Answers
Answer:
Step-by-step explanation:
a). [tex]\text{cos}^4(\frac{\theta}{6})-\text{sin}^4(\frac{\theta}{6})=\text{cos}\frac{\theta}{3}[/tex]
By solving left hand side of the equation,
= [tex][\text{cos}^2(\frac{\theta}{6})-\text{sin}^2(\frac{\theta}{6})][\text{cos}^2(\frac{\theta}{6})+\text{sin}^2(\frac{\theta}{6})][/tex]
= [tex][\text{cos}^2(\frac{\theta}{6})-\text{sin}^2(\frac{\theta}{6})](1)[/tex] [Since, cos²a + sin²a = 1]
= [tex]\text{cos}\frac{\theta}{3}[/tex] [Identity used → cos²a - sin²a = cos(2a)]
Hence, left hand side of the given equation = Left hand side of the equation.
Related Questions
An equation for the line whose slope is 4 and which passes thorough the point (-5,3)
Answers
Answer:
y = 4x + 23
Step-by-step explanation:
[tex]y-y_{1}=m(x-x_{1} )\\y-3=4(x-(-5))\\y-3=4(x+5)\\y-3=4x+20\\y=4x+23[/tex]
The equation of the line is required.
The equation of the line is [tex]y=4x+23[/tex]
Equation of line[tex]m[/tex] = Slope of line = 4
Point = [tex](-5,3)[/tex]
[tex]x_1=-5[/tex]
[tex]y_1=3[/tex]
Equation of a line is given by
[tex]y-y_1=m(x-x_1)\\\Rightarrow y-3=4(x-(-5))\\\Rightarrow y-3=4x+20\\\Rightarrow y=4x+20+3\\\Rightarrow y=4x+23[/tex]
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Approximate the percent of values on the box and whisker plot that lie below 68?
25
49
50
75
Answers
You work as a cashier for a grocery store and earn $5 per hour. You also mow lawns and earn $10 per hour. You want to earn at least $50
per week, but would like to work no more than 10 hours per week.
Which system of inequalities, along with y0 andx
0, would you use to solve the real-world problem?
Answers
The required inequalities are x + y ≤ 10 and 5x + 10y ≥ 50
What is an inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given that, You work as a cashier for a grocery store and earn $5 per hour. You also mow lawns and earn $10 per hour. You want to earn at least $50 per week, but would like to work no more than 10 hours per week.
Let, you work at grocery story (x), and you work mowing lawns (y)
You want to work no more than 10 hrs
So, first inequality will deal with hrs.
x + y ≤ 10....(i)
A less than or equal to sign tells that you do not want to work more than 10 hrs, but you can still work 10 hrs, so we include the equal sign as well.
And,
Grocery store (x) earning $5 per hr and lawn mowing (y) earning $10 per hr, making at least $50...
Now we will make an inequality dealing with the $
5x + 10y ≥ 50.....(ii)
A greater than or equal to sign tells that, you want to make 50 or more, so we include the equal sign.
So, the inequalities are :
x + y ≤ 10
5x + 10y ≥ 50
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67 x 10 to the fourth power
Answers
Answer:
670000
Step-by-step explanation:
67 * 10^4
67 * (10*10*10*10)
= 670000
Answer:
670,000
Step-by-step explanation:
You'd do 10^4 first which is 10,000.
Then multiply 10,000 by 67.
67*1 is 67. Add the 4 zeros and you get...
670,000
What is the solution of the equation:
[tex] \sqrt{5 - 2x } = 3i[/tex]
O 1
О 4
O 7
О -2
Answers
Because 5-2 is seven so x =7
write an equation that is perpendicular to x - 3y =3 and passes through the point (5,-9) in slope-intercept form.
Answers
9514 1404 393
Answer:
y = -3x +6
Step-by-step explanation:
The perpendicular line will have the coefficients of x and y swapped (and one of them negated), and will have a constant appropriate to the point the line needs to go through.
The equation will look like ...
x -3y = 3 . . . . . . . . . . . . . given line
3x +y = constant . . . . . . perpendicular line
where "constant" can be found by substituting for x and y.
3x +y = 3(5) +(-9)
3x +y = 6 . . . . equation in standard form
To put this in slope-intercept form subtract 3x:
y = -3x +6
Just need 15 and 16 help will mark as brainliest answer
Answers
Answer:
15. 12, 16. 18
Step-by-step explanation:
a = pi*r^2
15) 36pi = pi*r^2 --> 36 = r^2 --> 6 = r --> 12 = d
16) 81pi = pi*r^2 --> 81 = r^2 --> 9 = r --> 18 = d
What is the slope of the line containing A(6,-2) and
B(-4,4)?
Answers
Answer: -0.6 or -3/5.
Step-by-step explanation: m = 6 / -10 = 3 / -5 = -0.6
Answer:
-0.6
Step-by-step explanation:
Hopefully this helps
Jesse uses the function f(x) = 0.25x + 20 to calculate her phone bill each month, in dollars, where x is the number of minutes she uses. What does 0.25 represent?
Answers
Answer:
c hope this helps!
Step-by-step explanation:
HELP ASAP!! WILL MARK BRAINLIST!!!!!!!
Derek Jeter, the short stop for the New York Yankees, a major league baseball team, played in 159 games in 2012 and hit 15 home runs. If he plays a total of 1272 games in his career, approximately how many home runs will he hit?
[A] Write a proportion that is defined by this situation.
[B] Explain how the cross product is used to solve the problem.
[C] Answer the question.
Answers
Answer:
120 home runs.
Step-by-step explanation:
Let x be the number of home runs after playing 1272 games.
We have been given that Derek Jeter, the short stop for the New York Yankees, a major league baseball team, played in 159 games in 2012 and hit 15 home runs.
Let us find the probability of hitting home runs in next game.
To find the total number of home runs Derek will hit in his career, we will use relative probability, which is the ratio of the occurrence of a singular event and the total number of outcomes.
So we can set a proportion as:
Let us multiply both sides of our equation by 1272.
Therefore, Derek Jeter will hit approximately 120 home runs in his career.
In his career, Derek Jeter will probably hit 120 home runs.
What is a proportion?A proportion is an equation that sets two ratios at the same value.
Let x be the number of home runs after playing 1272 games.
And given, Derek Jeter hits 15 home runs in 159 games.
To find the number of home runs he hit in 1272 games,
x = 1272 x 15 / 159
x = 120
And to find the proportion:
15x = 120
x = 120/15
x = 8
We can calculate the Cross Product this way:
cross product with angle and unit vector
a × b = |a| |b| sin(θ) n
Therefore, Derek Jeter will hit approximately 120 home runs in his career.
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a line with the slope of 1/3 passes through the points of (6,0). what is the equation in slope intercept form?
Answers
Answer:
y = 1/3x -2
Step-by-step explanation:
the equation for slope intercept form is y= mx + b.
m is the slope and b is where the line crosses the y-axis which is called the y-intercept.
to find the y-intercept plug in a coordinate on the line (6,0)
0 = 1/3(6) + b
then solve for b by first multiplying 1/3 by 6
0 = 2 + b
subtract 2 from both sides
-2 = b
and then you can plug b into the equation
y = 1/3x - 2
need help on work!!!
Answers
Answer:
you have chosen the correct answer
Step-by-step explanation:
the answer is 9.45
3/6.30=4.5/x
4.5*6.30=28.35
28.35/3= 9.45
can someone help me please
Answers
Answer:
the third one ( -7+u+8t)
Step-by-step explanation:
first you add the ts together and you get 8. Then u keep the U and cancel out the +2 nad the -2. Then you are left with your answer. have a nice day
tatiana earns money by babysitting her little cousin. when she babysits for 7 hours she earns 94.50. which equation represents her total wages based on the hours that she works?
answers:
y=2x
y=7x
y=27x
y=13.50x
Answers
Answer:
y=13.50x
Explanation:
94.50/7 = 13.5
hold on i think im wrong who knows sorry
true or false a rectangle with four right angles is a square
Answers
Answer:
False.
Step-by-step explanation:
Every rectangle had 4 right angles, including squares, which are also rectangles! ^^ Squares are basically just special rectangles!
Will mark brainliest
Answers
Answer:b),c),d) are correct for sure. e) may be correct ,y= -2, so,f is not correct
Step-by-step explanation:
Investors buy a studio apartment for $200,000 of this amount they have a down payment of $50,000 their down payment is what percent of the purchase price what percent of the purchase price would a $70,000 down payment be their down payment is what percent of the purchase price
Answers
Answer: 35%
Step-by-step explanation:
$70,000 was the down payment for a total price of $200,000.
Down payment percentage = 70,000 / 200,000
= 0.35
= 35%
Identify the x-intercept and the y-intercept of the graph of 6x + 15y = −30.
A. x-intercept: 2; y-intercept: 5
B. x-intercept: −2; y-intercept: −5
C. x-intercept: 5; y-intercept: 2
D. x-intercept: −5; y-intercept: −2
Answers
Answer:
D
Step-by-step explanation:
CAN U PLZ HELP MEE DONT SCROLL DOWN ILL GIVE BRAINLLEST PLZ PLZZZZ
Answers
Answer:
75.4
Step-by-step explanation:
v = pi * r^2 * h
v = 3.14 * 4 * 6
v= 3.14 * 24
v= 75.36 m^3
to the nearest tenth is 75.4 m^3
Pls explain how you got the answers
Answers
Answer:
1. 2.64172
2. 9.94194
3. 76.2
4. 10.9728
5. 49.2126
6. 443.603
7. 402.336
8. 259.08
9. 328.084
10. 7.57082
11. 7.25748
12. 55.1156
13. 127
14. 22.7125
15. 189.598
Step-by-step explanation:
1. liters to gallons 1:0.264172
10 L = 2.64172 gal.
2. kilometers to miles 1:0.621371
16 Km = 9.94194 mil.
3. inches to centimeters 1:2.54
30 in = 76.2 cm
4. yards to meters 1:0.9144
12 yd. = 10.9728 m
5. meters to feet 1:3.28084
15 m = 49.2126 ft
6. fluid ounces to milliliters 1:29.5735
15 fl oz = 443.603 mL
7. miles to kilometers 1:1.60934
250 mi = 402.336 km
8. feet to meters 1:0.3048
850 ft = 259.08 m
9. meters to feet (see problem 5)
100 m = 328.084 ft
10. quarts to liters 1:0.946353
8 qt = 7.57082 L
11. pounds to kilograms 1:0.453592
16 lbs = 7.25748 kg
12. kilograms to pounds 1:2.20462
25 kg = 55.1156 lbs
13. inches to centimeters (see problem 3)
50 in = 127 cm
14. gallons to liters 1:3.78541
6 gal = 22.7125 L
15. kilograms to pounds (see problem 12)
86 kg = 189.598 lbs
PLEASE HELP!!! the values in the table reresent a function
Answers
Answer:
7/3 or 3/7
Step-by-step explanation:
it says it on the thing you just have to find the numbers and we're they go
The function d = 8f + 24 represents the monthly cost d (in dollars) of a group of f members joining the fitness club. a. Identify the independent and dependent variables (don’t say f and d).
Answers
Answer:
D represents the dependent variable: the monthly cost in dollars is your independent variable
F represents the independent variable: the number of members joining the fitness club
Step-by-step explanation:
The amount of money depends on how many members come and join the fitness club because more money is spent more with more members
(help asap!!!!) Wyatt is 6 years older than 2 times the age of his nephew. Wyatt is 32 years old. How old is his nephew?
Answers
Answer:
His nephew is 13
Step-by-step explanation:
Reverse the given process,
32 - 6 = 26,
26 ÷ 2 = 13,
The answer is 13.
Answer:
13
Step-by-step explanation:
13 times 2 plus 6 is 32
A car travels 56 miles per hour. At this rate, how long will it take for the car to travel 336 miles?
Answers
Answer:
it will take 6 hours
Step-by-step explanation:
336/56=6
Need help?????????!!!!!!!!!!!!!
Answers
Answer:
29=b
30=a
Step-by-step explanation:
Juan's meal costs $15.35. He leaves a 25% . Find the total cost of the meal
Answers
Answer:
$19.19
Step-by-step explanation:
15.35 x 0.25 = 3.8375
15.35 + 3.8375 = 19.1875
Rounded it will be $19.19
If the coordinates of point E are (-4, y), what is the value
of y?
O -8
O -4
O0
O8
Answers
The value of y is -8
What is slope of the line?"The slope of tee line passing through points [tex](x_1,y_1),(x_2,y_2)[/tex] is [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]"
What is y-intercept?"The point at which the graph intersects the Y-axis."
What is slope intercept form of the line?"y = mx + c, where m is the slope of the line and c is the Y-intercept."
For given question,
We have been given the graph of a line.
From the graph, we can observe that the line is passing through the points (4, 4) and (-6, 0)
Using slope formula the slope of the line would be,
[tex]\Rightarrow m=\frac{4-(-6)}{4-0}\\\\\Rightarrow m=\frac{10}{4}\\\\\Rightarrow m=\frac{5}{2}[/tex]
Also, the line intersects y-axis at y = 2
This means the y-intercept is c = 2
Using the slope-intercept form of the line the equation of the line would be,
[tex]y=mx+c\\\\y=\frac{5}{2}x+2[/tex]
Point E(-4, y) lies on the given line.
So, this point satisfies the equation of the line.
[tex]\Rightarrow y=\frac{5}{2}(-4)+2\\\\ \Rightarrow y=-10+2\\\\\Rightarrow y=-8[/tex]
Therefore, the value of y is -8
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At the beginning of the month, Leslie's lunch account has a balance of $48.07. If lunch costs $2.53 per day, for how many days will Leslie be able to purchase lunch before her account runs out of money?
Answers
Answer:
19 days
Step-by-step explanation:
Step one:
given data
Leslie's lunch account has a balance of $48.07.
the cost of lunch per day is $2.53 per day
Required
The duration that the account will last if Leslie purchases lunch every day
Step two:
to get the answer we need to divide the account balance by the cost of the lunch
= 48.07/2.53
=19 days
2 math question please help me 30 point
Answers
Answer:
1. B: 12 BB 18 FB,, 2.
Step-by-step explanation:
1. make the equation (198 + 33x) + 24x = 882 because there are a certain number of each ball (x) and 6 more footballs. since each football is 33 dollars, you do 33 x 6 which is 198, and then keep 33x and 24x. It is all equal to 882 since that is the final price. First, you subtract 198 on each side and combine the like terms (33x + 24x). Now it is 684= 57x and you divide 684 by 57, which equals 12. That means that there are 12 basketballs and 12 + 6 footballs, which is 18.
2. You cannot solve the problem or do any problem without distributing first. I'm unsure how else to explain it.
can someone help me !
Answers
Answer:
Your answer is 3 100000000000% i did the math lol
Step-by-step explanation:
