Answers
Answer: A
Step-by-step explanation:
The standard form of a cosine equation is: y = A cos (Bx - C) + D where
Amplitude (A) is the distance from the center to the maxPeriod (P) is the length of the function = 2π/B Phase Shift is the distance the max is moved from the y-axis = C/BCenter (D) is the imaginary line between the max and minPlot the points (see graph below).
A = 28
[tex]\dfrac{1}{2}P=6\quad \rightarrow \quad P=12\\\\\\P=\dfrac{2\pi}{B}\qquad \rightarrow \qquad 12=\dfrac{2\pi}{B}\qquad \rightarrow \qquad \large\bold{B=\dfrac{\pi}{6}}[/tex]
Phase Shift = 7 = C/B
[tex]7=\dfrac{C}{\frac{\pi}{6}}\qquad \rightarrow \qquad \large\bold{C=\dfrac{7\pi}{6}}[/tex]
D = 49
Input the values of A, B, C, and D into the standard form of a cosine equation to get:
[tex]\large\boxed{y=28\cos \bigg(\dfrac{\pi}{6}x-\dfrac{7\pi}{6}\bigg)+49}[/tex]
Related Questions
Which of the following is the equation of a line that passes through the point
(3.2) and is parallel to the yaxis?
Answers
Answer:
y=2 is the correct ans.
here, tge equn of st line passing through the point (3,2) and is also parallel to y axis.
we have, equn of st line parallel to y xaus is y= b
so , the equn of st line passing through the point (3,2) is y= 2 (where 2 is likely to b).
Can someone give me the answer?
Answers
Answer:
the answer is exactly one solution
Answer:
Step-by-step explanation:
No
Mrs. Brown has 11 more boys than girls in her class and has a total of 28 students. Which of the following systems of equations could be used to solve this problem?
Answers
Answer:
g=number of girls in the class b=number of boy in the class
g+b=28
g=11+b
y=(x+9)÷(x-3)
Find the value of y when x=5
Answers
solution,
X=5
[tex]y = \frac{x + 9}{x - 3} \\ = \frac{5 + 9}{5 - 3} \\ = \frac{14}{2} \\ = 7[/tex]
hope this helps...
Good luck on your assignment..
Answer:
When x=5
Y=(5+9)÷(5-3)
= 14 ÷2
= 7
4. Two ropes are attached to a heavy object. The ropes are given two strong physics
students (is there any other kind?) with instruction for each to pull with 1000 N of force.
Determine the resultant force is the two students pull:
a. In the same direction east
b. In opposite directions
c. At right angles, south and east
Answers
Answer:
A.) 2000N
B.) 0
C.) 1414.2 N
Step-by-step explanation:
Given that the force on the rope = 1000N
A.) If the two students pull in the same direction, the resultant force will be addition of the two forces. That is
1000 + 1000 = 2000 N
B.) If the two students pull in the opposite direction, the resultant force will be sum of the two forces equal to zero. That is,
F1 + F2 = 0
F1 = positive 1000N
F2 = negative 1000N
Therefore, 1000 - 1000 = 0
The resultant force of the two forces is zero.
C.) If the two forces are at right angles, south and east to each other, the resultant force R will be achieved by using pythagorean theorem.
R = sqrt( 1000^2 + 1000^2 )
R = sqrt( 2000000 )
R = 1414.2 N
The resultant force of the two forces will be 1414.2N
HELP PLZ It is your turn to wash the dishes. When you are finished, you begin to drain the water from the sink. The water's draining can be defined by the function V = -.75t + 10 where V is the volume of water in gallons and t is the time in minutes. What is the rate of change and would you interpret that?
Answers
Answer:
The rate of change is -0.75
Step-by-step explanation:
For each unit of t the volume of water is decreasing by 0.75.
At t=13.333 the volume of water is 0. at t=0 the volume of water is 10
Hope this helps
Are triangles ABD and CDB congruent by AAS, ASA, SAS or SSS?
Answers
Answer:
They are congruent by AAS.
Step-by-step explanation:
Side BD is common to both triangles and 2 pairs of corresponding angles are congruent.
Filipe practiced 12 fewer hours than Bianca. If Filipe practiced for 16 hours, how long did Bianca practice? Bianca practiced for hours.
Answers
Answer:
She practiced for 28 hours.
Step-by-step explanation:
x = 16 - Filipe's hours
y =? - Bianca's hours
Filipe practiced 12 hours less than Bianca so we get the following equation:
y - 12 = x which is y - 12 = 16.
Now we solve the equation by adding 12 to the both sides:
y - 12 + 12 = 16 + 12
y + 0 = 28
y = 28.
Answer:
equation: a statement that two expressions are equal operation: a mathematical process such as addition, subtraction, multiplication, or division solution: a value of the variable in an equation or inequality that makes the equation or inequality true variable: a letter or symbol used to represent an unknown quantity
Section 1 00:00:00 TEACHER: Welcome. In this lesson, we're going to be answering the question what situations can you model with one-step equations? Let's begin. Section 2 00:00:00 TEACHER: We'll start with the goals for this lesson. We're going to be writing and solving one-step equations. And to do this, we're going to use one-step equations to solve word problems. And we're also going to be using one-step equations to solve word problems involving rational numbers. Now there's some words you're going to need to know in this lesson. 00:00:21 We have equation, operation, solution, and variable. Make sure you familiarize yourself with the definitions for these words before we continue. Section 3 00:00:00 TEACHER: We're answering the question, what situations can you model with one-step equations? Now, you already know that inverse operations like multiplication and division, they undo each other. In this lesson, you're going to learn how to use what you already know in order to learn how to solve real world problems.
Section 1 00:00:00 TEACHER: In this lesson, we're answering the question, what situations can you model with one-step equations? Now, you already know how to use inverse operations and equality properties to solve equations. In the first part of this lesson, we're going to learn how to solve real world problems by writing and solving one-step equations. Section 2 00:00:00 TEACHER: Let's take a look at equations and word problems. Now, there are some steps that you can use in order to be able to write and solve a one-step equation involving a word problem. The first step is to identify the variable. We need to find out what is unknown in the problem and then let our variable represent that unknown. Next, we identify the operation, whether we're using 00:00:21 addition, subtraction, multiplication, or division. And we can do that by looking at key words in our scenario. Then we can write the equation. Once we have an equation, then we can solve it. And we can solve that expressing it as an equation, like an x equals 5, or even model that value on a number line. We can then check the solution. 00:00:43 We want to check back with the original problem to see if that answer make sense. Let's go ahead and take a look at this scenario right here. And we're going to identify what the equation would be for this scenario. Now, the total cost of 3 tickets to a play was $42. What was the cost of each ticket? Notice the question. 00:01:02 What was the cost of each ticket? That's unknown. I don't know what the cost is yet. So in identifying my variable, we're going to identify that unknown. We're going to let c equal the cost of 1 ticket because that is unknown at this time. Well, now that we've done that, we've 00:01:22 completed step one. So now let's go ahead and see what we can do to write the equation. But we need to identify the operation. Well, knowing the variable, let's go ahead and go back to the clues that we were given. The total cost of 3 tickets to a play was $42. Now, here in my table, I have different words in a situation 00:01:42 that would describe what operation I'm using. If I see words like increasing, I know that means addition. Difference means subtraction. Finding part of a total means multiplication. And that's what we're looking at in this scenario, the total cost of 3 tickets to a play. We're finding part of a total. 00:02:00 Let's look at the last thing in the table-- sharing or grouping. That would tell us we were using a division problem. So let's go back to this multiplication. Since we're going to be finding part of a total because I'm trying to find out the cost of 1 ticket, which is a part of the total cost of tickets, then I can go ahead and use the fact that 3 tickets times the cost of 1 00:02:24 ticket is equivalent to $42. So notice I have the equation 3 times c is equal to 42. And then once you have your equation, you would be able to move to the next step in solving that equation.
Step-by-step explanation:
Which statement is true about the equations –3x + 4y = 12 and 1/4x-1/3y=1
Answers
Answer: No solution
Step-by-step explanation:
This system of equation has no solution because...
-3x+4y=12
1/4x-1/3y=1
[tex]-3x+4y-4y=12-4y[/tex]
[tex]-3x=12-4y[/tex]
[tex]\frac{-3x}{-3}=\frac{12}{-3}-\frac{4y}{-3}[/tex]
[tex]\frac{12}{-3}-\frac{4y}{-3}[/tex]
[tex]x=-\frac{12-4y}{3}[/tex]
substitute
[tex]\frac{1}{4}\left(-\frac{12-4y}{3}\right)-\frac{1}{3}y=1[/tex]
[tex]-1=1[/tex]
-1=1 is false so therefore this system has no solution
Which of the following are solutions to the equation below?
Check all that apply.
x2 + 4x-9 = 5x + 3
A. -3
B. 5
| C. 2
D. -4
E. 4
F-7
Answers
Answer:
The answers are options A and E
x² + 4x-9 = 5x + 3
Group like terms
x² + 4x - 5x - 9 - 3 = 0
x² - x - 12 = 0
Using factorization method
(x + 3)( x - 4) = 0
x = - 3 x = 4
Hope this helps
Which expression is equivalent to.......
See pictures
Answers
Answer:
[tex] \sqrt{ {2}^{5} } [/tex]
Step-by-step explanation:
[tex]\huge \bigg( {2}^{ \frac{1}{2} }. {2}^{ \frac{3}{4}} \bigg)^{2} \\ \\ \huge = {2}^{ \frac{1}{2} \times 2 }. {2}^{ \frac{3}{4} \times 2} \\ \\ \huge = 2 \times {2}^{ \frac{3}{2} } \\ \\ \huge = {2}^{ \frac{3}{2} + 1 } \\ \\ \huge = {2}^{ \frac{3 + 2}{2} } \\ \\ \huge = {2}^{ \frac{5}{2} } \\ \\ \huge = \sqrt{ {2}^{5} } [/tex]
Which situation is best modeled by the inequality g ≤ 13? A. You cannot play a game at age 13. B. You must be at least 13 to play a game. C. You must be no older than 13 to play a game. D. You must be younger than 13 to play a game.
Answers
Answer:
C)you must be no older than 13 to play the game.
Step-by-step explanation:
≤this means equal to or less than which in this case is 13
The situation represented by the inequality g ≤ 13 will be option C. You must be no older than 13 to play the game.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the inequality is g ≤ 13.
The inequality can be represented by the situation you must be no older than 13 to play a game.
To know more about inequality follow
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Through any 2 points there is exaclty_____line.
Answers
Answer:
One
Step-by-step explanation:
Through any 2 points, there is exactly one line.
Answer:
ONE
Step-by-step explanation:
Through any 2 points there is exaclty ONE line.
The graphs below have the same shape. What is the equation of the blue
graph?
Answers
Answer:
Option (A)
Step-by-step explanation:
Parent function (in red) graph is represented by,
f(x) = x²
If this function is translated by 'a' units to the right, rule to be followed,
f(x) → f(x - a)
If the parent function is shifted by 4 units to the right (blue graph), the new function will be,
g(x) = f(x - 4)
g(x) = (x - 4)²
Therefore, Option (A) will be the correct option.
I need help please help
Answers
Answer:
21u-16v+18w
Step-by-step explanation:
(7u-4v+4w) 14u-12v+14w
21u-16v+18w
Answer:
= 21u−16v+18w
Step-by-step explanation:
Let's simplify step-by-step.
7u−4v+4w−2(−7u+6v−7w)
Distribute:
=7u+−4v+4w+(−2)(−7u)+(−2)(6v)+(−2)(−7w)
=7u+−4v+4w+14u+−12v+14w
Combine Like Terms:
=7u+−4v+4w+14u+−12v+14w
=(7u+14u)+(−4v+−12v)+(4w+14w)
=21u+−16v+18w
Answer:
=21u−16v+18w
what is the volume of the cylinder below?
Answers
Answer:
A
Step-by-step explanation:
vol of a cylinder = pie* r^2×h
r= 5
h= 9
......vol= 9×5^2 pie= 225pie units ^3
A shop advertises 25% off its prices in a sale a dress is 90% how much was it before the price reduction
Answers
Answer:
120
Step-by-step explanation:
90→75%
X→100%
⇒X=(90×100)÷75=120
Before the price reduction, the cost was 120 dollar.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that shop advertises 25% off its prices in a sale a dress is 90% .
Here 90 percent is equivalent to 75%
Let X = 100%
So,X=(90×100)÷75
x =120
The price was 120 dollar.
Learn more about multiplications;
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What is the range? Explain
Answers
Answer:
Range = [5, ∞)
Step-by-step explanation:
The initial number of snakes is 5 and it is increasing at a high rate so the maximum number is infinite. The population is increasing exponentially according to the equation P = 5(2)^t where t = the number of years.
Complete the equation of the line through (-8,8)(−8,8)left parenthesis, minus, 8, comma, 8, right parenthesis and (1,-10)(1,−10)left parenthesis, 1, comma, minus, 10, right parenthesis.
Answers
Answer:
[tex]y = -2x - 8\\OR\\2x+y+8=0[/tex]
Step-by-step explanation:
Given that there are 2 points
[tex]A(-8,8)[/tex] and
[tex]B(1,-10)[/tex]
So, the coordinates are:
[tex]x_2 = 1\\x_1 = -8\\y_2 = -10\\y_1 = 8[/tex]
Equation of a line is given as:
[tex]y =mx+c[/tex]
where 'm' is the slope of the line, formula for 'm' is given as:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex](x,y)[/tex] are the points that satisfy the equation of the line.
[tex]c[/tex] is the [tex]y -[/tex] intercept.
Calculating the value of m using the given coordinates:
[tex]m=\dfrac{-10-8}{1-(-8)}\\\Rightarrow m=\dfrac{-18}{9} = -2[/tex]
So, the equation of line becomes:
[tex]y =-2x+c[/tex]
Now, putting the coordinates of point [tex]A(-8,8)[/tex]
[tex]8 =-2\times (-8)+c\\\Rightarrow 8 = 16+c\\\Rightarrow c = -8[/tex]
Please refer to the graph of given equation of line.
The equation of line is:
[tex]y =-2x+-8\\OR\\2x+y+8=0[/tex]
(Plz hurry) Given that cosθ=817 and sinθ=−1517 . What is the value of tanθ? 815 −815 158 −158
Answers
Answer:
D. -15/8Step-by-step explanation:
Given the following;
cosθ=8/17 and sinθ=−15/17
In trigonometry identity, tanθ = sinθ/cosθ
Substituting the given values in the equation;
tan θ = (−15/17)/(8/17)
tanθ = −15 /17 * 17/8
tanθ = -15/8
Answer:
D. -15/8
Step-by-step Explanation
find a18 of the arithmetic sequence 2, -5, -12, -19
Answers
Answer:
The 18th term of the sequence is -117.
Step-by-step explanation:
The given sequence is 2,-5,-12,-19
From this AP,
First term, a = 2
Common difference, d = -5-2 = -7
It is required to find the 18th term of the sequence. The nth term of an AP is given by :
[tex]a_n=a+(n-a)d\\\\a_{18}=a+17d\\\\a_{18}=2+17\times (-7)\\\\a_{18}=-117[/tex]
So, the 18th term of the sequence is -117.
A machine can wrap 360 packages of muffins in 12 minutes. At this rate, how
many packages will be wrapped in 1 hour?*
Answers
Answer:
1800 (packages )muffins
Step-by-step explanation:
360 muffins x muffins
-------- = --------
12 min 60 min
Answer:
1800 maybe
Step-by-step explanation:
in 12 minutes can wrap 360
in 1 hr have 60 minutes
60/12=5
than 360*5 = 1800
find the quadratic polynomial if zeros of it are 2 and 1/3 respectively
Answers
Answer:
[tex]\boxed{\sf \ \ \ 3x^2-7x+2 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
There are a lot of polynomials which have 2 and 1/3 as zeroes,
I can show you one below
[tex]3(x-2)(x-\dfrac{1}{3})=(x-2)(3x-1)=3x^2-x-6x+2=3x^2-7x+2[/tex]
hope this helps
sector of a circle is given with radius 7cm and angle subtended by the sector of a circle is 500
,
Calculate,
(i) area of sector,
Answers
Answer:
The area of the sector is 21.39 cm^2
Step-by-step explanation:
Mathematically, to calculate the area of a sector, the formula to use is;
A = Theta/360 * pi * r^2
where Theta is the angle subtended at the center of the circle = 50 degrees
r is the radius of the circle = 7cm
pi = 22/7
Substituting these values into the area of sector equation, we have;
A = 50/360 * 22/7 * 7 * 7 = (5 * 22*7 )/36 = 21.39 cm^2
a line segment may have more than one midpoint true or false
Answers
Answer: false
Step-by-step explanation: A line segment may not have more than one midpoint.
24. A quantity represented by 3x - 4 is
subtracted from the quantity 5x – 7. What is
the result?
A 2x - 3
© 2x – 11
B 2x + 3
D 2x + 11
Answers
Answer:
The answer is option A. 2x - 3
The expression 3x - 4 is subtracted from
5x - 7 is written as
5x - 7 - (3x - 4)
= 5x - 7 - 3x + 4
= 2x - 7 + 4
= 2x - 3
Hope this helps
The play director spent 190190190190 hours preparing for a play. That time included attending 35353535 rehearsals that took varying amounts of time and spending 933493 \dfrac{3}{4}934393, start fraction, 3, divided by, 4, end fraction hours on other responsibilities related to the play. What question does the equation 35x+9334=19035x+93\dfrac{3}{4}=19035x+9343=19035, x, plus, 93, start fraction, 3, divided by, 4, end fraction, equals, 190 help answer?
Answers
Answer:
The equation above represents the total time the play director spent preparing for a play.
Step-by-step explanation:
The time spent by the play director for preparing for a play is, 190 hours.
Of these 190 hours, the director spent varying amounts of time attending 35 rehearsals for the play.
Let the varying amounts of time be denoted by, x.
The director also spent 3/4th of an hour, i.e. 45 minutes, on other responsibilities related to the play.
The equation provided is:
[tex]35x+\frac{3}{4}=190[/tex]
The equation above represents the total time the play director spent preparing for a play.
Write the point-slope form of an equation of the line through the points (-7, 7) and (4,1).
Answers
Answer:
The point-slope form of an equation of the line through the points (-7, 7) and (4,1):
(y - 7) = m(x + 7)
or
(y - 1) = m(x - 4)
with
m = (1 - 7)/(4+7) = -6/11
Answer:
y=-6/11 x +35/11
Step-by-step explanation:
(-7, 7) and (4,1)
m=y2-y1/x2-x1
m=1-7/4-(-7)
m=-6/11
y=mx+b take one point(4,1) to find b
1=-6/11(4)+b
1=-24/11 +b
b=1+24/11
b=(11+24)/11
b=35/11
y=-6/11 x +35/11
the price of a CD was decreased by 2% to £14. what was the price before the decrease?
Answers
Answer:
£14.29
Step-by-step explanation:
0.98x=14
x=14.29
Answer:
14.28
Step-by-step explanation:
In △ABC, m∠A=35°, a=12, and b=14. Find c to the nearest tenth.
Answers
Answer:
a b. c=19 it is equal to 19
Answer:
20.3854
Step-by-step explanation: