Given sin x = 8/10, 90° <x< 180° and tan y = -12/5, 270° ≤y≤ 360°. Without finding the values for angle x and y, determine cos x cos y + sin x sin y / tan x - tan y.
Answers
Answer:[tex]-\frac{189}{208}[/tex]
Step-by-step explanation:
Given
[tex]\sin x=\frac{8}{10}[/tex]
x lies in the second quadrant where sin and cosec is positive and rest trigonometric functions are negative
so, [tex]\cos x=-\sqrt{1-sin ^2 x}\\\cos x=-\sqrt{1-(\frac{8}{10})^2}=-\sqrt{\frac{36}{100}}\\\cos x=-\sqrt{\frac{6}{10}}[/tex]
[tex]\tan x=\frac{\sin x}{\cos x}=-\frac{4}{3}[/tex]
similarly, [tex]\tan y=-\frac{12}{5}[/tex]
Also, y lies in 4 th Quadrant where cos and sec is positive and rest trigonometric functions are negative
[tex]\sec y=\sqrt{1+\tan ^2y}=\sqrt{1+(-\frac{12}{5})^2}\\\sec y=\frac{13}{5}\\\cos y=\frac{5}{13}\\\sin y =\frac{\tan y}{\cos y}=-\frac{12}{13}[/tex]
Now putting the values
=[tex]\dfrac{\cos x \cos y+\sin x\sin y}{\tan x-\tan y}=\dfrac{(\frac{-6}{10})(\frac{5}{13})+(\frac{8}{10})(\frac{-12}{13})}{(\frac{-8}{6})-(\frac{-12}{5})}\\\dfrac{\cos x \cos y+\sin x\sin y}{\tan x-\tan y}=\dfrac{\frac{-126}{130}}{\frac{16}{15}}=-\frac{189}{208}[/tex]
Related Questions
4 and 9/10 minus 2 and 2/5 = (in fractions)
5 and 1/2 minus 2 and 2/5 = (answer in fractions)
5 and 1/2 plus 2 and 3/5 =
4 and 5/6 minus 2 and 1/4 =
Answers
Answer:
3 mark me brainlest
Step-by-step explanation:
Answer:
It is the 3rd one I think
Step-by-step explanation:
Hope this helps have an amazing day!
Which one is a cheaper buy, a 24-cm by 24-cmn pizza for
7350.00 or a 30-cin diameter circular pizza for the same price.
Explain.
Answers
Answer:
The circular pizza is cheaper because you pay less money for a unit area of the pizza
Step-by-step explanation:
Step one:
given data
The dimension of the square pizza is
24 X 24 cm
The area is
= 576cm^2
Also, the dimension of the circular pizza is
DIameter = 30cm
radius = 30/2 = 15cm
The area is
= πr^2
=3.142*15^2
=706.95cm^2
Step two:
let us find the cost per area of each of the shape of the pizzas
For the square pizza the cost per area is
= 7350/576
=$12.76 per area
For the circular pizza, the cost per area is
= 7350/706.95
=$10.40 per area
HELLPPPPPPPPPPP WILL GIVE BRAINLIEST YO CORRECT ANSWERRR
Answers
Answer: AS you can see Triangel A' B' C' has been dilated. You can see this is because it is still a tringle but its been made smaller. it has also has been reflected accross the y axis and then reflected accros the x asis
Step-by-step explanation:
what is different of the four shapes?
Answers
Answer:
It has only 1 pair of parallel sides.
Step-by-step explanation:
Answer:
It has only 1 pair of parallel sides
Step-by-step explanation:
A leaking pond loses 12 gallon of water in 23 hours How many gallons of water will it lose in 31 hours
Answers
Answer:
The volume of water the pond will lose in 31 hours is 17.71 gallons.
Step-by-step explanation:
Given;
Rate of water leakage, R = 12 gallon of water in 23 hours
[tex]R = \frac{12 \ gallons}{23 \ hours}[/tex]
In 31 hours the volume of water leaked is calculated as;
[tex]V = \frac{12 \ gallons}{21 \ hours} \times 31 \ hours\\\\V = 17.71 \ gallons[/tex]
Therefore, the volume of water the pond will lose in 31 hours is 17.71 gallons.
O MODULE 1: EXPRESSIONS AND EQUATIONS
Distributive property: Integer coefficients
Use the distributive property to remove the parentheses.
(-6+x+3y)(-6)
DO
X Х
?
Answers
Answer:
First, multiply the 5 by each of the terms inside the parentheses. Next, simplify each part of the expression and then add. The answer is 5(2+3)=25. The distributive property also works if there is subtraction inside the parentheses
Step-by-step explanation:
Evaluate the expression (3-2)2 (3.2) = 11
Answers
I believe the answer is 6.4 = 11.
20. Jorge conducted a survey by asking 120 students whether they use a pencil to take notes. Of the students surveyed, 90 responded favorably. Which margin of error matches each confidence level for this situation?
1. 90% =
2. 99% =
3. 95%=
options- 0.102, 0.338, 0.216, 0.077, 0.256, 0.065
Answers
Answer:
Margin of error for 90% C.I: 0.065
Margin of error for 99% C.I: 0.091
Margin of error for 95% C.I: 0.077
Step-by-step explanation:
In this question, for each student, there are only two possible outcomes. Either they use a pencil to take notes, or they do not. Students are independent of each other. So we use the binomial probability distribution to solve this question.
Binomial confidence interval:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
For this problem, we have that:
120 students, so [tex]n = 120[/tex]
90 responded favorably, so [tex]p = \frac{90}{120} = 0.75[/tex]
Margin of error for 90% CI:
Here [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}} = 1.645\sqrt{\frac{0.75*0.25}{120} = 0.065[/tex]
Margin of error for 99% CI:
Here [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.325[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}} = 2.325\sqrt{\frac{0.75*0.25}{120} = 0.091[/tex]
Margin of error for 95% CI:
Here [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}} = 1.96\sqrt{\frac{0.75*0.25}{120} = 0.077[/tex]
Answer: Margin of error for 99% CI: z=2.575 . input that into the equation and it give you .1017
Step-by-step explanation:
2 1/3 - 1 2/5 please help
Answers
Answer:
14/15
Step-by-step explanation:
2 1/3 - 1 2/5
1 4/3 - 1 2/5
0+14/15
final answer is 14/15
Select the number that would make this statement true: 361.2 ÷ ________ = 036.12 (3 points)
1,000
100
10
1
Answers
Answer: c
Step-by-step explanation:
You can take the blank as x
so 361.2 / x = 36.12
multiply by x
361.2 = 36.12x
divide
x = 10
thank me and mark me as brainlies
Answer:
10
Step-by-step explanation:
You owe $300 on your credit card. For every month that you fail to make a payment, your balance increases by 1%. Find a formula for the balance B owed after t months with no payment.
Answers
Answer:
[tex]B(t) = 300(1.01)^{t}[/tex]
Step-by-step explanation:
The balance owed after t months can be given by an exponential function in the following format:
[tex]B(t) = B(0)(1+r)^{t}[/tex]
In which B(0) is the initial balance owed and r is the growth rate, as a decimal.
You owe $300 on your credit card. For every month that you fail to make a payment, your balance increases by 1%.
This means, respectively, that [tex]B(0) = 300, r = 0.01[/tex]
So
[tex]B(t) = 300(1+0.01)^{t}[/tex]
[tex]B(t) = 300(1.01)^{t}[/tex]
Describe all the x-values at a distance of 25 or less from the number 12. Enter your answer in interval notation.
Answers
Answer: [-13, 37]
======================================================
Explanation:
The smallest x value possible is 12-25 = -13
The largest x value possible is 12+25 = 37
It might help to draw out a number line to see this.
x is between -13 and 37, including both endpoints. We can write [tex]-13 \le x \le 37[/tex]
This converts to the interval notation [-13, 37] which is the answer.
The use of square brackets is to indicate "include this endpoint".
4² - 3 + 7
pemdas please
Answers
Answer:
20
Step-by-step explanation:
4^2= 16
16+7=23
23-3=20
Answer: 6
Step-by-step explanation:
4^2 - 3 +7
16 - 3 +7
16 - 10
6
Help me please I hate Math
Answers
Answer:
112°
Step-by-step explanation:
Each of the interior angles that measure 34° and mentioned there are two of them will add up to 68°. A triangle must equal 180°. Subtract 68 from 180 to get 112° as your final answer.
Answer:
112
Step-by-step explanation:
180-(34+34)
180-68
112
Which expression represents the fourth term in the binomial expansion of (e + 2f)10?
10C3(e7)(2f)3
10C3(e7)(f)3
10C4(e6)(2f)4
10C4(e6)(f)4
Answers
Answer:
first one
Step-by-step explanation:
Answer:
a on edge
Step-by-step explanation:
91 points need help now . Emanuel put 12 marbles on one pan
of a scale. On the other pan, he put
4 marbles, then he added 8 more
marbles to that side. Each of the-
marbles weighs 1 ound. Is the scale
balanced? Explain.
Answers
Answer: I believe the scale is balanced.
Step-by-step explanation: I stated that because since the other side of the scale contained 12 marbles that were 1 pound each that would be 12 pounds and then since 4+8=12 12 pounds of marbles were also put on the other side.
Pls help I’m failing math I’ll brainlest for the right answer grades close today
Answers
answer: i think that it would increase by about 20 percent
i am not sure, if i m wrong then i am very sorry!
Step-by-step explanation:
Answer:
The change is a decrease by ~13.6%
Step-by-step explanation:
Formula:
[First Value – Second Value] ÷ [(First Value + Second Value) ÷ 2] × 100
48 - 84 ÷ 48 + 84 ÷ 2 × 100
-36 ÷ 132 ÷ 2 × 100
-0.2727272727272727 ÷ 2 × 100
-0.1363636363636364 × 100
-13.63636363636364
Or ~ 13.6
The change is a decrease by ~13.6%
It is common to leave a 10% tip when the service was just mediocre. At one such occasion, a patron left a 10% tip on a $23.45 bill.
What is the tip amount?
What is the total bill?
Answers
Answer: $2.3
Step-by-step explanation: well you need to find 10% of 23.45, so multiply .1 by 23.45.
[tex]23.45 \times 10\%[/tex]
[tex] = 23.45 \times 0.1[/tex]
[tex] = 2.345[/tex]
[tex] = 2.35[/tex]Answer:$2.35 is the tip amount
What is the total bill?Solution:[tex]23.45 + 2.345[/tex]
[tex] = 25.795[/tex]
[tex] = 25.80[/tex]
Answer:$25.80 is the total bill
#CarryOnLearning
#AnswerForTrees
#BrainlyBookSmart
can someone please prove that the expression (x-y)+(y-z)+(z-x) is equivalent to 0
Answers
Answer:
see below
Step-by-step explanation:
[tex](x-y)+(y-z)+(z-x)\\\\=x-y+y-z+z-x\\\\=(x-x)+(-y+y)+(-z+z)\\\\=0+0+0\\\\=0[/tex]
54 is 45% of _______________. fill in the blank
Answers
Answer:
Your answer is 120% of 45
Step-by-step explanation:
the product of two number is 42.they are two consecutive numbers. the two numbers are both less than 10. what is the answer?
Answers
Answer:
6 and 7
Step-by-step explanation:
You first want to find the factors of 42. They are:
1,2,3,6,7,14,21,42
The factor pairs are:
1 & 422&213&146&7The only factor pair with consecutive numbers is 6 and 7. They are both less than 10 as well, so 6 and 7 works.
HELP ASAP!! MARKING BRAINLIEST!!! WORTH 10 POINTS FIRST PERSON TO ANSER CORRECTLY GETS BRAINLIEST!!!!
Which expression represents a positive number?
A.) -3/4 divided by 2/3
B.) 3/4 divided by (-2/3)
C.) -2/3 divided by 3/4
D.) -3/4 divided by (-2/3)
Answers
Answer:
its d
Step-by-step explanation:
2 negs make a pos
A line graph does NOT:
a.
show trends clearly
c.
use percentages to display data
b.
allow viewers to make predictions about data
d.
show specific values of data
Answers
Answer:
show trends clearly. that's the answer
If 60 people were surveyed, how many of them would chose an SUV as their preferred vehicle?
60
57
36
39
Answers
Answer:
39
Step-by-step explanation:
Can someone help me will give brainliest thanks (:
Answers
10x + 20y = 690
Now get x by itself on one side by subtracting y
10x = 690 - 20y
Divide by 10 on both sides
X = 69 - 2y
Now plug this value for x into a separate equation just showing the amount of coins
(X+y=45)
69 - 2y + y = 45
Now solve for y
69 - y = 45
-y = -24
Y = 24
Now plug this y value into the same equation to solve for x
X + 24 = 45
X = 21
To check this work add both values into the original equation and solve
10(21) + 20(24) = 690
210 + 480 = 690
690 = 690
Answer:
$10 coins: 21
$20 coins: 24
Step-by-step explanation:
So we can create 2 equations where
x = number of $10 coins
y = number of $20 coins:
x + y = 45
10x + 20y = 690
we can move equation 1 around so that we can get a value of x
x = 45 - y
now we can substitute x into the second equation
10(45 - y) + 20y = 690
450 - 10y + 20y = 690
10y = 240
y = 24
Now plug in y back into the first equation
x = 45 - y
x = 45 - 24
x = 21
1a
the length of notes na inante are till wudhof
1
Innly
llon
117 and Itank
Answers
Answer:
can you please describe this more and what it is then i will answer it in the comments
Step-by-step explanation:
Henry is planning to create two rectangular gardens.
Part A
Henry has 96 feet of fencing to enclose the first rectangular garden. The garden will be x feet wide.
Which function, f(x), can Henry use to determine the area, in square feet, of the first garden?
a f(x) = 48x
f(x) = 48 - x
f(x) = 48 – x²
f(x) = 48x - x2
Answers
Answer:
Step-by-step explanation:
THANKS 4 POINTS!!!!!!!
What is the answer to 34/6?
Answers
Answer:
I don't Know if this is division or fraction
Step-by-step explanation:
But I divided
and my answer was 5r4
Spencer has a bank account with a balance of $75.00. Spencer owes $30.00 to her credit card and she owes $50.00 for a LCD TV. What would Spencer’s bank balance be, if both debits were paid?
Answers
Answer:
-5.00 dollars
Step-by-step explanation:
Answer:
-5
Step-by-step explanation:
75-50-30=-5
Solve the equation X-4/2=10
X=24
X=22
X=29
X=39
Answers
Glad I could help and have a fantastic day!
Also, can you please mark my answer as the brainliest answer?
Thanks.