The function that has the greatest rate of change is y = x
Which function has the greatest rate of change?From the question, we have the following parameters that can be used in our computation:
y = -x ,
y = 3/4x +1,
y = 1/2x +2,
y = x
A linear function is represented as
y = mx + c
Where
rate of change = m
So, we have
y = -x , rate = -1
y = 3/4x +1, rate = 3/4
y = 1/2x +2, rate = 1/2
y = x, rate = 1
This means that the function with the highest rate is y = x
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Lara chooses a number less than 20
She divides it by 2 and then adds 6
She then divides this result by 3
Her answer is 4.5
What was the number she started with?
Working backward, the number that Lara started with in performing the mathematical operations was 15.
How the number is determined:We can use mathematical operations to determine the initial number that Lara started with.
Mathematical operations include addition, subtraction, division, multiplication, etc.
Let the number that Lara started with = x
x < 20
x ÷ 2 + 6 = y
y ÷ 3 = 4.5
y = 13.5 (4.5 x 3)
x ÷ 2 + 6 = 13.5
x ÷ 2 = 7.5
x = 15 (7.5 x 2)
Thus, Lara started performing the mathematical operations with 15 and got a final result of 4.5.
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Answer pls my state test is cominggggg
(-3/4) x (3/4)
---When we multiply fractions, we multiply horizontally/across
(-3 x 3) / (4 x 4)
-9 / 16
Answer: -9/16
Hope this helps!
Which of the following numbers is shown plotted on the number line?
0
0 2.75 0 2 0-3 0-2 0-15
Answer:
-3 3/8
Step-by-step explanation:
The only number we're given on the number line is 0, but we can assume that each tick on the number line represents 1 units. We see that between the ticks that are 4 and 3 spaces away from 0.Since the point is to the left of 0, we know the number must be negative.The only answer that would make sense is -3 3/8, since the tick 4 places away from 0 is -4 and the tick 3 units away from 0 is -3 and -3 3/8 lies between -3 and -4A company gives a 12% discount to his customers on retail price. If the total is over $10,000 after the discount, they give an additional 3% discount on the remaining balance. A customer’s total came to $13,500 (discounted price). How much did he save?
Answer:
Therefore, the customer saved $2,448.45.
Step-by-step explanation:
To answer this question, we need to use the percentage discount formula to find the original price and the amount saved.
Let x be the original price of the product. Then, after applying the 12% discount, the price becomes 0.88x. If the total is over $10,000 after this discount, then an additional 3% discount is applied on the remaining balance, which means the final price becomes 0.97 * 0.88x.
We are given that the final price is $13,500, so we can set up an equation and solve for x:
0.97 * 0.88x = 13,500 x = 13,500 / (0.97 * 0.88) x = 15,948.45
Therefore, the original price was $15,948.45.
The amount saved is the difference between the original price and the final price:
15,948.45 - 13,500 = 2,448.45
math
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Two wading pools are being filled at the same time.
The orange pool contains 4 gallons when it starts willing at a rate of 4 galtons a minute.
The blue pool fills at a rate of 5 gallons a minute.
How should the axis be labeled?
The z-axis should be labeled
How should the y-axis be labeled?
The yaxis should be labeled
What does the slope of each line represent?
The slope of each line represents the
What should the x axis be labeled
What is the y axis labeled
What does the slope line of each represent
What does the y intercept of each line represent
What does the slope line of each represent?
The slope line represents the constant change in value.
What does the y intercept of each line represent
The y-intercept indicates the y-value when the x-value is 0.
The function h(t) = 4 + 64t – 16t2 models the height h, in feet, of a ball thrown in the air, after t seconds.
Part A
What is the vertex of the graph of the function, (t, h(t))?
(
,
)
Part B
What does the t-coordinate of the vertex represent?
A. the ball's maximum height
B. the time it takes for the ball to reach its maximum height
C. the time it takes for the ball to hit the ground
D. the height the ball was thrown from
Part C
What does the h(t)-coordinate of the vertex represent?
A. the ball's maximum height
B. the time it takes for the ball to reach its maximum height
C. the time it takes for the ball to hit the ground
D. the height the ball was thrown from
Part A) The vertex of the graph of the function, (t, h(t)) is (2, 68).
Part B) The t-coordinate of the vertex represent is the time it takes for the ball to reach its maximum height (option b)
Part C) The h(t)-coordinate of the vertex represent is the ball's maximum height (option a).
Part A asks for the vertex of the graph of the function, which is the point where the function reaches its maximum or minimum value. To find the vertex of a quadratic function like
=> h(t) = 4 + 64t – 16t²,
we can use the formula
=> t = -b/2a,
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c and t is the input variable (in this case, the time).
The t-coordinate of the vertex is simply the value we get when we plug this formula into our equation.
So, for
=> h(t) = 4 + 64t – 16t²,
we have a = -16, b = 64, and c = 4.
Plugging these values into the formula
=> t = -b/2a,
we get
=> t = -64/(2*(-16)) = 2.
The t-coordinate of the vertex is therefore 2.
To find the h(t)-coordinate of the vertex, we can simply plug t = 2 into the function h(t) = 4 + 64t – 16t² and evaluate it.
This gives us
=> h(2) = 4 + 64(2) – 16(2²) = 68.
Therefore, the vertex of the graph of h(t) is (2, 68).
Part B asks what the t-coordinate of the vertex represents. We know that the t-coordinate is the time at which the ball reaches its maximum height.
Therefore, the correct answer is B: the time it takes for the ball to reach its maximum height.
Part C asks what the h(t)-coordinate of the vertex represents. We just found that the h(t)-coordinate of the vertex is the maximum height of the ball.
Therefore, the correct answer is A: the ball's maximum height.
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Given the two concentric circles with center X below, find the area of the shaded region. Round your answer to the nearest tenth if necessary.
The area of the shaded region is given as follows:
298.3 units².
How to calculate the area of a circle?The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:
A = πr²
The larger circle has a radius of 7 + 5 = 12 units, hence it's area is given as follows:
A = 3.14 x 12²
A = 452.16 units².
The smaller circle has a radius of 7 units, hence it's area is given as follows:
A = 3.14 x 7²
A = 153.86 units².
Hence the area of the shaded region is given as follows:
452.16 - 153.86 = 298.3 units².
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In the diagram shown, points B and D lie on sides AC and AE such that BD is parallel to CE. If AB=10, AD=16, and De=22 then find the length of AC
In triangle ACE, with BD parallel to CE, using similar triangles and ratios, we get a quadratic equation with two possible solutions. Only the positive one is chosen, so AC is approximately 30.96 units long.
Since BD is parallel to CE, we can use the property of similar triangles to find the length of AC.
Triangles ABD and ACE are similar because they have the same corresponding angles. This means that the ratios of their corresponding side lengths are equal.
We know that AB = 10, AD = 16, and DE = 22.
Let x be the length of AC. Then, we have
AB/AD = CE/EA (by similarity of triangles ABD and ACE)
10/16 = CE/(x-16+22) (substituting CE = EA - DE and simplifying)
5/8 = CE/(x-6)
CE = (5/8)(x-6)
We also know that
BD/DE = AB/AE (by similarity of triangles ABD and ADE)
BD/22 = 10/(x-22) (substituting BD = CE and AE = AC - CE - DE, and simplifying)
CE = (220 - 10x)/(x-22)
Since CE is equal in both expressions, we can equate them and solve for x
(5/8)(x-6) = (220 - 10x)/(x-22)
5x² - 196x + 1320 = 0
x² - 39.2x + 264 = 0
Using the quadratic formula, we get
x = 30.96 or x = 8.54
The length of AC must be positive, so we choose x = 30.96.
Therefore, the length of AC is approximately 30.96 units.
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--The given question is incomplete, the complete question is given
" In the diagram shown, points B and D lie on sides AC and AE such that BD is parallel to CE. If AB=10, AD=16, and De=22 then find the length of AC "--
A number cube with faces labeled 1 to 6 is rolled once.
The number rolled will be recorded as the outcome.
Consider the following events.
Event A: The number rolled is odd.
Event B: The number rolled is greater than 3.
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
The possible outcomes for each of the given events are:
A --> {1, 3, 5}
B --> {4, 5, 6}
How to find the outcomes for each event?For a regular number cube, the sample space (possible outcomes) is:
S = {1, 2, 3, 4, 5, 6}
Now we have two events.
A = rolling an odd number
Here the outcomes can be any of the odd numbers in the sample space, so the possible outcomes are:
A --> {1, 3, 5}
The second event is:
B = the number rolled is greater than 3. Again, the outcomes are thevalues in the sample space that are larger than 3, these are:
B --> {4, 5, 6}
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A study of the consultants in a particular industry has determined that the standard deviation of the hourly fee of the consultants is $23. A random sample of
100 consultants in the industry has a mean hourly fee of $113. Find a 99% confidence interval for the true mean hourly fee of all consultants in the industry.
Then give its lower limit and upper limit.
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)
Lower limit:
Upper limit:
X
5
If a study of the consultants in a particular industry has determined that the standard deviation of the hourly fee of the consultants is $23. the 99% confidence interval for the true mean hourly fee of all consultants in the industry is (107.1, 118.9).
How to find the confidence interval?The formula for a confidence interval for the population mean is:
CI = X- bar ± z* (σ/√n)
where:
X- bar = sample mean
z* = z-score for the desired level of confidence (99% in this case)
σ = population standard deviation
n = sample size
Substituting the given values, we get:
CI = 113 ± 2.576 * (23/√100)
Calculating the standard error:
SE = σ/√n = 23/√100 = 2.3
Now we can substitute this value into the formula:
CI = 113 ± 2.576 * 2.3
CI = 113 ± 5.92
So,
Lower limit: 107.1
Upper limit: 118.9
Therefore, the 99% confidence interval for the true mean hourly fee of all consultants in the industry is (107.1, 118.9).
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Asynchronous activity
In the triangles given the analysis for same is given below
What is the analysis of the two triangles given above?1) the corresponding vertices are
R ~ C and
E ~ 0
2) The corresponding angle are
∠E ~∠O and
∠ R ~ ∠C
3)
The corresponding sides are;
ER ~ CO;
MO ~ EM
CM ~ RM
4) the congruent angles are:
∠REM ≅ ∠MOC
∠ERM ≅ ∠MCO
∠CMO ≅ EMR
5) the congruent sides are:
ER ≅ CO;
MO ≅ EM
CM ≅ RM
6) the congruent triangles are;
ΔMER ≅ ΔMOC
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The value of x in the following equation 4x-5=7 is .........
Answer:
Step-by-step explanation:
4x - 5 = 7
4x = 7 + 5
4x = 12
x = 12/4
x = 3
A gas can hold 10 L of gas how many cans could we filled filled with 7 L of
Answer:
2 cans
Step-by-step explanation:
What is the perimeter of the regular pentagon?
Answer:
To find the perimeter of a regular pentagon, you need to know the length of one side and the number of sides. In a regular pentagon, all sides have the same length and the shape has 5 sides.
Let's say the length of one side of the regular pentagon is 's'.
The formula for the perimeter of a regular pentagon is:
Perimeter = 5s
This is because a regular pentagon has 5 sides of equal length, so you can simply add the length of each side together 5 times.
Therefore, the perimeter of a regular pentagon with a side length 's' is 5s.
Step-by-step explanation:
Find the distance between the zeros of the (2x-8)^2-4=12
The distance between the zeros of the equation [tex](2x-8)^{2}[/tex] - 4 = 12 is 4 units.
First, we can simplify the equation [tex](2x-8)^{2}[/tex] - 4 = 12 by adding 4 to both sides:
[tex](2x-8)^{2}[/tex] = 16
Next, we can take the square root of both sides:
2x-8 = ±4
Solving for x in each case, we get:
2x-8 = 4: 2x = 12 → x = 6
2x-8 = -4: 2x = 4 → x = 2
So the zeros of the equation are x=6 and x=2. The distance between them is:
distance = |6 - 2| = 4
As a result, there are 4 units between zeros of the equation [tex](2x-8)^{2}[/tex] - 4 = 12.
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Trapezoid WXYZ is rotated 90 degrees clockwise around point A to create trapezoid WXYZ what must be true A angle W is half the measure of angle W B Wx is equal to WX
C WX is perpendicular to YZ D WZ is equal to WX
Answer:
B) Wx is equal to WX.
When a shape is rotated 90 degrees, the length of its sides and angles do not change. Therefore, the length of Wx in the original trapezoid will be the same as the length of WX in the rotated trapezoid.
In our chapter on inverse functions, we discussed several charcteristics related to inverse functions. Asumme that you were given information that the points P(2, 4) was on the graph of a function, y. Therefore, the point Q, (___, ___) would be on the graph of y-1, the inverse function of y.
Write at least three sentences to explain how you can identify the point Q. Explain how you would find the coordinates and be sure to include the actual coordinates of point Q.
Answer: you could reflect the points (2, 4) to both axisis to find the inverse, add a negative in front of both numbers, or multiply the function by -1.
Step-by-step explanation:
Have a great night.
50 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
Answer:
the answer for this question is x=8
What did Maleuvre write about Gauguin's views on Polynesian women?
Answer:
Step-by-step explanation:
Observation of the real life and way of life of the peoples of Oceania are intertwined in them with local myths.
campaign. Evaluate how community respond to women and children in (3x4)(12) light of the following aspects: Bill of Rights Discrimination Human Rights Violations ■ . B
The community's response to women and children in light of the Bill of Rights, Discrimination, and Human Rights Violations should prioritize the protection and promotion of their rights and freedoms.
Now, The evaluation of community response to women and children in the context of Bill of Rights, Discrimination, and Human Rights Violations can be done as follows:
Bill of Rights:
The Bill of Rights guarantees certain rights and freedoms to all individuals regardless of their gender or age. Therefore, any discrimination or violation of women and children's rights would be a direct violation of the Bill of Rights. The community must ensure that women and children are not denied their right to life, dignity, equality, and freedom from all forms of violence and exploitation.
Discrimination:
Discrimination against women and children is a prevalent issue in many societies. Women and children are often subjected to discrimination on the basis of their gender, age, race, religion, or socio-economic status. The community should work towards eliminating all forms of discrimination against women and children and provide them with equal opportunities in all spheres of life.
Human Rights Violations:
The community must also ensure that the human rights of women and children are protected. Human rights violations against women and children can include physical and emotional abuse, sexual harassment and assault, child labor, child marriage, and human trafficking, among others. The community must take a strong stance against such violations and work towards preventing and punishing the perpetrators.
In conclusion, the community's response to women and children in light of the Bill of Rights, Discrimination, and Human Rights Violations should prioritize the protection and promotion of their rights and freedoms. Any form of discrimination or violation of their rights should be condemned and punished to ensure that women and children are safe and empowered members of society.
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In a certain survey, 511 people chose to respond to this question: "Should passwords be replaced with biometric security (fingerprints, etc)?"
Among the respondents, 51% said "yes." We want to test the claim that more than half of the population believes that passwords should be
replaced with biometric security. Complete parts (a) through (d) below.
a. Are any of the three requirements vicated? Can a test about a population proportion using the normal approximation method be used?
OA. All of the conditions for testing a claim about a population proportion using the normal approximation method are satisfied, so the method
can be used.
B. The conditions np 25 and nq 25 are not satisfied, so a test about a population proportion using the normal approximation method cannot
be used.
OC. One of the conditions for a binomial distribution are not satisfied, so a test about a population proportion using the normal approximating
method cannot be used.
D. The sample observations are not a random sample, so a test about a population proportion using the normal approximating method
cannot be used.
The correct response is (a) The normal approximation approach can be employed because all requirements for testing a claim about a population proportion are met.
what is probability ?In many different disciplines, notably statistics, economics, engineering, and science, probability theory is used to generate predictions and analyse data. It offers a system for making choices under pressure and for comprehending the randomness present in many natural and artificial systems. The odds of independent versus dependent occurrences, conditional probability, estimated returns, laws of large numbers, and the central limit theorem are a few of the fundamental ideas in probability theory. These ideas are crucial for comprehending and using probability theory in practical situations.
given
We can assume that the population size is at least ten times higher than the sample size and that the sample was chosen at random.
We must compute np and nq in order to verify the second condition:
np = (511)(0.51) = 260.61nq = (511)(0.49) = 250.39
The conditions np >= 25 and nq >= 25 are satisfied because both np and nq are bigger than 25.
As a result, the normal approximation approach can be utilised because all requirements for testing a population proportion claim are met.
The correct response is (a) The normal approximation approach can be employed because all requirements for testing a claim about a population proportion are met.
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Answer:
D. The sample observations are not a random sample, so a test about a population proportion using the normal approximating method
cannot be used.
Step-by-step explanation:
The sample is not random.
Boyd's board shop grt a shipment of 92 new skateboards wheels. Boyd assembles the skateboards and puts 4 of the new wheels on each board. You can use a function to describe the number of new wheels Boyd has left after assembling x skateboards
The function to describe the number of new wheels Boyd has left is f(x) = 92 - 4x
From the question, we have the following parameters that can be used in our computation:
Shipment of 92 new skateboards wheels. 4 of the new wheels on each board.After assembling x skateboards, we have
f(x) = Shipmnet - Rate * x
Substitute the known values in the above equation, so, we have the following representation
f(x) = 92 - 4 * x
Evaluate
f(x) = 92 - 4x
Hence, the function is f(x) = 92 - 4x
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3.4 MIXED FACTORING
1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.
(2x^2 + 23x) - (3x - 18)
Answer:
2 (x + 1)(x + 9)
Step-by-step explanation:
The given expression is
[tex]\left(2x^2\:+\:23x\right)\:-\:\left(3x\:-\:18\right)[/tex]
and we are asked to factor it
Step 1
Remove parentheses
[tex]\left(2x^2\:+\:23x\right) = 2x^2 + 23x\\\\-\:\left(3x\:-\:18\right) = - (3x) - (-18) = -3x + 18\\\\[/tex]
Step 2
Add the individual terms to correspond to the original expression:
[tex]\left(2x^2\:+\:23x\right)\:-\:\left(3x\:-\:18\right) \\\\= 2x^2 + 23x -3x + 18\\\\= 2x^2 + 20x + 18[/tex]
Step 3
Factor out common term 2
[tex]2x^2+20x+18 \\\\= 2\left(x^2+10x+9\right)[/tex]
Step 4
Factor [tex]x^2+10x+9[/tex]
To do this find two numbers such that their sum = 10 and product = 9
We can easily see that these two numbers are 1 and 9 because 1 + 9 = 10 and 1 x 9 = 9
Therefore, splitting the expression into groups we get
[tex]x^2 + 10x + 9 = x^2 + 1x + 9x + 9\\\\[/tex]
Step 5
Factor:
[tex]x^2 + 1x = x(x+ 1)\\9x + 9 = 9(x + 1)\\\\[/tex]
Therefore
[tex]x^2 + 1x + 9x + 9 = x(x + 1) + 9(x + 1)\\\\[/tex]
Step 6
Factor common term (x + 1) from the expression
[tex]x(x + 1) + 9(x + 1) = (x + 1)(x + 9)[/tex]
Step 7
Putting it all together
Remember we factored out the 2 in step 3 so we got to put it back into the factored expression giving the final factored expression as
[tex]2 (x + 1)(x + 9)[/tex]
Can someone help me with this please
The matrix after the row operation is given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
How to do the row operation?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]
We want to have element 1 into row 1 and column 1, that is, the element of 7 must assume a value of -1.
A valid row operation is the multiplication of the row by a constant, and as the element has a value of 7, the constant to obtain a value of 1 is:
7/k = 1
k = 7.
Dividing every element of the first row by 7, the matrix is given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
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PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
The sum of both sides is 2x² + 4. The length of the third side is 5x³ - 4x² + 3x - 12
What is a triangle?A triangle is a polygon that has three sides and three angles. Types of triangles are isosceles, right angled, scalene, equilateral.
Given that the perimeter of the triangle is 5x³ - 2x² + 3x - 8. The length of side one is 3x² - 4x - 1 and that of side two is -x² + 4x + 5
The sum of side one and side two is:
Sum = side 1 + side 2 = (3x² - 4x - 1) + (-x² + 4x + 5) = 2x² + 4
The sum of both sides is 2x² + 4
The third side is:
Third side = Perimeter - Sum of two sides = (5x³ - 2x² + 3x - 8) - (2x² + 4) = 5x³ - 4x² + 3x - 12
The length of the third side is 5x³ - 4x² + 3x - 12
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How much money should Be deposited today in an account that earns 10.5 percent compounded monthly so that it will accumulate to $22,000 in four years
Answer:
$12,276.24
Step-by-step explanation:
22000 / (1 + 0.105/12)^4*12
12276.24
Tyler is simplifying the expression: 6-2x+5+4x Here is his work
6-2x+5+4x
(6-2)x+(5+4)x
4x+x
13x
a. Explain the error he made
b. Simplify the expression: 6-2x+5+4x
Answer:
11-2x not 13x
Step-by-step explanation:
\(6-2)x + (5-4)x does = 13x
If there were parentheses as in the 2nd line, everything else is correct
the mistake is going from
6-2x + 5-4x to
(6-2x) + (5-4)x
PEMDAS is the order of operations. P for parentheses 1st, Multiplication 3rd, addition 4th, subtraction 5th
(there are no exponents or division or parentheses, so it's just M, A and S that apply)
combine like terms, 2x-4x =-2x
combine the constant terms 6+5 = 11
6-2x +5-4x = 11-2x
The mistake was assuming parentheses when they aren't there.
correct answer is 11-2x not 13x
please answer the question in pic
Note that given the factors above, Orr should replace the above plant. This has to do with depreciation and book value.
Why is this so ?We need to first compute the current total cost of keeping the old plant.
Book value = $4,500,000 - $1,000,000/year x 4 years
= $500,000
Thi smean that the current total cost of keeping the old plan tfor the reamining 10 year is
Total cost of keeping old plant = $1,000,000/year x 10 years - $500,000 + $150,000
= $9 650 000
Now lets calculate the total cost of purchasing the new plant for 10 years.
$600,000 - $150,000
= $450,000 per year.
The salvage value after 10 years is $0.
Total cost of new plant = $3,500,000 + $450,000/year x 10 years = $8,000,000
Since the cost of keeping is higher than the new one, then Orr should get a new plant.
$9 650 000 > $8,000,000
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Write an Equation for the ellipse. The center is (1, -3).
The standard form of the equation of the ellipse is (x - 1)² / 16 + (y + 3) / 9 = 1.
How to define the standard form of the equation of an ellipse
In this problem we find the representation of an ellipse on Cartesian plane, whose center is at (h, k) = (1, - 3), whose major semiaxis length is 4 units and whose minor semiaxis length is 3 units. The standard form of the equation of the ellipse is described below:
(x - h)² / a² + (y - k)² / b² = 1
Where:
(h, k) - Coordinates of the center.a - Length of the major semiaxis.b - Length of the minor semiaxis.If we know that (h, k) = (1, - 3), a = 4 and b = 3, then the standard form of the equation of the ellipse is:
(x - 1)² / 16 + (y + 3) / 9 = 1
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which expresion shows 7+21 written as a product of two factors
As we used the distributive property of multiplication to rewrite 7+21 as a product of 7 x (1+3) or 7 x 4.
However, you are asked to express this sum as a product of two factors. A factor is a number that is multiplied by another number to produce a product. Therefore, to express 7+21 as a product of two factors, we need to find two numbers that, when multiplied together, give us the sum of 7+21.
One way to approach this problem is to use the distributive property of multiplication, which states that a(b+c) = ab + ac. We can apply this property by rewriting 7+21 as 7+3*7, since 21 is equal to 3 times 7. Then, we can factor out the common factor of 7 from the expression to get:
7+37 = 7(1+3)
Now, we have expressed 7+21 as a product of two factors: 7 and (1+3), or simply 7 and 4. Therefore, the expression that shows 7+21 written as a product of two factors is:
7 x (1+3) or 7 x 4
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