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)?
Answers
Answer:
B
Step-by-step explanation:
Im almost sure it B but if not then its for sure D.
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
Gemma makes a conjecture that the sum of an odd integer and itself is always an even integer. Which choice is the best proof of her conjecture?
A) Look at these different examples: 7 + 7 = 14, 13 + 13 = 26, 23 + 23 = 46. So the sum of an odd number and itself must be even
B) Let 2n + 1 be an odd number; (2n + 1) + (2n + 1) = 4n + 2. Because 4(n + 2) is divisible by 2, the sum of 2n + 1 and itself is even.
C) Let n represent an odd number, and let n + n be an even number. Therefore, n + n = n + n, which shows that the sum of an odd number and itself is even.
D) Every time you add an odd number and itself, the sum is an even number.Every time you add an odd number and itself, the sum is an even number.
Answers
Answer:
Let 2n + 1 be an odd number...... B/2nd option
Step-by-step explanation:
The best choice is
Let 2n + 1 be an odd number; (2n + 1) + (2n + 1) = 4n + 2.
Because 4(n + 2) is divisible by 2, the sum of 2n + 1 and itself is even.
What is Conjecture?A hypothesis in mathematics is a conclusion or a proposition made tentatively without supporting evidence. Some conjectures, like the Fermat's Last Theorem or the Riemann hypothesis, have significantly influenced the development of new branches of mathematics.
First, Only three examples are given which is not appropriate at all.
Second, This is the best proof is
Let 2n + 1 be an odd number; (2n + 1) + (2n + 1) = 4n + 2. Because 4(n + 2) is divisible by 2, the sum of 2n + 1 and itself is even.
Fourth, State the meaning of Title without proof.
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The equipment elevator descends 4 feet per second. The elevator for the miners descends 17 feet per second. The equipment elevator descends. After 25 seconds, the elevator for the miners begin to descend. What is the position of each elevator relative to the surface after another 12 seconds? At that time. Which elevator is deeper?
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Equipment elevator Descent = 4 fts per Second
Miners elevator descent = 17 ft/sec
Miner's elevator begins descent 25 seconds after equipment elevator :
Elevation after another 12 seconds :
Descent = (speed * time)
Equipment elevator = 4 * (25 + 12) = 148 ft descent
Miner's elevator = 17 * 12 = 204 ft descent
The Miner's elevator is deeper at 204 feets.
What is the equation of a line, in point-slope form, that passes through (-2,-6)and has a slope of 1/3 ?
Answers
Answer:
y +6 = 1/3(x+2)
Step-by-step explanation:
Point slope form:
y - y1 = m(x - x1)
m = slope
Since x and y are negative, the double negatives make a positive.
simplify 3x(4x-5)+3 and its value for X = 3
Answers
Answer:
Step-by-step explanation:
3x ( 4x - 5 ) + 3
12x^2 - 15x + 3
12 × 3^2 - 15 × 3 + 3
12 × 9 - 45 + 3
= 108 - 45 + 3
= 66
Hope this helps
plz mark as brainliest!!!!!!
answer this please :(
Answers
Find x and y in each figure.
Answers
Answer:
[tex]by \:alternate \: interiar \: angle \: \\ (8y + 2) + (25y - 20) = 180 \\ 8y + 2 + 25y - 20 = 180 \\ 33y - 18 = 180 \\ 33y = 180 + 18 \\ 33y = 198 \\ y = 6 \\ \\ now \\ by \: \: linear \: pair \: \\ 10x + 8y + 2 = 180 \\ 10x + 48 + 2 = 180 \\ 10x = 180 - 50 \\ 10x = 130 \\ x = 13[/tex]
so finallyX=13and y=6-------------------------Please help! I’ll give brainliest to anybody who answers correctly!
Answers
HELP MY GRADE IS HORRIBLE
Answers
Answer for y-2x^2-8x+ 10 is -10
Find the unit rate: $23.96 for 4 pounds
Answers
Answer:
5.99 dollars per pound
Step-by-step explanation:
Convert to a decimal by dividing the numerator by the denominator.
Ian left his house and drove to the store. He stopped and went inside. From there, he
drove in the same direction until he got to the bank. He stopped and went inside the
bank. Then he drove home. The graph below shows the number of blocks away from
home Ian is x minutes after he left his house, until he got back home.
Answers
Answer:
6 blocks
Step-by-step explanation:
If someone could help me I would really appreciate it!
Factor by slide and divide!
Answers
Answer:
(3x-4)(2x+5)
Step-by-step explanation:
6x^2 + 7x + 24
= 6x^2 + (15-8)x + 24
= 6x^2 + 15x - 8x + 24
= 3x( 2x+5 ) - 4( 2x+5 )
= (3x-4)(2x+5)
Just the last question thank you!!
Answers
Answer:
6 X 10^21
Step-by-step explanation:
What is the domain of the function on the graph?
Answers
Describe a sequence of translations, rotations, and reflections that takes Polygon P to Polygon Q. P
Answers
Answer:
train tracks
Step-by-step explanation:
They have simple rotations and movemental frequences
Describe how the value of the digit 2 changes in each place in the number 22.222.
Answers
Answer:
ones, ten, hundreds, thousands, ten thousand, ect.
on the right side of the decimal represents a part of a number Ex. .222 is equal to 222/1000 of a number.
11 is what percent of 41?
Answers
Answer: What do you mean?
Is this even correct question?
Answer:
4.51
Step-by-step explanation:
you have to divide
. Express each exponent in expanded form: StartFraction 6 times 6 times 6 times 6 times 6 times 6 times 6 Over 6 times 6 times 6 times 6 EndFraction 2. Divide common factors: StartFraction 6 times 6 times 6 times 6 times 6 times 6 times 6 Over 6 times 6 times 6 times 6 EndFraction. 4 sixes in the numerator and denominator are crossed out. What is the exponent of the simplified power?
Answers
Answer:
The exponent of the simplified power is 3
Step-by-step explanation:
Given:
6 × 6 × 6 × 6 × 6 × 6 × 6 / 6 × 6 × 6 × 6
Dividing common factors ( cancel out 4 6's in the Numerator and Denominator
= 6 × 6 × 6 / 1
= 6^3 /1
= 6^3
The exponent of the simplified power is 3
Answer:
The exponent of the simplified power is 3
Step-by-step explanation:
What is StartFraction 5 Over 8 EndFraction divided by One-fourth?
Answers
Answer:
tfollow me plzzz
Step-by-step explanation:
Rectangle ABCD has a length represented by the expression 2x-3, and a width represented by the expression 4x+5. Rectangle PQRS has a length represented by the expression x-1, and a width represented by the expression 3x+2. Which Expression can be used to represent the difference in the perimeter of Rectangle ABCD and Rectangle PQRS
Answers
This question is Incomplete
Complete Question
Rectangle ABCD has a length represented by the expression 2x – 3, and a width represented by the expression 4x + 5. Rectangle PQRS has a length represented by the expression x – 1, and a width represented by the expression 3x + 2. Which Expression can be used to represent the difference in the perimeter of Rectangle ABCD and Rectangle PQRS?
a) 2x + 1
b) 4x + 2
c) 4x + 6
d) 20x + 6
Answer:
b) 4x + 2
Step-by-step explanation:
The Formula for the Perimeter of a Rectangle = 2(L + W)
= 2L + 2W
Hence:
For rectangle ABCD
Length = 2x - 3
Width = 4x + 5
Hence, the Perimeter is :
P = 2L + 2W
P = 2(2x - 3) + 2(4x + 5)
P = 4x - 6 + 8x + 10
P = 4x + 8x -6 + 10
P = 12x + 4
For Rectangle PQRS
Length = x - 1
Width = 3x + 2
Hence, the Perimeter is :
P = 2L + 2W
P = 2(x - 1) + 2(3x + 2)
P = 2x - 2 + 6x + 4
P = 2x + 6x - 2 + 4
P = 8x + 2
The Expression that can be used to represent the difference in the perimeter of Rectangle ABCD and Rectangle PQRS is
Perimeter of Rectangle ABCD - Perimeter of Rectangle PQRS
(12x + 4) - (8x + 2)
12x + 4 - 8x - 2
12x - 8x +4 -2
4x + 2
Option b) 4x + 2 is the correct option.
what is the answer to x/2+3<12 ?
Answers
Answer:
x<18
Step-by-step explanation:
Help plz if someone could answer this problems soon as possible that would be great. It is a geometrical proof Given: angle 1 and angle 2 are complementary angle 1 is congruent to angle 3 and angle 2 is congruent to angle 4 prove: angle 2 and 3 are complementary
Answers
Answer:
<2 + <3 = [tex]90^{o}[/tex]
Thus, angles 2 and 3 are complementary.
Step-by-step explanation:
Complementary angles are two or more angles that their sum equals [tex]90^{o}[/tex]. Given that: i. <1 and <2 are complementary
ii. <1 ≅ <3
iii. <2 ≅ <4
Prove that: <2 and <3 are complementary
Proof:
<1 + <2 = [tex]90^{o}[/tex] (complementary angles)
<1 ≅ <3 (congruent property)
<2 ≅ <4 (congruent property)
⇒ <3 + <4 = [tex]90^{o}[/tex] (complementary angles by congruent property)
Since <1 ≅ <3,
∴ <2 + <3 = [tex]90^{o}[/tex]
Thus, angles 2 and 3 are complementary
Please help!
I will mark brainliest!! ;)
Answers
Answer:ok
Step-by step explanation:
please help, i need it done soon
Answers
Answer:
Point C i think is: (33/8, 0)
Step-by-step explanation:
I hope this helps -w-
Please help! I'm in a hurry
Answers
Answer:
the answer is 62
Step-by-step explanation:
you take 180 and subtract 118
Answer:
The answer should be 62, but i'm not positive so correct me if i'm wrong!
Explanation:
What I did is i added 118 and 118 then subtracted 360 by the sum. After that I divided the result by two which gave me 62, and I am almost sure that is the answer, but like I said i'm not positive. :)
if i won 10 games out of 16, how many games would i need to paly to win 50
Answers
Answer:
19
Step-by-step explanation:
Which equation has no solutions?
1. 2(x + 3) = 3(2x + 2)
2. -x + 3 + 5x = 4x + 3
3. 2(2x – 10) + 32 = 4(x+3)
4. 3(5x + 4) – 20 = 15x -4
Answers
Answer:
4. 3(5x+4)-20=15x-4 has no solution
Step-by-step explanation:
3(5x+4)-20 = 15x - 4
15x-8=15x-4
15x = 15x+4
0=4
No Solution
Answer:
3(5x + 4) – 20 = 15x -4
Step-by-step explanation:
2x + 6 = 6x + 6 One solution 4x = 0
4x + 3 = 4x + 3 infinite solutions
4x + 12 = 4x + 12 infinite solutions
15x - 8 = 15x - 4 no solutions -8 ≠ -4
I solved the problems ahead of time if you need the work tell me.
No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true. Note that we have variables on both sides of the equation.
√27
A. 3√3
B. 6√7
Which one?
Answers
Answer:
√27 = A. 3√3
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Exact Form:
3 √ 3
At an opening of a new art gallery, the owner hired a caterer to serve light snacks. The owner created a budget for 150 people to attend the opening, with a per person food cost of $4.25. If the number of guests attending the opening was 56% more than expected, then how much was the final food cost?
$234.00
$357.00
$637.50
$994.50
Answers
Answer: $994.50
Step-by-step explanation:
From the question, we are informed that the owner created a budget for 150 people to attend the opening, with a per person food cost of $4.25. This means that the total cost to cater for the 150 people will be:
= 150 × $4.25
= $637.5
We are further told that the number of guests attending the opening was 56% more than expected, then the final food cost will be represented by:
= $637.5 + (56% × $637.5)
= $637.5 + (0.56 × $637.5)
= $637.5 + $357
= $994.50
If your UBER and your bill is 20$ they will ask if you want to leave a 4$ tip. what percent tip would that be?
Answers
4 out of 20 is 20% so they left a 20% percent tip
find the equation of the line. Use exact numbers.
help
Answers
Answer:
y = 2x + 4
Step-by-step explanation:
the line intersects the y axis at 4. so, b = 4
For the slope, to make it really easy, you can find a point where the line is on a point purfectly and just count how many times you went up or down and then left or right. Or, you can pick 2points and use the slope formula (y2-y1)/(x2-x1). the slope is 2.