The function g(x) represents f(x) = 9 cosine (x minus StartFraction pi Over 2 EndFraction) + 3 after translating StartFraction pi Over 6 EndFraction units left and 4 units up.

Which equation represents g(x)?

The Function G(x) Represents F(x) = 9 Cosine (x Minus StartFraction Pi Over 2 EndFraction) + 3 After

Answers

Answer 1

Answer:

B

Step-by-step explanation:

Im almost sure it B but if not then its for sure D.

Answer 2

The equation that represents the function g(x) is [tex]g(x)=9cos(x-\frac{\pi }{3} )+7[/tex].

What is function?

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

What is translation?

Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.

The function is given as

[tex]f(x)=9cos(x-\frac{\pi }{2} )+3[/tex]

The function f(x) is first translated [tex]\frac{\pi }{6}[/tex] units left.

The rule of translation is:

[tex](x,y)=(x+\frac{\pi }{6},y)[/tex]

So, we have:

[tex]f'(x)=9cos(x+\frac{\pi }{6} -\frac{\pi }{2} )+3[/tex]

Take LCM

[tex]f'(x)=9cos(x+\frac{\pi-3\pi }{6} )+3[/tex]

[tex]f'(x)=9cos(x-\frac{2\pi }{6} )+3[/tex]

[tex]f'(x)=9cos(x-\frac{\pi }{3} )+3[/tex]

Next, translate f'(x) 4 units up.

The rule of this translation is:

[tex](x,y)=(x,y+4)[/tex]

So, we have:

[tex]g(x)=9cos(x-\frac{\pi }{3} )+3+4[/tex]

[tex]g(x)=9cos(x-\frac{\pi }{3} )+7[/tex]

Hence, the equation that represents the function g(x) is [tex]g(x)=9cos(x-\frac{\pi }{3} )+7[/tex].

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Related Questions

Students was 1: 8. However, this year the ratio of the number of middle school students to the number of high school students changed to 2: 7. If there are 18 middle school students in the band this year, how many fewer high school students are in the band this year compared to last year? Expla

Answers

Answer:

Step-by-step explanation:

Last year

Ratio of the number of middle school students to number of high school students = 1 : 8

Total ratio = 9

Middle school = 1

High school = 8

Total students in the band = x

Middle school = 1/9x

High school = 8/9x

Total = 1/9x + 8/9x

This year

Ratio of the number of middle school students to number of high school students = 2 : 7

Total ratio = 9

Middle school = 2

High school = 7

Total students = x

Middle school = 2/9x

High school = 7/9x

Total = 2/9x + 7/9x

If there are 18 middle school students in the band this year

2/9x = 18

x = 18÷2/9

= 18 × 9/2

= 81

x = 81

Last year:

1/9x + 8/9x

= 1/9 * 81 + 8/9 * 81

= 9 + 72

= 81

This year

2/9x + 7/9x

2/9*81 + 7/9*81

= 18 + 63

=81

Change in middle school =this year - last year

= 18 - 9

= 9 (increase)

Change in high school = this year - last year

= 63 - 72

= -9 (decrease)

a population of bears is decreasing the population this year is 200 bears after 1 year it is estimated that the population will be 160 bearsafter 2 years it is estimated that the population will be 128 bears what equation describes the bear population in any year x?

Answers

Answer:

200x-160

Step-by-step explanation:

A and \angle B∠B are supplementary angles. If m\angle A=(5x-19)^{\circ}∠A=(5x−19)

and m\angle B=(2x+10)^{\circ}∠B=(2x+10)

, then find the measure of \angle B∠B.

Answers

Answer: 52

Step-by-step explanation:

4x+8 = 5x-3 by the Vertical Angles Theorem that states the vertical angles are congruent.  

Subtract 4x from both sides and get:

8=1x -3

Add 3 to both sides:

11= 1x

if x =11, plug that in to angle A.  

4x+ 8 becomes 4(11)+8 =

44+ 8=

52

2. Determine the amount of interest owed after 2 years on a $850 loan at 12.25% if no payments
are made. LTD
Enter your answer

Answers

Answer:

Question example:

The amount of interest is 208.74$

Here we have given

Amount (P)=850$

Interest (r)=12.25%

Time (t)=2 years

we have to calculate the simple interest

What is the formula for simple interest?

[tex]I=\frac{PRT}{100}[/tex]

Plug the given value in above formula

[tex]I=\frac{850*12.25*2}{100}[/tex]

Simplify above equation we get

[tex]I=\frac{850*12.25*2}{100}\\\\I=\frac{20874}{100}\\\\I=208.74[/tex]

Therefore the amount of interest is 208.74$

To learn more about the interest visit:

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14.) George is designing a pool that will be 34 feet long. He plans to make
a scale drawing of the pool by letting 1/4 inch represent 1 foot. How long
should the line representing the length of the pool in the diagram be?

Answers

Answer:

I believe the answer is 8.5 inches long

Step-by-step explanation:

we have to find out how long 1/4 × 34 is, since each 1/4 represents one of the 34 feet of the pools length.

34×.25 = 8.5

AT&T charges $350 to get a plan with them, plus $60 per month. T-Mobile charges a $275 initial fee, plus $80 per month. Write an equation or inequality that can be used to determine the number of months it would take for T-Mobile to cost the same or more than AT&T.

Answers

Given :

AT&T charges $350 to get a plan with them, plus $60 per month.

T-Mobile charges a $275 initial fee, plus $80 per month.

To Find :

Write an equation or inequality that can be used to determine the number of months it would take for T-Mobile to cost the same or more than AT&T.

Solution :

Money-time relation of plan AT&T :

[tex]M_1 = 60x + 350[/tex]

Money-time relation of plan T-Mobile :

[tex]M_2 = 80y + 275[/tex]

( Here, x and y are number of months )

Let, after t months would take for T-Mobile to cost the same or more than AT&T.

So, [tex]M_2\ge M_1[/tex]

[tex]80t+275 \ge 60t + 350\\\\20t \ge 350 - 275\\\\20t \ge 75\\\\t \ge 3.75[/tex]

Hence, this is the required solution.

plz help i dont know the answer

Answers

Answer:

Im not 100 percent sure but I think you have to do this

Step-by-step explanation:

Add all numbers together to find total students

Then add the students in Chemistry and Physics and both together

Then find what that number is in percent to the total students

how do you solve X+17=-12​

Answers

Answer:

Subtract 17 from -12, you sould get x= -29

Step-by-step explanation:

Click through and select the graph that correctly shows the following points:

X(-2, 0), Y(3, -5), and Z(0, 3).

Answers

Answer:

The second graph

Step-by-step explanation:

each of the points you listed are graphed on there.

Answer:

the answer is graph number 2

it has X(-2, 0), Y(3, -5), and Z(0, 3) points on it !

Al saves pennies. He agreed to give 3/7 of his pennies to Bev if she would give 3/7 of what she got from Al to Carl and if Carl in turn would give 3/7 of what he got from Bev to Dani.​ Bev, Carl, and Dani agreed and Dani received pennies. How many pennies did Al have​ initially

Answers

Answer:

2744

Step-by-step explanation:

Let Al had x pennies initially.

Al agreed to give 3/7 of his pennies to Bev if she would give 3/7 of what she got from Al to Carl and if Carl in turn would give 3/7 of what he got from Bev to Dani.

So, as per the given condition,

The number of Pennies received by Ben from Al [tex]= \frac{3}{7} x[/tex]

The number of Pennies received by Carl from Bev

[tex]=\frac{3}{7} \times \frac{3}{7} x=\frac{9}{49}x[/tex]

The number of Pennies received by Dani from Carl

[tex]= \frac{3}{7}\times \frac{9}{49}x=\frac{27}{343} x[/tex]

Now, as Dani received 216 Pennies, so

[tex]\frac{27}{343} x =216[/tex]

[tex]\Rightarrow \frac{216\times 343}{27}=2744.[/tex]

Hence, initially, Al had 2744 Pennies.

There are (64)2 ⋅ 60 pigs on a farm. What is the total number of pigs on the farm?

Answers

I’m bot sure if you ask 64^2 x 60 or 64 x 2 x 60. If you ask the first one, the answer is 245760. But if you ask the second one, the answer is 7680.

Answer:

If the question is (64)2 x 60, then the answer is 7,200

Step-by-step explanation:

What are the following properties:
4k−3−2k=2k+5−2k

2k−3=5

2k−3+3=5+3

2k=8

2k2=82

k=4

Answers

Answer:

k4-3+3=10k

Step-by-step explanation:

Answer:

4k-3+3=10k

Step-by-step explanation:

4k-3+3=10k

To encourage recycling many states require a $.70 deposit or drink containers the total deposit di you pay depends on the number of containers N You by the function D =0.07N could be used to describe the situation if you deposit $1.40 how many containers do you buy?

Answers

Answer:

20 containers

Step-by-step explanation:

Given:

D = 0.07N

Where,

D = Amount of deposits

N = Number of containers

If D = $1.40 find N

D = 0.07N

1.40 = 0.07N

Divide both sides by 0.07

N = 1.40 / 0.07

= 20

N = 20 containers

if you deposit $1.40, you will buy a total of 20 containers.

determine the unit rate for each ratio.
The gas station charges $180 for 3 hours of work. How much
they charge for 1 hour of work?

Answers

Answer:

$60

Step-by-step explanation:

180/3 = 60

I hope this helps :)

Answer:60 per hour

Step-by-step explanation: you divide 180 by 3

Can someone please help

Answers

Answer:

( -1 , 0.5)

Step-by-step explanation:

If the 16 boys in the classroom are 40% of the class how many students are there in the class

Answers

Answer:

56

Step-by-step explanation:

40+16=56

Answer:

40

Step-by-step explanation:

Set up the equation.

Let the full number of people in the classroom = x

(40%) x = 16                Change 40% to a fraction

(40/100) x = 16            Reduce 40/100 to a decimal

0.4 x = 16                     Divide by 0.4

0.4/0.4 x = 16/0.4

x = 40

Answer for brainliest.

Answers

Answer:

t > 28

Step-by-step explanation:

Given

[tex]\frac{t}{4}[/tex] > 7 ( multiply both sides by 4 to clear the fraction )

t > 28

Answer:

[tex]t>28[/tex]

Step-by-step explanation:

[tex]\frac{t}{4} >7\\[/tex]

Times both sides by 4

[tex]t>28[/tex]

Hope this helps and pls do mark me brainliest:)

This recipe makes 15 cupcakes.
Deepak only wants to make 12 cupcakes.
How much of each ingredient does he need?

Recipe: Makes 15 cupcakes
12 ounces butter
10 ounces sugar
15 ounces flour
5 eggs
I WILL GIVE BRAINLIEST TO THE BEST ANSWER IF ITS RIGHT

Answers

He will only need 3 ounces of butter, 1 ounce of sugar, 3 ounces of flour, and 5 eggs hope I helped

3/4 change 3/4 to a decimal show work

Answers

Answer:

0.75

Step-by-step explanation:

You just need to convert 3/4 into a decimal.

For example: If you get 3 out of 4 problems right on a quiz, in percent form it will be a 75%, in decimal form 0.75 because you'll move the percent sign 2 spaces to the left. That will then be a decimal if you're converting 75% to 0.75.

3 divided by 4 is also going to give you 0.75. Because, a "fraction slash" is the dividing point. So,

3/4 = 0.75

8c + 20 = -180

c =

can some one help me please

Answers

Answer:

c = -25

Step-by-step explanation:

8c + 120 = -180

Subtract 20 from both sides.

8c = -200

Divide both sides by 8.

c = -25

Answer:

C = -25

Step-by-step explanation:

Start by getting C alone, subtract 20 from the left side of the equal sign and subtract 20 from the right. (what you do on one side you MUST do to the other) this gives you 8c= -200. Divide 8 from 8c on the right side and divide 8 from -200 on the left side. This will give you c= -25

A line passes through the point (-2, 7) and has a slope of -5.
What is the value of a if the point (a,2) is also on the line?​

Answers

Answer:

-1

So the answer would be (-1, 2)

Hopefully, this is correct, sorry if not.

bailey ran 0.674 times aound her school track. what percentage of the track did she run around?

f: 0.0674%
G: 6.74%
H:64.4%
j: 674%

Answers

Answer:

0.674 as a percent. 0.674 is equivalent to 67.4%.

Hope this helps!

PLEASE HELP WILL MARK BRAINLIEST FOR RIGHT ANSWER!!

Answers

Answer:

Population 2 pattern is that every year the population goes down by 2

Step-by-stepation:

Substitute the given value for x into each equation to determine the value of y.
1. y = 3x + 6; x = -4
2.3.2 - 8y = 12; x = 4
3. y = -43; x = -2

Answers

Answer:

Y=-6

Y= -1.1

Y=-43

Step-by-step explanation:

Urvi solved a fraction division problem using the rule "multiply by the reciprocal." Her work is shown below. StartFraction 14 divided by StartFraction 2 Over 7 EndFraction. StartFraction 1 Over 14 EndFraction times StartFraction 2 Over 7 EndFraction = StartFraction 2 Over 98 EndFraction or StartFraction 1 Over 49 EndFraction Which is the most accurate description of Urvi's work? Urvi solved the problem correctly. Urvi multiplied the dividend by the divisor instead of finding the reciprocal. Urvi multiplied the denominators instead of finding a common denominator. Urvi multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Answers

Given:

The equation is

[tex]\dfrac{14}{\dfrac{2}{7}}[/tex]

To find:

The correct description of Urvi's work.

Solution:

We have,

[tex]\dfrac{14}{\dfrac{2}{7}}[/tex]

Using the rule "multiply by the reciprocal", we get

[tex]\dfrac{14}{\dfrac{2}{7}}=14\times \dfrac{7}{2}[/tex]

[tex]\dfrac{14}{\dfrac{2}{7}}=\dfrac{98}{2}[/tex]

[tex]\dfrac{14}{\dfrac{2}{7}}=49[/tex]

Urvi multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Therefore, the correct option is D.

Answer:

D

Step-by-step explanation:

Find the square root.

±√1.69 = ____ and ____

Answers

Answer:

             ±√1.69 = +1.3 and -1.3

Step-by-step explanation:

√169 = 13

square root and two digits after dot means the result need to has one digit after dot (number of digits after dot divided by 2 because of square root)

so √1.69 = 1.3

Please help! I'm in a hurry.

Answers

Answer:

13

Step-by-step explanation:

15 and 13 have the same angle because they are opposit each other on the intersection of both lines.

Which of the following situations have a sum of zero? Select all that apply.

1. Shawna spends $20 on materials to make bracelets for her friends. She then earns $20 from selling the bracelets.

2. A diver dove down 20 1/4 feet under water and then descended 20 1/4 feet.

3. A golfer shot 2 over par (+2) on a hole. They then then shot 2 under par (−2) on the next hole.

4. You have $5.50 in your pocket and then you receive $5.50 for doing your chores.

Answers

I’m pretty sure it’s 1. And 2.
The first and the third.

Write the linear equation in slope intercept form y-2=1/2(x+4)

Answers

Answer:

y = 1/2x + 4

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

m - slope

b - y-intercept

Step 1: Define

Point-slope form; y - 2 = 1/2(x + 4)

Step 2: Rewrite

Distribute 1/2 to both sides: y - 2 = 1/2x + 2Add 2 to both sides: y = 1/2x + 4

Answer:

y=1/2x+4

Step-by-step explanation:

y-2=1/2(x+4)

(distribute the 1/2)

y-2=1/2x+2

(add 2 to both sides)

y=1/2x+4

8.
Which of the following is a negative
rational number that is not an integer?
А -pi
B -4.5
C -2
D 5 squared

Answers

The answer is B, 4.5
It is not an integer because it’s a decimal, it’s a rational number, unlike pi, and it’s negative, so it the answer is 4.5
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