Answers
Answer:
[tex]\sf\:Negative = \boxed{\sf\:\theta =\pi n_{1}+\frac{5\pi }{6}\text{, }n_{1}\in \mathbb{Z}}\\\sf\: Positive = \boxed{\sf\:\theta =\pi n_{1}+\frac{\pi }{6}\text{, }n_{1}\in \mathbb{Z}}[/tex]
Step-by-step explanation:
[tex]4 - 3 \sec ^ { 2 } \theta = 0[/tex]
Let's solve this.
Isolate sec²θ.
[tex]4 -3 \sec ^ { 2 } \theta = 0\\- 3 \sec^{2}\theta = -4\\3 \sec^{2}\theta=0\\\sec^{2} \theta=\frac{4}{3}[/tex]
Now, we now that, cos θ is the reciprocal of sec θ. Therefore,
[tex]\sec^{2}\theta = \frac{4}{3}\\\cos^{2}\theta = \frac{3}{4}[/tex]
Bring the square root on both the sides of the equation to remove the square.
[tex]\sqrt{\cos^{2}\theta} = \sqrt{\frac{3}{4} }\\\cos^{2}\theta = (+/-) \frac{\sqrt{3} }{2}[/tex]
If,
[tex]\cos\theta = + \frac{\sqrt{3}}{2}\\= cos \left( \frac{\pi}{6} \right)\\\Longrightarrow \boxed{\sf\:\theta =\pi n_{1}+\frac{\pi }{6}\text{, }n_{1}\in \mathbb{Z}}[/tex]
Also if,
[tex]\cos\theta = -\frac{\sqrt{3}}{2}\\= \cos \left(\pi - \frac{\pi}{6}\right)\\= \cos \left({\frac{5\:\pi}{6}\right)\\\Longrightarrow \boxed{\sf\:\theta =\pi n_{1}+\frac{5\pi }{6}\text{, }n_{1}\in \mathbb{Z}}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
Related Questions
The height of a triangle is 4 feet less than the length of its base, b. The area of the triangle is 30 square feet.
Find the base and the height of the triangle.
Answers
Answer:
b = 10 ft , h = 6 ft
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
let base = b theh height h = b - 4
given A = 30 , then
[tex]\frac{1}{2}[/tex] b(b - 4) = 30 ( multiply both sides by 2 to clear the fraction )
b(b - 4) = 60 ← distribute parenthesis on left side by b
b² - 4b = 60 ( subtract 60 from both sides )
b² - 4b - 60 = 0
(b - 10)(b + 6) = 0
equate each factor to zero and solve for b
b - 10 = 0 ⇒ b = 10
b + 6 = 0 ⇒ b = - 6
however, b > 0 , then b = 10
and h = b - 4 = 10 - 4 = 6
then base is 10 ft and height is 6 ft
Joe does 25 sit ups each day.How many sit ups does he do in three weeks remember,, one week has seven days
Answers
25x21= 525 sit ups
Answer:
525
Step-by-step explanation:
So its 25 a day and hes doing it for 21 days because 7*3=21.
so 25*21= 525
What is the slope of a line that passing through the points ( 6 , -10 ) and ( 8, -18) ?
Answers
Answer:
Slope = -4
Step-by-step explanation:
Given:
Point 1: (6,-10)Point 2: (8,-18)Rate of change (Slope) formula:
[tex]\text{Slope} = \dfrac{\text{Rise}}{\text{Run}} = \dfrac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1} }[/tex]
Where:
y₂ = y-coordinate of second point = -18y₁ = y-coordinate of first point = -10x₂ = x-coordinate of second point = 8x₁ = x-coordinate of first point = 6Substitute the coordinates of the given points in the formula to determine the slope of the line (Rate of change).
[tex]\implies \text{Slope} = \dfrac{(-18) - (-10)}{8 - 6 }[/tex]
Finally, let's simplify the fraction on the right hand side as needed.
[tex]\implies\text{Slope} = \dfrac{(-18) + 10}{8 - 6 }[/tex]
[tex]\implies \text{Slope} = \dfrac{-8}{2 } = -4[/tex]
Therefore, the slope of a line that passes through (6 , -10 ) and (8, -18) is -4.
With explanation pls
Answers
Two siblings, Miko and Cheko, receive some pocket money every month. This month, the ratio of Miko's pocket money to Cheko's pocket money is 8:12. Cheko's pocket money is $660. How much must Cheko give to Miko such that each of them have an equal amount of pocket money?
Answers
Cheko must give $110 to Miko so that each of them has an equal amount of pocket money, which is $550.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
The ratio of Miko's pocket money to Cheko's pocket money.
= 8:12
= 2:3
Now,
Let's represent Miko's pocket money as 2x and Cheko's pocket money as 3x.
We know that,
3x = $660
x = $220
Miko's pocket money.
= 2x
= 2($220)
= $440.
To make their pocket money equal,
Cheko needs to give half of the difference between their pocket money to Miko.
The difference between their pocket money.
= $220 (i.e., $660 - $440).
Half of that is $110.
Therefore,
Cheko must give $110 to Miko so that each of them has an equal amount of pocket money, which is $550.
Learn more about ratios here:
https://brainly.com/question/2462048
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can someone help i’ll give brainlist
Answers
Answer: A pet store had a total of 24 fish. And they separated the fish into 4 different fish tanks tanks.
Step-by-step explanation: 24 fish / 4 fish tanks :)
A number cube is rolled two times. The first time it lands showing an even number. The second time it lands showing the number 5. Identify whether this event is independent or dependent. Explain your answer.
A. Independent; the first roll of the number cube affects the probability of the second roll.
B. Dependent; the first roll of the number cube does not affect the probability of the second roll.
C. Independent; the first roll of the number cube does not affect the probability of the second roll.
D. Dependent; the first roll of the number cube affects the probability of the second roll
Answers
Answer:
Independent; the first roll of the number cube does not affect the probability of the second roll.
Step-by-step explanation:
Johnny went to the park at 10:45am and left at 12:00pm. How long was he at the park?
Answers
[tex]\huge\mathcal{\fbox{\fbox\red{Hello}}}[/tex]
[tex]\large\underline{\mathbb{AnSwEr}:}[/tex]
10:45 am to 11:00 am : 15 minutes
11:00 am to 12:00 pm= 1 hour
Total Time= 1 hour 15 minutes.
so he was 1 hour 15 minutes at the park.
went at 10:45 AM
left at 12:PM
to find:the duration he was at the park.
solution:( to find the duration just find the difference of the time he left and went.
= 1 hour 15 mins.
therefore, he was at the park for 1 hour 15 mins.
What is the median, first quartile third quartile and interquartile of 38 46 55 56 558 59 61 65 67 75
Answers
Answer:
Median = 58.5
Q1 = 55
Q3 = 65
Interquartile = 10
Step-by-step explanation:
first let’s correct the data set :
It’s 38 46 55 56 58 59 61 65 67 75 not 38 46 55 56 558 59 61 65 67 75
Data set : 38 46 55 56 58 59 61 65 67 75
Median:
After we put Our data set from Smallest to largest
we define the median as the middle number of the data set but our set consists of an even number which is 10
In this case the median is the average of the two middle numbers which are the 5th and 6th numbers
38 46 55 56 [58 59] 61 65 67 75
Then
Median = (58+59)/2 = 117/2 = 58.5
quartile 1 : It’s just the median of the lower set of numbers which means it’s the median of : 38 46 55 56 58
Then Q1 = 55 because it’s the middle number.
quartile 3 : It’s just the median of the upper set of numbers which means it’s the median of : 59 61 65 67 75
Then Q3 = 65 (Easy to spot)
Interquartile = Q3 - Q1 = 65 - 55 = 10
is y=-x+2 a linear equation
Answers
Answer:
yes it is
Step-by-step explanation:
it is linear because the number can fall on both the x and y axis
Answer:
y = -x + 2 is a Linear Equation.
Step-by-step explanation:
The equation is in slope-intercept form of a linear function.
Slope-intercept form: y = mx + b ---> y = y, -x = mx, b = 2
a high school club is researching a tour package offered by the island kayak company. the company charges $35 per person and $245 for the tour guide. which function represents the total cost, c(x), of this kayak tour package for x club members? A. C(x) = 35x B. C(x) = 35x+245 C. C(x) = 35(x+245) D. C(x) = 35 + (x+245)
Answers
The function that represents the total cost, c(x), of this kayak tour package for x club members is 245 + 35x
How to calculate the total cost on a package?According to the given question, we have the following parameters
Amount charged on tour guide = $245
Let the total number of club members charged be "x", such that if the company charges $35 per person, the total cost on "x" members will be 35x
Determine the total costTotal cost = Amount charged on tour guide + cost of "x" members
Total cost = 245 + 35x
Hence the function that represents the total cost, c(x), of this kayak tour package for x club members is 245 + 35x
Learn more on functions and values here: https://brainly.com/question/2284360
Drag the tiles to the correct boxes to complete the pairs.
Match the x-coordinates with their corresponding pairs of y-coordinates on the unit circle.
tile: 1 (4/5,y), 2(1/3,y) 3(squared2/3,y), 4(2/3,y)
matching graph:
y=+/- squared5/3
y=+/- squared7/3
y=+/-3/5
y=+/-2squared2/3
Answers
Answer:
the answer is b
Step-by-step explanation:
y=+/- squared5/3
y=+/- squared7/3
y=+/-3/5
y=+/-2squared2/3
Simplify the expression. Write your answer as a power.
Answers
When multiplying two powers, if their bases are the same, then you simply add the exponents:
[tex]\frac{8^5*8^3*8^2}{8^8} =\frac{8^{5+3+2}}{8^8} =\frac{8^{10}}{8^8}[/tex]
When dividing two powers, if their bases are the same, you simply minus the exponents.
[tex]\frac{8^{10}}{8^8}=8^{10-8}=8^2[/tex]
Thus when the expression is simplified, the answer as a power is [tex]8^2[/tex]
Answer: 8^2
Hope that helps!
4. Triangle D is the image of Triangle A~You can show that Triangle An Triangle D using a sequence of transformations. Which of these statements about Triangle A and Triangle D is true?
A. triangle D is to the left and down from triangle A.
B. triangle D is dilated from triangle A.
C. triangle A and triangle D have interior angle measures that sum to less than 180°
D. triangle A and triangle D are congruent.
Answers
Answer:
C or A po Yan sagut ko sa dalawa pumili Lang ako9. Elena is selling tickets for an amusement
park. She sells triple the number of
student tickets as adult tickets and
she sells 8 fewer senior tickets than
adult tickets
a Write expressions for the number of
adult tickets, student tickets, and
senior tickets, using a as the number of adult tickets
b. Using your answers from part b, write
a simplified expression for the total
number of tickets Elena sells
1
C. Elena sells 15 adult tickets, does
she sell at least 100 total tickets?
Show your work
Answers
Step-by-step explanation:
A) a = students tickets
3a = adult tickets
3a+8 = senior tickets
B) a + 3a + 3a + 8 = Tt
C) 15 + 3(15) + 3(15) + 8 = 113
Therefore, she sells at least 100 total tickets
Janet wants to solve the equation y startfraction y squared minus 5 over y squared minus 1 endfraction = startfraction y squared y 2 over y 1 endfraction. what should she multiply both sides of the equation by? y y2 – 1 y 1 y2 y 2
Answers
An equation is formed of two equal expressions. Janes should multiply both sides of the equation by (y²-1).
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The equation that is given is an equation with a mixed fraction, therefore, the denominator with the highest power should be multiplied on both sides of the equation. The equation that is given to us
[tex]y + \dfrac{y^2-5}{y^2-1} = \dfrac{y^2+y+2}{y+1}[/tex]
As we can see in the equation that there are 2 denominators, which are,
y²-1y+1In the two of the expressions that are stated above the expression (y²-1) is of a higher power.
Hence, Janes should multiply both sides of the equation by (y²-1).
Learn more about Equation:
https://brainly.com/question/2263981
homework help please!!!!!!!!!!
Answers
Answer:
the line is equal to 180 degrees so knowing that we can make our equation
(2x+3)+(x-6)=180
now all we have to do is combine like terms
3x-3=180
3x=177
x=59
plug back in
Value of A (2(59)+3)= 121
Value of B (59-6)= 53
What is the shape of A(-5,1) B(-2,4) C(3,1) D(0,-4)
Answers
Answer: Parallelogram
Step-by-step explanation: Roughly sketched.
what is 1,200 x 1,300
Answers
Answer:
It's 1,560,000
Step-by-step explanation:
You can just put it into a calculator.
Answer:
1,560,000
Step-by-step explanation:
When you multiply 1,200 by 1,300, you would get 1,560,000.
compare |-0.658| and |-0.653|.
Answers
Can I have brainliest?
right triangles trigonometry
I dont understand how to solve this.
Answers
(60)tan(x/4sq14)
Once you find this answer, apply it to the opposite of the 60° angle on the far right.
Then you are going to do the solution of the equation I just stated above, times 4sq14 using the Pythagorean theorem theory shown down below.
a^2 + b^2 = c^2
first answer^2 + 4sq14^2 = C^2
C^2 will then provide the short legs of the larger triangle (they are congruent lengths in a 45-45-90 triangle)
Multiply the value of c times c without squaring either of them, like so, this will lead to the answer of X
C times C = “x”
Hope this helps!
Luke’s payment on his new phone will be $70 per month for 12 months. Assuming the phone costs $830 at sale, how much interest will he have paid when he pays the loan on fuel
Answers
Because 830 times .012048192771084 equals 840 which is 70 times 12
please help asap i need this for my essay (35 points)
ʏᴏᴜ’ᴠᴇ ʟᴇᴀʀɴᴇᴅ ᴀʙᴏᴜᴛ ꜰᴜɴᴄᴛɪᴏɴ ɴᴏᴛᴀᴛɪᴏɴ ɪɴ ᴘʀᴇᴠɪᴏᴜꜱ ʟᴇꜱꜱᴏɴꜱ,
ʙᴜᴛ ᴄᴏᴜʟᴅ ʏᴏᴜ ᴜꜱᴇ ꜰᴜɴᴄᴛɪᴏɴ ɴᴏᴛᴀᴛɪᴏɴ ᴛᴏ ᴀᴅᴅ ᴛᴡᴏ ꜰᴜɴᴄᴛɪᴏɴꜱ?
ʜᴏᴡ ᴅᴏ ʏᴏᴜ ᴛʜɪɴᴋ ʏᴏᴜ ᴄᴏᴜʟᴅ ꜱɪᴍᴘʟɪꜰʏ ꜰ(x) + ɢ(x) ɪꜰ ꜰ(x) = 3x + 2 ᴀɴᴅ ɢ(x) = 4x?
ᴡʜᴀᴛ ᴀʙᴏᴜᴛ ᴀ ꜰᴜɴᴄᴛɪᴏɴ ᴏꜰ ᴀ ꜰᴜɴᴄᴛɪᴏɴ ꜱᴜᴄʜ ᴀꜱ ꜰ(ɢ(x))?
ʜᴏᴡ ᴅᴏ ʏᴏᴜ ᴛʜɪɴᴋ ꜰ(ɢ(x)) ᴄᴏᴜʟᴅ ʙᴇ ꜱɪᴍᴘʟɪꜰɪᴇᴅ?
ᴡʜᴀᴛ ꜱɪᴛᴜᴀᴛɪᴏɴꜱ ᴄᴀɴ ʏᴏᴜ ᴛʜɪɴᴋ ᴏꜰ ᴡʜᴇʀᴇ ᴄᴏᴍʙɪɴɪɴɢ ꜰᴜɴᴄᴛɪᴏɴꜱ ᴡᴏᴜʟᴅ ʙᴇ ᴜꜱᴇꜰᴜʟ?
different font because brainly is censoring it for no reason?
Answers
Answer:
I think you could combine functions (not sure don't hold me to it), but im not sure of the actual process. Furthermore, combining functions could be useful if you were an architect.
Step-by-step explanation:
30 POINTS IF YOU ANSWER CORRECTLY!!!! I NEED HELP ASAP PLEASE!!! ALL THE ANSWERS OF THIS ONLINE ARE INCORRECT SO PLEASE HELP!!! Byron is conducting an experiment to determine whether a new medication is effective in reducing coughing. He finds 1,200 volunteers with coughing issues and divides them into two groups. The control group does not receive any medication; the treatment group receives the medication. The patients in the treatment group show reduced signs of coughing. What can Byron conclude from this experiment?
Answers
Answer:
Step-by-step explanation:
Given Byron's discovery of 1,200 volunteers with coughing problems.
He separates them into two categories:
1. There is no medication given to the control group.
2. The medication is given to the treatment group.
In addition, patients in the treatment group have fewer signs of coughing. As a result, Byron can conclude that the new medication works in the treatment group to reduce coughing.
The medicine given to the people, according to Byron, worked because the treatment group showed signs of less coughing.
Answer: Deduction is the effectiveness of the medication is positive since purpose for the trial was achieved. The cough symptoms responded to the medication while the control method used on the other group yielded no visible result. Medication was a better choice to the control method
Step-by-step explanation: Those who received the medication had their symptoms reduced while those who had other control measures showed no form of improvement.
Use whole numbers and decimals to write 19.06 in expanded form.
Answers
Answer:
90.125
Step-by-step explanation:
Answer:
Step-by-step explanation:
19.125
Which comparison is not correct?
02>-3
0 -7<-5
0-9<1
0<-4
Answers
Answer:
last one its not correct
Step-by-step explanation:
what is the area of base for 7mm height and 7mm radius cylinder?
Answers
Answer:
153.94 mm^2
Step-by-step explanation:
area of base = area of a circle = Pi * radius squared
radius squared = 49
area of base = Pi * 49
area of base = 153.94
Answer number 16 please
Answers
Jim's cards increased more
what is -2(-y) in expanded form
Answers
Answer:
2y
Step-by-step explanation:
[tex](-2)(-y) = (-1)(2)(-1)(y) = (-1)^2\ccdot 2y = 2y[/tex]
Solve for X and Y
Picture above
Answers
Answer...
ok done. Thank to me >:3