The transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:
vertical stretch of 0.35horizontal compression of period of [tex]\dfrac{\pi}{4}[/tex]phase shift of [tex]\dfrac{\pi}{4}[/tex] to right How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is [tex]y=f(x)[/tex]A, assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift):[tex]y=f(x+c)[/tex]Left shift by c units: earlier)Right shift by c units: [tex]y=f(x-c)[/tex] output, but c units late)Vertical shift:Up by d units: [tex]y=f(x)+d[/tex]Down by d units: [tex]y=f(x)-d[/tex]Stretching:Vertical stretch by a factor k: [tex]y=k\times f(x)[/tex]Horizontal stretch by a factor k: [tex]y=f(\dfrac{x}{k})}[/tex]For this case, we're specified that:
y = cos(x) (the parent cosine function) was transformed to
[tex]y=0.35cos(8(x-\pi/4)[/tex]
We can see its vertical stretch by 0.35, right shift by horizontal stretch by 1/8
Period of cos(x) is of length. But 1.8 stretching makes its period shrink to
[tex]\dfrac{2\pi}{8}=\dfrac{\pi}{4}[/tex]
Thus, the transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:
vertical stretch of 0.35
horizontal compression to period of (which means period of cosine is shrunk to which originally was )
phase shift of to right
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Answer:
C on ed
Step-by-step explanation:
got it right
Find the value of x using the diagram below
Answer:
x=19
Step-by-step explanation:
9x-17
(9*19)-17
=95
5*19=95
if you put 19 in x you will get the same degree
Sam has 3 candy bars and he wants to divide them into 8 equal portions to give to friends. What fraction will each person receive?
Answer: [tex]\frac{3}{8}[/tex] of the 3 candy bars
Step-by-step explanation:
We will divide the total number of candy bars by the portions.
3 candy bars / 8 portions = [tex]\frac{3}{8}[/tex]
Each friend will receive [tex]\frac{3}{8}[/tex] of the 3 candy parts
Samantha has 67 cents in her pocket. Write two coin combinations she could have that would equal the same amount
Which of the following equations does not have an x-intercept? Select all that apply.
A) y=x+0
ОВ) y=x
C) y=0x + 3
OD) y=0
E)y=5
F) y 3x+0
We can conclude from the slope intercept result, the equation with no x-intercept is C) y=0x + 3, D) y=0, E) y=5
What is slope intercept?In mathematics, the slope-intercept form of a linear equation is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point on the line where it intersects the y-axis.
Because it allows you to easily view the line and identify its slope and y-intercept, the slope-intercept form is a useful way to describe a line's equation. The slope of the line denotes its steepness, while the y-intercept indicates where the line intersects the y-axis.
The x-intercept of an equation is the point at which the equation's graph intersects the x-axis. When the value of y is zero, something happens. As a result, an equation lacks an x-intercept horizontal line that does not intersect the x-axis.
C) y=0x + 3 (A horizontal line with a y-intercept of 3 that does not cross the x-axis.)
D) y=0 (This is a horizontal line that passes through the origin but does not intersect the x-axis.)
E) y=5 (This is a horizontal line that passes through (0,5) but does not cross the x-axis.)
F) y=3x+0 (This is a straight line travelling through the origin and does cross the x-axis) (This is a straight line passing through the origin and does cross the x-axis)
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Answer:
C and E
Step-by-step explanation:
because i did the assignment and got it right
1. Which of the following is 60% in fraction form? A. 2/5 B. 3/5 2. What is 2/5 in percent? C. 4/5 D. 1/5 A. 20% B. 40% C. 80% D. 30% 3. What is 1/3 in decimal? A. 0.222 B. 0.333 C. 0.667 D. 0.445 4. What is 250 in the statement 24% of 250 is 60? A. base B. rate C percent D. percent 5. What is the equivalent of 48/100 in decimal form? A. 0.48 B. 0.048 C. 0.408 D. 0.0048 6. What do you call the quantity that represents the whole? A. base B. rate C. percent D. percentage 7. Which term is described as the quantity that is part of the base? A. base B. rate C. percent D. percentage 8. Which represents base in 30% of 300 is 90? A. 30 B. 90 C. 300 D. 30% 9. In the statement 24% of 250 is 60, which represents rate? A.0.24 B. 24% C. 60 D. 250 10. If 30% of 300 is 90, what do you call 90? A. base B. rate C. portion D. percentage 11. In the statement "18 is girls in the class of 60 learners? A. 3:12 B. 5:20 C. 1:4 D. All of these 16. Seven of the 35 boys in the class wear eyeglasses. What percent of the boys wear eyeglasses? Which of the following is asked in the problem? A. Base B. Rate C. Percentage D. Proportion any one help meg
1. 60% can be written as 60/100, simplified as 3/5
2. 2/5 is 40/100, can be written as 40%
3. 1/3 is 33.33333...% -> 0.(3) [ infinite recurring decimals if i remember correctly]
4. 250 here is the base (original number)
5. 48/100 can be written as 48% -> 0.48
6. base
7. percentage
8. 300
9. 24%
10. portion
11. (i dont know what this mean, next time write it more carefully)
12. percentage
Easy question simplify
Answer:
144
Step-by-step explanation:
-12 * -12 = 144
12² =144
but the question was not 12², but -12²
so the answer is -144
if the exercise was between (), so writen like this (-12)²
then you would need to do the - to the power of 2 as well
13/6 renamed as a mixed number
Answer:
2 1/6
Step-by-step explanation:
13/6 is 6/6 + 6/6 + 1/6... each 6/6 = 1 sooo. 2 and 1/6 :)
orrr
6*2 is 12 (closest multiple of 6 to 13, so 2 is whole number w/ 1(/6) as a remainder
Which statements about the graph of the function f(x) = –x2 – 4x 2 are true? select three options. the domain is {x|x ≤ –2}. the range is {y|y ≤ 6}. the function is increasing over the interval (–[infinity] , –2). the function is decreasing over the interval (−4, [infinity]). the function has a positive y-intercept.
The graph of the function f(x) = –x^2 – 4x +2 are true options 1 and 4 are correct.
We have the given,
The graph of the function f(x) = –x^2 – 4x+ 2
The statements that agree with the graph of the equation are as follows:
1. The domain is {x|x ≤ –2}.
What is the domain?The set of points at which function is defined.
4. The function is decreasing over the interval (−4, ∞).
From the given graph,
We can say that the above statements are true.
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Answer:
yes
Step-by-step explanation:
please help with this question
Determine values of m, n, p, and q so that
Answer:
Step-by-step explanation:
[tex]\frac{x^{2}+mx+n }{9-x^{2} } /\frac{x^{2} +6x-16}{x^{2} +px+q} = \frac{-x+3}{x+8}[/tex]
Change the division of the two fractions in to multiplication
[tex]\frac{x^{2}+mx+n }{9-x^{2} } * \frac{x^{2} +px+q}{x^{2} +6x-16} = \frac{-x+3}{x+8}[/tex]
Factor what we can
[tex]\frac{x^{2}+mx+n }{(3-x)(3+x)} * \frac{x^{2} +px+q}{(x-2)(x+8)} = \frac{(3-x)}{x+8}[/tex]
Cross multiply and simplify (x+8)/(x+8)
(x² +mx +n) (x² +px +q) = (x -3) (x -3) (x +3)( x -2)
Now we look to see what values for m, n, p, and q will give those factors.
m= 1 n= 2 p= 3 q= 4
(x² +x +2) (x² +3x +4) ≠ (x -3) (x -3) (x +3)( x -2) ❌
m= 1 n= -6 p= -6 q= 9
(x² +x -6) (x² -6x +9) = (x+3)(x-2) (x-3)² ✅
m= -5 n= 6 p= 0 q= -9
(x² -5x +6) (x² -9) = (x-3)(x-2)(x-3)(x+3)✅
m= 7 n= -4 p= 2 q= 0
(x² +7x -4) (x² +2x) ≠ (x-3)(x-2)(x-3)(x+3)❌
m= 3 n= -6 p= 1 q= 7
(x² +3x -6) (x² +x+7) ≠(x-3)(x-2)(x-3)(x+3)❌
m= -6 n= 9 p= 1 q= -6
(x² -6x +9) (x² +x -6) = (x-3)(x-3)(x-2)(x+3)✅
m= 0 n= -9 p= -5 q= 6
(x² -9) (x² -5x +6) ≠(x-3)(x-3)(x+3)(x-2)❌
What is the solution to the equation below?
Blog4x = log232+ log 2
O X=-8
O
X=-4
O x=4
X-
X-8
Answer:
x = 4
Step-by-step explanation:
When you have a coefficent in front of a logarithm function, you can take the argument to the power of that coefficient. For example, the 3 in front of the logarithm can be brought into the argument, and you can take 'x' to the third power. You get:
[tex] log_{4}( {x}^{3} ) = log_{4}(32) + log_{4}(2) [/tex]
When you add logarithms, it is equivalent to multiplying their arguments:
[tex]log_{4}( {x}^{3} ) = log_{4}(32 \times 2) = log_{4}(64) [/tex]
Since both sides are log base 4, the arguments must equal each other:
[tex] {x}^{3} = 64[/tex]
[tex]x = \sqrt[3]{64} = 4[/tex]
here it is, this is ur answer x=4
How do you solve this
Answer:
x = 8
Step-by-step explanation:
Use the Intersecting Chords Theorem...
A football is thrown into the air from an initial height of 4 feet with an upward velocity of 46 ft/sec. The function h = -16t² + 46t + 4 gives the height after t sec.
whats the vertex?
axis of symmetry?
solutions?
2 other points?
and i know the balls max height is 37.06
Answer:
Vertex = (1.4375, 37.0625)
Axis of symmetry: t = 1.4375
x-intercept: (2.9595, 0)
y-intercept: (0, 4)
another point: (2, 32)
Step-by-step explanation:
Given function: [tex]h(t)=-16t^2+46t+4[/tex]
(where h is the height in feet and t is the time in seconds)
The vertex is the turning point of the parabola.
To find the x-value of the turning point, differentiate the function:
[tex]\implies h'(t)=-32t+46[/tex]
Set it to zero:
[tex]\implies h'(t)=0[/tex]
[tex]\implies -32t+46=0[/tex]
Solve for t:
[tex]\implies 32t=46[/tex]
[tex]\implies t=\dfrac{23}{16}[/tex]
Input found value of t into the function to find the y-value of the vertex:
[tex]\implies h(\frac{23}{16})=-16(\frac{23}{16})^2+46(\frac{23}{16})+4=\dfrac{593}{16}[/tex]
Therefore, the vertex is [tex]\left(\dfrac{23}{16},\dfrac{593}{16}\right)[/tex] or (1.4375, 37.0625) in decimal form.
The axis of symmetry is the x-value of the vertex.
[tex]\implies \textsf{Axis\:of\:Symmetry}:t=\dfrac{23}{16}=1.4375[/tex]
To find the x-intercepts, use the quadratic formula.
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\implies t=\dfrac{-46 \pm \sqrt{46^2-4(-16)(4)} }{2(-16)}[/tex]
[tex]\implies t=\dfrac{-46 \pm \sqrt{2372}}{-32}[/tex]
[tex]\implies t=\dfrac{23 \pm \sqrt{593}}{16}[/tex]
As time is positive,
[tex]\implies t=\dfrac{23 + \sqrt{593}}{16}=2.959474458...\:\sf s\quad only[/tex]
The y-intercept is when t = 0:
[tex]h(0)=-16(0)^2+46(0)+4=4[/tex]
So the curve intercepts the y-axis at (0, 4)
Because of the modelling of the function, there will be a restricted domain: 0 ≤ t ≤ 2.9595
Therefore, to find another point, input a value in the domain into the function and solve:
[tex]t=2 \implies h(2)=-16(2)^2+46(2)+4=32[/tex]
⇒ (2, 32)
at what time do u have to get out of the house if your walking 32 min to school school starts at 8 opens at 7:40
Answer:
7:10 or 7:20
Step-by-step explanation:
it allows time for the doors to open and time to get to class
A volleyball player hits a ball from a height of 6 feet with an initial vertical velocity of 16 feet per second. What is the maximum height of the volleyball? Assuming it is not hit by another player, when will the volleyball hit the ground? Round the answers to two decimal places if necessary.
The maximum height of the volleyball is ___
feet.
The volleyball will hit the ground after ___
seconds.
Considering a quadratic equation, it is found that:
The maximum height of the volleyball is of 19.06 feet.The volleyball will hit the ground after 3.6 seconds.What is the quadratic equation for an object's height?Considering the height in feet, it is given by:
h(t) = -4.9t² + v(0)t + h(0)
In which:
v(0) is the initial velocity.h(0) is the initial height.In this problem, we have that h(0) = 6, v(0) = 16, hence the equation is given by:
h(t) = -4.9t² + 16t + 6
Which is a quadratic equation with coefficients a = -4.9, b = 16, c = 6. Hence the maximum height is found as follows:
[tex]\Delta = b^2 - 4ac = 16^2 - 4(-4.9)(6) = 373.6[/tex]
[tex]h_{MAX} = -\frac{\Delta}{4a} = -\frac{373.6}{-4(4.9)} = 19.06[/tex]
The maximum height of the volleyball is of 19.06 feet.
It hits the ground at the roots, hence:
The solutions are:
[tex]x_1 = \frac{-16 + \sqrt{373.6}}{-9.8} = -0.34[/tex]
[tex]x_2 = \frac{-16 - \sqrt{373.6}}{-9.8} = 3.6[/tex]
Time is a positive measure, hence:
The volleyball will hit the ground after 3.6 seconds.
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Please help i will give brainliest
Answer:
c
Step-by-step explanation:
Answer:
its C bro i dont copy her/he
dont be suspiciousful
Step-by-step explanation:
ita right mark me as brainlest
Mark works 40 hours per week at a store.
He earns $8.75 per hour.
Each week $36 is deducted from his paycheck for taxes.
how much money does mark earn, after taxes have been deducted,during a 4-week period
A. $314
B. $386
C. $1,256
D. $1,364
Answer
not to sure but i think its number 3
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Write these numbers in standard form:
A. 400
B. 6000
C. 2000000
D. 0.4
= 4 × 10^2
B. 6000= 6 × 10^3
C. 2000000= 2 × 10^6
D. 0.4= 4 × 10^-1
( to find the standard form just count the zeros. )
a)= 4×10^2
b)= 6×10^3
c)= 2×10^6
d)= 4×10^-1
hope this helps
5(x + y) what is tje anser
Use the distributive property:
5(x + y) becomes 5x + 5y
with the information provided in the question that is as much as can be done.
answer: 5x + 5y
What is the final answer ?
Answer:
16 feet
Step-by-Step Explanation:
If you graph it, the vertex will be (3,16) and that means 16 feet is the maximum height of the diver.
Part A
Which statements are central ideas of Library on Wheels: Mary Lemist Titcomb and America's First Bookmobile?
Select the two correct answers.
Mary was not afraid to be a pioneer.
Mary worked hard to better the library experience.
Mary believed libraries were mainly for the rich.
Mary's friends supported her decision to move to Maryland.
Question 2
Part B
Which two details from the text best support the answers in Part A?
"But Mary, always independent, was eager to take on this new challenge."
"'…It remained for Miss Titcomb to show us that libraries are intended for the middle class of people, the working man and woman and children particularly.'"
"She continually looked for ways to improve librarianship, to render it both more efficient and more far-reaching."
"Mary's friends and family thought it would be unwise for her to leave her secure position in Vermont to go by herself to rural Maryland."
Answer:
Part 1:
A. Correct
B. Correct
Part 2:
A. Correct
C. Correct
Answer:
I got 100 % on the quiz
Step-by-step explanation:
check the photo below for the awnser
Given C = 119º, B= 44°, and c = 15, use the
Law of Sines to solve the triangle for the
value of a. Round answer to two decimal
places.
Step-by-step explanation:
A+B+C=180° (Sum of angles in a triangle)
A+44°+119°=180
A+163°=180°
A=17°
Using Sine Rule
a/Sin A=c/Sin C
Subtitute the value of A, c and C into the formula
a/Sin 17°=15/Sin 119°
Cross Multiply
a=15Sin17°/Sin119°
a=5.01 (2 d.p)
A lizard is 412 inches long.
How long is the lizard in centimeters?
Answer: 1046.48cm
Step-by-step explanation: Multiplying by 2.54 To convert
PLS HELP!!! No links pls and Ty <3333
Answer:
The area is 176.6
Step-by-step explanation:
The formula for the area of a circle is "πr²"
This means you square the radius, and multiply it by pi.
Our diameter is 15, and the radius is half of the diameter.
15 ÷ 2 = 7.5
Next, we square the radius. (7.5)
Let's fill it into the formula.
π7.5²
After squaring, it's this:
π56.25
In your question, pi is 3.14, so let's replace that.
(3.14)56.25
After multiplying we get 176.625, after we round, we get 176.6
176.6 is the area.
Brainliest please?
Answer:
The area is 176.6
Step-by-step explanation:The formula for the area of a circle is "πr²"This means you square the radius, and multiply it by pi.Our diameter is 15, and the radius is half of the diameter.15 ÷ 2 = 7.5Next, we square the radius. (7.5)Let's fill it into the formula.π7.5²After squaring, it's this:π56.25In your question, pi is 3.14, so let's replace that.(3.14)56.25After multiplying we get 176.625, after we round, we get 176.6176.6 is the area.
Step-by-step explanation:
Jenna's has invested 3000 at a 5% Simple rate how much interest will she earn in three years
Answer:
simple interest=Principal +Time+Rate÷100
Interest=3000+3+5÷100=3005.03
interest=3005.03
If an orthocenter lies inside of a triangle, then the triangle must be
isosceles.
obtuse.
right.
acute.
Answer:
acuteStep-by-step explanation:
Remember :the orthocenter of a triangle is the point of concurrency of the 3 altitudes.
[tex]\large \text{If an orthocenter lies inside of a triangle, then the triangle must be}\ :\\\\\large isosceles. \\\\\large obtuse. \\\\\large right. \\\\\large acute \checkmark[/tex]
If an orthocenter lies inside of a triangle, then the triangle must be acute.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Orthocenter of a triangle is the intersection of any two of three altitudes of a triangle.
The third altitude usually pass through the point of the first two altitudes.
When the orthocenter lies inside a triangle, the angles formed by the intersection of the three altitudes is less than 90 degrees.
An acute triangle is a type of triangle whose angles are less than 90 degrees.
Hence, If an orthocenter lies inside of a triangle, then the triangle must be acute.
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PLS HELP!!!!
No links pls and Ty<33!!!!
Answer:
r=20
d=40
40*3.14=125.6
circumference = 125.6
Step-by-step explanation:
please help! What fractional part of one semicircle does the labeled angle represent? Express
your answer as a fraction in simplest terms. Then, express the labeled angle in radian
measure.
225°
Answer:
Fraction: 5/8
Radians: 5pi/4 Radians
Step-by-step explanation:
1A Fraction
A circle has a total of 360 degrees, in order to solve the first part we must use this preknowledge.
As we are given 255 degrees, we simply order a fraction:
Degrees Given/360 Hence,
255/360
Simplify
5/8
1B Radians
In order to convert degrees to radians we use a simple trick, we must multiply the degree measure (225) by pi/180 because a full circle = 2pi radians or 360 degrees hence,
225 x pi/180
Simplify
5pi/4 radians
. A rectangular tank is 32 cm wide and 45 cm long. It
contains three identical plastic water plants and is
filled with water to a height of 10 cm. When Amy
pulls all three plastic water plants out of the tank,
the height of the water drops to 8 cm. Find the
volume of one plastic water plant.
PLEASE HELP!! WILL GIVE BRAINLIEST
Answer: 960^3 cm or 960 cubic centimeters
Step-by-step explanation:
Cubic because measuring 3 dimensions.
32x45 = area of given face
32x45= 1440
height of water = 10 cm
so,
area of given face x 10 =
32x45x10 or lxwxh (Volume)
so
1440x10= 14,400
1440x8= 11,520
so 14,400 - 11,520 = 2880
V of three plants = 2880
so, 2880/3 = volume of one plant
2880/3=960
V of singe plant = 960 units ^ 3
The difference in volumes represents the total volume of three plants, so answer should be divided by 3.
Hope This Helped!
Answer: one plastic water plant volume = 960 cm³
Step-by-step explanation:
Total volume = Water Volume + 3 plants volume
Total Volume = 32 cm x 45 cm x 10 cm = 14 400 cm³
Water volume = 32 cm x 45 cm x 8 cm = 11 520 cm³
3 Plants volume = 14,400 cm³ - 11,520 cm³ = 2880 cm³
1 Plant volume = 2,880 cm³ : 3 = 960 cm³
2 |3x-5| - 4 = 12
Solve for x
Show work
Isolate the absolute-value term:
2 |3x - 5| - 4 = 12
2 |3x - 5| = 8
|3x - 5| = 4
Recall the definition of absolute value:
[tex]|x| = \begin{cases}x & \text{if }x \ge0\\-x&\text{if }x<0\end{cases}[/tex]
We consider two cases:
• If 3x - 5 ≥ 0, then |3x - 5| = 3x - 5, and the equation resolves to
3x - 5 = 4
3x = 9
x = 3
• Otherwise, if 3x - 5 < 0, then |3x - 5| = -(3x - 5) = -3x + 5, hence
-3x + 5 = 4
-3x = -1
x = 1/3