Find a translation that has the same effect as the composition of translations.
(x y) → (–x + 6,y + 7) followed by (x y) → (x - 2,y + 5)
Answers
The translation that has the same effect as the composition of translations will be;
⇒ (x, y) → (x + 4, y + 12)
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The translation is,
⇒ (x y) → (- x + 6,y + 7) followed by (x y) → (x - 2,y + 5).
Now,
In this case we have this Composition of translations:
⇒ (x y) → (- x + 6,y + 7) followed by (x y) → (x - 2,y + 5).
Here, You can notice that 6 units are add from the x-coordinate in the first transformation and then 2 units are subtracted. So, the sum is:
⇒ 6 + (-2) = 4
And, Observe that, in the first transformation, 7 units are added to the y-coordinate and then 5 units are added. The sum is:
⇒ 7 + 5 = 12
Thus, The single Translation that has the same effect as the given Composition of translation is:
⇒ (x, y) → (x + 4, y + 12)
Therefore, The translation that has the same effect as the composition of translations will be;
⇒ (x, y) → (x + 4, y + 12)
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Related Questions
A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by h(t)= −4.9t^2+11t+7. How many seconds does it take to reach maximum height? Enter the answer with at least 3 decimal places.
Answers
Given statement solution is :- It takes approximately 1.122 seconds for the ball to reach its maximum height.
To find the time it takes for the ball to reach its maximum height, we need to determine the vertex of the parabolic function given by the equation h(t) = \(-4.9t^2 + 11t + 7.\)
The vertex of a parabola in the form y = \(ax^2 + bx\) + c is given by the formula t = -b / (2a).
Comparing the equation h(t) = \(-4.9t^2 + 11t + 7\) to the standard form, we have:
a = -4.9
b = 11
Using the formula for the vertex, we can calculate the time it takes to reach the maximum height:
t = -11 / (2 * -4.9)
t = -11 / -9.8
t ≈ 1.122
Therefore, it takes approximately 1.122 seconds for the ball to reach its maximum height.
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1)
On the basis of extensive tests, the yield point of a particular type of mild steel-reinforcing bar is known to be normally distributed with ? = 100. The composition of the bar has been slightly modified, but the modification is not believed to have affected either the normality or the value of ?.
(a) Assuming this to be the case, if a sample of 49 modified bars resulted in a sample average yield point of 8459 lb, compute a 90% CI for the true average yield point of the modified bar. (Round your answers to one decimal place.)
( ? , ? )
(b) How would you modify the interval in part (a) to obtain a confidence level of 98%? (Round your answer to two decimal places.)
2)
An article reported that for a sample of 48 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was 162.85.
(a) Calculate and interpret a 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.)
( ? , ? )
(b) Suppose the investigators had made a rough guess of 170 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 47 ppm for a confidence level of 95%? (Round your answer up to the nearest whole number.)
Answers
1) On the basis of extensive tests, the yield point of a particular type of mild steel-reinforcing bar,
a) 90% CI for the true average yield point of the modified bar is 8459 +/- 23.5
b) 98% CI for the true average yield point of the modified bar is 8459 +/- 23.49
2) An article reported that for a sample of kitchens with gas cooking appliances monitored during a one-week period,
a) 95% (two-sided) confidence interval for true average CO2 level in the population is 654.16 +/- 185.0632
b) Sample size is 12.
What is Confidence Interval ?The confidence interval for the population mean is constructed about the sample mean i.e. sample mean lies at the center of the interval.
1) The yield point of a particular type of mild steel-reinforcing bar is normally distributed with
Sample size,n = 49
Sample mean , X-bar = 8459 lb,
Standard deviations, σ = 100
We have to compute 90% CI for the true average yield point of the modified bar.
α = 1 - 90% = 1- 0.90 = 0.10
a)From Standard Normal Table, the critical value at the Zα/2 = Z₀.₀₅ level of significance is 1.645.
Confidence interval formula ,
X-bar +/- Zα/2(σ /√n)
90% CI for the true average yield point of the modified bar, is
8459 +/- 1.645(100/√49)
=> 8459 +/- 1.645(100/7)
=> 8459 +/- 1.645(14.2857) = 8459 +/- 23.5
b)
Now, we have to compute 98% CI for the true average yield point of the modified bar.
α = 1 - 98% = 1 - 0.98 = 0.02
From Standard Normal Table, the critical value at the Zα/2 = Z₀.₀₁ level of significance is 2.326.
Then, Confidence interval is,
CL = 8459 +/-2.326(100/√49)
= 8459 +/- 1.645( 14.285) = 8459 +/- 23.49
2) An article reported that for a sample of kitchens with gas cooking appliances monitored during a one-week period,
Sample size, n = 48
Sample mean , X-bar= 654.16
standard deviations, σ = 162.85
a) We have to calculate and interpret a 95% (two-sided) confidence interval for true average CO2 level. α = 1 - 0.95 = 0.05 ; α/2 = 0.025
From Standard Normal Table, the critical value at the Zα/2 = Z0.025 level of significance is 1.96
95% (two-sided) confidence interval for true average CO2 level is 654.16 +/- 1.96(654.16 /√48)
= 654.16 +/- 1.96(94.42)
= 654.16 +/- 185.0632
b) The distance between the two ends limits of the interval is known as the width of the interval and it is twice the margin of error.
We have width of the interval = 47 ppm
so, Margin of error , MOE = 94
Significance level, 95%
we have to determine sample size
Margin of error formula is
MOE = Zα/2(σ/√n)
where n is sample size.
94 = 1.96 (162.85/√n)
=> √n = 162.85 × 1.96/94 = 3.39559574468
=> n = 11.53 ~ 12
Hence, sample size is 12..
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The following histogram displays the test score results for Ms. Garrison's Algebra class.
Drop down menus:
1st: Symmetric, skewed right, skewed left
2nd: 50-60 and 60-70, 60-70, 50-60
3rd: 5, 8, 4, 1
Answers
Answer:
1) scewed left
2) 60-70
3) 5
Step-by-step explanation:
i took the test on edmentum and got it correct
From the histogram graph, it is clear that the graph is skewed left. Anabelle's score should be added to 60 - 70. 5 students scored below 70 on that day.
What is a histogram graph?''A histogram is a graphical representation that organizes a group of data points into user-specified ranges. Similar in appearance to a bar graph, the histogram condenses a data series into an easily interpreted visual by taking many data points and grouping them into logical ranges or bins.''
Given, a histogram that shows the test score results of Ms. Garrison's Algebra class.
1. Data in the histogram is skewed left as the graph is pretty higher on the right hand side and deeper on the left hand side.
2. Anabelle was absent on the day of the test but appeared on the next week. She scored 60. It will be added in the column of 60 - 70.
3. The students who scored less than 70 on that day of exam is = (3 + 2) = 5.
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What are the coordinates of the vertices of the final image? A. P’(12, -6), Q’(8, -7), R’(4, -4), and S‘(7, -1) B. P’(12, 8), Q’(8, 9), R’(4, 6), and S‘(7, 3) C. P’(-12, 6), Q’(-8, 7), R’(-4, 4), and S‘(-7, 1) D. P’(12, 6), Q’(8, 7), R’(4, 4), and S’(7, 1)
Answers
Answer:
Given that the vertices of quadrilateral PQRS are P(6,3), Q(4,2), R(2,4) and S(4,5) and the quadrilateral is dilated with a scale factor of 2, about the origin.
Now, let's find the new vertices of the dilated image:
Vertex P is dilated by a scale factor of 2, its new coordinates will be (2 × 6, 2 × 3) = (12, 6). Therefore, the new vertex P' is at (12, 6).
Vertex Q is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 2) = (8, 4). Therefore, the new vertex Q' is at (8, 4).
Vertex R is dilated by a scale factor of 2, its new coordinates will be (2 × 2, 2 × 4) = (4, 8). Therefore, the new vertex R' is at (4, 8).
Vertex S is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 5) = (8, 10). Therefore, the new vertex S' is at (8, 10).
Therefore, the coordinates of the vertices of the final image are P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).So, the correct option is D. P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).
Step-by-step explanation:
Hope this helps you!! Have a good day/night!!
7%of£40
show working out plz
Answers
Answer:
7% of 40 is 2.80
Step-by-step explanation:
0.07 x 40 = 2.8
Answer:
17.5%
Convert fraction (ratio) 7 / 40
then divide 7 by 40 and multiply by 100 and you get 17.5%
plz mark brainliest
anwser it pls aaaaaaaassaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answers
Answer:
Step-by-step explanation:
Volume = Bh
Turn the shape so the trapezoid is on the bottom/base
h=18 for overall shape
B = area of base, trapezoid
B = 1/2 (b₁ + b₂) h
b₁ = 11
b₂ = 25
h = 24 for trapezoid
B = 1/2 (11 + 25)(24)
B = 432
V = Bh
V = (432)(18)
V= 7776 in³
Marco wants to know how much the other students in his mathematics class study. He recorded the data he collected in
the following table.
Time spent studying per week (in hours)
2.0
5.0
1.0
2.5
2.5
3.5
0.0
4.5
2.5
4.0
3.5
3.0
2.0
1.5
4.0
2.0
0.5
3.0
1.0
3.0
3.5
1.5
1. Construct a histogram for the data.
Answers
Answer:
Step-by-step explanation:
This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.
Hurry!
The following is a function, true or false?
Answers
Answer:
Step-by-step explanation: true
If the variance for a set of data equals 8.1, find the standard deviation.
Answers
The standard deviation for this set of data is approximately 2.85.
To find the standard deviation, we first need to take the square root of the variance. Therefore, the standard deviation for the given data set is the square root of 8.1, which is approximately 2.846.
To find the standard deviation of a set of data when the variance is given, you simply need to take the square root of the variance. In this case, the variance equals 8.1.
Step 1: Identify the variance, which is 8.1.
Step 2: Take the square root of the variance.
Standard Deviation = √(Variance) = √(8.1)
Step 3: Calculate the square root of 8.1.
Standard Deviation ≈ 2.85
So, the standard deviation for this set of data is approximately 2.85.
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Kesia is writing a report about two of the world's fastest fish. She wants to put the faster fish on the cover of her report. The fastest speed for a sailfish is 67.85 mph. The fastest speed for a swordfish is 60 mph.
Which fish should go on the cover of Kesia's report?
Choose 1 answer:
(Choice A)
A
Sailfish
(Choice B)
B
Swordfish
Answers
Answer:
A. Sailfish
Step-by-step explanation:
Looking at the problem, we need to focus on the speeds of the fishes. The sailfish has a max speed of 67.85 and the swordfish's is 60. Comparing the two values, 67.85 is greater, so Kesia should put the sailfish (A) on the cover of her report.
The fastest fish that should go to the cover of Kesia's report is Sailfish. Option A is correct.
How do you determine the speed of an object?The speed of an object is the amount of distance covered by an object within a specified period of time. The higher the distance, the higher the speed covered.
From the given information,
Speed of the Sailfish = 67.85 miles/hourSpeed of the Swordfish = 60 miles/hourProvided the time is constant for both fish, we can conclude that the speed of the Sailfish is faster than the speed of the Swordfish.
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Twenty percent of adults in a particular community have at least a​ bachelor's degree. Suppose x is a binomial random variable that counts the number of adults with at least a​ bachelor's degree in a random sample of 100 adults from the community. If you are using a calculator with the binompdf and binomcdf​ commands, which of the following is the most efficient way to calculate the probability that more than 60 adults have a​ bachelor's degree, ​P(x?>60)?
a. P(x < 60)=binompdf(100,0 20,59)
b. P(x<60)=binompdf(100.0.20.60)
c. P(x<60)= binomcdf(100,0,20,59)
d. P(x<60)=binomcdf (100.0.20.60)
Answers
Answer:
Step-by-step explanation:
Since we are dealing with binomial probability in this scenario, then the outcome is either a success or a failure. A success in this case means that a chosen adult has a bachelor's degree. The probability of success, p would be 20/100 = 0.2
The number of adults sampled, n is 100
The number of success, x is 60
The probability that more than 60 adults have a bachelor's degree P(x >60) would be represented as
d. P(x<60)=binomcdf (100.0.20.60)
binompdf is used when we want to determine P(x = 60)
41 is 82% of what number?
Enter your answer in the box.
Answers
Answer:
The answer is 50.
Step-by-step explanation:
Set up a proportion: \(\frac{41}{y} =\frac{82}{100}\)
Step 2- Multiply 41 by 100 to get 4100
Step 3. Divide 4100 by 82 to get 50.
Hope this helps! :)
Simplify (2x-3)(5x squared-2x+7)
Answers
To simplify the expression (2x-3)(5x^2-2x+7), we can use the distributive property.
First, multiply 2x by each term inside the second parentheses:
2x * 5x^2 = 10x^3
2x * -2x = -4x^2
2x * 7 = 14x
Next, multiply -3 by each term inside the second parentheses:
-3 * 5x^2 = -15x^2
-3 * -2x = 6x
-3 * 7 = -21
Combine all the resulting terms:
10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21
Now, combine like terms:
10x^3 - 19x^2 + 20x - 21
So, the simplified expression is 10x^3 - 19x^2 + 20x - 21.
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What is the quotient?
x-3) 4x2+3x+2
+2
O 4X2 + 15 +
47
X-3
43
0 4x + 15 +
X-3
O 4x2 + 15 +
43
X-3
0 4x + 15 +
47
X-3
Answers
Answer:
13
Step-by-step explanation:
the answer is 13
the answer is 13
the answer is 13
the answer is 13
the answer is 13
The quotient obtained by dividing 4x²+3x+2 will be 4x + 15 hence option (A) will be correct.
What is the equation?An equation can be defined in numerous ways. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.
A formula known as an equation uses the same sign to denote the equality of two expressions.
In another word, the equation must be constrained with some constraint.
Given that
dividend = 4x²+3x+2
divider = x -3
⇒ (x - 3) / 4x²+3x+2
⇒ (x - 3) / 4x²+3x+2
→ First it will goes for 4x time so 4x × (x - 3) = 4x² - 12x
Quotient = 4x
so (4x²+3x+2) - ( 4x² - 12x ) = 15x + 2
(x - 3) / 4x²+3x+2
→ Second time it goes for 15 so 15 × (x - 3) = 15x -45
Quotient = 15
so (15x + 2 ) - ( 15x -45 ) = 47
Hence, 47 will be the remainder and the quotient will be (4x + 15).
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During her first year of college, Sara put $2000 in the bank to save for a trip to Italy after graduation. The money earned 3% simple annual interest. After 4 years, how much money did she have in the bank for her trip?
$ ____
Answers
The money she will have in the bank after her trip is $2240.
How much will she have in the bank?Simple interest is when the amount deposited increase by a fixed percentage over a period of time. The amount Sara would have in her account is a function of the amount deposited, the interest rate and the number of years.
The amount she would have = simple interest + amount deposited
Simple interest = principal x time x interest rate
2,000 x 0.03 x 4 = $240
The amount she would have = $240 + $2000 = $2240
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Answer:
The Answer Is: 2240 I Just did the question
Step-by-step explanation:
Which triangle’s area would be calculated using the trigonometric area formula?
Triangle E F D is shown. The length of E F is 10, the length of D F is 7, and the length of D E is 12.
Triangle Q R P is shown. The length of Q R is 5 and the length of R P is 6. Angle Q R P is 40 degrees.
Triangle A B C is shown. The length of A B is 4 and the length of B C is 5. Angle B C A is 25 degrees.
Triangle X Y Z is shown. The length of Y Z is 4. Angle Z X Y is 29 degrees and angle X Y Z is 110 degrees.
Answers
Answer:
Triangle Q R P is shown. The length of Q R is 5 and the length of R P is 6. Angle Q R P is 40 degrees.
Step-by-step explanation:
The trigonometric formula refers the two sides length of the triangle and it also consists of included angle to find out the area
A = \(\frac{1}{2}\) ab sin C
QPR contains two sides and the included angle
XYZ has one side and the two angles
DEF has only three sides
And, the ABC contains two sides but does not have the included angle
Based on the explanation above, the correct option is B
Answer: the second option aka B
Step-by-step explanation: The other person explained it and I'm just here to tell you they gave the correct and answer for edge 2020.
Find the center and radius of the circle with a diameter that has endpoints (-6,10)
and (2,3)Enter the center as an ordered pair, : Enter the radius as a decimal correct to three decimal places :
Answers
Step-by-step explanation:
the center of the circle is the midpoint of the diameter.
and the radius is the distance of the midpoint to either endpoint (or simply half of the distance between the diameter endpoints).
the midpoint between points A and B
(xm, ym) = ((xa + xb)/2, (ya + yb)/2)
in our case the midpoint (center of the circle) is
((-6 + 2)/2, (10 + 3)/2) = (-4/2, 13/2) = (-2, 6.5)
about the radius
diameter² = (-6 - 2)² + (10 - 3)² = (-8)² + 7² = 64 + 49 =
= 113
diameter = sqrt(113) = 10.63014581...
radius = diameter / 2 = 5.315072906... ≈ 5.315
FInd the measure of the arc using the picture provided , please and thanks
Answers
The measure of arc angle QTP is 204 degrees.
How to find arc angle?When a tangent and a secant intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
Therefore, let's find the measure of arc angle QTP as follows:
90 = 0.5(x - 68)
90 = 0.5x - 34
0.5x = 124
x = 124 / 0.5
x = 248 degrees
Where
x = arc angle TSQ
Therefore,
arc QP = 44 degrees
Therefore,
arc QTP = 248 - 44
arc QTP = 204 degrees
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a red ant traveled 1/12 inch in. 6 seconds. what's the ants speed in inches per second?
Answers
a red ant traveled 1/12 inch in. 6 seconds. what's the ants speed in inches per second?
To find out the speed, divide the total distance by the total time
so
(1/12)/(6)=1/72 inches per second
answer is
1/72 inches per secondChristian and Tanae both leave Disneyland at the same time. Christian travels north at 65 mph. Tanae travels south at 55 mph. How long will it take them to be 540 miles apart? Which of the following equations would you use to solve this word problem?
65t + 55(t − 1) = 540.
65t + 55t = 540.
65t + 55(t + 1) = 540.
None of these choices are correct.
Answers
Answer:
Step-by-step explanation:
B looks like it would work.
You add speeds * time when you are travelling in opposite directions.
I don't know why you would add or subtract 1 as in A and C
120 * t = 540
t = 540/120
t = 4.5 hours.
So after 4.5 hours they are 540 miles apart.
Answer:
b
Step-by-step explanation:
Find |37|.
0
-37
37
i have 3 minutes to finish HELPP :(
Answers
The ratio of the number of boys to the number of
girls in choir is 6 to 5. There are 70 girls in the choir.
How many boys are in the choir?
Answers
Answer:
48 boys
Step-by-step explanation:
use distributive property to rewrite this problem: -2(n-7)
Answers
To rewrite the expression -2(n-7) using the distributive property, we need to distribute the -2 to both terms inside the parentheses. The distributive property states that for any numbers a, b, and c:
a(b + c) = ab + ac
Applying this property to the given expression:
-2(n-7) = -2 * n + (-2) * (-7)
Simplifying further:
-2(n-7) = -2n + 14
Therefore, the rewritten expression is -2n + 14.
The right rectangular prism is filled with cubes that have a side length of 1/8
foot.
How many cubes does it take to fill the prism? (Look at the photo please!!)
Answers
Volume of cube = side measure ^ 3
Cube = (1/8)^3 = 1/512
Volume of prism = l x w x h
Prism = (1/4)(1/2)(3/8) = 3/64
3/64 / 1/512
3/64 x 512/1
3 x 512 / 64
1536 / 64
24
Please answer ive been searching for answers will give brainliest and 5 star pleaseeeee
Answers
[-9, 7]
Step-by-step explanation:The domain describes the x-values contained in a graph.
Finding the Domain
As stated above, the domain shows the x-values that are covered by a function. The x-values are listed on the horizontal axis. Starting on the left, the x-values range from -9 to 7. Additionally, the circles on points -9 and 7 are both closed. This means that both of the values are included within the domain.
Interval Notation
There are different ways to write a domain. One way is interval notation. In this notation, the minimum x-value is listed, then the maximum x-value is listed. If the min and max values are included, then surround the values with brackets. If they are not included, then use parentheses.
In the graph above, the minimum domain value is -9 and the max is 7. Since both are included, the interval notation for the domain is [-9, 7].
Calculate the trade discount for 15 boxes of computer paper if the unit price is $14.26 and a single trade discount rate of %45 is allowed.
Answers
So, the trade discount for 15 boxes of computer paper if the unit price is $14.26, and a single trade discount rate of 45% allowed is $96.255.
Trade discount refers to the reduction in list price known as a discount, allowed by a supplier to the consumer while selling the product generally in bulk quantities to the concerned consumer to increase the sales of the business as more customers are attracted when the discount is given on the list price of the product.
We have to calculate the trade discount for 15 boxes of computer paper.
the unit price of computer paper is $ 14.26, and a single trade discount rate is 45% allowed.
The trade discount on one unit computer paper is.
= 45%×14.26
= $6.417
now, trade discount on 15 unit of computer paper box is.
=6.417×15
=$96.255.
So, the trade discount for 15 boxes of computer paper if the unit price is $14.26, and a single trade discount rate of 45% allowed is $96.255.
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Which is equivalent to 80 Superscript one-fourth x? (StartFraction 80 Over 4 EndFraction) Superscript x RootIndex 4 StartRoot 80 EndRoot Superscript x RootIndex x StartRoot 80 EndRoot Superscript 4 (StartFraction 80 Over x EndFraction) Superscript 4
whoever can answer this gets brainliest
Answers
The expression that is equivalent to \(80^{(1/4}\) * x is \(80^{4/x}\)
How to calculate the valueTo determine the equivalent expression to \(80^{1/4}\) * x, let's analyze each option:
\(80/4^{x}\)
This expression simplifies to \(20^{x}\), but it is not equivalent to the original expression.
Applying the power of a power rule, this expression simplifies to \(80^{x/4}\) , which is not equivalent to the original expression.
\(80/x^{4}\)
This expression can be simplified as \(80^{4 x^{4} }\) , which is not equivalent to the original expression.
Therefore, the expression that is option d.
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NO LINKS!! Please assist me with this problem Part 1m
Answers
Answer:
(x + 8)² + (y - 8)² = 64=======================
Given ConditionsTangent to x-axis,Tangent to y-axis,In the second quadrant,Radius is 8 units.SolutionEquation of circle:
(x - h)² + (y - k)² = r², where (h, k) is center and r - radiusThe center is the radius long distance from the x- axis to left and y-axis up same distance, this makes it in the second quadrant.
So the coordinates of the center are:
x = - 8, y = 8The equation is:
(x - (-8))² + (y - 8)² = 8²(x + 8)² + (y - 8)² = 64
Answer:
\((x+8)^2+(y-8)^2=64\)
Step-by-step explanation:
Required conditions:
Tangent to both axes.Center in the second quadrant.Radius = 8 units.If the circle is tangent to both axes, its center will be the same distance from both axes. That distance is its radius.
If the center of the circle is in quadrant II, the center will have a negative x-value and a positive y-value → (-x, y).
Therefore, the coordinates of the center will be (0-r, 0+r) where r is the radius.
If the radius is 8 units, then the center is (-8, 8).
\(\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)
Substitute the found center and given radius into the formula to create an equation for the circle that satisfies the given conditions:
\(\implies (x-(-8))^2+(y-8)^2=8^2\)
\(\implies (x+8)^2+(y-8)^2=64\)
PLEASE HELP ME QUICK!!!
Answers
Answer:
Option D. \(g(x)=5(0.8)^{x}+2\)
Step-by-step explanation:
Main concepts
Concept 1: identifying horizontal asymptote
Concept 2: assuring decreasing exponential function
Concept 1. identifying horizontal asymptote
Any exponential function of the form \(y=a*b^x\) has a horizontal asymptote on the x-axis. A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number. Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units. Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.
Concept 2. assuring decreasing exponential function
Exponential functions of the form \(y=a*b^x\) increase or decrease based on the value of "b".
If "b" is between 0 and 1 (a "small" number), the function will decrease.If "b" is larger than 1 (a "big" number), the function will increase.Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.
To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.
Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.
unction g is a transformation of the parent tangent function such that
. Which graph represents function g?
A.
The graph shows trigonometric functions intercept the x-axis at minus 3, 0.2, and 3.5 units also pass parallel to the g of the x-axis.
B.
The trigonometric functions intercept the x-axis at minus 4.2, minus 1.1, 2, and 5 units also pass parallel to the g of the x-axis.
C.
The trigonometric functions intercept the x-axis at minus 3.5, minus 0.2, and 3 units also pass parallel to the g of the x-axis.
D.
The trigonometric functions intercept the x-axis at minus 5, minus 2, 1, and 4.2 units also pass parallel to the g of the x-axis.
Answers
Answer:
A.
The graph shows trigonometric functions intercept the x-axis at minus 3, 0.2, and 3.5 units also pass parallel to the g of the x-axis.