Answer:
[tex]\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}[/tex]
Step-by-step explanation:
Given
[tex]\cos(\theta) = -\frac{2}{3}[/tex]
[tex]\theta \to[/tex] Quadrant III
Required
Determine [tex]\tan(\theta) \cdot \cot(\theta) + \csc(\theta)[/tex]
We have:
[tex]\cos(\theta) = -\frac{2}{3}[/tex]
We know that:
[tex]\sin^2(\theta) + \cos^2(\theta) = 1[/tex]
This gives:
[tex]\sin^2(\theta) + (-\frac{2}{3})^2 = 1[/tex]
[tex]\sin^2(\theta) + (\frac{4}{9}) = 1[/tex]
Collect like terms
[tex]\sin^2(\theta) = 1 - \frac{4}{9}[/tex]
Take LCM and solve
[tex]\sin^2(\theta) = \frac{9 -4}{9}[/tex]
[tex]\sin^2(\theta) = \frac{5}{9}[/tex]
Take the square roots of both sides
[tex]\sin(\theta) = \±\frac{\sqrt 5}{3}[/tex]
Sin is negative in quadrant III. So:
[tex]\sin(\theta) = -\frac{\sqrt 5}{3}[/tex]
Calculate [tex]\csc(\theta)[/tex]
[tex]\csc(\theta) = \frac{1}{\sin(\theta)}[/tex]
We have: [tex]\sin(\theta) = -\frac{\sqrt 5}{3}[/tex]
So:
[tex]\csc(\theta) = \frac{1}{-\frac{\sqrt 5}{3}}[/tex]
[tex]\csc(\theta) = \frac{-3}{\sqrt 5}[/tex]
Rationalize
[tex]\csc(\theta) = \frac{-3}{\sqrt 5}*\frac{\sqrt 5}{\sqrt 5}[/tex]
[tex]\csc(\theta) = \frac{-3\sqrt 5}{5}[/tex]
So, we have:
[tex]\tan(\theta) \cdot \cot(\theta) + \csc(\theta)[/tex]
[tex]\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \tan(\theta) \cdot \frac{1}{\tan(\theta)} + \csc(\theta)[/tex]
[tex]\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 + \csc(\theta)[/tex]
Substitute: [tex]\csc(\theta) = \frac{-3\sqrt 5}{5}[/tex]
[tex]\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 -\frac{3\sqrt 5}{5}[/tex]
Take LCM
[tex]\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}[/tex]
HELP ASAP PLEASEE!!
Simplify this expression.
5^6 x 5^-2 over 5^-7
a
5^1
b
5^11
c
5^-3
d
5^-19
Answer:
5^6 × 5^(-2) × 5^(-7)
= 5^{6+(-2)+(-7)}
= 5^{6-2-7}
= 5^(-3)
Option c 5^-3
7. Murray spins the pointer of the spinner shown at the right
a. What is the sample space for the probability model?
b. What is the probability of each event in the sample space?
Answer:
a)
Sample Space of Probability model is - S' = { [tex]\frac{1}{4}[/tex] , [tex]\frac{1}{4}[/tex] , [tex]\frac{1}{4}[/tex] , [tex]\frac{1}{4}[/tex] }
b)
Probability of Event 1 , P(1) = [tex]\frac{2}{8} = \frac{1}{4}[/tex]
Probability of Event 2 , P(2) = [tex]\frac{2}{8} = \frac{1}{4}[/tex]
Probability of Event 3 , P(3) = [tex]\frac{2}{8} = \frac{1}{4}[/tex]
Probability of Event 4 , P(4) = [tex]\frac{2}{8} = \frac{1}{4}[/tex]
Step-by-step explanation:
Given - Murray spins the pointer of the spinner as shown .
To find - a. What is the sample space for the probability model?
b. What is the probability of each event in the sample space?
Proof -
The Sample space is the set of all possible outcomes.
So,
Sample space becomes -
S = { 3, 5, A, Y, 3, 5, A, Y}
Total number of outcomes, n(S) = 8
Now,
We can see that There are 4 types of event
Event 1 : 3
Event 2 : 5
Event 3 : A
Event 4 : Y
So,
Probability of Event 1 , P(1) = [tex]\frac{2}{8} = \frac{1}{4}[/tex]
Probability of Event 2 , P(2) = [tex]\frac{2}{8} = \frac{1}{4}[/tex]
Probability of Event 3 , P(3) = [tex]\frac{2}{8} = \frac{1}{4}[/tex]
Probability of Event 4 , P(4) = [tex]\frac{2}{8} = \frac{1}{4}[/tex]
Now,
Sample Space of Probability model is -
S' = { [tex]\frac{1}{4}[/tex] , [tex]\frac{1}{4}[/tex] , [tex]\frac{1}{4}[/tex] , [tex]\frac{1}{4}[/tex] }
∴ we get
a)
Sample Space of Probability model is - S' = { [tex]\frac{1}{4}[/tex] , [tex]\frac{1}{4}[/tex] , [tex]\frac{1}{4}[/tex] , [tex]\frac{1}{4}[/tex] }
b)
Probability of Event 1 , P(1) = [tex]\frac{2}{8} = \frac{1}{4}[/tex]
Probability of Event 2 , P(2) = [tex]\frac{2}{8} = \frac{1}{4}[/tex]
Probability of Event 3 , P(3) = [tex]\frac{2}{8} = \frac{1}{4}[/tex]
Probability of Event 4 , P(4) = [tex]\frac{2}{8} = \frac{1}{4}[/tex]
Need help with this question please!!
Answer:
11.1
Step-by-step explanation:
Use the Pythagorean theorem to find the unknown side.
[tex]a^{2} +b^{2} =c^{2} \\AB^{2} +BC^{2} =AC^{2} \\AB^{2} +19^{2} =22^{2} \\\\AB^{2}=22^{2}-19^{2\\AB=\sqrt{123} \\AB=11.1[/tex]
Select the correct text in the passage.
In this excerpt from A Christmas Carol by Charles Dickens, which sentence indicates that Scrooge formed relationships primarily for selfish
reasons?
"I don't mind going if a lunch is provided," observed the gentleman with the excrescence on his nose. "But I must be fed, if I make one."
Another laugh.
"Well, I am the most disinterested among you, after all," said the first speaker, "for I never wear black gloves, and I never eat lunch. But I'll offer
to go, if anybody else will. When I come to think of it, I'm not at all sure that I wasn't his most particular friend; for we used to stop and speak
whenever we met. Bye, byel
Speakers and listeners strolled away, and mixed with other groups. Scrooge knew the men, and looked towards the Spirit for an explanation.
The Phantom glided on into a street. Its finger pointed to two persons meeting. Scrooge listened again, thinking that the explanation might lie
here.
He knew these men, also, perfectly. They were men of business: very wealthy, and of great importance. He had made a point always of standing
well in their esteem: in a business point of view, that is strictly in a business point of view.
Answer: it's the last
Step-by-step explanation:
If the radius of a sphere is 6cm, then it’s volume is____
A. 288pi cm^3
B. 576pi cm^3
C. 72pi cm^3
D. 36pi cm^3
Answer:
[tex]A. \: 288\pi( {cm}^{3} )[/tex]
Step-by-step explanation:
Hint:
Formula = [tex] \frac{4}{3} \pi {r}^{3} [/tex]Radius = 6 cmSimplify:
[tex] \frac{4}{3} \pi (radius {)}^{3} [/tex][tex] \frac{4}{3} \pi \times {6}^{3} [/tex][tex] \frac{4\pi}{3} \times 216[/tex][tex]4\pi = \frac{216}{3} [/tex][tex]4\pi \times 72[/tex]
[tex]288\pi( {cm}^{2} )[/tex]
Hope it is helpful....This is what I have so far I just need the last step
Answer:
-2
HOPE THIS HELPS
- Todo ❤️
Step-by-step explanation:
-6/3=-2
Ameer uses \dfrac14 4 1 start fraction, 1, divided by, 4, end fraction of a bottle of shampoo to give each of his dogs a bath. He has 555 dogs all together.
Answer:
138 3/8
Step-by-step explanation:
total shampoo used for 555 dogs = 1/4 x 555 = 138 3/8 bottles
Mr lance designed a class banner shaped like a the polygon shown. What is the name of the polygon?
Answer:
hexagon
Step-by-step explanation:
i g
Write the equation of the line that goes through the point (-2, 8) with a slope of 1/2
Answer:
The answer is Y = 1/2x + 9
Step-by-step explanation:
The general equation with a slope and intercept is:
y=mx+b
We are given a slope of 1/2, which represents the "M" part of the equation.
So we have:
Y = 1/2x + b
We do not know what "b" is, so the equation is not complete.
We plug in "-2" for X and "8" for Y:
8 = 1/2 (-2) + b
b = 9
So, the full equation is: Y = 1/2x + 9
Help please how do I find x and y
Answer:
Option 3
Step-by-step explanation:
tan33°=x/7
x=4.5
4.5^2+7^2=y^2
20.25+49=y^2
y=√69.25
y=8.3
please answer accurately with a full explanation and please don't do short answers thank u, and if u spam this question u will be reported. please answer with a proper answer, not a short one thank u so much
Answer:
When buying a backpack you want to pick the one with the greatest volume. Backpack A has the highest volume (5200) which means that it's the backpack that will allow me to fit the most stuff.
Step-by-step explanation:
This questions i just asking which bag has the greatest volume
the formula for that is just l*w*h
calculate the volume for each backpack:
a: 26*20*10=5200
b: 32*16*8=4096
c: 28*14*12= 4704
We can see that backpack A has the greatest volume, so we should pick it.
Henry spent 37.88 at the grocery store.he know has 26.92 left .how much money did Henry originally have?
Answer:
64.8
Step-by-step explanation:
37.88+ 26.92
64.80
Answer:
He had 64.8
Step-by-step explanation:
Just add 37.88 and 26.92 together :)
37.88
+26.92
64.8
Hope it helps!! :D
The longest sides of a right triangle is called the?
Answer:
hypotenuse
Step-by-step explanation:
Answer:
HYPOTENUSE
Step-by-step explanation:
No need to explain
°^°
1. Find six rational numbers between 2/7 and 5/2
Answer:
5/14
6/14
7/14
8/14
9/14
10/14
Step-by-step explanation:
We need to find the six rational numbers between 2/7 and 5/2. Firstly convert the fractions into like fractions.
LCM of 7 & 2 = 14=> 2/7 = 2×2/7×2 = 4/14
=> 5/2 = 5 ×7/2×7 = 35/14
Therefore the six rational numbers are
5/146/147/148/149/1410/14How long could a student take to paint their canvas if they are slower than 75% of the other students?
Answer:
multiply the other kid's time by 3/4
Step-by-step explanation:
there's some info missing but hope this helps!
What is the length of KL?
A 24
B 37
C 33
D 12
A standard American deck of cards contains 52 cards in four “suits”:
♣ clubs
♦ diamonds
♥ hearts
♠ spades
Each card also has a “rank”. There are 13 ranks: 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king), A(ace). Every suit-rank combination occurs in the deck, so a typical card might be called “the 7 of clubs” or “the queen of hearts”. Suppose we shuffle a deck (meaning that we put the cards in random order), then we draw a card
off the top. What is the probability that this card has an even number on it? (Jacks, queens, kings, and aces do not have numbers on them.)
I need the answer quickly pls
Answer:
5/13
Step-by-step explanation:
We can first start by finding the number of even numbers in one suit and then multiply by 4. The even numbers are:
2, 4, 6, 8, 10
There are 5, and since there are 4 suits, there is a total of 20 even cards.
Probability is equal to the amount of desirable outcomes over the total number of outcomes. The desirable outcomes are when we pull out an even number, and as we calculated earlier, there are 20 of those. There are 52 total cards, so that is the number of total outcomes. We get the expression:
20 / 52 which simplifies to 5/13
a. Find the mean, median, and mode of 12, 9, 17, 15, 10.
mean:
median:
Create an equation which contains the solution (-1,3)
Answer:
3x + y =0
Step-by-step explanation:
We need to create equation whose solution is (-1,3) . So let another point through which it passes be ( 0,0) .
Since at least two points are required for making a line .Slope :-
=> m = -1-0/3-0
=> m = -1/3
Using point slope form :-
=> ( x - x1) = m( y - y1)
=> ( x - (-1)) = -1/3( y - 3)
=> (x + 1 )3= -y + 3
=> 3x +3 = -y + 3
=> 3x + y = 0
✔️ Checking :-
(-1,3)=> 3(-1) + 3 = 0
=> -3+3=0
=> 0 = 0
• Hence the equation can be 3x + y = 0 .You want to fill up a jar with lemonade.
Is this the characteristic of total surface area or volume?
Multiple Select: Multiply and match each of the following
expressions.
A. (x − p) (x + p)
B. (x – 5) (x + 7)
C.(x + p) (x + p)
A.isz? - 2px – pº A.isx? – p2 B.isz? + 2x – 35
B.isx? - 20 – 35 Cisx2 + 2px +p?
Answer:
A. (x − p) (x + p) = x² - p²
B. (x – 5) (x + 7) = x² + 2x - 35
C. (x + p) (x + p) = x² + 2px + p²
Step-by-step explanation:
To find - Multiply and match each of the following expressions.
A. (x − p) (x + p)
B. (x – 5) (x + 7)
C.(x + p) (x + p)
Proof -
A.)
The expression is - (x − p) (x + p)
Now,
(x − p) (x + p) = x(x + p) - p(x + p)
= x(x) + x(p) - p(x) - p(p)
= x² + xp - px - p²
= x² - p²
⇒(x − p) (x + p) = x² - p²
B.)
The expression is - (x – 5) (x + 7)
Now,
(x − 5) (x + 7) = x(x + 7) - 5(x + 7)
= x(x) + x(7) - 5(x) - 5(7)
= x² + 7x - 5x - 35
= x² + 2x - 35
⇒(x − 5) (x + 7) = x² + 2x - 35
C.)
The expression is - (x + p) (x + p)
Now,
(x + p) (x + p) = x(x + p) + p(x + p)
= x(x) + x(p) + p(x) + p(p)
= x² + xp + px + p²
= x² + 2px + p²
⇒(x + p) (x + p) = x² + 2px + p²
true or false the values [x] and [-x] are always equal
Answer:
If you mean |x| and |-x| yes they are equal.
Step-by-step explanation:
Brackets do not exactly specify the meaning of absolute value.
On most keyboards, above the enter button on the main keyboard part (not the keypad one) there is a back slash symbol \ and if you hold shift, there might be another symbol | which more accurately represents absolute value,
If you aren't talking about the absolute value, then no.
Henry is planning to attend a public university after he graduates from high school in 3 years. He is devising a plan to save money each month to help with the expenses of attending the university. The cost of attending the public university for one-year is $26,500. His family has promised to contribute $13,450 each year he is in school. What is the minimum amount of money Henry must contribute to his savings per month for the next 3 years to have enough money to pay for his first year of tuition?
a
$501.32
b
$362.50
c
$294.38
d
$482.35
brainliest goes to whoever answers the question correctly also if you want more points answer my other questions
Answer:
D
Step-by-step explanation:
I am pretty sure it is D because the numbers on the chart don't seem inconsistent. You go from 11 to 2 which would give a big drop so it wouldn't be a linear function.
Help please. Find the area of this circle
Answer:
8
Step-by-step explanation:
I need help finding the anwser for 52 divided (13 x 2)
Answer:
52÷(13x2) 13×2 = 26 52÷26=2
Abby and Bill share a 20-ounce bucket of clay. By the end of the week, Abby has used
1/10
of the bucket, and Bill has used
2/5
of the bucket of clay. How many ounces are left in the bucket?
Answer:
A little brain/willpower.....Im sure you can figure it out!!!
find equation so EASY PLZ HELPPP URGENT WILL GIVE BRAINESD MARK 11+ POINTS
Answer:
y= -4x+4
Step-by-step explanation:
there you go!!!
Answer:
m= -4 would be the equation
Step-by-step explanation:
super urgent will give u 5 rating and thansk if u answer
A jar contains 12 oatmeal cookies, 13 sugar cookies and 5 chocolate chip cookies. The percent of cookies that are oatmeal is ?
Answer:
40%
Step-by-step explanation:
I added all the cookie numbers together to get 30 then I found the percentage of 12 in 30 which is equal to 40 percent
What is mZPQR in radians?
Answer:
7pi/20 radians
Step-by-step explanation:
63 pi
------ x---------- = 63pi/180
1 180
63pi/180 simplified is 7pi/20 radians.