The statement "If f(n) = O(g(n)) and g(n) = Ω(h(n)), then f(n) = Θ(h(n))" is actually true.
This can be proven using the formal definitions of the O-notation, Ω-notation, and Θ-notation:
f(n) = O(g(n)) means that there exist positive constants c and n0 such that |f(n)| ≤ c|g(n)| for all n ≥ n0.
g(n) = Ω(h(n)) means that there exist positive constants c' and n0' such that |g(n)| ≥ c'|h(n)| for all n ≥ n0'.
f(n) = Θ(h(n)) means that there exist positive constants c1, c2, and n1 such that c1|h(n)| ≤ |f(n)| ≤ c2|h(n)| for all n ≥ n1.
If we assume that f(n) = O(g(n)) and g(n) = Ω(h(n)), we can use the definitions above to show that f(n) = Θ(h(n)).
Since g(n) = Ω(h(n)), we have |g(n)| ≥ c'|h(n)| for some positive constants c' and n0', and since f(n) = O(g(n)), we have |f(n)| ≤ c|g(n)| for some positive constants c and n0.
Combining these two inequalities, we get:
|f(n)| ≤ c|g(n)| ≤ c(c'/c)|h(n)|
Therefore, f(n) = Θ(h(n)) with constants c1 = 1 and c2 = c(c'/c), and n1 = max(n0, n0').
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I don’t understand this can someone help
The ordered pair (2,10) means that the cost to feed 200 animals is of $10,000.
How to interpret the ordered pair?The general format of an ordered pair is given as follows:
(x,y).
The meaning of an ordered pair (x,y) is that y = f(x), meaning that the numeric value of the function at the value of x is of y.
The variables for this problem are given as follows:
x -> number of animals, in hundreds, hence x = 2 means that there are 200 animals.y -> cost to feed the animals, in thousands, hence y = 10 means that the cost is of $10,000.More can be learned about ordered pairs at brainly.com/question/1528681
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Please help me it’s a drag and drop
Which cylinder has a volume of 45% cm³?
Answer:
Right cylinder
Step-by-step explanation:
Right cylinder
i wasnt here when we did this, please help?
Answer:
25°
Step-by-step explanation:
look at the picture, that's the ans
Answer:
x = 25.4
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
139° is an exterior angle of the triangle, then
5x - 25 + 37 = 139
5x + 12 = 139 ( subtract 12 from both sides )
5x = 127 ( divide both sides by 5 )
x = 25.4
LA Galaxy have won 36%of their soccer matches .If they have played 50 matches ,how many have they won ?
If LA Galaxy has won 36% of their soccer matches, this means that they have won 36/100 * 50 = 18 matches.
So, they have won 18 matches out of 50.
Step-by-step explanation:
percentage of soccer matches won = 36%
total matches = 50
matches won = 36/100 * 50
=18
in a normal distribution with a mean of 90 and a standard deviation of 5, which of the following scores lie within one standard deviation of the mean? select one: a. 5-90 b. 80-100. c. 85-95. d. 90-95.
The range of 85-95 is within one standard deviation of the mean in a normal distribution with a mean of 90 and a standard deviation of 5,the correct answer is c. 85-95.
The normal distribution is a bell-shaped curve that is centered around the mean and symmetrical about the mean. In a normal distribution with a mean of 90 and a standard deviation of 5, one standard deviation of the mean would be 85-95. This means that any score within this range is within one standard deviation of the mean.
To calculate this, we first look at the mean, which is 90. To find the value of one standard deviation from the mean, we need to subtract 5 from 90 to get 85. To find the upper limit of one standard deviation, we add 5 to 90 to get 95. Therefore, any score between 85 and 95 is within one standard deviation of the mean.
To summarize, any score within the range of 85-95 is within one standard deviation of the mean in a normal distribution with a mean of 90 and a standard deviation of 5. Therefore, the correct answer is c. 85-95.
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Joe and Martha shared 56 books joe had 2 more books than Martha how many did Martha have
Answer:
26
Step-by-step explanation:
56/2 -2
an analyst has a sample of 28 observations of the weekly return of an index portfolio that includes 50 stocks. the weekly returns are approximately normally distributed, and the sample mean and sample variance are 1.2% and 0.00175. a 90% confidence interval for a weekly return is closest to:
We are 90% confident that the true weekly return of the index portfolio is between 1.186% and 1.214%.
One important concept in statistics is a confidence interval, which is a range of values that is likely to contain the true value of a parameter, such as a population mean or proportion.
The analyst has a sample of 28 observations of the weekly return, which is assumed to be normally distributed. The sample mean is 1.2% and the sample variance is 0.00175. With this information, we can calculate the standard error of the mean, which measures the variability of the sample mean from one sample to another. The formula for the standard error is:
standard error = sample standard deviation / square root of sample size
In this case, the sample standard deviation is the square root of the sample variance, which is approximately 0.0418%. The square root of the sample size is 5.2915. Therefore, the standard error of the mean is:
standard error = 0.0418 / 5.2915 = 0.0079%
To construct a 90% confidence interval for the weekly return, we need to use the t-distribution, which is a probability distribution that takes into account the sample size and the level of confidence. The t-distribution has more variability than the normal distribution, which results in wider confidence intervals for smaller sample sizes.
The formula for a t-confidence interval is:
sample mean ± t-value x standard error
The t-value depends on the sample size and the level of confidence. For a sample size of 28 and a 90% confidence level, the t-value is 1.699. Therefore, the confidence interval is:
1.2 ± 1.699 x 0.0079 = [1.186%, 1.214%]
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What are the coordinates of(D0.25∘rx-axis)(ABCD) for A(2, 6), B(0, 0), C(-5, 8), and D(-2, 10)?
(express ordered pairs as decimal)
Answer: The coordinates of the image of a figure after a rotation of 0.25 degrees about the x-axis can be found using the following formulas:
x' = x
y' = y * cos(θ) - z * sin(θ)
z' = y * sin(θ) + z * cos(θ)
where (x, y, z) are the original coordinates and (x', y', z') are the new coordinates. In this case, we only need to find the y' coordinate because the rotation is about the x-axis and the x coordinate will not change.
For each point, we can use the formula to find the y' coordinate:
A (2, 6) -> y' = 6 * cos(0.25) - 0 * sin(0.25) = 5.99911... ~ 6
B (0, 0) -> y' = 0 * cos(0.25) - 0 * sin(0.25) = 0
C (-5, 8) -> y' = 8 * cos(0.25) - 0 * sin(0.25) = 7.99823... ~ 8
D (-2, 10) -> y' = 10 * cos(0.25) - 0 * sin(0.25) = 9.99649... ~ 10
So, the new coordinates after rotating 0.25 degrees about the x-axis are:
A (2, 6) -> (2, 6)
B (0, 0) -> (0, 0)
C (-5, 8) -> (-5, 8)
D (-2, 10) -> (-2, 10)
The coordinates of the points have not changed after the rotation because the rotation angle is very small.
Step-by-step explanation:
How much money in dollars and cents did Julie have to spend after buying the chair?
How are lim p(x) and lim p(x) calculated if p is a polynomial function?
Limits function lim p(x) can be calculated if p is a polynomial function by:
Identify the degree of the polynomial.Substitute the defined limits with xSimplify and solve the limits function.To calculate the limits of a polynomial function, p(x), first identify the degree of the polynomial. Then, use the formula Lim p(x) = aₙ xⁿ + aₙ₋₁ xⁿ⁻¹ + ... + a₀, where an is the leading coefficient. For example, if the polynomial is of degree 3, then the formula would be:
Lim p(x) = a₃ x³ + a₂ x² + a₁ x + a₀.
Next, we need to subtitute the variable x with the defined limits. For example, if the defined limit of the function is 2, then the limit function would be:
Lim p(2) = a₃ (2)³ + a₂ (2)² + a₁ (2) + a₀
Then, we just need to simplify our finding:
Lim p(2) = 8a₃ + 4a₂ + 2a₁ + a₀
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Pete is saving $0. 45 each week to buy a video game that cost $9. 0. How many weeks will he have to save?
If , Pete is saving $0. 45 each week to buy a video game that cost $9.0. Pete will have to save for 20 weeks to have enough money to buy the video game.
The problem asks us to find out how many weeks Pete will have to save to buy a video game that costs $9.0 if he is saving $0.45 each week. To solve this problem, we can use division to find out how many times $0.45 goes into $9.0.
We first divide the total cost of the game by the amount Pete saves each week, which gives us the number of weeks he will need to save.
In this case, the division of $9.0 by $0.45 yields 20, which means that Pete will have to save for 20 weeks to buy the video game. This calculation is important for Pete because it helps him plan his savings and gives him a goal to work towards. By saving $0.45 every week, he can keep track of his progress and stay motivated to reach his goal.
This problem highlights the importance of basic arithmetic skills, specifically division, in practical situations like budgeting and financial planning. By applying mathematical concepts to everyday situations, we can make informed decisions and manage our resources more effectively.
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A haiku is a poem with three lines: the first line contains 5 syllables, the second line 7 syllables, and the last line 5 syllables. If each word in each list shown is used at most once, how many different haiku can be made with these words?
2 syllable words:
UNKNOWN
MEASURE
COUNTING
LOGIC
3 syllable words:
ALGEBRA
TRIANGLE
REASONING
There will be 350 different haiku that can be made with the given words.
How to calculate the valueIn this case, there are 5 syllables in the first line, 7 syllables in the second line, and 5 syllables in the last line, so the number of different haiku is given by the number of combinations of 3 elements taken from the set containing 5 elements (for the first and last lines) and 7 elements (for the second line), respectively.
This can be calculated as:
C(5,3) * C(7,3) = 10 * 35
= 350
So, there are 350 different haiku that can be made with the given words.
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Hello can somebody please explain thank you
The correct option is C which is out of 30000 there will be 27000 deaths.
What is the percentage?According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.
Given, according to the website, 90% of the 30,000 deaths caused by unsafe water and filthy living conditions that occur every week around the world involve children under the age of five. All of the following interpretations of this statistic are accurate.
The percentage of deaths will be calculated as:-
Percentage = 30000 x 90%
Percentage = 30000 x 0.9
Percentage = 27000
Therefore, the number of deaths will be 27000.
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How many solutions does the system of linear equations represented in the graph have?
Coordinate plane with one line that passes through the points negative 2 comma negative 3 and 0 comma negative 2 and another line that passes through the points 0 comma 3 and 1 comma 1.
a.One solution at (−1, 2)
b. One solution at (2, −1)
c. No solution
d. Infinitely many solutions
The system of linear equations represented in the graph have (b) ne solution at (2, −1)
How to determine the number of solutionsFrom the question, we have the following parameters that can be used in our computation:
The graph
The graph represents two linear functions
The point of intersection of the linear functions represent the solution
In this case, the linear functions intersect at (2, −1)
Hence, it has one solution at (2, −1)
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Answer:
I picked "d. Infinitely many solutions" but it turned out to be wrong lol, so I'm guessing the person above is correct.
at 12 noon the count in a bacteria culture was 400; at 3:00 pm the count was 1200. let p(t) denote the bacteria count at time t and assume that the culture obeys the population growth law. what was the bacteria count at 9 am, rounded off to the nearest bacterium?
At 12 noon the count in a bacteria culture was 400, at 3:00 pm the count was 1200. The bacteria count at 9 am, rounded off to the nearest bacterium, was 255.
The problem involves finding the bacteria count at 9 am, given the counts at 12 noon and 3 pm, and assuming that the bacteria culture obeys the population growth law.
To solve the problem, we use the population growth law, which states that the rate of growth of a population is proportional to the size of the population at any given time. This can be expressed as a differential equation, and its solution gives the population as a function of time.
Assuming the bacteria culture grows exponentially between 9 am and 3 pm, we can use the population growth law to find the bacteria count at 9 am. Let the initial count at 9 am be denoted by P, and let the growth rate be denoted by r.
Then we have:
P * (1 + r)^3 = 1200
Solving for P, we get:
P = 1200 / (1 + r)^3
Similarly, assuming the bacteria culture grows exponentially between 12 noon and 3 pm, we have:
400 * (1 + r)^3 = 1200
Solving for r, we get:
r = (1200/400)^(1/3) - 1
Plugging this value of r into the equation for P, we get:
P = 1200 / (1 + (1200/400)^(1/3) - 1)^3
Using a calculator, we get:
P ≈ 255
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A wellness director at a company in New York City wants t0 investigate whether it is unusual for one person working in the city who wears an activity tracker to record approximately 8,500 steps on typical workday: Is it appropriate to use the confidence interval found in part (a) to conduct the investigation? Explain your answer: In the STATE, DO, PLAN, CONCLUDE
The population mean, 9,009, 10,585 employees, and 9,009, 10,585 steps are the solution.
What is mean?A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency.
The term "activity tracker" refers to gadgets, including watches and bands, that record your physical activity, such as walking, jogging, and skipping. They only count your steps and inform you of your daily objectives. They are quite useful for tracking blood pressure and other things.
The 95% confidence interval between 9,009 and 10,585 steps was used to estimate the mean number of steps taken by City employees.
The likelihood of the various values may be estimated using the confidence interval. It may be utilised to derive conclusions about the population mean.
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the variance in the thickness values of 20 textbooks for this class is 0.0665 (inch)2 with a mean of 1.013 inch. what is the random error in the mean value and the confidence interval for the true mean of populaiton at 95%?
If the variance in the thickness of 20 textbooks is 0.0665 , then the random error in the mean value is ±0.1207 inches and the confidence interval is (1.013 ± 0.1207) inches .
The number of textbooks (number of observations) , n = 20 ;
So , v = n - 1 = 20 - 1 = 19 ;
For v = 19 and 95% confidence interval , we have t = 2.093 ;
The variance (σ²) is = 0.0665 ;
So , σ = √0.665 = 0.258 inches ;
We know that , Random Error (Δ) = tσ/√n = (2.093 × 0.258)/√20
= 0.1207 ;
The mean of the thickness of textbooks is ( [tex]\bar x[/tex] ) = 1.013 inches ;
So , the Random Error in the mean is = ±Δ = ±0.1207 inches ;
and the 95% confidence interval is = [tex]\bar x[/tex] ± Δ
⇒ (1.013 ± 0.1207) inches ;
Therefore , the Random Error is ±0.1207 inches , and the interval is (1.013 ± 0.1207) inches .
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Solve for system of equation 2 equations 6x+3y=8 and 8x+4y=-1
The solution of the given system of equations 6x+3y=8 and 8x+4y=-1 is x=0 and y==-8/9
What is system of equations?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously. In order to solve a system of equations, one must find all the sets of values of the variables that constitutes solutions of the system. (5, 4) is a solution of the first equation, but not the second.
We are given that;
The equation 1; 6x+3y=8
The equation 2; 8x+4y=-1
Now,
In equation 1
6x=8-3y
x=(8-3y)/6
Substituting the value of x in equation 2
8((8-3y)/6)+4y=-1
4((8-3y)/3)+4y=-1
(8-3y)/3)+4y=-1/4
8-3y+12y=-3/4
8+9y=-3/4
9y=-3/4-8
9y=-3-32/4
9y=-35/4
y=-32/36=-8/9
Putting the value of y in equation 1
6x+3(-8/9)=8
54x-8=8
x=0
Therefore, the solution of the equations will be x=0, y=-8/9.
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There were 50 guests in a marriage ceremony. 30 were from the groom's family and 20 were from the brides's family. There's a tradition of giving hugs among the groom's family although there's no such traditions in the bride's family. They only shake hands. what's the number of total handshakes?
Note that the members from the bride's family will shake hands with the groom's family too.
Answer:
1020 handshakes including the bride and the groom. 980 excluding the groom and the bride.
Step-by-step explanation:
(20*19) twenty people on the brides side shake hands with the other 19 people (19 because you can't really shake your own hand).
+(20*30) twenty people on the brides side shake hand with 30 people on the grooms side.
+(20*2) twenty people on the brides side shake hands with the bride and the groom.
this equalssss......
1020!!!!
Since the grooms family does hugs instead of handshakes, you'd only calculate how many the brides side does.
-36<-3x-9 or -42≥-3x-9
Step-by-step explanation:
= 9>x or. = 11<x.
Here is the answer
State if the lines are Parallel, Perpendicular, or Neither. 6x-12y=24 4x+2y=8
Answer:
Step-by-step explanation:
The lines are neither parallel nor perpendicular.
Two lines are parallel if and only if they have the same slope. Two lines are perpendicular if and only if the product of their slopes is -1.
To find the slope of a line given in the form of Ax + By = C, we can rearrange the equation into slope-intercept form (y = mx + b), where m is the slope.
The first line, 6x - 12y = 24, can be rearranged into slope-intercept form as follows:
12y = -6x + 24
y = -0.5x + 2
The slope of the first line is -0.5.
The second line, 4x + 2y = 8, can be rearranged into slope-intercept form as follows:
2y = -4x + 8
y = -2x + 4
The slope of the second line is -2.
Since the product of the slopes is not -1, the lines are not perpendicular. And since the slopes are not the same, the lines are not parallel. So, the lines are neither parallel nor perpendicular.
Find X then find angle PSQ
The value of angle PSQ is 136. 9 degrees
How to determine the valueIt is important to note the following;
Supplementary angles sum up to 180 degreesAngles on a straight are equivalent to 180 degreesThen, we have that;
30x + 6 + 11x - 5 = 180 degrees
Now, let's collect the like terms
30x + 11x + 6 - 5 = 180
add or subtract the like terms
41x = 180 - 1
41x = 179
Divide the values, we get;
x = 4. 36
Then,
PSQ = 30x + 6
PSQ = 136. 9 degrees
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€100 was invested in a savings account. After 10 years, there is
€300 in the account.
Work out how much money would have been in the account after
only 5 years if it had been gathering
a) annual simple interest.
b) annual compound interest.
Give each of your answers to the nearest €1.
c) Will the savings account have more money in it after 15 years if
it is gathering annual simple interest or annual compound interest?
Answer:
Simple Interest
SI=PRT/100
P=€100
SI=€300-€100 = €200
T=10 years
rate = unknown
Rate = SIx100/(pxt)
Rate = 200x100/(100x10)
= 20%
b)Compound interest
CI = P(1+i)ⁿ
CI= €300
P =€100
n = 10
€300 = €100(1+i)¹⁰
take the tenth root of both sides
€1.77 = €1.58(1+i)
divide both sides by 1.58
1.12 = 1 + i
i = 1.12 - 1
i = 12%
c)si=prt/100
=(100x20x15)/100
= €300
total = 300+100
€400
CI = P(1+i)ⁿ
= 100(1+0.12)¹⁵
=€547.35
It is gathering more money with annual compound interest
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Darnell solved a system of equations by graphing. When he graphed the lines,
he saw that the two lines intersected. What should Darnell conclude about the
solution to this system of equations?
There are infinitely many solutions.
There is exactly one solution.
There are exactly two solutions.
There are no solutions.
The point of intersection of two lines implies a system has one solution, therefore, Darnell should conclude that: B. there is exactly one solution to the system of equations.
What is the Solution of a System by Graphing?If the two lines in a system of equations intersect when graphed, then there is exactly one solution to the system of equations. This is because the point of intersection represents the values of the variables that satisfy both equations simultaneously.
If the two lines in a system of equations are parallel and do not intersect when graphed, then there are no solutions to the system of equations. If the two lines are the same and coincide when graphed, then there are infinitely many solutions to the system of equations.
Therefore, Darnell should conclude that: B. there is exactly one solution to the system of equations.
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Combine like terms to create an equivalent expression.
−
3.6
−
1.9
�
+
1.2
+
5.1
�
−3.6−1.9t+1.2+5.1tminus, 3, point, 6, minus, 1, point, 9, t, plus, 1, point, 2, plus, 5, point, 1, t
The equivalent expression with combined like terms is -5.5t + 6.3.
What is Equivalent expression?
Equivalent equations are algebraic equations with the same roots or solutions. We get an analogous equation by adding or subtracting the same number or expression from both sides of an equation. We can also get an equivalent equation by multiplying or dividing both sides of an equation by the same non-zero value.
To combine like terms, we can group the terms with the variable t together, and group the constant terms together:
(-3.6t) + (-1.9t) + (1.2 + 5.1)
We can simplify the constant terms:
(-3.6t) + (-1.9t) + 6.3
Finally, we can combine the terms with the same variable by adding their coefficients:
-5.5t + 6.3
Therefore, the equivalent expression with combined like terms is -5.5t + 6.3.
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The student can combine like terms in the given expression by adding and subtracting the corresponding pairs. This gives the equivalent expression as 3.2t - 2.4.
Explanation:To combine like terms in the equation -3.6 - 1.9t + 1.2 + 5.1t, you need to group together the like terms. The two like terms we have are the terms with the variable t, -1.9t and +5.1t, and the two constant terms -3.6 and +1.2 without the variable t.
When you add and subtract these pairs accordingly, you get:
-1.9t + 5.1t = 3.2t
-3.6 + 1.2 = -2.4
So, the equivalent expression that combines these like terms is: 3.2t - 2.4.
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in a game of chance, a fair die is tossed. if the number is 1 or 2, you will win $3. if the number is 3, you win $5. if the number is 4 or 5, you win nothing, and if the number is 6 you lose $2. should you play the game, based on the long run expected amount you would win?
Answer:
Expected amount = $1.50
Step-by-step explanation:
Let's get a couple of definitions out of the way to understand how to compute the expected value given probabilities
Random Variable is a set of possible values from a random experiment.
We usually denote a random variable using the sets of possible values that the variable can take.
When we toss a fair die, the probability of getting a single number = 1/6 since there are 6 possible outcomes
The probability of getting 2 given numbers say 1 or 2 is twice 1/6 = 2 x 1/6 = 2/3 and so on
The expected value of each outcome is the value attached to each outcome x probability of that outcome
As an example, P(1 or 2) = 2/6 = 1/3
Payout = $3
Expected payout = 3 x 1/3 = $1
The table below summarizes the outcomes, probabilities, payouts and expected payouts
Outcome Probability Payout Expected Payout
(Payout x probability)
X = {1 or 2} 2/6 = 1/3 $3 $3 x 1/3 = $1
X = {3} 1/6 $5 $5 x 1/6 = $5/6
X = {4 or 5} 2/6 = 1/3 $0 $0 x 1/3 = $0
X = {6} 1/6 -2$ -$2 x 1/6 = -$2/6
The expected payout in the long run is the sum of the individual expected payouts
= $1 + $5/6 + $0 - $2/6 (5/6 - 2/6 = 3/6)
= $1 + $3/6 (3/6 = $0.50)
= $1 + $0.50
= $1.50
The expected value of the game is $2. This means that if you play the game many times, you can expect to win an average of $2 per game in the long run.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
To determine whether you should play the game, we need to calculate the expected value of the game.
The expected value is the sum of the product of each outcome and its probability.
The outcomes and their corresponding probabilities are:
Win $3 with probability 1/3 (if the number is 1 or 2)
Win $5 with probability 1/6 (if the number is 3)
Win $0 with probability 2/6 = 1/3 (if the number is 4 or 5)
Lose $2 with probability 1/6 (if the number is 6)
Using these probabilities and outcomes, we can calculate the expected value as:
Expected value = (3 × 1/3) + (5 × 1/6) + (0 × 1/3) + (-2 × 1/6)
= 1 + 5/6 - 1/6
= 1.666
= 2
Hence, the expected value of the game is $2. This means that if you play the game many times, you can expect to win an average of $2 per game in the long run.
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In the function rule p(t) - 700 what does 700 mean in the context of the situation
In the function rule p(t) - 700, the number 700 represents a constant value that is subtracted from the value of the function p(t).
Assuming that p(t) is a function of time t, it is possible that p(t) represents a physical quantity such as the population of a city, the price of a stock, or the number of customers in a store, among other things. If we know what p(t) represents, we can interpret the meaning of 700 in the context of the situation.
For example, if p(t) represents the population of a city, then p(t) - 700 would represent the difference between the population and a reference value of 700. This could mean that 700 is the estimated minimum viable population of the city, or it could represent a reference population for comparison with other cities.
If p(t) represents the price of a stock, then p(t) - 700 would represent the difference between the stock price and a target value of 700, such as a price floor or a strike price.
In general, the meaning of 700 in the function rule p(t) - 700 depends on the specific context of the situation and the physical quantity that p(t) represents.
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A tree that is 18 feet tall is growing at a rate of 2 feet each year. A different tree that is 20.5 feet tall is growing at a rate of
3/4
feet each year. At this rate, when will the trees be the same height? What will
the height of the trees be?
The trees will be the same height in 2 years and the height of these trees will be 22 ft.
Linear Expression
A linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=x+10. Where:
m= the slope.
b= the constant term that represents the y-intercept
For the given example: m=1 and b=10.
For solving the question you should convert the given text into an algebraic expression.
Tree01= 18+2*y
Tree02= 20.5+0.75*y (Note that 3/4=0.75)
y= number of years
Therefore,
18+2*y=20.5+0.75*y
2y-0.75*y=20.5-18
1.25y=2,5
y=2
Thus, at 2 years the trees will be the same height.
When y=2, you have:
Tree01= 18+2*y= 18+2*2=18+4=22
Tree02= 20.5+0.75*y =20.5+1.5=22
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Someone help me with this equation please!!
The given proof follows the symmetric property of angle congruence. Therefore, option C is the correct answer.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Given that,
Statements Reasons
1. ∠ABC≅∠DEF 1. Given
2. m∠ABC=m∠DEF 2. Definition of congruent angles
3. m∠DEF=m∠ABC 3. Symmetric property of equality
4. ∠DEF≅∠ABC 4. Definition of congruent angles
The symmetric property says that if one geometric shape is congruent to another, than the second shape is also congruent to the first. The symmetric property of congruence says that for any angles A and B, if ∠A≅∠B then ∠B≅∠A.
Therefore, option C is the correct answer.
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