Given:
is a right angle
Prove:
A perpendicular line between AC and BD has a point of intersection of midpoint O
Since
is a right angle, it is. Is supplementary to
, so. By the substitution property of equality,. Applying the subtraction property of equality,. What statement is missing from the proof?
The statement missing from the proof is "A perpendicular line drawn between two parallel lines creates congruent alternate interior angles."
We know that the right angle is. Thus, m∠ADC = 90°And as ∠ADC is supplementary to ∠ACB,∠ACB = 90°. We have AC ⊥ BD and it intersects at O. Then we have to prove O is the midpoint of BD.
For that, we need to prove OB = OD. Now, ∠CDB and ∠BAC are alternate interior angles, which are congruent because AC is parallel to BD. So,
∠CDB = ∠BAC.
We know that ∠CAB and ∠CBD are also alternate interior angles, which are congruent, thus
∠CAB = ∠CBD.
And in ΔCBD and ΔBAC, the following things are true:
CB = CA ∠CBD = ∠CAB ∠BCD = ∠ABC.
So, by the ASA (Angle-Side-Angle) Postulate,
ΔCBD ≅ ΔBAC.
Hence, BD = AC. But we know that
AC = 2 × OD
So BD = 2 × OD.
So, OD = (1/2) BD.
Therefore, we have proven that O is the midpoint of BD.
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The ratio of two numbers is 5:6. The product of these numbers is 120. What is the smaller of these two numbers?
The smaller of the two number is 10.
What are Ratios?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
In simple words, the ratio is the number that can be used to express one quantity as a fraction of the other ones. The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things.
Given:
Ratio of two Positive number = 5:6
Let , the smaller number be 5x
then , the bigger number = 6x
According to the question,
product of these numbers = 120
Therefore,
\(5x * 6x = 120\\30x^{2} = 120\\x^{2} =4\\x = 2\)
Smaller number = 5x = 5*2 = 10.
Hence, the smaller of the two number is 10.
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Please solve using the image. No links.
Answer:
(A) True. False. True.
(B) 4
Step-by-step explanation:
Use the graph to complete the statements.
The period is ✔ 2pi/3
The amplitude of the corresponding cosine function is 2..
The vertical shift of the graph of the parent secant function is 1 unit down.
The graph is of the function ✔ 2sec(3x) – 1
THESE ARE THE ANSWERS
The exercise has to do with the Graphing of a Cosecant Function. From the graph, the completed statements have been indicated below.
What are the completed statements?The completed statements are:
The period is 2pi/3The amplitude of the corresponding cosine function is 2.The vertical shift of the graph of the parent secant function is 1 unit down.It is to be noted that the graph is of the function 2Sec (3x) – 1.
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Answer:
2pi/3
corresponding cosine function is 2.
1 unit down.
graph 2sec(3x) – 1
Step-by-step explanation:
please help ASAP
please
Answer:
I think its b
Step-by-step explanation:
good luck!!!!
(Factorize): x² + 2x - (Ans: (x + 6) (x - 4))
Answer:
x²+2x
x(x+2)
Step-by-step explanation:
take x common and thats it either tou gave incomplete question or wrong ans
Answer:
See below
Step-by-step explanation:
This should be your expressions: \(\displaystyle{x^2+2x-24}\), this can be factored by applying in the form of:
\(\displaystyle{x^2+(\alpha + \beta)x+\alpha \beta = (x+\alpha)(x+\beta)}\)
This simply means you have to find two numbers that add up or subtract and obtain the middle term, and that two numbers must also satisfy the last terms as well. (Hence, two numbers adding up to middle term and multiply to last term.)
We can check by seeing into the factor of 24 which are:
1, 242, 123, 84, 6These numbers have product of 24. Next, we find the middle term -- since the middle term is positive value. This means that the highest value is in positive.
From factors that we list, we can cancel off the followings:
1, 24 (This never makes 2 but rather 23)2, 12 (This never makes 2 but rather 10)3, 8 (This never makes 2 but rather 5)Therefore, the only factors left are 4 and 6. These two also make 2 (6-4), so we will have \(\alpha\) = 6 and \(\beta\) = -4. Therefore:
\(\displaystyle{x^2+(6-4)x+6(-4) = (x+6)(x+(-4))}\\\\\displaystyle{x^2+2x-24= (x+6)(x-4)}\)
And there you have it, the factor of x² + 2x - 24
If you send ppl links- I hope your phone can only charge at an angle
Anyways my discord is rosexlyn#6833 so add me hœs
Answer:
nah
Step-by-step explanation:
Can someone help me plss
in herrnstein's matching equation, the letters and numbers to the left of the equals sign refer to what?
In Herrnstein's matching equation, the letters and numbers to the left of the equals sign refer to behaviour.
THE MATCHING LAW
Herrnstein's Experiment Herrnstein (1961) conducted an experiment with pigeons in a room with two response buttons, red and white. Each key was assigned its own VI gain schedule. For example, under one condition, the left button pick was boosted on a VI 135 second schedule, and the right button pick was boosted on a VI 270 second schedule.
After the birds have learned as much as possible about this electoral situation, how do they distribute their responses? We trained them for days and then measured their reactions. As is often the case with VI schedules, birds returned many responses for each reinforcer received. Most interesting, however, is that in this condition, where two-thirds of the reinforcers came from the left button, the birds performed about two-thirds of the responses with the left button. That is, the proportion of left button responses equaled or matched the proportion of reinforcers delivered by the left button. In another condition, two birds received only about 15% of reinforcers from the left key and responded about 15% to that key.
Based on these results, Herrnstein proposed the following general principle for individual behavior when presented with alternative sequences. So, what you think makes sense rather than other options available at that particular moment.
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Please help! I will mark as brainliest IF answer is right. <3
Answer:
Explanation
Step-by-step explanation:
First, we work on the inequality, we're given the total that can be spent, and price of what is required, hence we can build the inequality following:
\(3.30x\leq 95\)
With the information given, we solve for x and round:
\(3.30x=95\\x=28.78\\\)
We can round 28.78 to 28, 29 would break the inequality.
Which is the best probability to determine the outcome of rolling seven with two dice? subjective empirical classical random
The classical probability of rolling a seven with two dice is 6/36 or 1/6.
Which is the best probability to determine the outcome of rolling seven with two dice?The best probability to determine the outcome of rolling seven with two dice is the classical probability.
Classical probability is based on the assumption that all outcomes in a sample space are equally likely, and it involves counting the number of favorable outcomes and dividing by the total number of possible outcomes.
In the case of rolling two dice, there are 36 possible outcomes, each with an equal chance of occurring. The number of ways to roll a seven is 6, as there are six combinations of dice rolls that add up to seven: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). Therefore, the classical probability of rolling a seven with two dice is 6/36 or 1/6.
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what feature(s) about a relationship can be observed from examining a scatterplot of two quantitative variables x and y?
By examining a scatterplot, you can gain valuable insights into the relationship between the two quantitative variables x and y, such as direction, strength, form, and outliers.
From examining a scatterplot of two quantitative variables x and y, you can observe the following features about the relationship between the variables:
1. Direction: You can determine whether the relationship between the variables is positive (both variables tend to increase or decrease together) or negative (one variable tends to increase while the other tends to decrease).
2. Strength: You can assess the strength of the relationship by observing how closely the data points are clustered around an imaginary line (e.g., a straight or curved line). A strong relationship has points closely clustered, while a weak relationship has points more scattered.
3. Form: You can identify the form of the relationship, such as linear (points form a straight line) or nonlinear (points form a curve).
4. Outliers: You can detect any outliers, which are data points that do not follow the general pattern of the relationship between the variables.
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On a number line, what is the distance between 6 and 6? between 24 and 17? between 17 and 24? between t and 4? This last question is harder to answer because it depends on whether t is smaller than or greater than 4. Is the answer t 4 or 4 t? This is an absolute value calculation: use absolute value signs to express the distance between t and 4. What is the distance between the numbers a and b on the number line? What is the relationship between |p q| and |q p|?
On a number line, the distance between any number and itself is always 0. Therefore, the distance between 6 and 6 is 0.
The distance between 24 and 17 can be calculated by subtracting the smaller number from the larger number, considering only the magnitude: |24 - 17| = 7.
Similarly, the distance between 17 and 24 can be calculated as |17 - 24| = 7. The absolute value ensures that the distance is always positive, regardless of the order of subtraction.
For the distance between a variable "t" and 4, the answer depends on the relationship between t and 4. If t is smaller than 4, the distance is expressed as |t - 4|. If t is greater than 4, the distance is expressed as |4 - t|. In either case, the absolute value ensures a positive value.
The distance between any numbers a and b on the number line can be calculated as |a - b|.
The relationship between |p - q| and |q - p| is that they are equal. The absolute value function disregards the sign of the argument, so whether you subtract p from q or q from p, the result will have the same magnitude. Therefore, |p - q| = |q - p|.
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In this lab, you will figure out who was guilty of the classroom food mess by determining which macromolecules are present in the mystery food sample.
Rephrase this statement as a scientific question you can answer through investigation
Answer:
In this food sample testing lab, you will figure out who was guilty of the classroom food mess by determining which macromolecules are present in the mystery food sample.
Step-by-step explanation:
Answer:
In the mystery food sample, what macromolecules are present?
Step-by-step explanation:
Edge… you’re welcome.
Mark me brainliest please.
sanji has a room with a perimeter of 42.5 feet if she wants to hand a curtain along one full side of the room how long dose the curtain need to be
Answer:
The length of the curtain is 10.625 feet
Step-by-step explanation:
The length of the curtain to cover one side of the room depends on the shape of the room
Given a room shape of a square, we have;
Perimeter = 4 × Side length of the room
Length of the curtain = Side length of the room
Therefore;
Perimeter = 4 × Length of the curtain
42.5 feet = 4 × Length of the curtain
Length of the curtain = (42.5 feet)/4 = 10.625 feet
The length of the curtain = 10.625 feet.
what's the upper bound of 206.264 to 3 decimal places?
The upper bound of 206.264 to 3 decimal places would be 206.265.
What is upper bound?
In mathematics, an upper bound is a value that is greater than or equal to all of the values in a set. For example, if we have a set of numbers {1, 2, 3}, then 3 is an upper bound of this set because it is greater than or equal to all the numbers in the set.
An upper bound can be either a member of the set or not. If the upper bound is a member of the set, then it is called a maximum element of the set. If the upper bound is not a member of the set, then it is called a strict upper bound of the set.
In the context of rounding, the upper bound refers to the next highest value that a number could be rounded to. For example, if we are rounding a number to the nearest integer, the upper bound would be the next integer greater than the original number.
The upper bound of 206.264 to 3 decimal places would be 206.265.
This is because the third decimal place of the original number is 4, and any number greater than or equal to 5 in the next decimal place would round the number up to the next value. Therefore, rounding 206.264 to 3 decimal places gives 206.265.
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29/1000
The fraction can be written as which decimal?
1,000
A)
0.0029
B)
0.029
0.29
2.9
Pls help ASAP
The question is in the picture
Value of quadratic equation is x = -1 and 11.
Define quadratic equation.In mathematics, a quadratic equation is one with degree 2, which means that its maximum exponent is 2. A quadratic has the standard form y = ax² + bx + c, where a, b, and c are all numbers and a cannot be zero. All of these are examples of quadratic equations: the square root of the sum of the squares of the values, given by y = x² + 3x + 1. a degree 2 equation with just one variable. Ax² + bx + c = 0, where x is the variable and a, b, and c are constants (a 0), is its general form.
Given Data
Equation
x² - 10x -11 = 0
x² -11x + x -11 = 0
Completing the square,
x(x - 11) + 1(x -11) =0
Taking common,
(x+1)(x -11) =0
x = 11. -1
Value of quadratic equation is x = -1 and 11.
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a researcher claims that 62% of voters favor gun control. determine whether the hypothesis test for this claim is left tailed, right tailed, or two tailed.a. rightb. leftc. two
As no explicit alternative hypothesis is supplied, we should use the two-tailed test, which includes both possibilities of the proportion being less or greater than 62%. As a result, the correct answer is (c) two-tailed test.
To determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed, let's consider the possible alternatives to the researcher's claim:
1. The proportion of voters favoring gun control is less than 62%.
2. The proportion of voters favoring gun control is more than 62%.
3. The proportion of voters favoring gun control is not equal to 62%.
If we were to test against alternative 1, it would be a right-tailed test.
If we were to test against alternative 2, it would be a left-tailed test.
If we were to test against alternative 3, it would be a two-tailed test.
Since we are not provided with any specific alternative hypothesis, it is most appropriate to choose the two-tailed test, as it covers both possibilities of the proportion being either less or more than 62%. Therefore, the answer is (c) two-tailed test.
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Pls help pls I need help on this
Answer:
I think it is B
Step-by-step explanation:
Answer:
Choice 4
Step-by-step explanation:
From the question, we know that something divided by 8 is 6. From the choices, we know that the missing number is represented as an x and an n.
We can change the information the question gives us to the equation something / 8 = 6
Choice 4 is the correct one because if we change the “something” to the letter n, it is the same.
I hope this helped and please mark me as brainliest!
If x and y vary directly and y is 6 when x is 8, find y when x is 12?
Given: x=8 when y= 6.
To find: We have to find y when x=12.
Solution:
The value of x and y are respectively -
x=8 when y= 6.
To get x=12 we have to multiple a number with 8 which will result in 12.
So, let the number be x.
We can write-
Thus the value of x is 3/2.
Now we have to multiply the value of y which is 6 with 3/2 to get the new value of y.
Thus the value of y is 9.
X
Dogs
0
16
12
10
10
Name
Problem # 1 (worth 50 points)
Carlos and Clarita are making a lot of some of the issues they need to consider as part of their business plan to care for
cats and dogs while their owners are on vacation.
Cats
40
0
12
14
10
Space Used
A
Date
Space: Cat pens will require 6/r of space, while dog runs require 24/r. Carlos and Clarita have up to 360 f
available in the storage shed for pens and runs, while still leaving enough room to move around the cages.
Start-up costs: Carlos and Clarta plan to invest much of the $1280 they earned from their last business venture
to purchase cat pens and dog runs. It will cost $32 for each cat pen and $80 for each dog run
0-24 n 40-6n
Complete the table below based on the scenario. Determine whether the combinations of cats and dogs fit within the
conditions of the constraints listed above.
-
ZOOM +
. Pampering time constraint: (25 points)
2 TS
Cost
R0-580 40-$32-5
Period
Works?
Yes if Used
Space 5360¹
and
Costs$1280
Points
10
10
10
10
10
Problem #2 (worth 50 points)
Carlos and Clarita have been worried about space and start-up costs for their pet sitting business, but they
realize they also have a limit on the amount of time they have for taking care of the animals they board. To
keep things fair, they have agreed on the following time constraints.
. Feeding time: Carlos and Clarita estimate that cats will require 6 minutes twice a day-moming and
evening to feed and clean their litter boxes, for a total of 12 minutes per day for each cat Dogs will
require 10 minutes twice a day to feed and walk, for a total of 20 minutes per day for each dog. Carlos
can spend up to 8 hours each day for the moming and evening feedings but needs the middle of the
day off for baseball practice and games.
Pampering time: The twins plan to spend 16 minutes each day brushing and petting each cat, and
20 minutes each day bathing or playing with each dog. Clarita needs time off in the morning for the
swim team and evening for her art class, but she can spend up to 8 hours during the middle of the
day pampering and playing with the pets.
Write each of these additional time constraints symbolically
. Feeding time constraint: (25 points)
a
Answer:
problem 2
Step-by-step explanation:
The feeding time constraint for cats can be written symbolically as:
12 minutes/day * number of cats <= 8 hours/day
The feeding time constraint for dogs can be written symbolically as:
20 minutes/day * number of dogs <= 8 hours/day
The pampering time constraint for cats can be written symbolically as:
16 minutes/day * number of cats <= 8 hours/day
The pampering time constraint for dogs can be written symbolically as:
20 minutes/day * number of dogs <= 8 hours/day
A metal fabricator produces connecting rods with an outer diameter that has a 0.98 inch to 1.02
inch specification and standard deviation of 0.03. A machine operator takes several sample
measurements over time and determines the sample mean outer diameter to be 1.005 inches
with a standard deviation of 0.007 inch. What is the Cpk?
A. More than 0.6 but not more than 0.8. The process is capable.
B. More than 1.1 but not more than 1.2. The process is not capable.
C. More than 0.6 but not more than 0.8. The process is not capable.
D.More than 1.1 but not more than 1.2. The process is capable.
The correct answer is A. More than 0.6 but not more than 0.8. The process is capable. To calculate the process capability index (Cpk), we need to consider the specifications and the process variability.
Cpk measures how well a process meets the specifications, and it is calculated as the minimum of two values: Cpk = min(Cpk_upper, Cpk_lower), where Cpk_upper = (USL - mean) / (3 * standard deviation) and Cpk_lower = (mean - LSL) / (3 * standard deviation).
In this case, the upper specification limit (USL) is 1.02 inches, the lower specification limit (LSL) is 0.98 inches, the sample mean is 1.005 inches, and the sample standard deviation is 0.007 inch.
1. Calculate Cpk_upper:
Cpk_upper = (USL - mean) / (3 * standard deviation)
Cpk_upper = (1.02 - 1.005) / (3 * 0.007)
Cpk_upper ≈ 0.715
2. Calculate Cpk_lower:
Cpk_lower = (mean - LSL) / (3 * standard deviation)
Cpk_lower = (1.005 - 0.98) / (3 * 0.007)
Cpk_lower ≈ 1.19
Since Cpk is the minimum of Cpk_upper and Cpk_lower, we have Cpk ≈ 0.715.
From the given answer choices, we can see that the Cpk value falls within the range specified in option A: "More than 0.6 but not more than 0.8. The process is capable."
Therefore, the correct answer is A. More than 0.6 but not more than 0.8. The process is capable.
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A runner is traveling at a constant rate of 8 meters per second. How long does it take for the runner to travel 100 meters?
Answer:
Total time taken = 12.5 second
Step-by-step explanation:
Given:
Speed of runner = 8 m/s
Total distance cover = 100 m
Find:
Total time taken
Computation:
Time taken = Distance / Speed
Total time taken = 100 / 8
Total time taken = 12.5 second
Eight friends want to play enough games of chess to be sure everyone plays everyone else. How many games will they have to play?
The number of games, the friends have to play is an illustration of combination.
They have to play 28 games to ensure that they all play
Given
\(n = 8\) --- number of friends
\(r = 2\) --- only two friends can play at a time
For everyone else to play, we will make use of the following combination formula;
\(^nC_r = \frac{n!}{(n - r)!r!}\)
So, we have:
\(^8C_2 = \frac{8!}{(8 - 2)!2!}\)
\(^8C_2 = \frac{8!}{6!2!}\)
Expand
\(^8C_2 = \frac{8 \times 7 \times 6!}{6! \times 2 \times 1}\)
\(^8C_2 = \frac{8 \times 7}{2 \times 1}\)
\(^8C_2 = 4 \times 7\)
\(^8C_2 = 28\)
Hence, the 8 friends have to play 28 games to ensure that everyone else plays
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find the domain and range of the function represented by the graph.
Solve the differential equations 2xy(dy/dx)=1 y^2. y(2)=3
The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).
To solve the given differential equation
2xy(dy/dx) = y²
We will use separation of variables and integrate to find the solution.
Start with the given equation
2xy(dy/dx) = y²
Divide both sides by y²:
(2x/y) dy = dx
Integrate both sides:
∫(2x/y) dy = ∫dx
Integrating the left side requires a substitution. Let u = y², then du = 2y dy:
∫(2x/u) du = ∫dx
2∫(x/u) du = ∫dx
2 ln|u| = x + C
Replacing u with y²:
2 ln|y²| = x + C
Using the properties of logarithms:
ln|y⁴| = x + C
Exponentiating both sides:
|y⁴| = \(e^{x + C}\)
Since the absolute value is taken, we can remove it and incorporate the constant of integration
y⁴ = \(e^{x + C}\)
Simplifying, let A = \(e^C:\)
y^4 = A * eˣ
Taking the fourth root of both sides:
y = (A * eˣ\()^{1/4}\)
Now we can incorporate the initial condition y(2) = 3
3 = (A * e²\()^{1/4}\)
Cubing both sides:
27 = A * e²
Solving for A:
A = 27 / e²
Finally, substituting A back into the solution
y = ((27 / e²) * eˣ\()^{1/4}\)
Simplifying further
y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)
Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is
y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)
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Define Chi square test OR Tests of significance based on Chi-Square. A: -Various tests of significance described previously have mostly applicable to only quantitative data and usually to the data which are approximately normally distributed. It may also happens that we may have data which are not normally Inference: (i) If Z0 ≤ Ze we accept the H0 (ii) If Z0 >Ze we reject the H0 Example: A test of the breaking strengths of two different types of cables was conducted using samples of n1 = n2 = 100 pieces of each type of cable. Do the data provide sufficient evidence to indicate a difference between the mean breaking strengths of the two cables? Use 0.01 level of significance. x = 1925 and sigm = 40 and X2 = 1905, sigma = 30
The Chi-square test is a statistical test used to determine if there is a significant difference between observed and expected frequencies in categorical data. In this example, the test is used to assess whether there is a significant difference in the mean breaking strengths of two types of cables.
The Chi-square test of significance is employed when dealing with categorical or nominal data. It compares the observed frequencies with the frequencies that would be expected if the variables were independent. In this case, the breaking strengths of the two cables are the variables of interest.
To perform the test, the first step is to define the null hypothesis (H0) and the alternative hypothesis (Ha). In this example, H0 assumes that there is no difference in the mean breaking strengths of the two cables, while Ha suggests that there is a difference.
Next, the test statistic, denoted by X2 (chi-square), is calculated using the formula X2 = Σ[(O - E)²/E], where O represents the observed frequencies and E represents the expected frequencies under the assumption of independence.
To determine the expected frequencies, we need to estimate the means and variances of the breaking strengths. Here, x = 1925 and sigma = 40 for the first cable, and x = 1905 and sigma = 30 for the second cable.
Once the test statistic is calculated, it is compared to a critical value from the Chi-square distribution with degrees of freedom equal to (r - 1)(c - 1), where r is the number of rows and c is the number of columns in the contingency table. The significance level of 0.01 determines the critical value.
If the calculated X2 value is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to indicate a difference in the mean breaking strengths of the two cables. Conversely, if the calculated X2 value is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is no significant difference.
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What is the equation of y = x^3 with the given transformations?
vertical compression by a factor of 1/7 , horizontal shift 8 units to the left, reflection across the x-axis
EXPLAIN PLEASE!
The transformed equation is y=-(1/7)(x+8)³ when 1/7 vertical compression, an 8-unit horizontal shift to the left, and an x-axis reflection.
Given that,
We have to find what does y=x³ with the specified transformations look like. 1/7 vertical compression, an 8-unit horizontal shift to the left, and an x-axis reflection
We know that,
The equation is y=x³
We must multiply the function by 1/7 in order to get a vertical compression of a factor of 1/7.
So,
y=(1/7)x³
We must add 8 to x in order to obtain a horizontal shift of 8 units to the left.
So,
y=(1/7)(x+8)³
Finally, we need to multiply the function by one in order to have a reflection over the x-axis.
So,
y=-(1/7)(x+8)³
Therefore, the transformed equation is y=-(1/7)(x+8)³ when 1/7 vertical compression, an 8-unit horizontal shift to the left, and an x-axis reflection.
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If 96 as a product of its prime factors is 2x2x2x2x2x3, find the greatest common divisor of 72 and 96
Answer:
24
Step-by-step explanation:
72=2*2*2*3*3
96=2*2*2*2*2*3
Hcf=2*2*2*3=24#