Answer:
g(x)= 9 cos (x - [tex]\frac{\pi}{3}[/tex]) +7
Step-by-step explanation:
What is given is f(x) = g cos (x - pi/2) + 3
Note that the standard form of cosine function is a cos (bx + c) + d
a= amplitude
-c/b = phase shift
d = vertical shift
After moving pi/6 to the left --
x = pi/2 - pi/6 = pi/3
once moving pi/6 left, it is at pi/3
moving 4 units up just means adding 4 + 3, and that equals 7, that would be the vertical shift once applied.
So the equation that represents g(x) is C. 9 cos (x - pi/3) + 7
The equation that represents the function g(x) is [tex]g(x)=9 \cos (x- \frac{\pi}{3})+7[/tex]
The function is given as:
[tex]f(x)=9 \cos (x-\frac{\pi}{2})+3[/tex]
The function f(x) is first translated [tex]\frac{\pi}{6}[/tex] units left.
The rule of this translation is:
[tex](x,y) \to (x + \frac{\pi}{6},y)[/tex]
So, we have:
[tex]f'(x)=9 \cos (x+ \frac{\pi}{6}-\frac{\pi}{2})+3[/tex]
Take LCM
[tex]f'(x)=9 \cos (x+ \frac{\pi - 3\pi}{6})+3[/tex]
[tex]f'(x)=9 \cos (x- \frac{2\pi}{6})+3[/tex]
Divide 2 by 6
[tex]f'(x)=9 \cos (x- \frac{\pi}{3})+3[/tex]
Next, we translate f'(x) 4 units up.
The rule of this translation is:
[tex](x,y) \to (x,y+4)[/tex]
So, we have:
[tex]g(x)=9 \cos (x- \frac{\pi}{3})+3 +4[/tex]
[tex]g(x)=9 \cos (x- \frac{\pi}{3})+7[/tex]
Hence, the equation that represents the function g(x) is [tex]g(x)=9 \cos (x- \frac{\pi}{3})+7[/tex]
Read more about function transformation at:
https://brainly.com/question/1548871
a and b are positive numbers.
a is inversely proportional to b.
when a=4,b=36
find value of a when b=a
Answer:
a = 12
Step-by-step explanation:
Given that a is inversely proportional to b then the equation relating them is
a = [tex]\frac{k}{b}[/tex] ← k is the comstant of proportion
To find k use the condition when a = 4, b = 36, then
4 = [tex]\frac{k}{36}[/tex] ( multiply both sides by 36 )
144 = k
a = [tex]\frac{144}{b}[/tex] ← equation of proportion
When b = a , then
a = [tex]\frac{144}{a}[/tex] ( multiply both sides by a )
a² = 144 ( take square root of both sides )
a = ± [tex]\sqrt{144}[/tex] = ± 12
However a is a positive number, thus a = 12
4 equal piece of rope out of 2 1/2 inch how long is each piece
Answer:
1/4 inches
Step-by-step explanation:
To get 4 equal pieces you need to cut the 2 equal pieces in half, which half of 1/2 inches is 1/4 inches.
please help me with this
Answer:
its yes
I'm fighting ransome cuz I need at least 20 characters
Which ordered pair is the solution to the system of linear equations Negative 5 x + y = 26 and 2 x minus 7 y = 16?
9514 1404 393
Answer:
(-6, -4)
Step-by-step explanation:
If you're going to use technology to answer your questions, you may as well use appropriate technology: a graphing calculator. It shows the solution to the system is the ordered pair (-6, -4).
__
The first of the given equations can be solved for y, then that used to substitute for y in the second equation.
y = 5x +26
2x -7(5x +26) = 16
2x -35x -182 = 16
-198 = 33x . . . . . . . . add 33x-16
-6 = x . . . . . . . . . . . . divide by 33
y = 5(-6) +26 = -4 . . . find y
The solution is (x, y) = (-6, -4).
Solve for x when 4x+x+2=10x−13
Answer:
x = 3
Step-by-step explanation:
First lets add 4x + x so that we can get one x value on that side of the equation.
4x + x + 2 = 10x - 13
5x + 2 = 10x - 13
Then we can solve for x from there
5x + 2 = 10x - 13
-5x + 2 = -13 [Subtract 10x from both sides of the equation]
-5x = -15 [Subtract 2 from both sides of the equation]
-x = -3 [Simplify]
x = 3 [Simplify]
Hope this helps! I apologize if I got this incorrect
Answer: x = 3
Steps: 4x + x + 2 = 10x - 13
Combine like terms: 5x + 2 = 10x - 13
Subtract 2 from both sides: 5x + 2 - 2 = 10x - 13 - 2
Simplify: 5x = 10x - 15
Subtract 10x from both sides: 5x - 10x = 10x - 15 - 10x
Simplify: -5x = -15
Divide both sides by -5: -5x ÷ -5 = -15 ÷ -5
Simplify: x = 3
Plz mark brainliest:)
Jackson was solving the problem below for k. However, he made a mistake.
19 - 2k = 3k - 1
+3k +3k
19 +1k = -1
-19 -19
k = -20
Part A: Identify the FIRST mistake Jackson made.
Part B: Solve for k.
Please help me with this
Answer:
B.
[tex](x + 2) ^{3} - 9 [/tex]
A group of people were asked if Marilyn Monroe had an affair with JFK. 184 responded "yes", and 387 responded "no". Find the probability that if a person is chosen at random, the person does NOT believes Marilyn Monroe had an affair with JFK.
Probability (round to 4 decimal places)
Answer:
0.6778 to 4 dec. places.
Step-by-step explanation:
That is 387 / (184+387)
= 387 / 571
= 0.677758
Which of the following is equal to 5/7-4/7 (a) 0 (b) 1 (c) undefined (d) 1/7
Answer:
It's 0.142857
Step-by-step explanation:
Answer:
your answer is d.1/7
Step-by-step explanation:
all you have to do is subtract 5-4 which is 1 then add 7 as the denominator
Jimmy deposits $5000 into an account that pays 4.5% interest compounded weekly. How much would he have when he goes to withdraw his funds? There is not enough information to complete this problem. What part is missing if you are using the formula given below?
Answer: TIME
Step-by-step explanation: I cant see the formula, but I think the one you are using is Interest = (principal)(interest rate)(time). You have the interest rate and principal, but you need the amount of time to figure out how much he has earned.
Ryan is taking a survey to find out how many people prefer soda A over soda B. He surveyed 100 people and forty-nine preferred soda A. Seven percent had no preference for soda A or soda B. What percentage of peoples surveyed preferred soda B?
Answer:
44%
Step-by-step explanation:
An atom is neutral. Its nucleus contains two protons and two neutrons. How
many electrons does the atom have?
Answer:
2 electrons
Step-by-step explanation:
An atom is neutral if it has no charge. That means the positive and negative charge balance each other out.
There are two protons, so that is a charge of +2. To make the charge 0, there needs to be a charge of -2. -2= 2 electrons.
Answer:
Answer is 2
Step-by-step explanation:
What do solving absolute value equations and solving quadratic equations have in common?
Answer:
They often have more than one solution.
Answer:
Step-by-step explanation:
Quadratic equations are equations that when rearranged using the 5 operations can yield a polynomial of degree 2 on one side of the equation and 0 on the other. There are 3 commonly taught methods for solving quadratic equations. These methods are factoring, completing the square, and the quadratic formula. These functions are most commonly used to model projectiles, disregarding air resistance.
When using the factoring method one attempts to write a degree 2 polynomial as the product of two degree 1 polynomials. This method works because if we multiply two degree one polynomials together we find
For example: When factoring , we want to find two number a, b whose product is 6 and sum to 5. The values of a and b we are looking for are 2 and 3.
The method of completing the square centers around using the five operations to replace the original equation with an equivalent equation of the form by taking advantage of the fact that
The absolute value function takes the value of a number, regardless of whether it is positive or negative. Some problems that the absolute value is useful for modeling include an object bouncing on the ground.
For example, , since we do not care about the negative sign.
Example: Solve
Solution: Since the absolute value does not care about whether a number is positive or negative, if then or . Then we can solve each equation individually to find that x = 1 or 5.
Find the equation of line b described below, in slope-intercept form
Line a is perpendicular to line b
Line a passes through the points (1,-8) and (9,-12)
Line b passes through the point (-8, -16)
The equation of line b is y= ______
Given:
Line a is perpendicular to line b .
Line a passes through the points (1,-8) and (9,-12) .
Line b passes through the point (-8, -16).
To find:
The equation of b.
Solution:
Line a passes through the points (1,-8) and (9,-12) . So, slope of line a is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m_a=\dfrac{-12-(-8)}{9-1}[/tex]
[tex]m_a=\dfrac{-12+8}{8}[/tex]
[tex]m_a=\dfrac{-4}{8}[/tex]
[tex]m_a=-\dfrac{1}{2}[/tex]
Product of slopes of two perpendicular lines is -1.
[tex]m_a\times a_b=-1[/tex]
[tex]-\dfrac{1}{2}\times a_b=-1[/tex]
[tex]b=2[/tex]
Slope of line b is 2.
If a line passing through a point [tex](x_1,y_1)[/tex] with slope m, then equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
Line b passing through (-8,-16) with slope 2. So, equation of line b is
[tex]y-(-16)=2(x-(-8))[/tex]
[tex]y+16=2(x+8)[/tex]
[tex]y+16=2x+16[/tex]
Subtract 16 from both sides.
[tex]y=2x[/tex]
Therefore, the equation of line b is [tex]y=2x[/tex].
Find the measures of the interior angles and please tell me all angles
Which ordered pair is a solution to the system of inequalities
Y<3x-1
Y>|x-2|
A. (-2,0)
B. ( 0,1)
C. (4,4)
D. (3,-1)
How do I plot the coordinates (2,-4)
Answer:
the first number is the x axis and the second is the y axis so first find the x axis and plot the first number on there then do the same to the y.
Step-by-step explanation:
if the roof building is 46 feet off the ground and the floor of the basement is 15 feet under ground what is the total distance from roof to basement floor
Answer:
61
Step-by-step explanation:
46 then you have to add another 15 feet for underground and you get 61 because it is asking form the roof to the basement floor
hope this helps
If Hector is 8 years old and Mary is 3 years old, how old will Mary be when Hector is 16? Can I use proportional reasoning in here
Answer: Mary will be 11, and yes you can
Step-by-step explanation: hector will be 16 in 8 years so you just add the 8 on to the 3
Morgan can type 18 words
per minute. How long will it
take her to type 3
paragraphs? (Each
paragraph has 30 words)
Answer: it will take 5 minutes.
Ryan and his brother are at a carnival. They separate from each other at the ferris wheel at 1:00 PM, and they agree that they will each meet back at the ferris wheel from time to time to see whether the other is ready to leave. Ryan checks the ferris wheel every 15 minutes. His brother checks in every 24 minutes. At what time will they meet at the ferris wheel again. (Hint: Don't forget you're looking for a time)
Answer:
3:00pmStep-by-step explanation:
The idea hear is to find the least common multiples of 15 and 24
Given that they separated at exactly 1:00pm
the multiples are
15= 15,30,45,60,75,90,105,120
24= 24, 48,72,96,120
the multiples common is 120
Therefore they will meet in 120minute, which is 2 hours time \
hence the time will be 3:00pm
(2a-b-c)³+(2b-c-a)³+(2c-a-b)³ factorise
Answer:
Sowy but try Mathwa y
Step-by-step explanation:
the registration fee for a used car is 0.8% of the sale price of 5,700. How much is the fee
Answer:
1,140
Step-by-step explanation:
subtract the percentage from the total
The following graph shows a proportional relationship
Answer:
for every 5 units to the right, there is 1 unit up
the slope is y = 1/5
help me answer this slope problem (10 points)
What is the equation of a quadratic function that has zeros -6 and -2?
Answer:
[tex]y=x^{2} +8x+12[/tex] is the quadratic function.
Step-by-step explanation:
We know that -6 and -2 are the zeros. So, they are both equal to x.
x = -6 and x = -2
Add them to x.
(x + 6) (x + 2)
Now, multiply the two binomials together.
[tex]x^{2} +6x+8x+12[/tex]
Combine like terms.
[tex]y=x^{2} +8x+12[/tex]
[tex]y=x^{2} +8x+12[/tex] is the answer.
helpppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! pleaseeeeeee
Answer:
Step-by-step explanation:
y= money earned , x is the number of hours
k is the constant=y/x=12
a- y=12 xb- if she worked 18 hours:
y=12(18)
y=216 dollarsc- if she earned 330 dollars:
330=12x
x=330/12
x=27.5 hourscan medicine cure depression if you have it because of someone you’ve loved for 2 years but they just don’t care about you..? i’ve tried for 2 years to get over them and till this day i’m still ✨crying✨ every night :/ i need help i need answers to why this is happening.. i’m sorry for being depressed but i just can’t stop how much i love them.. and i pray for god but he never answers he just puts more pain in my life.. love you all and thank you for reading this if you did your all amazing..
Answer:
there is mutable ways to cure depression rather it would be therapy or antidepressants if you need help find a therapist or cirotherapist that can solve your pain and can prescribe medication
what number can be added to 55 and have 45 and 9 as thier greatest common factor?
Answer:
36
Step-by-step explanation:
At the zoo, the ratio of elephants to hippos is 1.2. So for every elephant, there
are hippos
Answer:
2 hippos
Step-by-step explanation:
Answer:
For every elephant, there are 2 hippos.