will provide a sample mean within 1 week of the population mean.
The standard error of the sample mean is given by the formula
standard error = population standard deviation / sqrt(sample size) = 4 / sqrt(40) = 0.6325
Using the central limit theorem, we can assume that the sample mean follows a normal distribution with a mean of 18.5 weeks and a standard deviation of 0.6325 weeks.
To find the probability that the sample mean will be within 1 week of the population mean, we need to calculate the z-score for the lower and upper limits of the sample mean
z1 = (18.5 - 1 - 18.5) / 0.6325 = -1
z2 = (18.5 + 1 - 18.5) / 0.6325 = 1
Using calculator, we can find that the area between z = -1 and z = 1 is 0.6827.
Therefore, the probability that a simple random sample of 40 unemployed individuals will provide a sample mean within 1 week of the population mean is 0.6827 or 68.27% (rounded to four decimal places).
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3-7 If a hip roof has a slope of 6 inches per foot ( hip slope factor = 1.5) and a hip run of 14 feet. The length of the hip on feet will be:A. 15.B. 21.C. 22.D. 28.
The length of the hip on a hip roof rises 1.5 feet vertically.
The hip roof has a slope of 6 inches per foot ( hip slope factor = 1.5) and a hip run of 14 feet
Length of hip = (square root of (hip run squared + (hip slope factor x roof span squared)))
Plugging in the given values, we get:
Length of hip = (square root of (14 squared + (1.5 x 14 squared)))
Length of hip = (square root of (196 + 294))
Length of hip = (square root of 490)
Length of hip = 22 feet (rounded to the nearest whole number)
Therefore, the correct answer is C. 22.
It's important to note that the hip slope factor is a value used to calculate the actual slope of the hip, which is typically steeper than the pitch of the roof. In this case, the hip slope factor of 1.5 means that for every foot of horizontal run, the hip rises 1.5 feet vertically.
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Emily predicted her car payment to be $250 each month. Her actual car payment is $275 each month. By what percent was Emily’s prediction off?
Answer:
10%
Step-by-step explanation:
Express 660 parts per million as a percentage (answer must be numeric, no units or commas, include a leading zero when answer is less than 1)
When expressed as percentage, 660 parts per million will equal to 0.0066%.
Part per million (ppm) should be multiplied by 0.001 of it could be divided by 10000 to convert it into percentage. In order to convert 660 ppm to a percentage, divide it by 10,000, which yields 0.066.
This needs to be multiplied by 100 to achieve the final result of 0.066%, which is how we may describe it as a percentage. Because the answer is less than 1%, you'll see that we added a leading zero.
As a result, the answer is 0.066%.
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7PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answer: 26 degrees
Step-by-step explanation:
12/24 = 1/2
5
Select the correct answer,
Solve the following inequality for %.
z-9≤2(9)
O A. X=<9
OB. X> =11
OC. x<-7
OD. x<10
Answer:
1) -4<x<-2
2) x<-7 or x75
3) 2<x<7
4) x<-5 or x<6
5) x<-8 or x74
Step-by-step explanation:
if you throw exactly two heads in two tosses of a coin you win $120 . if not, you pay me $37 . step 2 of 2 : if you played this game 742 times how much would you expect to win or lose? round your answer to two decimal places. losses must be expressed as negative values.
If we throw, a coin in twice, then pay off for throw exactly two heads is $120. The expected win value in the game in 742 trials is equals to the $1669.5.
We have to two tosses a coin and we gift with payouts according to results of tossing. When we throw exactly two heads in two tosses of a coin, then pay out is $120. If not throw two heads then payout is $37… Now, number of times we play the game that is trials = 742
We have to determine value of expected value to win or loss for 742 trials. First we determine the excepted value of proposition. Total possible outcomes on two tosses of a coin = 4 = {HH,TT, HT, TH}
Probability of throwing two heads = 1/4
= 0.25
Probability of not throwing two heads
= 1 - 1/4 = 3/4 = 0.75
That is when x (pay off) = $120, P( x)
= 0.25 ; x (payout) = -$37, P( X) = 0.75. Now, the excepted value formula is written as, [tex]E( x) = \sum x× P(x) [/tex]
= $120 × 0.25 - $37 ×0.75
= $2.25
So, the expected value of win with 575 trials of gane = 2.25 × 742
= 1669.5
Hence, required excepted win value is $1669.5.
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Eat your cereal: Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 14 boxes. It is reasonable to assume that the population is approximately normal. 14.07 13.99 14.16 14.17 14.15 14.11 14.24 13.99 14.14 14.13 14.20 14.21 14.06 14.05 Send data to Excel Part: 0 / 20 of 2 Parts Complete Part 1 of 2 (a) Construct a 99.9% confidence interval for the mean weight. Round the answers to at least three decimal places. A 99.9% confidence interval for the mean weight is <<μ.
The 99.9% confidence interval for the mean weight is (14.042, 14.202).
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
To construct a 99.9% confidence interval for the mean weight, we can use the formula:
CI = X ± Zα/2 * (σ/√n)
where X is the sample mean, Zα/2 is the critical value from the standard normal distribution corresponding to a 99.9% confidence level (which is 3.291), σ is the population standard deviation (which we don't know, so we will use the sample standard deviation as an estimate), and n is the sample size.
First, we need to calculate the sample mean and sample standard deviation:
X = (14.07 + 13.99 + 14.16 + 14.17 + 14.15 + 14.11 + 14.24 + 13.99 + 14.14 + 14.13 + 14.20 + 14.21 + 14.06 + 14.05) / 14 = 14.122
s = sqrt((1/(n-1)) * ∑(xᵢ - X)²) = 0.072
where n is the sample size and ∑(xᵢ - X)² is the sum of squared deviations from the sample mean.
Plugging in the values, we get:
CI = 14.122 ± 3.291 * (0.072/√14) = (14.042, 14.202)
Therefore, the 99.9% confidence interval for the mean weight is (14.042, 14.202).
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A method of assigning probabilities based on historical data is called the
A method of assigning probabilities based on historical data is called the Empirical Probability method.
Empirical probability refers to the probability of an event based on observed data or past experience.
It is also known as experimental probability because it is determined through experimentation or observation.
This approach involves analyzing past events and their outcomes to calculate the probability of a particular event happening in the future.
To calculate empirical probability, you can use the formula:
Empirical Probability = (Number of successful outcomes) / (Total number of outcomes)
In this method, you collect and analyze historical data to make predictions about future events.
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the scores on a standardized test are normally distributed with a mean of 105 and standard deviation of 10. what test score is 0.6 standard deviations above the mean?
The test score that is 0.6 standard deviations above the mean is 111.
We can use the formula for z-score to find the test score that is 0.6 standard deviations above the mean:
z = (x - μ) / σ
where z is the number of standard deviations from the mean, x is the test score, μ is the mean, and σ is the standard deviation.
In this case, we want to find x when z = 0.6, μ = 105, and σ = 10:
0.6 = (x - 105) / 10
Multiplying both sides by 10, we get:
6 = x - 105
Adding 105 to both sides, we get:
x = 111
Therefore, the test score that is 0.6 standard deviations above the mean is 111.
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The test score that is 0.6 standard deviations above the mean is 111.
To find the test score that is 0.6 standard deviations above the mean, we can use the formula
z = (x - μ) / σ
where z is the number of standard deviations from the mean,
x is the test score we want to find,
μ is the mean of the distribution (105), and
σ is the standard deviation of the distribution (10).
We know that the desired test score is 0.6 standard deviations above the mean,
so we can set z = 0.6 and solve for x:
0.6 = (x - 105) / 10
Multiplying both sides by 10, we get:
6 = x - 105
Adding 105 to both sides, we get:
x = 111
Therefore, the test score that is 0.6 standard deviations above the mean is 111.
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is -6 greater than 3
Answer: no 3 is grade then -6 as 3 is positive number and 6 is negative number so positive is greater then negative number.
Step-by-step explanation:
In order to indicate if a number is greater than or less than another, we use the symbols > and <. For example, 10 is greater than 3, so we write it 10 > 3.
The variables x and y vary inversely. Use the given values to write an equation relating x and y . Then find y when x=−3 .
x = 1, y = 5
The equation is y =
Step-by-step explanation:
to vary inversely means that
y = k/x
the opposite would be to vary directly :
y = kx
so, in our case
5 = k/1
k = 5
y = 5/x
therefore, for x = -3
y = 5/-3 = -5/3 = -1.666666666...
Bryan is training for a triathlon and needs to swim a certain distance for today's workout. If he swims at the rec center pool, he will complete a 100-yard warmup and then swim laps in a lane that is 39 yards long. If Bryan swims at the indoor pool at his gym, he will complete a 104-yard warmup, plus a main set that consists of 37 yards per lap. If Bryan swims the correct number of laps, he can complete the same distance in either pool. How long will Bryan's workout be in total? How many laps will that take?
In linear equation, The required days for which Bryan's workout would be the same in either pool is 2 days.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
Here.
Let the number of days of B'ryan workout be x, the total yard he swims be y,
According to the question,
he swims at the rec center pool, will complete a 100-yard warm-up, and then swim laps in a lane that is 39 yards long.
y = 100 + 39x
Jason swims at the indoor pool at his gym, he will complete a 104-yard warmup, plus the main set that consists of 37 yards per lap.
y = 104 + 37x
Equating both the equation,
100 + 39x = 104 + 37x
39x - 37x = 104 - 100
2x = 4
x = 2 days
Thus, the requried days for which Bryan's workout would be the same in either pool is 2 days.
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I can’t solve Question 5, can anyone help?
6. Suppose the object hits the top of a tree that is 44 feet above the
ground. Write and solve an equation that allows you to find how many
seconds after being dropped that this occurs.
According to the Equation, the provided question's conclusion is that the object strikes the top of the tree in roughly 4 seconds.
What is Equation?An equation is a mathematical statement that demonstrates the equality of two expressions and is typically denoted by the equals symbol (=). Equations can be used to solve issues and make predictions as well as to express a wide variety of mathematical relationships.
The formula for the distance travelled by an object under constant acceleration can be used to solve this issue:
d = 1/2 * g * t²
where:
The distance travelled is d.
Gravitational acceleration (g) is around 32.2 feet per second squared.
T is the passing of time
Since the object is being dropped in this scenario, we know that its initial height is 0 feet and its ending height is 44 feet. For the duration of the trip, we may construct the following equation:
The required time is t seconds.
h(t) = 44
Simplifying:
-16t² + 300 = 44
16t² = 300 - 44
t² = 256/16
t² = 16
When both sides are squared:
t = 4 seconds
The time it takes for the object to strike the tree's top is therefore 4 seconds.
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The complete question is,
Let's say the object lands 44 feet above the ground, at the top of a tree. You may calculate the number of seconds after being dropped by writing and solving an equation.