Answer:
0 degrees
120 degrees
240 degrees
Step-by-step explanation:
The solutions to the equation √3sin(x/2) + cos(x) = 1, for 0º < x < 360°, are x = 0°, 120°, and 240°.
The given equation is √3sin(x/2) + cos(x) = 1.
Rearrange the equation to isolate the term with sin(x/2):
√3sin(x/2) = 1 - cos(x)
Square both sides of the equation to eliminate the square root:
3sin²(x/2) = (1 - cos(x))²
Apply the trigonometric identity sin²(x/2) = (1 - cos(x))/2:
3(1 - cos(x))/2 = (1 - cos(x))²
Multiply both sides by 2 to remove the fraction:
3(1 - cos(x)) = 2(1 - cos(x))²
Expand the square on the right side:
3 - 3cos(x) = 2(1 - 2cos(x) + cos²(x))
Simplify and rearrange the equation:
3 - 3cos(x) = 2 - 4cos(x) + 2cos²(x)
Combine like terms:
2cos²(x) - cos(x) - 1 = 0
Factor the quadratic equation:
(2cos(x) + 1)(cos(x) - 1) = 0
we can solve for x by setting each factor equal to zero:
2cos(x) + 1 = 0:
cos(x) = -1/2
x = 120°, 240° (in the range 0° < x < 360°)
cos(x) - 1 = 0:
cos(x) = 1
x = 0° (in the range 0° < x < 360°)
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True or False
100% of any number must greater than or
equal to 100
Pleaseeeee help meeee
I will mark brainliste
Answer:
24
Step-by-step explanation:
Cross-multiply 8 times 9
Then divide the answer to 8 x 9 by 3
I have no idea what I'm doing pls help.
Answer:
Step-by-step explanation:
You did the number 3 right because you multiply 3 x 25 is 75.
All you have to do is find what to multiply by the "x" numbers and find the "y" equal answers.
Hope this helps.
Have a good day ma'am/sir.
Be safe!
Ram has 35 gel pens.. please help this is for kahn academy
Answer:
After the 35 gel pens??
Step-by-step explanation:
What is the formula for calculating a residual value
The residual value indicates how well the regression model fits the observed data, with a residual of zero indicating a perfect fit.
In the context of linear regression analysis, the residual value represents the difference between the observed value of the dependent variable and the predicted value. The formula for calculating the residual value can be expressed as:
Residual = Observed Value - Predicted Value
To calculate the residual value, you need to have a regression model that predicts the value of the dependent variable based on the independent variable(s). Once you have the predicted value, you subtract it from the corresponding observed value to obtain the residual.
For example, if you have an observed value of 10 and the predicted value from the regression model is 8, the residual would be:
Residual = 10 - 8 = 2
The residual value indicates how well the regression model fits the observed data, with a residual of zero indicating a perfect fit.
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y = -6x
y = -8x + 6
?????
Answer:
x=3
Step-by-step explanation:
-6x=-8x+6
+8 +8
2x=6
2/2 6/2
x=3
A new car is purchased for $49,000 and over time its value depreciates by one half
every 4.5 years. What is the value of the car 21 years after it was purchased, to the
nearest hundred dollars?
Answer: it’s 1900
Step-by-step explanation:
The value of the car 21 years after it was purchased, to then earest hundred dollars is $1900.
What is the value of the car in 21 years?
When an asset depreciates, it means that it declines in value with the passage of time.
The formula for calculating future value:
FV = P (1 +-r)^n
FV = Future value P = Present value R = rate of decline = 50%N = number of years : 21 / 4.5 = 4.6749,000(0.5^4.67) = $1900
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Evaluate 4a if a =2 so what is the answer
Answer:
The answer is 8.
Step-by-step explanation:
hope that helps
4a
4(2)
=8
Which point would map onto itself after a reflection across the line y = –x?
(–4, –4)
(–4, 0)
(0, –4)
(4, –4)
Answer:
its D
Step-by-step explanation:
Answer:
D. (4,-4)
Step-by-step explanation:
because y (the second one) equals x but just with a minus
plz do this ill mark brainly and its worth 15 points plz
Answer:
Step-by-step explanation:
9. discount is 9 dollars. sale price is 36 dollars
10. discount is 135 dollars sale price is 315
11. discount is 7.20 dollars, sale price is 41.80
12. discount is 37.50. sale price is 112.50
13. discount is 590. sale price is 870
14. discount is 42. sales price is 42
15. discount is 32.50. sales price is 292.50
16. discount is 29.75. sales price is 56.25
17. The similarities is that there's a difference in the original price, usually in a percentage. The difference is that a markup is a increase whereas a discount is a decrease
Answer:
just look up the questions on the internet
for exaple look up 20% of 45 is what for discount then do 45-discount=sales price
Step-by-step explanation:
1. Choose the value for x that would make this inequality true. x > 5
a. 3
b.-6
c. 7
d.4
Divide. Write the quotient in lowest terms. 1 7/9÷4/5
Answer:
2 units and 2/9
Step-by-step explanation:
Answer: 236.25
Step-by-step explanation:
The Sheikra roller coaster at Busch Gardens in Tampa, Florida, features a 138-foot vertical drop.
What is the slope of the coaster track at this part of the ride?
PLEASE DO IT it is due in 5 minutes
If a, b are real numbers and 7a + i(3a - b) = 14 - 6i , then find the values of a and b.
If a, b are real numbers and 7a + i(3a - b) = 14 - 6i, then find the values of a and b. Therefore, the value of a = 2 and the value of b = 12. 3.
The value of the variables 'a' and 'b' of the complex equation will be 2 and 12, respectively.
What is a complex number?The complex number is the combination of the real part and the imaginary part. Then the complex number is given as a+bi where the value of i is √(-1) and the value of i² is -1.
The equation is given below.
7a + (3a - b)i = 14 - 6i
Compare the real part of the equation, then we have
7a = 14
a = 14 / 7
a = 2
Compare the imaginary part of the equation, then we have
3a - b = - 6
3 x 2 - b = -6
6 - b = - 6
b = 6 + 6
b = 12
The value of the variables 'a' and 'b' of the complex equation will be 2 and 12, respectively.
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Someone say 3x1 is 5 it that correct why or why not
Answer:
Wrong
Step-by-step explanation:
Any number times one equals that number
3x1=3 not 5
Directions are on the picture. I just need to figure out
Answer:
Bruh so easy hahahahahaha
When would we need to calculate circumference of a circle? Area of a circle?
Select the correct answer from the drop-down menu.
Javier has a basket of oranges and apples. The number of oranges is 2 more than twice the number of apples in the basket. The difference of half the number of oranges and half the number of apples is 4.
An equation created to find the number of apples Javier has in the basket will have _________
A. No Solution
B.One Solution
C.Infinitely many solutions
Answer:
D
Step-by-step explanation:
Got 100%
Answer:
I think that it's C.Infinitely many solutions
Step-by-step explanation:
Hope this helps
df+gh=k
solve for h.
please help!!
Answer:
15
Step-by-step explanation:
Solve the following quadratic equation
2x²+7x=15
Answer:
x = - 5 ; x = 3/2
Step-by-step explanation:
Start by subtracting 15 from both sides to get to an equation in standard form: a x^2 + b x + c= 0 so we can use the quadratic formula to solve for "x".
2 x^2 + 7x - 15 = 0
Then:
[tex]x=\frac{-7+/-\sqrt{49-4(2)(-15)} }{4} \\x=\frac{-7+/-\sqrt{169} }{4}\\x=\frac{-7+/-13}{4}\\x =-5\\or\\x=3/2[/tex]
At a little-known vacation spot, taxi fares are a bargain. A 16-mile taxi ride takes 24 minutes and costs $9.60. You want to find the cost of a 42-minute taxi ride. What unit price do you need?
Answer:
$32.90
Step-by-step explanation:
You would need $32.90 to get travel by the taxi.
how much of a 3/4 of cup serving is in a 2/3 cup of yogurt?
Answer:
8/9
Step-by-step explanation:
could i have brailiest plz it isnt a must tho thx
Although the first quarter of 2002 was quite dismal on Wall Street, mutual funds investing in gold companies rose an average of 35.2%. Assume that the distribution of returns in the first quarter of 2002 for mutual funds specializing in gold companies is fairly symmetrical with a mean of 35.2% and a standard deviation of 20%. If random samples of 16 gold stock funds were selected:
Complete Question
Although the first quarter of 2002 was quite dismal on Wall Street, mutual funds investing in gold companies rose an average of 35.2%. Assume that the distribution of returns in the first quarter of 2002 for mutual funds specializing in gold companies is fairly symmetrical with a mean of 35.2% and a standard deviation of 20%. If random samples of 16 gold stock funds were selected:
90% of the sample mean returns are between what two values symmetrically distributed around the mean?
Answer:
The two values symmetrically distributed around the mean are
21.87\% and 43.17\%
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 16[/tex]
The sample mean is [tex]\= x = 0.352[/tex]
The standard deviation is [tex]\sigma = 0.20[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n -1[/tex]
=> [tex]df = 16 -1[/tex]
=> [tex]df = 15[/tex]
From the question we are told the confidence level is 90% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally from the t distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of [tex]df = 15[/tex] is
[tex]t_{\frac{\alpha }{2} , 15 } = 2.13 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 2.13 * \frac{ 0.20 }{\sqrt{16} }[/tex]
=> [tex]E = 0.1065 [/tex]
Generally 90% confidence interval is mathematically represented as
[tex]0.3252 -0.1065 < \mu < 0.3252 + 0.1065 [/tex]
=> [tex]0.2187 < \mu < 0.4317 [/tex]
converting to percentage
[tex]0.2187 * 100 < \mu < 0.4317 * 100 [/tex]
=> [tex] 21.87\% < \mu < 43.17\% [/tex]
Hence the 90% of the sample mean returns are between 21.87\% and 43.17\%
This is just a made up question I made.
6(2 + 9) - 11
Answer:
55
Step-by-step explanation:
2+9=11x6=66-11=55
In 7 hours of driving, Vince travelled 364 kilometers. If he travels at the same rate, what distance will he travel in 12 hours? kilometers
Answer:
52 times 12 = 624
Step-by-step explanation:
364 divided 7 = 52
52 times 12 = 624
How much is 10% of 65 gallons? Write your answer as a decimal number.
Answer:
6.5 Gallons
Step-by-step explanation:
If 10% is 6.5 then just divide 65 by 10
will mark brainliest please yall
Answer:
c
Step-by-step explanation:
Just think about the question
c look at the picture carefully
you will understand it more clearly
Select all the correct answers.
Which expressions are equivalent to this exponential expression?
(52)-3.54
5-4
25
0 0 0 0 0
52
5-1
051
Reset
Reset
Next
Answer:
first and third and fifth
Step-by-step explanation:
big brain time
Answer:
25 and 5^2
5 to the power of two is 25, because 5 * 5 is 25. Therefore the two are the same.
Step-by-step explanation:
♩ What can I say except your welcome? ♪ ♫
4t^2-6 when t is 3
Math question
Answer:
30
Step-by-step explanation:
4t^2-6 when t is 3
Since we know t=3, we can substitute that in
4(3^2) - 6
Simplify.
3^2 = 9
= 4(9) - 6
= 36 - 6
= 30