Answer: Thus, after the transformation, the graph consists of points (x,y) satisfying y=2(x−3)2. This is the equation of the transformed graph.
Step-by-step explanation:
Consider the graph y=x2. Suppose the graph is dilated from the x-axis by a factor of 2, and then translated 3 units to the right. What is the equation of the resulting graph?
Solution
The transformation given is Trans(3,0)∘Dilx-axis,2. Denote by (x′,y′) the image of a point (x,y) under this transformation. A point (x,y) is sent to (x,2y) by the dilation, and then to (x+3,2y) by the translation, so (x′,y′)=(x+3,2y).
The original graph consists of points (x,y) such that y=x2. Then it is transformed so that (x,y)↦(x′,y′)=(x+3,2y). We must find what equation is satisfied by x′ and y′.
Since x′=x+3 and y′=2y, we have x=x′−3 and y=y′/2. Thus y=x2 implies
y′2=(x′−3)2or equivalentlyy′=2(x′−3)2.
Explain the differences and similarities of the steps for dividing whole numbers and decimals.
Answer: Comparing a whole numbers and a decimals:
First let’s talk about the similarities of comparing whole numbers and decimals:
=> their place value always matters.
Now, let’s proceed to their differences
=> in comparing whole numbers, we don’t care about the value to the nearest decimal points or the value of ones. We always look at the highest value, not unless the highest values are all the same.
=> In comparing decimals, the value to the nearest decimal points or the tenths place value always matters.
Step-by-step explanation:
Plss answer I give you branlistb
can some one awnser this i got 2 more questions for this test.
Answer:
and question is
Step-by-step explanation:
What is the amplitude and period of the function shown below?
The features of the sine function in this problem are given as follows:
Amplitude: 2.
Midline: y = -4.
Period: 3 units.
What is trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Here, we have,
The equation is given as follows:
y = 2sin(2πx/3) - 4.
we have to define the sine function:
The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For which the parameters are given as follows:
A: amplitude.
B: the period is 2π/B.
C: phase shift.
D: vertical shift.
The function has a minimum value of -6 and a maximum value of -2, for a difference of 4, hence the amplitude is given as follows:
2A = 4.
A = 2.
Without vertical shift, a function with amplitude of 2 would oscillate between -2 and 2, while this one oscillates between -6 and -2, hence the vertical shift is given as follows:
D = -4.
The shortest distance between repetitions can be given by 2 - (-1) = 3, hence the period is of 3 units and the coefficient B is given as follows:
2π/B = 3
B = 2π/3.
The function is at it's midline at the origin, hence it has no phase shift, and thus the equation is given as follows:
y = 2sin(2πx/3) - 4.
More can be learned about trigonometric functions at brainly.com/question/21558626
#SPJ2
Use technology to find the P-value for the hypothesis test described below.
The claim is that for a smartphone carrier's data speeds at airports, the mean is p = 19.00 Mbps. The sample size is n = 21 and the test statistic is t= 1.401
P-value = (Round to three decimal places as needed)
Using the t-distribution, it is found that the p-value is of 0.177.
At the null hypothesis, it is tested that for a smartphone carrier's data speeds at airports, the mean is 19 Mbps, that is:
[tex]H_0: \mu = 19[/tex]
At the alternative hypothesis, it is tested if the mean is different than 19 Mbps, that is:
[tex]H_1: \mu \neq 19[/tex]
We are testing if the mean is different from a value, hence it is a two-tailed test.The test statistic is t = 1.401.Sample size of n = 21, hence there are 21 - 1 = 20 df.Inputting this information into a calculator, the p-value is of 0.177.
A similar problem is given at https://brainly.com/question/13873630
PLZZZ HELPPP
What are the domain and range of f (x) = 1/2 (x+4)^2 - 11
Domain: All real numbers
Range: f(x) > -11
Domain: 3 > -11
Range: f(x) > -11
Domain: All real numbers
Range: All real numbers
Domain: 2 > -11
Range: All real numbers
Answer:
D. Domain: 2 > -11
Range: All real numbers
Step-by-step explanation:
Correct me if I’m wrong UwU
Answer:
Domain: All real numbers
Range: f(x) ≥ - 11
Step-by-step explanation:
Given the quadratic function in vertex form, f(x) = ½(x + 4)² - 11:
The vertex, (h, k) is (-4, -11).
Range: f(x) ≥ -11.The parabola opens upward (where a = ½, which is greater than 0), and k = -11 is the minimum value for f(x). Hence, the range of the given function must be at least -11, or f(x) ≥ -11.
Domain: all real numbersThere is no restriction for the value of x. Therefore, the domain of the given function is all real numbers.
chapter 6.4 : Problem 4
Answer:
wdym
Step-by-step explanation:
Anne bought an aquarium priced at $44.96. Shipping and handling cost an additional 25%of the price. What was the total cost of the aquarium, including shipping and handling?
If 10 candy cost $35. How much candy can I buy with $20
Answer:
6 candies
Step-by-step explanation:
(find unit rate, cost / quantity)
35/10 = 3.5
20/3.5 = = 5.7142857142857
candies cannot be in decimal so you must round to the nearest whole
18x+5=-1+8x+46 find value of x
Answer:
3
Step-by-step explanation:
18x + 15 -8x = 8x + 45 -8x
10x + 15 = 45
10x + 15 - 15 = 45 - 15
10x = 30
10x/10 = 30/10
× = 3
Please help me with these questions. I’m genuinely confused.
Answer:
16: 5
17: 6 4/9
Step-by-step explanation:
I only will give u the answer for a few questions
Solve the equation for B. PLEASE SHOW YOUR WORK.
2(B + 3.5 - B = -3(6 - 2B)
9514 1404 393
Answer:
B = 5
Step-by-step explanation:
The given equation has mismatched parentheses. We assume the intent is ...
2(b +3.5) -b = -3(6 -2b)
Eliminating parentheses, we have ...
2b +7 -b = -18 +6b
25 = 5b . . . . . . . . . . . add 18-b to both sides and collect terms
b = 5 . . . . . . . . . . . . divide both sides by 5
Jamie Lee needs to save a total of $9,000 in order to get started in her cupcake café venture. She is presently depositing $1,800 a year in a regular savings account. Calculate the future value of these deposits.
Answer: 16,200,000
Step-by-step explanation: divide both numbers
The future value of her deposit would be in 5 years.
The total amount needed to start a cupcake cafe venture
= $9,000
Deposit per year = $1,800
Therefore, if $1,800 = 1 year
$9,000 = X
[tex]x = \frac{9000}{1800} [/tex]
[tex]x = 5[/tex]
Therefore in 5 years, Jamie Lee would be able to start her cupcake café venture.
Learn more about savings here:
https://brainly.com/question/25787382
biografía completa de Pitágoras
Answer:
hiiiiiiiiiíiiiiiiiiiii
Question 21: In January, Michelle walked 15.73 miles. In February she walked 3.6 miles. In March,
she walked 8.01 miles. How many miles did she walk in all?
Answer:
27.34 milesStep-by-step explanation:
Add all together:
15.73 + 3.6 + 8.01 = 27.3415.73miles + 3.6miles + 8.01miles = ...
= 19.33miles + 8.01miles
= 27.34miles
Please help thank you! Solve for x and y
Answer:
x = 2
y = 7
I aced this lesson in 6th grade.
Step-by-step explanation:
hope this helps. . . <3
good luck! uωu
Answer:
Step-by-step explanation:
All 4 sides are equal. (They are marked that way).
8x = 5x + 6 Subtract 5x from both sides
8x - 5x = 5x - 5x + 6 Combine
3x = 6 Divide by 3
3x/3 = 6/3
x = 2
Consecutive angles of a rhombus are supplementary
97 + 12y - 1 = 180 Combine
96 + 12y = 180 Subtract 86 from both sides
12y = 180 - 96
12y = 84 Divide by 12
y = 84/12
y = 7
The letters A, B, and C can be arranged in six ways. Five ways are listed below.
Find the sixth way.
АВС ACB BAC ВСА САВ
Answer:
CBA would be the sixth
Step-by-step explanation:
Please help! Grade 7 math
Answer:
[tex]-\frac{5}{8}\\-9.2%\\\\-0.001[/tex]
-3/4, -5/8, -9.2%, -0.001, 4.6%, 5%, 33%
Step-by-step explanation:
[tex]-\frac{3}{4}=-75[/tex]% 4.6%
Let's do the process of elimination to find our answers
[tex]-\frac{5}{8}=-62.5[/tex]% this would be in between because - 62.5% would be after -75%
[tex]\frac{5}{100}=5[/tex]% this fraction equals to a positive percentage which would be after 4 so not this one
[tex]-0.001 = -0.1[/tex]% this number would come after -75%, -62.5%, -9.2%and before 4.6% so this would be one
[tex]-0.75= -75[/tex]% we already have the percentage so not this one
33% this number would come after 4.6% so not this one
-9.2% this would be between them because its -9 and it will be after -75% and -62.5%
Find the 6th term of the geometric sequence whose common ratio is
1/3
and whose first term is 5.
Step-by-step explanation:
geometric sequence means every new term is created by multiplying the previous term by a certain constant (here 1/3).
s1 = 5
s2 = s1 × 1/3 = 5 × 1/3
s3 = s2 × 1/3 = s1 × 1/3 × 1/3 = 5 × 1/9
sn = sn-1 × 1/3 = s1 × (1/3)^(n-1) = 5 × (1/3)^(n-1)
s6 = 5 × (1/3)⁵ = 5 × 1/243 = 5/243
For the right angle shown, the length of two sides are given. Find the third side. Leave your answer in simplified, radical form.
b=9, c=16
a=
Answer:
a is about 13.2
Step-by-step explanation:
the formula for this type equation is a²+b²=c²
plug in the numbers to make the equation a²+9²=16²
do the multiplication and it gives u a²+81=256
subtract 81 from both sides and a²=175
take the square root of both sides and it gives u 13.22
For the amusement of the guests, some hotels have elevators on the outside of the building. One such hotel is 400 feet high. You are standing by a window 100 feet above the ground and 150 feet away from the hotel, and the elevator descends at a constant speed of 20 ft/sec, starting at time t = 0, where t is time in seconds. Let θ be the angle between the line of your horizon and your line of sight to the elevator. 4 (a) Find a formula for h(t), the elevator's height above the ground as it descends from the top of the hotel. h(t) = (b) Using your answer to part (a), express θ as a function of time t. θ(t) = Find the rate of change of θ with respect to t. dθ dt = (c) The rate of change of θ is a measure of how fast the elevator appears to you to be moving. At what time does the elevator appear to be moving fastest? time = seconds At what height does the elevator appear to be moving fastest?
9514 1404 393
Answer:
a. h(t) = -20t +400
b. θ(t) = arctan(2 -2/15t); dθ/dt = -30/(1125 -120t +4t^2)
c. 15 seconds; 100 ft
Step-by-step explanation:
a. The initial height of the elevator is 400 ft. The rate of change of height is -20 ft/s, so the height equation can be ...
h(t) = -20t +400
__
b. The tangent of the angle above the line of sight is "opposite"/"adjacent":
tan(θ) = (h(t) -100)/(150) = -2/15t +2
θ(t) = arctan(2 -2/15t) . . . . radians
The derivative of the angle function is ...
dθ/dt = 1/(1+(2 -2/15t)^2)(-2/15)
dθ/dt = -30/(1125 -120t +4t^2)
__
c. The value of dθ/dt will have a peak where the denominator has a minimum, at t = -(-120)/2(4)) = 15. (The quadratic vertex coordinate is t=-b/(2a).)
The elevator appears to be moving fastest at t=15 seconds.
The height at that time is ...
h(15) = 400 -20(15) = 100
The elevator appears to be moving fastest when it is at eye level, 100 ft above the ground.
A 6 sided die is rolled 2 times. What is the probability of getting a 1 both times ?
Answer:
Step-by-step explanation: If you roll the die twice, the probability of getting a even number both times is (1/2)(1/2) ... A probability experiment consists of rolling a 6 sided die
) Which value is equivalent
[tex] {7}^{3} [/tex]
Answer:
343
Step-by-step explanation:
[tex]7^{3} = 7 * 7 * 7[/tex]
[tex]7^3 = 343[/tex]
-Chetan K
In parallelogram HJKL if JM=19 find ML.
Answer:
19
Step-by-step explanation:
in any parallelogram the diagonals bisect each other evenly. that means if JM = 19, ML is also 19. hope this helps
due in an hour please help!!! :(
Answer:
Step-by-step explanation:
1,7 are same side exterior
1,8 alternate exterior
2,4 none
3,5 same side int
2,6 corrosponding
4,6 same side int
4,7 is none
5,4 alternate int
8,5 vertical
8,7 alternate exterior
Becca hikes 9/10 mile in 5/3 hour.
Answer:
(9/10 mile)/(5/3 hour) = 27/50 miles/hour
Step-by-step explanation:
If you are looking for the speed, then speed = distance/time
speed = (9/10 mile)/(5/3 hour)
speed = 9/10 ÷ 5/3 miles/hour
speed = 9/10 × 3/5 miles/hour
speed = 27/50 miles/hour
Answer:
1. 9/10/3/5
2. 3/2
Step-by-step explanation:
Got it correct on iReady.
Look at attached photo. Will give brainiest to correct answer. Trigonometry.
Answer:
Step-by-step explanation:
Which number line shows the solution of –5x + 10 > –15? A. B. C. D.
[tex]-5x+10>-15\\\\\implies -5x> -10 -15\\\\\implies -5x > -25\\\\\implies x< 5\\\\\text{Interval,} ~(-\infty,5)[/tex]
Answer:
add the options, then we'll talk
Step-by-step explanation:
the difference between factors and factor pairs
Answer:
Factors are often given as pairs of numbers, which multiply together to give the original number. These are called factor pairs. A square number will have one factor pair consisting of one factor multiplied by itself. This factor is called the square root of the given number.
The city commission would like to install new flagpoles that are each 15 yards tall. If there are 3 feet in 1
yard, how tall are the flagpoles in the model?