Three trigonometric functions for a given angle are shown below. sin theta = -77/85, cos theta=36/85 tan theta=77/36 What are the coordinates of point (x, y) on the terminal ray of angle theta assuming that the values above were not simplified?
A) (-77,-36)
B)(-77,36)
C) (-36,77)
D) (36, -77)
Answers
Answer:
The correct option is D.
Step-by-step explanation:
It is given that
[tex]\sin \theta =\frac{-77}{85}[/tex]
[tex]\cos \theta =\frac{36}{85}[/tex]
The angle of terminal ray is θ, it means the angle between x-axis and terminal ray is θ.
[tex]\sin \theta =\frac{perpendicular}{hypotenuse}[/tex]
[tex]\cos \theta =\frac{base}{hypotenuse}[/tex]
Therefore the length of perpendicular is 77 and the base of the triangle is 36.
Since sinθ is negative and cosθ is positive, it means point must be lies on fourth quadrant because in fourth quadrant cosine in positive but sine is negative.
The point of terminal ray is (base, perpendicular) and the sign are used according to the quadrant.
Therefore the point of terminal ray is (36,-77) because in fourth quadrant x is positive but y is negative. Option D is correct.
The coordinates of the point (x, y) on the terminal ray of angle theta are (36, -77).
Given
Three trigonometric functions for a given angle are shown below.
sin theta = -77/85, cos theta=36/85, tan theta=77/36.
What is a terminal ray of angle?A ray is defined as the initial side of the angle.
The second ray which is called the terminal side of the angle.
The value of the sin and cos theta then, the co-ordinate lies in the fourth quadrant.
Therefore, the coordinates of the point (x, y) on the terminal ray of angle theta are (36, -77).
To know more about Terminal ray click the link given below.
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Related Questions
the results of a survey showed that 7 tenths of the housholds surveyed used a computer what fraction of the household surveyed did not use a computer
Answers
Hope this helps.
Joey has 8 pairs of socks in his drawer five of them are white what percent of colored socks does Joey have
Answers
Answer:
0.375 or 37.5%
Step-by-step explanation:
To do this you divide 8 by 3 because he has 3 colored socks out of 8 socks.
Seymour is twice as old as Cassandra. If 16 is added to Cassandra’s age and 16 is subtracted from Seymour’s age, their ages will be equal. What are their present ages?
Answers
Cassandra: Seymour:
16 48
+ -
16. 16
_____ _____
32 32
The ages are =
Answer:
The age of Cassandra is 32 years and Seymour is 64 years old.
Step-by-step explanation:
Let the age of Cassandra be x.
The age of Seymour = 2x
If 16 is added to Cassandra’s age and 16 is subtracted from Seymour’s age, their ages will be equal.
x + 16 = 2x - 16
2x - x = 16 + 16
x = 32 years
x = 32 years
The age of Seymour = 2x = 2 × 32 years = 64 years
The age of Cassandra is 32 years and Seymour is 64 years old.
Seven days ago, I put 60 jelly beans in a bowl. Now there are 4 jelly beans left.
If I ate the same number of jelly beans each day, how many jelly beans did I eat each day?
Get's Brainliest if best answer
Please help ASAP!
Answers
Answer:
You ate 8 jellybeans a day
Step-by-step explanation:
60-4=56
56/7=8
The student ate 8 jelly beans per day, calculated by subtracting the number of jelly beans left from the original amount and dividing by the number of days.
To determine how many jelly beans were eaten each day, we can subtract the number of jelly beans left in the bowl from the original amount and then divide by the number of days that have passed.
If there were originally 60 jelly beans and now there are only 4 left, then 60 - 4 jelly beans have been eaten.
Over the course of 7 days, this amount should be divided by 7 to find the daily consumption.
= 60 jelly beans - 4 jelly beans = 56 jelly beans have been eaten in total.
To find the number eaten per day: 56 jelly beans / 7 days
= 8 jelly beans per day.
Therefore, 8 jelly beans were eaten each day.
A leak in a water tank causes the water level to decrease by 3.6×10−23.6×10−2 millimeters each second. About how many millimeters does the water level in the tank decrease in 5 hours, or 1.8×1041.8×104 seconds? Drag and drop the values to the boxes to express the answer in scientific notation.
Answers
Answer:
[tex]6.48\times 10^{2}[/tex] millimeters.
Step-by-step explanation:
We have been given that a leak in a water tank causes the water level to decrease by [tex]3.6\times 10^{-2}[/tex] millimeters each second.
To find the decrease in water level in 5 hours let us multiply water decrease in one second by number of seconds in 5 hours.
[tex]\text{The decrease in water level in the tank}=3.6\times 10^{-2} \times 1.8\times 10^4[/tex]
Using the exponent product rule let us add the exponents with same base (10).
[tex]\text{The decrease in water level in the tank}=3.6 \times 1.8\times 10^{-2+4}[/tex]
[tex]\text{The decrease in water level in the tank}=3.6 \times 1.8\times 10^{2}[/tex]
[tex]\text{The decrease in water level in the tank}=6.48\times 10^{2}[/tex]
Therefore, the water level in tank decreased [tex]6.48\times 10^{2}[/tex] millimeters in 5 hours.
Convert 5 square root of a into exponential form?
Answers
Answer:
The answer is: " [tex]5a^\frac{1}{2}[/tex] " .
_____________________________________________
Step-by-step explanation:
______________________________________________
We are asked to convert "5 square root of a" ; into "exponential form".
Note that "5 square root of a" ;
or; " 5 root a " ;
means: " 5 times the {square root of the variable, "a" };
or : " 5 multiplied by the {square root of the variable, "a" }.
_______________________________________________
This can be written as: " [tex]5\sqrt{a}[/tex] " .
_______________________________________________
Note the following property of exponents:
[tex]\sqrt[n]{a^m} = (\sqrt[n]{a})^m = a^m^n[/tex] .
_____________________________________________
So; to write: " √a " ; as an exponent :
______________________________________________
Note:
" [tex]\sqrt{a} = \sqrt[2]{a} = \sqrt[2]{a^1} = (\sqrt[2]{a})^1 = a^\frac{1}{2}[/tex] " .
_______________________________________________
So:
" [tex]\sqrt{a} = a^\frac{1}{2}[/tex] " ;
_______________________________________________
And:
________________________________________________
" [tex]5\sqrt{a} = 5a^\frac{1}{2}[/tex] " .
________________________________________________
→ The answer is: " [tex]5a^\frac{1}{2}[/tex] " .
________________________________________________
Hope this helps!
Best wishes in your academic endeavors
— and within the "Brainly" community!
________________________________________________
there are 24 students at the class picnic if 3/4 of the class is at the picnic how many students are in the class
Answers
Answer:
32
Step-by-step explanation:
To find the number of students in the class, use the equation 3/4x = 24 and solve for x.
Explanation:To find the number of students in the class, we can set up the equation 3/4x = 24, where x represents the total number of students in the class.
To solve for x, we need to isolate it. We can do this by multiplying both sides of the equation by the reciprocal of 3/4, which is 4/3.
3/4x * 4/3 = 24 * 4/3
x = 32
Therefore, there are 32 students in the class.
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The difference of 11 and 4 times a number equals 3
Answers
Hello there!
An equation to model this situation is 11 - 4n = 3.
The unknown number has a value of 2.
Okay, so let's start by breaking down the question - we'll use n to model the unknown number.
The difference of 11 and 4 times a number equals 3
This means we are using subtraction.
The difference of 11 and 4 times a number equals 3
This means the numbers we are subtracting are 11 and 4n. (11 - 4n)
The difference of 11 and 4 times a number equals 3
This means our equation is equal to 3. (11 - 4n = 3)
Now we solve for N.
11 - 4n = 3
Start by subtracting 11 from both sides to work to isolate N.
11 - 11 - 4n = 3 - 11
-4n = -8
Next, divide both sides by -4 to finish isolating n.
-4/-4n = -8/-4
n = 2
I hope this helped you and have a great day!
The number in the equation is 2, as that when multiplied by 4 results in 8, and when subtracted from 11 gives 3.
Explanation:The question is looking for a number that, when multiplied by 4 and subtracted from 11, equals 3. We can represent this with the equation 11 - 4x = 3. To solve for x, we first move 4x to other side by adding 4x to both sides. This gives us 11 = 4x + 3. Then, we subtract 3 from both sides which gives us 8 = 4x. Finally, to solve for x, we divide both sides by 4. Therefore, x = 8 / 4 = 2.
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pls help with number 2 will give brainliest
Answers
Answer:41% i think i am pretty sure
Step-by-step explanation:
don't have one
what is the solution to −1.2b−5.3≥1.9
Answers
Answer:
If you want me to solve for b then
b ≤ − 6
The solution to the given inequality is b≤-6.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is -1.2b-5.3≥1.9.
Add 5.3 on both the sides of an inequality, we get
-1.2b≥7.2
Divide -1.2 on both the sides of an inequality, we get
b≤-6
In interval notation: (-∞,-6]
Therefore, the solution is b≤-6.
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Solve for X. Each figure is a parallelogram.
Answers
Answer:
x = 3
Step-by-step explanation:
m < T = m < R (Because they are opposite angles of a parallelogram). Therefore:-
40x + 2 = 122
40x = 120
x = 120/40
x = 3
Parallelogram is the closed shaped quadrilateral which has opposite site equal and the opposite angle are equal. The value of the x is 3 units.
Given-For the parallelogram angle T is (40x+2) degrees.
The angle R is 122 degrees.
To solve this the it should be known about the angle of the parallelogram.
Parallelogram-Parallelogram is the closed shaped quadrilateral which has opposite site equal and the opposite angle are equal.
As in the given figure the angle T and angle R is the opposite angle. Thus angle T and angle R will be equal to the each other. Thus,
[tex]\angle T= \angle R[/tex]
Put the values of the angle in the above equation. Thus,
[tex]40x+2=122[/tex]
[tex]40x=122-2[/tex]
[tex]40x=120[/tex]
[tex]x=\dfrac{120}{40}[/tex]
[tex]x=3[/tex]
Hence the value of the x is 3.
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Find the quotient. 1,458/26
Answers
1458/26 = 56.0769230769
Hope this helps! <3
The quotient is 56, and there is a remainder of 2.
The quotient of 1,458 divided by 26 is 56. In long division, you would set up the problem as follows:
56
__________
26 | 1,458
You start by asking how many times 26 can fit into 145 (the first two digits of 1,458). The answer is 5 (5 times 26 equals 130).
You write the 5 above the line and subtract 130 from 145, leaving you with 15.
Then, you bring down the next digit, which is 8, making it 158. You repeat the process, finding that 26 goes into 158 six times (6 times 26 equals 156).
Write the 6 above the line, and you're left with a remainder of 2. So, the quotient is 56, and there is a remainder of 2.
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PLEASE HELP 29 POINTS!
What is the difference between direct variation and constant variation?
Answers
Hi,
Direct variation
When two variables quantities have a ratio, then their relationship is called a direct variation.
Constant variation
The constant ratio between two variables quantities is called constant variation.
X varies directly and inversely with z. X=20 when y=8 and z=4 . Find x when y=4 and z =8
Answers
Answer:
Value of x = 5 .
Step-by-step explanation:
Combined variation states that describes a situation where a variable depends on two (or more) other variables, and varies directly with some of them and varies inversely with others.
Given: x varies directly with y and inversely with z.
i.e [tex]x \propto y[/tex] and [tex]x \propto \frac{1}{z}[/tex]
then we have the combined variation as;
[tex]x = k\frac{y}{z}[/tex] ......[1] where k is the constant variation.
Substitute the value of x =20 when y =8 and z = 4 to solve for k;
[tex]20 = k\frac{8}{4}[/tex]
Simplify:
[tex]20 = 2k[/tex]
Divide both sides by 2 we get;
[tex]k = 10[/tex]
Now, substitute k =10 , y =4 and z = 8 to find x;
Using [1] we have;
[tex]x = 10 \times \frac{4}{8} = 10 \times \frac{1}{2} = 5[/tex]
Therefore, the value of x is, 5
The problem involves the concept of direct and inverse variation. From the given conditions, a constant of variation 'k' is calculated as 1.6. Using this 'k', x is found to be 20 when y is 4 and z is 8.
Explanation:This question involves the concept of direct and inverse variation. When it is stated that 'x varies directly and inversely with z', it implies a relationship which can be written in the form of y = kx/z, where k is a constant of variation.
To find the constant, we plug in the provided values for x, y, and z into our equation. Hence, using the known values (x=20, y=8, and z=4), our equation becomes 8 = 20k/4. Simplifying this gives us k = 1.6.
Now, to find the value of x when y=4 and z=8, we substitute these into the equation giving us 4 = 1.6x/8. Solving for x, we find that x = 20.
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what is the definition of exponential decay
Answers
Answer:
When a population or group of something is declining, and the amount that decreases is proportional to the size of the population, it's called exponential decay. In exponential decay, the total value decreases but the proportion that leaves remains constant over time.
Step-by-step explanation:
Answer:
[tex]y =Ae^{-kx}[/tex]
would be the exponential decay function for initial population A and decaly rate is -k.
Step-by-step explanation:
Exponential decay occurs when rate of change of population or any other quantity is proportional to the present population or quantity present
i.e. if y is the population
then dy/dx = -ky where k is a positive constant of proportionality
[tex]\frac{dy}{y} =-kdx\\ln y = -kx+C\\y = e^{-kx+C} =Ae^{-kx}[/tex]
Based on the graph below, what are the solutions to the equation f(x) = g(x)?
A. x = −2.4, 1.4, 3.9
B. x = −2.4, 0.25, 1.4
C. x = −2, 2, 3
D. x = −2, 1, 3
Answers
Look at the picture.
f(x) = g(x) - x for which the graphs intersect.
Answer: A. x = -2.4, x = 1.4, x = 3.9Answer by YourHope:
HI! :)
Based on the graph below, what are the solutions to the equation f(x) = g(x)?
A. x = -2.4, x = 1.4, x = 3.9!
:)
A country with an area of 425 square miles has a population of 9,350 residents. Which rate best represents the relationship between the population and the area of the country
Answers
Answer:
22 residents per square mile is the correct answer.
Step-by-step explanation:
One way to find the answer is the following:
The first number to be considered is 425, which is the total amount of square miles.
The second one is 9,350 that represents the amount of residents.
To find the answer, we have to perform the following calculation:
9350%425=22, which is the correct answer.
Step-by-step explanation:
hahaha have a great weekend and happy birthday to you i q and happy birthday really want to get together
A recipe calls for 12 cups of blueberries to make 7 jars of blueberry jam.
What is true about the number of cups of blueberries in each jar?
Each jar has 7/12 cup of blueberries.
Each jar has 1/12 of 7 cups of blueberries.
Each jar has 12/7 cups of blueberries.
Each jar has 1 5/12 cups of blueberries.
Answers
Answer:
Each jar has 12/7 cups of blueberries.
Step-by-step explanation:
To find out how many cups of blueberries per jar, we take the number of cups of blue berries and divide by the number of jars
12 cups/7 jars
12/7 cups of blueberries per jar
Each jar has 12/7 cups of blueberries.
Answer:
Step-by-step explanation:
you are making scarves for presents each scarf needs 3/4 yards of fabric how many yards of fabric do you need for 6 scarves
Answers
Answer: 8/1
Step-by-step explanation: 6/1 x 3/4= 24/3( divide both numbers by 3) and you get 8/1 yards of fabric.
Answer:
18/4
Step-by-step explanation:
3/4 per scarf
6 scarfs
6*(3/4)=(18/4)=4.5 yards
GEOMETRY HELP PLEASE!!!!!!! Josh is building an enclosure with recycled cardboard for his collection of model cars his design is as shown below:
What is the length of side BC in inches?
A) 14
B) 43
C) 49
D) 63
Answers
Chole bought 4 movie tickets. Each ticket cost $6. What was the total cost of the movie tickets
Answers
Answer:
$24
Step-by-step explanation:
So, Basically you multiply 4 times 6 because you have 4 tickets that cost $6
and you would get 24 and add a dollar sign you should be good.
Can you help me I can’t figure it out!
Answers
Answer:
C, 17.3
Step-by-step explanation:
Mean is the average of the numbers. To get the mean, add all the numbers up, and divide them by how many numbers there were. Let's do that.
(16.8 + 12.3 + 19 + 17.5 + 18.2 + 17.5)/6
Simplify
101.3/6
Simplify.
~16.88
The closest estimate to that is C, 17.3
if the pet store had 10 more birds the number of dogs would be double the number of birds what number should be on the scale explain how you solved
Answers
Answer:
one that fits
Step-by-step explanation:
#Bird+10 so #dog=2(#birds+10)
Answer:
We are gonna called birds [tex]x[/tex] and dogs [tex]y[/tex]. So, if pet store had 10 more birds the number of dogs would be double, this means that:
[tex]y=2(x+10)[/tex]
In the expression we have 10 more birds [tex]x+10[/tex], and the number of dogs is the double of these birds, which give us the expression.
So, the range of values would be:
If there are 10 birds, there would be 20 dogs.
If there are 11 birds, there would be 22 dogs.
If there are 12 birds, there would be 24 dogs, and so on...
13 birds, 26 dogs.
14 birds, 28 dogs.
All these results are given by the expression we found.
Solve for the compound inequality 6b<24 or 4b+12>4
Answers
6b < 24 divide both sides by 6
b < 4
4b + 12 > 4 subtract 12 from both sides
4b > -8 divide both sides by 4
b > -2
Answer: -2 < b < 4 → b∈(-2, 4)As Saturn revolves around the sun, it travels at a speed of approximately 6
miles per second. Convert this speed to kilometers per second. At this speed, how many kilometers will Saturn travel in 2 seconds? In your computations, assume that 1
mile is equal to 1.6 kilometers. Do not round your answers.
Answers
Answer:
Speed = 9.6 km/s
Distance traveled in 2 seconds = 19.2 km
Step-by-step explanation:
Given that revolving speed of the Saturn around the sun = 6 miles per second
We need to convert this speed into kilometers per second.
Given that 1 mile = 1.6 kilometers so plug that into above speed. We get:
Revolving speed of the Saturn around the sun = (6)(1.6) kilometers per second.
Revolving speed of the Saturn around the sun = 9.6 kilometers per second.
Now to find distance travelled in 2 seconds, we just need too multiply the speed by time.
Distance = (9.6)(2)= 19.2 Kilometers.
Hence final answer is:
Speed = 9.6 km/s
Distance traveled in 2 seconds = 19.2 km
Answer:
Speed: 9.6 km/s
Distance traveled in 2 seconds: 19.2 km
Step-by-step explanation:
Speed: S=6 miles per second=6 miles/s
S=(6 miles/s)(1.6 km/1 mile)→S=(6)(1.6) km/s→S=9.6 km/s
S=9.6 km per second, that means in 1 second the distance traveled is 9.6 km, then in 2 seconds the distance traveled is 2(9.6 km)=19.2 km or
S=d/t
Distance: d
Time: t
Replacing the known values:
9.6 km/s=d/(2 s)
Solving for d: Multiplying both sides of the equation by 2 s:
(2 s)(9.6 km/s)=(2 s)d/(2 s)
19.2 km=d
d=19.2 km
heelp will give brianliest
Answers
Answer:
256
Step-by-step explanation:
4(7)^2 + 30(2)
196 + 60 = 256
Solve the system of elimination -2x+2y+3z=0 -2x-y+z=-3 2x+3y+3z=5
Answers
Answer:
x = 1 , y = 1 and z = 0
Step-by-step explanation:
-2x+2y+3z=0 ------(1)
-2x-y+z=-3 --------(2)
2x+3y+3z=5 ---------(3)
To find the values of x,y and z
(3) - (2)⇒ 2y + 4z = 2
y + 2z = 1 --------(4)
(1) - (2)⇒ 3y +2z =3 ---(5)
(5) - (4)⇒ 2y = 2
y = 1
Substituting the value of y in (4) we get z =0
Substituting the value of y and z in (1) we get x = 1
Therefore x = 1 , y = 1 and z = 0
An equation that expresses a mathematical rule or relationship is a ___.
proportion
conversion factor
formula
ratio
Answers
C. Formula.
The equation that expresses a mathematical rule or relationship is called a formula.
What is a formula?A formula in mathematics is an assertion of a fact, rule, or principle using mathematical symbols. Equations, equalities, identities, inequalities, and asymptotic expressions are a few examples of formulae.
Few examples of formulae are:
(a + b)^2 = a^2 + b^2 + 2ab
(a - b)^2 = a^2 + b^2 - 2ab
(a + b)^3 = a^3 + b^3 + 3ab(a + b)
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A rectangle has a length of \sqrt[3]{81} and a width of 3^{\frac{2}{3}} inches. Find the area of the rectangle.
Answers
[tex] \sqrt[3]{81} \times 3^{ \frac{2}{3 } } = \sqrt[3]{ {9}^{2} } \times {3}^{ \frac{2}{3} } = {9}^{ \frac{2}{3} } \times {3}^{ \frac{2}{3} } = \\ 3^{ \frac{4}{3} } \times {3}^{ \frac{2}{3} } = 3^{ \frac{6}{3} } = 9[/tex]
Answer:
The area of the rectangle is 9.
Step-by-step explanation:
The first thing to take into account is that the area of a rectangle is obtained by multiplying its length and width.
[tex]area=length\times width[/tex]
The problem says that the length is [tex]\sqrt[3]{81}[/tex] and the width is [tex]3^{\frac{2}{3}}[/tex]. So, to find the area we must replace the values of length and width into the previous expression.
[tex]area=length\times width[/tex]
[tex]area=(\sqrt[3]{81})\times (3^{\frac{2}{3}})[/tex]
The previous seems to be difficult but with a little of manipulation we can get a result without a calculator.
First step: the term [tex]\sqrt[3]{81}[/tex] could be written as exponential expression.
[tex]area=(81^{\frac{1}{3}})\times (3^{\frac{2}{3}})[/tex]
Second step: the term [tex]3^{\frac{2}{3}}[/tex] could be written in other way.
[tex]area=(81^{\frac{1}{3}})\times ((3^2)^{\frac{1}{3}})[/tex]
Third step: in the same way, the term [tex]81^{\frac{1}{3}}[/tex] could be written in other way taking into account that [tex]81=9^2[/tex].
[tex]area=((9^2)^{\frac{1}{3}})\times ((3^2)^{\frac{1}{3}})[/tex]
Forth step: the two terms must have the same base to apply other exponential rules; for example, the base could be 9.
[tex]area=(9^{\frac{2}{3}})\times (9^{\frac{1}{3}})[/tex]
Fifth step: as both terms have the same base, we must add the exponents and simplify the expression.
[tex]area=9^{\frac{2}{3}}\times 9^{\frac{1}{3}}[/tex]
[tex]area=9^{\frac{2}{3}+\frac{1}{3}}[/tex]
[tex]area=9^{\frac{3}{3}}[/tex]
[tex]area=9^1[/tex]
[tex]area=9[/tex]
Thus, the area of the rectangle is 9.
Please help me quick! I need this before tomorrow!
Round each number to the nearest tenth.
What is the best estimate for the answer to 26.73 + 89.42?
Answers
Answer:
116.1
Step-by-step explanation:
If you round each decimal to the nearest tenth it would be 26.7 + 89.4 because you round up if it is 6 and above and round down for 5 and below. The rest is just simple addition.