Answer:
21 degrees
Step-by-step explanation:
I did it on the calculator
Functions, f and g are given by f(x)= 3+ cos x and g(x) = 2x, x is a real number. Determine the value of c for which f(g(x))= g(f(x)) where 0[tex]\leq[/tex] x<2[tex]\pi[/tex]
9514 1404 393
Answer:
x = π
Step-by-step explanation:
You want f(g(x)) = g(f(x)):
3 +cos(2x) = 2(3 +cos(x))
cos(2x) -2cos(x) = 3 . . . . . . . rearrange
2cos(x)²-1 -2cos(x) = 3 . . . . . use an identity for cos(2x)
2(c² -c -2) = 0 . . . . . . . . . . . . substitute c = cos(x)
(c -2)(c +1) = 0 . . . . . . . . . . . factor
c = 2 (not possible)
c = -1 = cos(x) . . . . . true for x = π
The value of x that makes f(g(x)) = g(f(x)) is x = π.
_____
Additional comment
The substitution c=cos(x) just makes the equation easier to write and the form of it easier to see. There is really no other reason for making any sort of substitution. In the end, the equation is quadratic in cos(x), so is solved by any of the usual methods of solving quadratics.
Instructions: Determine if the two triangles in
the image are congruent. If they are, state how
you know by identifying the postulate.
th
The 2 triangles are congruent
by solving a pair of linear equation X + Y is equal to 20 and x-y=10 the value of 'x' and 'y' are
Answer:
x=15, y=5
Step-by-step explanation:
x+y=20
x-y=10
Adding both equations;
(x+x) + (y-y) = 20+10
2x = 30
x = 30/2 = 15
Substitute x=15 into x+y=20
y= 20-x = 20-15= 5
Select the correct answer.
As part of a class project, a university student surveyed the students in the cafeteria lunch line to look for a relationship between eye color and hair color among students. The table below contains the results of the survey.
Answer: Choice B) 0.27
=========================================================
Explanation:
There are a lot of data values here, and it's possible to easily get lost in them. However, we're asked only about students with blond hair. So we only focus on the first row. Ignore everything else.
We see that there are 78 of these students total. Of this total, 21 have green eyes.
Therefore, the relative frequency of blonds with green eyes is 21/78 = 0.2692 which rounds to 0.27; so that's why the answer is choice B.
find the value and express it in standard form : 5×10^8×2×10^11
Answer:
1*10^20
Step-by-step explanation:
5×10^8×2×10^11= 5*2*10^(8+11)= 10*10^19= 10^ (1+19)= 10^20= 1*10^20.
please mark this answer as brainlist
If 2/3 of the girls in class have brown eyes and 1/4 of the girls have blue eyes what fraction of the girls in class have neither blue or brown
Cheyenne's bi-weekly gross pay is $529.81. She sees that $18.54 was deducted for Medicare tax. What percent of Cheyenne's gross pay has been withheld for Medicare tax? Round to the nearest tenth. (2 points)
0.35%
2.2%
3.5%
Answer:
I got 3.5%
Step-by-step explanation:
Hope this helps
what is 2x2x2x3x3 please give me answer
Answer:
The answer is 72.
I am right .
In a certain country people own a total of about 352 million fish, cats, and dogs as pets. The number of fish owned is 14 million more than the total number of cats
and dogs owned, and 11 million more cats are owned than dogs. How many of each type of pet do people in this country own?
Answer:
dogs = 79
dats = 90
fish = 183
Step-by-step explanation:
let the total number of dogs owned be x
no. of cats owned = x+11
no. of fish owned = x+11+x+14= 2x+25
hence,
2x+25+x+11+x=352
4x=316
x=316/4= 79mil
no. of cats owned = 79 + 11 = 90
no. of fish owned = 2(79)+25=183
Chen rode his skateboard 3/3/4 miles in 34 of an hour.
What was his average speed in miles per hour?
_[blank]_ miles per hour
Answer:
5 miles per hour
Step-by-step explanation:
3¾ ÷ ¾ =
15/4 ÷ ¾ =
15/4 x 4/3 =
15/3 = 5
N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to
N?
A) 1 1/2
B 1 1/3
C) 5/3
D) 3/2
Answer:
it should be letter c 5/3 I could be wrong but I hope this help
Ronald types 360 words in 9 minutes.
If he types at a constant rate, how many words does Ronald type in 1 minute?
Answer:
40 per minute.
Step-by-step explanation:
360/9=40
A garden table and a bench cost $717 combined. The garden table costs $67 more than the bench. What is the cost of the bench?
Subtract the difference form the total:
717 - 67 = 650
Divide the remaining amount by 2:
650/2 = 375
The bench cost$375
Solve for the value of x
Answer:
Step-by-step explanation:
This is the Law of Cosines. Use the following formula:
[tex]5.1^2=3.3^2+3.3^2-2(3.3)(3.3)cos(x)[/tex] and simplify to
26.01 = 10.89 + 10.89 - 21.78cos(x) and a bit more to
4.23 = -21.78cos(x) and finally to
-.194214876 = cos(x) and use the 2nd button along with the cos button to find that the missing angle is 101.2 degrees
In a standardized normal distribution the mean is ____ while the standard deviation is ____.
A. 0; 1
B. 1; 0
C. 0; 0
D. 1; 1
Answer:
A. 0; 1
Step-by-step explanation:
Required
Mean and standard deviation of a standardized normal distribution
A standardized normal distribution is represented as:
[tex](\mu,\sigma) = (0,1)[/tex]
This implies that:
[tex]\mu = 0[/tex] -- mean
[tex]\sigma = 1[/tex] --- standard deviation
Hence, (a) is true
find the LCM of 220,440,660 by common division method
Answer: LCM = 1320
Step-by-step explanation:
2 | 220, 440, 660
2 | 110, 220, 330
2 | 55, 110, 165
3 | 55, 55,165
5 | 55, 55 , 55
11 | 11, 11, 11
| 1, 1, 1
= 2 × 2 × 2 × 3 × 5 × 11
= 1320
Therefore the LCM is 1320
Must click thanks and mark brainliest
What is the perimeter of the triangle?
units
Answer:
Does the answer help you?
Determine whether (a) x = -1 or (b) x = 2 is a solution to this equation
Answer:
x = 2 is the solution to x + 1.5 = 3.5
Step-by-step explanation:
x + 1.5 = 3.5
-1.5 -1.5
--------------------
x = 2
Find y when x = 22, if y varies directly as x,
and y = 42 when x = 5.
Answer:
184.8
Step-by-step explanation:
y =kx
k=y/x
k=42/5=8.4
y=8.4*22
Independent simple random samples are selected to test the difference between the means of two populations whose standard deviations are not known. We are unwilling to assume that the population variances are equal. The sample sizes are n1 = 25 and n2 = 35. The correct distribution to use is the:
1) t distribution with 59 degrees of freedom.
2) t distribution with 58 degrees of freedom.
3) t distribution with 61 degrees of freedom.
4) t distribution with 60 degrees of freedom.
Answer:
2) t distribution with 58 degrees of freedom.
Step-by-step explanation:
Population standard deviations not known:
This means that the t-distribution is used to solve this question.
The sample sizes are n1 = 25 and n2 = 35.
The number of degrees of freedom is the sum of the sample sizes subtracted by the number of samples, in this case 2. So
25 + 35 - 2 = 58 df.
Thus the correct answer is given by option 2.
properties of exponents. the answer is 1/2^3 i need help with the work
(2^-1)^2/2×2^0
2^(-1×2)/2^1
2^-2/2^1
2^(-2-1)
2^(-3)
(1/2)^3
Properties used (m^n)^a = m^na
(m)^-n = (1/m)^n
m^0 = 1
m^n/m^a = m^(n-a)
Must click thanks and mark brainliest
Multiplying and bmbFREE BRAINLIST AND POINTS!! Fast! RIGHT ANSWERS ONLY! Scam and wrong answers will be reported and dealed with.
1. 6x(-4)=
3. (-11) x 5=
4. (-12) x (-7)=
5. (-2) x (-10)
6. 4 x (-15)=
Answer:
Step-by-step explanation:
-24
-55
84
20
-60
What is the slope of the points (-2,7) and (2,-5)?
4
-3
-12
3
Answer:
-3
Step-by-step explanation:
Slope is equal to (-5-7)/(2-(-2)=-12/4=-3
Annie is opening a savings account which earns 5.2% interest compounded continuously how much will she need to deposit in the account so she has $2300 after seven years
Hi
let's call X the initial deposit.
the interest rate is 5.2 %
so each year X increase by 1.052.
so we have : X *1.052^7 =2300
X = 2300/1.052^7
X = 1612,94
please note that the deposit was rounded to the next cent. as the result would be 1612,937...
Answer:
1686.22
Step-by-step explanation:
1686.22
2300=P(1+(0.052x7))
2300=P1.364
P=2300/1.364
=1686.217...
=1686.22..
=1686 for the nearest dollar
The table below shows the number of pets kept by the students in a class.
-----------------------------------------------------------
No. of pets | No. of students
-----------------------------------------------------------
0 | 9
1 | k
2 | 2
3 | 1
4 | 2
-----------------------------------------------------------
If the median number of pets is 1, what is the smallest value of k ?
Answer:
The answer for this question is 5
Canada has a population of 33 million while Russia has 144 million inhabitants. Indonesia population is 50% greater then that of Russia while it is only 72% of the population of the United States. How many million people must be added to the United States so that the population of that country becomes 10 times of Canada?
Answer: 30 million people must be added.
Step-by-step explanation: 50% of 144 million is 72 million. You add these to find Indonesia’s population. 144 million + 72 million= 216 million. If 216 million is only 72% of the US population, then divide 216 million by 72 to find 1%. 216 million/72=3 million. Multiply this by 100 to find the US population. 3 million times 100= 300 million. Now, multiply Canada’s population by 10. 33 million times 10= 330 million. Finally, subtract 300 million from 330 million to find the amount needed to make the US population 10 times that of Canada’s. 330 million-300 million=30 million. So , you need 30 million people in order to make the US population 10 times that of Canada’s.
3,6,6,12,9,?,12 what comes next. Options
A.15
B.18
C.11
D.13
Answer:
a
Step-by-step explanation:
3x tables
vhhvffffhhgfgfccf
Answer:
a
Step-by-step explanation:
Has pattern 3x tables. Answer is 15 A.
The polynomial p(x) = x3 – 7x - 6 has a known factor of (x + 1).
Rewrite p(x) as a product of linear factors.
p(x)
Hi there!
[tex]\large\boxed{(x -3)(x + 2)(x + 1)}[/tex]
We can use long division to find the other roots of p(x).
We know that x + 1 is a factor, so:
Set up:
Find how many times that the first term in the divisor goes into the first of the dividend. Subtract from like terms.
x² - x - 6
x + 1 | x³ + 0x² - 7x - 6
x³ + x²
0 - x² - 7x
- x² - x
0 - 6x - 6
-6x - 6
0 0
Therefore, x² - x - 6 is another factor. We can factor this further:
Find two numbers that add up to -1 and multiply into -6. We get:
-3, 2
(x - 3)(x + 2)
The entire polynomial factored is:
(x -3)(x + 2)(x + 1)
The function f(x) = −x2 + 18x − 72 models the daily profit, in dollars, a gym makes for selling memberships, where x is the number of memberships sold, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
(10 points)
Answer:
Step-by-step explanation:
The way to do this so as to streamline both the vertex and finding the zeros is to complete the square. That method will provide us with the vertex, and then we can continue on to factor from that form to find the zeros. Completing the square requires us to set the quadratic equal to 0 then move over the constant, giving us
[tex]-x^2+18x=72[/tex] The leading coefficient HAS to be a positive 1; ours is negative 1 so we factor out the negative to get:
[tex]-(x^2-18x)=72[/tex] Now we're ready to complete the square.
Take half the linear term, square it, and add it to both sides. Our linear term is 18 (from -18x; don't worry about the negative because squaring it makes it positive anyway). Half of 18 is 9, and 9 squared is 81.
BUT on the left we have that -1 sitting out front that refuses to be ignored. What we actually added on to the left side, inside the parenthesis, is -1(81) which is -81. -81 is what we add to the right since that turns out to be what we added to the left:
[tex]-(x^2-18x+81)=72-81[/tex] and we clean that up.
The reason we complete the square is because when we simplify the left side, we end up with a perfect square binomial found from taking the square root of x-squared, the first sign we come to, then the square root of 81:
[tex]-(x-9)^2=-9[/tex]. Move the constant back over to get
[tex]-(x-9)^2+9=y[/tex] telling us that the vertex is (9, 9). In the context of the problem that means that the gym sells on average 9 memberships a day and the profit it makes on average per day is $9.
To factor, we will go back one step to
[tex]-(x-9)^2=-9[/tex] and begin by dividing both sides by -1 to get
[tex](x-9)^2=9[/tex] and undo the squaring by taking the square root of both sides to get
x - 9 = ±3 so
x = 9 + 3 and
x = 9 - 3 so
x = 6 and 12
Those are the zeros. This means that if they sell either 6 or 12 memberships they have a 0 profit. That may sound strange, but in business it does often work like that...selling too many of something makes your company lose money (this is often due to the cost required by you to produce or manufacture the product).
6 times the sum of 5 and K
Answer:
6(5+k)
Step-by-step explanation:
The sum of 5 and k
5+k
6 times the sum
6(5+k)
