The required solutions are θ = π/2 + 2πn, θ = 3π/2 + 2πn, 4πn, 2π + 4πn to the equation of trigonometry functions tan(θ/2) = sin(θ).
The equation of trigonometry functions is given in the question
tan(θ/2) = sin(θ)
Subtract sin(θ) from both sides of the equation,
tan(θ/2) - sin(θ) = 0
sin(θ/2) / cos(θ/2) - sin(θ) = 0
Take LCM in the above equation,
{sin(θ/2) - sin(θ)cos(θ/2)} / cos(θ/2) = 0
sin(θ/2) - sin(θ)cos(θ/2) = 0
-cos(θ)sin(θ/2) = 0
cos(θ) = 0 or sin(θ/2) = 0
cos(θ) = 0 : θ = π/2 + 2πn, θ = 3π/2 + 2πn
sin(θ/2) = 0 : 4πn, θ = 2π + 4πn
Combine all solutions, and we get
θ = π/2 + 2πn, θ = 3π/2 + 2πn, 4πn, 2π + 4πn
θ = 2π + 4πn
Thus, the required solutions are θ = π/2 + 2πn, θ = 3π/2 + 2πn, 4πn, 2π + 4πn to the equation of trigonometry functions tan(θ/2) = sin(θ).
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Answer: c
Step-by-step explanation:
just did it
The point A = (7,4) is dilated from the origin by a scale factor r = 3. What are the coordinates of A' ?
Given:
The coordinates of point A are (7,4).
It is dilated from the origin by a scale factor r = 3.
To find:
The coordinates of A'.
Solution:
If a figure is dilated from the origin by a scale factor k, then
[tex](x,y)\to (kx,ky)[/tex]
Here, the figure is dilated from the origin by a scale factor 3, so the rule of dilation is given by:
[tex](x,y)\to (3x,3y)[/tex]
Using this rule, we get
[tex]A(7,4)\to A'(3(7),3(4))[/tex]
[tex]A(7,4)\to A'(21,12)[/tex]
Therefore, the coordinates of point A' are (21,12).
Willow has 3/4 of a gallon of milk left that has an expiration date in 6 days. If she splits the milk equally among her next 6 bowls of cereal, how much milk will she use in each bowl
Answer:
[tex]\dfrac{1}{8}\ \text{gallons}[/tex]
Step-by-step explanation:
Amount of milk remaining is [tex]\dfrac{3}{4}\ \text{gallons}[/tex]
Number of bowls is [tex]6[/tex].
So, each bowl will contain
[tex]\dfrac{\dfrac{3}{4}}{6}[/tex]
[tex]=\dfrac{3}{4}\times \dfrac{1}{6}[/tex]
[tex]=\dfrac{3}{24}[/tex]
[tex]=\dfrac{1}{8}\ \text{gallons}[/tex]
Hence, each bowl will have [tex]\dfrac{1}{8}\ \text{gallons}[/tex] of milk.
Violet has a points card for a movie theater.
• She receives 20 rewards points just for signing up.
• She earns 12.5 points for each visit to the movie theater.
• She needs 170 points for a free movie ticket.
Write and solve an equation which can be used to determine V,
the number of
visits Violet must make to earn a free movie ticket.
There are 20 pieces of fruit in a bowl and 7 of them
are apples. What percentage of the pieces of fruit in
the bowl are apples?
Answer: 35%
Step-by-step explanation:
What is the solution to the system of linear equations graphed below?
5
4
3
1
+
++
-5 4 3 2
+
1
-11
3
4
x
4
5
Answer: the answer should be B
Step-by-step explanation:
[Function Composition] could someone help me with this answers or show work either is fine
Answer:
f(g(t)) = 2t² + 1
Step-by-step explanation:
You can solve this simply by substituting g(t) into f(t), and solving for f(g(t)):
[tex]f(t) = 2t + 5\\\\g(t) = t^2 - 2\\\\f(g(t)) = 2(g(t)) + 5\\\\f(g(t)) = 2(t^2 - 2) + 5\\\\f(g(t)) = 2t^2 - 4 + 5\\\\f(g(t)) = 2t^2 + 1[/tex]
what is the y intercept of
y=5x-8
Answer:
-8
Step-by-step explanation:
The equation is written in the form y=mx+b, where m is the slope and b is the intercept. So here the intercept is -8.
lightining strikes earth 1000 times per second how many times does it strike in 10 seconds
Answer:
10,000
Step-by-step explanation:
1000 times 10 is 10000
What is the measure of Zx?
Angles are not necessarily drawn to scale.
B
539
Determine whether lines L and m are parallel. Explain your reasoning.
Answer:
Parallel
Step-by-step explanation:
Since, exterior Alternate angles are congruent.
The football team has a total of 50jerseys. There are 35 medium sized jerseys. What percent of the jerseys are medium sized jerseys?
Answer: 70%
Step-by-step explanation:
Total number of jersey = 50.
Total number of medium sized jersey = 35
The percent of the jerseys that are medium sized jerseys will be:
= Number of medium sized / Total number of jersey × 100
= 35 / 50 × 100
= 70%
What is the solution to the following system of equations:
7x + 2y = 24
8x + 2y = 30
A (6, -9)
B (5, -1)
C (-6,4)
D) Infinitely Many
Answer: A, (6, -9)
hope this helps:)
The recommended amount of vitamin c for young adults is 75 milligrams. You drank a new sports drink that has 165 mg of vitamin C. What precent of the daily amount of vitamin C did you drink??
Answer
not sure
Step-by-step explanation:
Answer: 220%
Step-by-step explanation:
165 of 75 can be written as:
165 /75
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
165 /75 × 100 /100 = ( 165 × 100 /75 ) × 1 /100 = 220 /100
Therefore, the answer is 220%
y-2/3x=-6 solve for
Explain and answer plz
thank you
ill mark brainiest
i need help on these questions
Answer:
9. m = -3
11. m = 1
13. m = [tex]\frac{3}{5}[/tex]
Find the slope of the line passing through the points(-3, 7) and (2, -6).
Answer:
-13/5
Step-by-step explanation:
The formula for slope is [ y2-y1/x2-x1 ].
-6-7/2-(-3)
-13/5
Best of Luck!
Katrina is going to order sweatshirts for her girls mentoring group. The sweatshirts will have the group logo printed on the front. Katrina asks two local companies to give her a price.
• MH Designs will charge $21.50 for each of the sweatshirts.
• Print Rich will charge $18 for each sweatshirt plus a one-time setup cost of $70.
Justify how to determine the number of sweatshirts Katrina would need to order from
each company for the costs to be the same.
Answer:
Katrina would need to buy 20 sweatshirts.
Step-by-step explanation:
The number of sweatshirts Katrina would need to order from each company can be determined by forming the linear equation in two variables.
Given :
Katrina is going to order sweatshirts for her girl's mentoring group.Katrina asks two local companies to give her a price.MH Designs will charge $21.50 for each of the sweatshirts. Print Rich will charge $18 for each sweatshirt plus a one-time setup cost of $70.Let the number of sweatshirts orders from company MH Designs be 'x' and the number of sweatshirts orders from company Print Rich be 'y'.
So, the cost for ordering the sweatshirt from the company MH Design is:
[tex]21.50x = c[/tex]
Now, the cost for ordering the sweatshirt from the company Print Rich is:
18y + 70 = c'
Given that the number of sweatshirts Katrina would need to order from each company for the costs to be the same. So :
21.5x = 18y + 70
Now, put the value of x and y so, that in the above equation, both sides become equal.
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An elevator in a high-rise building moves upward at a constant rate. The table shows the height of the elevator above the ground floor after various
The function that models the
table of values is f(t) =
where "t" is the =
and f(t) is the=
determine the height, in feet, of the elevator at 14 seconds
Answer:
168
Step-by-step explanation:
1.3.2 - Harry has a 14 foot pole. He cuts off 4 1/2 feet of it and then cuts off
another 2 %s foot section. How big in the pole now?h
Answer:
9.31 is what I got
So 9.31 feet
Step-by-step explanation:
Helpppppppppppppppppppp
Answer:
option a
1/3=x/42
..........
Which vectors represent the reflection of the vector across the x-axis?
Answer:
<3, 7> and [3 7], b and c
Step-by-step explanation:
multiply the vector by the matrix {1 0} (top row) {0 -1} bottom row. So you flip the sign of the -7 and this gives us +7.
If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?
Answer:
Step-by-step explanation:
Hi! You didn't list the components of the two sets. Both M and T
2x + 3y = -4
y=x+4
What is the solution to the system of linear equations?
Answer:
Step-by-step explanation:
2x+3y=-4
-x+y=4 /*2
2x+3y=-4
-2x+2y=8
5y=4
y=4/5
x=y-4=4/5-4= - 3.2
At yesterday's ball game, 2,842 tickets were sold. The price of each ticket was 7.50. Which amount is closest to the total amount of money received from the ticket sales yesterday's ball game.
Answer
21315
Step-by-step explanation:
URGENT!!!!!!!!!!!!!!! Please help! Will mark brainlest
Answer:
2 nd one
Step-by-step explanation:
Rico bicycles at an average speed of 15.5 miles per hour. What distance will Rico bicycle in 180 minutes?
Answer:
46.5 miles
Step-by-step explanation:
Average speed × Time in hours = Distance
Average speed = 15.5 Miles per hour
Time = 180 minutes
We convert to hours
60 minutes = 1 hour
180 minutes = x
Cross Multiply
60x = 180
x = 180/60
x = 3 hours
Distance = 15.5 miles per hour × 3 hours
Distance = 46.5 miles
The distance Rico will ride his bicycle is 46.5 miles
Find IK
Please help me I’m stuck here Also I don’t feel good I’m sick and this is a quiz
Answer:
30
Step-by-step explanation:
49 - 31 = 18
12 + 18 = 30
In a game of luck, a turn consists of a player rolling 121212 fair 666-sided dice. Let X=X=X, equals the number of dice that land showing "111" in a turn. Find the mean and standard deviation of XXX.
Answer:
mean = 2
standard deviation = 1.3
Step-by-step explanation:
For a binomial random variable X, we can use this formula for mean:
meanX = np
We use this formula for the standard deviation:
sdX = sqrt(np(1 - p))
--------------------------------------------------------------------------------------------------
Since a turn consists of rolling 12 dice, we have n = 12.
The dice are fair and 6-sided, so the probability that each die lands showing "1" is p = 1/6.
meanX = np
= (12)(1/6)
= 2 dice
sdX = sqrt(np(1 - p))
= sqrt((12)(1/6)(5/6))
≈ sqrt(1.667)
≈ 1.291 dice
The mean and standard deviation of the game of luck are;
Mean = 2
Standard deviation = 1.29
We are told that a turn consists of rolling 12 fair six sided dice.
Thus;
n = 12
Probability of each one six sided die showing 1 is;
p = 1/6
Now,the formula for the mean is;
E(X) = np
Plugging in the relevant values gives;
E(X) = 12 × 1/6
E(X) = 2
Now, for the standard deviation, we will use the formula;
Standard deviation = √(np(1 - p))
Plugging in the relevant values;
Standard deviation = √((12 × 1/6)(1 - 1/6))
Standard deviation = 1.29
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pls help due soon !!!!!!!!!!!!!!!!!!!!!!!!!
Answer: B) 12.5
Step-by-step explanation:
In a box-and-whisker plot, the first line(dot) is the smallest value, the second line is the first quartile, the third line is the median, the fourth line is the third quartile, and the last line(dot), is the maximum.
Hope it helps :D
Twelve pounds of oranges are shared equally among 5 people. How many
pounds of oranges does each person get? *
Answer:
12/5 = 2.4 pounds of oranges per person
Step-by-step explanation:
Answer:
2.4 lbs of oranges
Step-by-step explanation:
12÷5
2.4