Which sequence of transformations was applied to the parent tangent function to create the function m(x) = 2tan(3x+4)
The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.
To determine the sequence of transformations, let's break down the given function:
1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.
2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.
3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.
4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.
5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.
In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.
Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.
After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)
This example helps illustrate the effect of the transformations on the graph of the function.
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Write an equation of a line with the given slope and y-intercept.
m = 4, b = -1
a. y = -x + 4
b. y = 4x + 1
C. y = -x - 1
d. y = 4x - 1
Please provide explanation :)
Answer:
D. y=4x-1
Step-by-step explanation:
y=mx+b (This is the slope intercept formula) The M(X) represents the slope and the B represents the y intercept.
y=4x-1
Answer:
d. y = 4x -1
Step-by-step explanation:
y = mx + b
m= 4
b= -1
y = (4)x + (-1)
y = 4x - 1
can i get brainliest please?
Here are the endpoints of the segments AB, CD, and EF.
A(7,4), B (2,8)
C(5,0), D (1, -5)
E (-3,5), F (-8, 1)
Answer:
this is not a question
Step-by-step explanation:
How much would you have to deposit today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would
earn?
Round to 2 decimal places and do not include the $
symbol.
Answer:
To calculate how much you would have to deposit today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn, we can use the formula for the present value of an annuity due:
PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)
where:
- PV is the present value of the annuity due (the amount you would have to deposit today)
- PMT is the monthly payment ($75)
- r is the annual interest rate (3.5%)
- n is the number of times interest is compounded per year (12 for monthly compounding)
- t is the number of years (10)
PV = 75 × ((1 - (1 + 0.035/12)^(-12×10)) / (0.035/12)) × (1 + 0.035/12) = **$7,360.47**
Therefore, you would have to deposit **$7,360.47** today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn.
Can someone explain what equivalent fraction and what I do to get one?
sue eats 3/8 of a cherry pie. Jan
eats
Answer:
If you're saying Jan ate 1/4 of what was left. How much of the pie did Jan eat?
then the answer is 5/32
Step-by-step explanation:
What percent of a 120-gallon tank is full if it contains 90 gallons?
Answer:
The vertical tank is basically a cylinder that is sometimes referred to as a V-120 cylinder. Both 120-gallon tanks can hold up to 96 gallons of propane when full (not 120 gallons). That’s due to the 80% rule; all propane tanks can be filled up to 80% of their maximum capacity.
Answer:
75%
Step-by-step explanation:
Help help help please in a hurry!!!!!!!!!!!!!!!!!!!
Answer:D
Step-by-step explanation:
please mark brainliest
lease Help!! And Fast!! Will give Brainliest to the Best Answers (75 points) --- The historical society hired an artist to restore a stained glass window panel. After studying the original drawings, the artist knows that panel ABCD is square. He also knows that FG is a perpendicular bisector of BC and BC ≅ BE. However, in order to restore the panel to match its original specifications, he needs to know the measure of ∠BED. Given: ABCD is a square FG ⊥ BC BC ≅ BE Step 1: Draw EC on the diagram. Use the given information to explain how you know △EGC ≅ △EGB. Add the appropriate notation to the diagram. (5 points) Step 2: Building on the information from Step 1, use the spaces below to prove that m∠BEC = 60°. Add the appropriate notation to the diagram. (5 points; 4 points for the proof, 1 point for the diagram) Statements Reasons 1. △EGC ≅ △EGB 1. Given 2. EB ≅ EC 3. Given 4. EB ≅ EC ≅ BC 5. m∠BEC = 60° Step 3: Next, use the spaces below to prove the measure of ∠ECD = 30°. Add the appropriate notation to the diagram. (5 points; 4 points for the proof, 1 point for the diagram) Given: ABCD is a square FG ⊥ BC BC ≅ BE △ECG ≅ △EBG △BEC is equilateral m∠BEC = 60° Prove: m∠ECD = 30° Statements Reasons 1. △BEC is equilateral 2. m∠GCE = 60° 3. ABCD is a square 4. Substitution Step 4: Find m∠BED. Show your work and explain your reasoning. Add the appropriate notation to the diagram. (6 points; 4 points for showing work and explaining reasoning; 1 point for final answer; 1 point for diagram) Given: ABCD is a square FG ⊥ BC BC ≅ BE △ECG ≅ △EBG △BEC is equilateral m∠BEC = 60° △ECD is isosceles Find: m∠BED
Answer:
\(\angle BED = 135^\circ\)
Step-by-step explanation:
First of all, let us do a construction in the given question image.
Let us connect the points E and C.
Please refer to the image attached in the answer area.
Step 1:
EC is drawn in the diagram.
Now, consider the triangles △EGC and △EGB.
1. Side BG = GC (G is the point on perpendicular bisector of AC)
2. \(\angle EGB =\angle EGC\) (G is the point on perpendicular bisector of AC)
3. Line EG is common to both the triangles.
So,from SAS (Side Angle Side) congruence i.e. two sides and angle between them are equal in two triangles.
△EGC ≅ △EGB
Step 2:
Now, we know that △EGC ≅ △EGB, we can say that the corresponding sides CE and BE must be equal to each other i.e. CE \(\cong\) BE .
And we are already given that BC \(\cong\) BE.
\(\therefore\) In \(\triangle BEC\):
EB ≅ EC ≅ BC that means \(\triangle BEC\) is an equilateral triangle.
Hence, every angle of \(\triangle BEC\) must be equal to \(60^\circ\).
\(\therefore\) ∠BEC = 60°.
Step 3:
Let us find ∠ECD= ?
ABCD is a square, so \(\angle BCD =90^\circ\)
\(\angle BCE + \angle ECD = 90^\circ\\\Rightarrow 60^\circ+ \angle ECD = 90^\circ\\\Rightarrow \angle ECD = 30^\circ\)
Step 4:
We know that ABCD is a square, so side BC = CD.
We have proved in the previous step that BC = EC
\(\therefore\) in \(\triangle CED\), two sides are equal so it is isosceles triangle.
One angle ∠ECD= \(30^\circ\)
As it is an isosceles triangle, the other two angles will be equal.
Let them be equal to \(x^\circ\).
The sum of all 3 angles of a triangle is equal to \(180^\circ\)
\(x+x+30=180\\\Rightarrow x = 75^\circ\)
OR
we can say \(\angle CED =75^\circ\)
Now, from the diagram, we can see the following:
\(\angle BED = \angle BEC + \angle CED\)
\(\Rightarrow \angle BED = 60^\circ+75^\circ\\\Rightarrow \angle BED = 135^\circ\)
Compute the missing x and y values so that each ordered pair will satisfy the given equation y=2x+4
The missing ordered pairs that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).
The equation given is y = 2x + 4. To compute the missing x and y values, we need to substitute the given ordered pairs into the equation and solve for the missing variable.
Let's assume we have an ordered pair (x, y) that satisfies the equation y = 2x + 4.
For example, let's say one missing value is x = 3. We can substitute this into the equation:
y = 2(3) + 4
y = 6 + 4
y = 10
So, the missing ordered pair is (3, 10).
Similarly, if another missing value is y = 8, we can substitute this into the equation and solve for x:
8 = 2x + 4
4 = 2x
x = 2
So, the missing ordered pair is (2, 8).
In summary, the missing x and y values that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).
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what is ninety two thousand one hundred seventy
Answer:
92170
I hope it's helps you
Can you guys answer both of these questions
Answer:
2+18
Step-by-step explanation:5+123
a basketball team wants to paint half of a free-throw circle grey. If the circumference of the free-throw circle is 30.77 feet, what is the are, in square feet, that will be painted grey? use 3.14 for PI, and round to the nearest square foot.
The area that will be painted grey is approximately 38 ft².
The circumference of the free-throw circle is given as 30.77 feet, and we know that the free-throw circle is a perfect circle. We can use the formula for circumference to find the radius of the circle, which will be necessary to calculate its area.
Circumference of a circle = 2πr
30.77 = 2 x 3.14 x r
r = 30.77 / (2 x 3.14) = 4.9 feet
Half of the circle will be painted grey. Find the area of half the circle using the formula for the area of a circle.
Area of a circle = π x r²
Area of half the circle = 0.5 x π x r²
Area of half the circle = 0.5 x 3.14 x 4.9²
Area of half the circle = 37.73 ft²
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5.6.8 let f be a uniformly continuous function on a set e. show that if {xn} is a cauchy sequence in e then {f(xn)} is a cauchy sequence in f(e). show that this need not be true if f is continuous but not uniformly continuous.
Proof. (1): To prove {f(xn)} is a Cauchy sequence just need to prove ∀ > 0, ∃N, s.t.,∀n, m > N,
have |f(xn) − f(xm)| < . Since f is uniformly continuous on set E, thus ∀ > 0, ∃δ > 0, s.t.,
∀x, y ∈ E, if |x − y| < δ,then |f(x) − f(y)| < .as {xn} is a Cauchy sequence, then ∃N, s.t.,
∀n, m > N, |xn − xm| < δ, thus |f(xn) − f(xm)| < which proves {f(xn)} is a Cauchy sequence.
(2): for example f(x) = 1
x
, x ∈ (0, 2) which is continuous but not uniformly continuous. {
1
n
} is
a Cauchy sequence, however, {f(xn)} does not converge which proves that it is not a Cauchy
sequence.
Showing that this need not be true if f is continuous but not uniformly continuous.
Given :
let f be a uniformly continuous function on a set e. show that if {xn} is a cauchy sequence in e then {f(xn)} is a cauchy sequence in f(e).
( 1 )
If f is uniformly continuous on E, then given ε > 0 there is δ > 0 such that if x, y are in E and |x−y| < δ,
then |f(x) − f(y)| < ε. Let (xn) be a Cauchy sequence in E. Then given δ > 0 there is N such that if p, q > N,
then |xp − xq| < δ, and thus |f(xp) − f(xq)| < ε, implying that (f(xn)) is a Cauchy sequence.
( 2 )
Let E = {1, 1/2, 1/3, · · } and f(1/n) = 1 is n is odd, f(1/n) = −1 if
n is even. Then f is continuous but not uniformly continuous. The sequence (xn) = (1/n) in E is Cauchy but the
sequence (f(xn)) = (1, −1, 1, −1, · · ·) is not Cauchy.
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The graph of a function f(x) passes through the following points:(0, - 2),(1,0), (- 1, –4)Which of the following could be f(x)?
Hello!
First, let's make a graph with these points:
As we can see, it is a function in the form ax + b = 0 (1st degree).
To solve this exercise, we can calculate the slope and then write the equation of the line in the slope-intercept form.
So, let's calculate the slope:
\(Slope=\frac{y_B-y_A}{x_A-x_B}=\frac{0-(-2)}{1-0}=\frac{+2}{1}=2\)Now, let's write it in the slope-intercept form as y = mx + b:
• m, is the slope
,• b ,is the y-intercept
,• x ,and ,y ,are generic coordinates
To solve it, let's replace x and y with the coordinates of point C (third):
\(\begin{gathered} y=mx+b \\ y=2\cdot x+b \\ -4=2\cdot(-1)+b \\ -4=-2+b \\ -4+2=b \\ b=-2 \end{gathered}\)Now, we know all unknows, let's rewrite it:
\(\begin{gathered} y=mx+b \\ y=2x-2 \end{gathered}\)Oops! But we don't have this option, right?
So, we must remember one thing: when we are talking about functions, f(x) and y mean the same.
So, we just have to replace y with f(x) and the answer will be:
\(f(x)=2x-2\)
Which statement is not a step used when constructing an inscribed hexagon?
Geometry: The base of a triangle is 12 in. Its height is (x + 6) in. Its area is no more
than 72 in.2. What are the possible integer values of x?
Please help meee I’m so bad at triangles!
Answer:
The area of a triangle= bh/2. Substitute
12(x+6)/2 ≤ 72
12(1/2x+3) ≤ 72
6x+36 ≤ 72
6x ≤ 72-36
6x ≤ 36 Divide both sides by 6
x ≤ 6
x|x ≤6 (read: x, where x is equal or smaller than 6)
Step-by-step explanation:
Maggie and her friends are each able to recruit a certain number of people each year to sample a product. The number of people per year is represented by the function f(t) = 3(2)t. What does the t represent? How many people were recruited in year 6?
t represents the year number; 36 people were recruited in year 6.
t represents the year number; 192 people were recruited in year 6.
t represents the number of people; 192 people were recruited in year 6.
t represents the number of people; 36 people were recruited in year 6.
A function assigns the values. The number of people that were recruited in year 6 is 192.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that the number of people per year is represented by the function \(f(t)=3(2)^t\).
In the given function, t represents the number of years.
Now, the number of people that were recruited in year 6 can be calculated by putting the value of t as 6 in the given function,
\(f(t)=3(2)^t\)
f(6) = 3(2)⁶
= 3(64)
= 192
Hence, the number of people that were recruited in year 6 is 192.
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Answer:
The answer is t represents the year number; 192 people were recruited in year 6
Step-by-step explanation:
10+ points if you answer correctly
Answer:
\(\sqrt[9]{3}\)
Step-by-step explanation:
The screenshot is proof that it’s the correct answer, because I used a calculator.
Sam studied 2 hours for her math test. She studied 4 hours for her history test. How many more hours did she study for the
history test? (Simplify the answer and write it as a mixed number.)
Sam studied 1 29/40 hours more for history than math, solved using fraction subtraction, making option C, the right choice.
In the question, we are given that Sam studied 2 13/20 hours for her math test. She studied 4 3/8 hours for her history test.
We are asked to find how many more hours did she study for the history test.
The time she study for history test = 4 3/8 hours.
Converting the mixed fraction to an improper fraction we get, 4 3/8 hours = 35/8 hours.
The time she study for math test = 2 13/20 hours.
Converting the mixed fraction to an improper fraction we get, 2 13/20 hours = 53/20 hours.
To find the time for which Sam studies history more than math, we do fraction subtraction, to get:
35/8 - 53/20
= (35*5 - 53*2)/40 hours
= (175 - 106)/40 hours
= 69/40 hours
= 1 29/40 hours, converting to mixed fraction.
Thus, Sam studied 1 29/40 hours more for history than math, solved using fraction subtraction, making option C, the right choice.
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The provided question is incomplete. The complete question is:
Sam studied 2 13/20 hours for her math test. She studied 4 3/8 hours for her history test. How many more hours did she study for the history test? (Simplify the answer and write it as a mixed number.)
A. 6 41/40 hours
B. 2 29/40 hours
C. 1 29/40 hours
D. 2 11/40 hours.
3 2/5 divided by 1 1/5 pleaseeee help its due on may 24
Answer:
2.83333333333
Step-by-step explanation:
(3 2/5) / (1 1/5) = 2.83333333333
Answer:
85/30 or 2.833333333
Step-by-step explanation:
When dividing fractions, you must find the reciprocal of the second number and multiply it as usual.
It is also much easier to solve after you convert these numbers to improper fractions.
In this case,
3 2/5 = 17/5
1 1/5 = 6/5
17/5 ÷ 6/5
17/5 x 5/6
85/30 (17/6 reduced)
or
2.83333333333333333333
PLEASE HELP ITS MATH THANK YOUUUU
1.) Solve the following equation for w: 3w-4(w-3) = 6
Answer: w=6
Step-by-step explanation: 1. Simplify. Distribute the -4 to the w and the -3. -4*w is -4w and -4*-3 is +12, so your left with 3w-4w+12=6.
2. simplify again. 3w-4w is -w.
3. -w+12=6. Subtract w to both sides, so its -w=-6. The negatives cancel out, so w just equals 6.
Kaitlynn needs 3 pounds of fruit for a salad.
She already has 34 pound of apples and 13 pound of grapes.
How many more pounds of fruit does she need to buy?
Answer:
She has 1 and 1/12 pounds of fruit already and she needs 1 and 11/12 pounds more to have 3 total pounds
Find the missing side
By using trigonometry, the missing sides are
Example 1: x = 16.7
Example 2: x = 3.2
Example 3: x = 23.5
Example 4: x = 9.3
Trigonometry: Determining the values of the missing sidesFrom the question we are to determine the value of the missing sides in the given triangles
We can determine the value of the missing sides by using SOH CAH TOA
Example 1
Angle = 42°
Opposite side = x
Hypotenuse = 25
Thus,
sin (42°) = x / 25
x = 25 × sin (42°)
x = 16.7
Example 2
Angle = 75°
Opposite side = 12
Adjacent side = x
Thus,
tan (75°) = 12 / x
x = 12 / tan (75°)
x = 3.2
Example 3
Angle = 36°
Hypotenuse side = x
Adjacent side = 19
Thus,
cos (36°) = 19 / x
x = 19 / cos (36°)
x = 23.5
Example 4
Angle = 53°
Opposite side = x
Adjacent side = 7
Thus,
tan (53°) = x / 7
x = 7 × tan (53°)
x = 9.3
Hence,
The missing sides are 16.7, 3.2, 23.5 and 9.3
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A rectangular rug has a perimeter of 460 meters. The width of the rug is five meters more than 4 times the length. Find the
length and the width.
Answer:
Length = 45 m
Width = 185 m
Step-by-step explanation:
Given:
Perimeter of rectangular rug = 460 m
width of the rug is five meters more than 4 times the length
To find:
Width and length of rug = ?
Solution:
Let the length = \(l\) m
As per given statement,
Width = \(4l+5\) m
Formula for perimeter of a rectangle = \(2\times (Length +Width)\)
\(460=2\times (l+4l+5)\\\Rightarrow 230 = 5l+5\\\Rightarrow l = \dfrac{225}{5} = 45\ m\)
Width = \(4l+5\) m
Width = \(4\times 45+5 = 185\ m\)
So, the answer is:
Length = 45 m
Width = 185 m
Use the quadratic formula to find the exact solutions of 3x2 − 6x + 2 = 0.
a. negative 1 plus or minus the square root of 3 divided by 3
b. 1 plus or minus the square root of 3 divided by 3
c. negative 1 plus or minus the square root of 15 divided by 3
d. 1 plus or minus the square root of 15 divided by 3
The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:
a. negative 1 plus or minus the square root of 3 divided by
3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.
To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:
x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))
x = (6 ± √(36 - 24)) / 6
x = (6 ± √12) / 6
x = (6 ± 2√3) / 6
x = (3 ± √3) / 3
Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:
a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)
So, option a is the correct answer.
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Kathy purchased cereal in bulk on two different trips to a grocery store. She paid $5.79 per pound each time. She purchased 2.25 pounds the first time and 1.8 pounds the second time. Rounded to the nearest cent, what is the total amount Kathy paid for both cereal purchases?
Answer:
$23.45
Step-by-step explanation:
5.79 x 2.25 = 13.03
5.79 x 1.8 = 10.42
total = 23.45
En una ruleta hay números del 1 al 24.
1. Cuál es la probabilidad que la ruleta pare en un tres.
2. Cuál es la probabilidad que la ruleta pare en un número primo.
3. Cual es la probabilidad que la ruleta pare en un número compuesto.
4. Cuál es la probabilidad que la ruleta pare en un número dividido entre 5.
5. Cuál es la probabilidad que la ruleta pare en un múltiplo de 2.
2. Cuál es el único número primo y par.
3. Defina lo que es un número primo.
4. Defina lo que es un número compuesto.
The probabilities in these cases are 0.125, 0.375, 0.58, 0.16, 0.5 and the only prime and even number is 2.
How to calculate the probability?The probability is defined by the formula: specific outcome/ total possible outcomes. Based on this, let's calculate the probability in each case:
3/24 = 0.1259/ 24= 0.37514/ 24 = 0.584 / 24 = 0.1612/ 24 = 0.5What is a prime and a composite number?A prime number can be defined as a number that can be divided only by 1 and the number itself. On the opposite, a composite number can be divided by at least another number than 1 and itself.
The only prime and even number is 2.
Note: Here is the question in English:
What is the probability of getting a 3?What is the probability of getting a prime number?What is the probability of getting a composite number?What is the probability of getting a number that can be divided into 5?What is the probability of getting a multiple of 2?What is the only prime and even number?Define a prime numberDefine a composite numberLearn more about probability in https://brainly.com/question/30034780
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PLease help me and answer the questions in the picture below you will make my day!
Answer:
b the solution is (3,5)
Step-by-step explanation:
look at the points where the lines intersect