if p(x,y) is the point on the unit circle defined by real number theta, then csc theta= _____. a. x/y. b. y/x. c. 1/x. d. 1/y.
Answers
Answer:
Option d is correct
[tex]Csc \ \theta =\frac{1}{y}[/tex]
Step-by-step explanation:
Here P(x,y) is the point on unit circle ( unit circle has radius 1 and center (0,0))
Now in a diagram we can see that
OA= x
AP= y
radius OP =1
∠POA =θ
Now in ΔAOP
[tex]Csc\ \theta =\frac{hypotenuse }{opposite \ side} \\Csc\ \theta =\frac{OP}{AP}[/tex]
[tex]Csc \ \theta =\frac{1}{y}[/tex] ( since OP =1 and AP =y)
Answer:
1/y
Step-by-step explanation:
apex
Related Questions
a scale model of a statue is 7 inches tall. The scale of the model is 1in./1.5ft. what is the actual height of the statue?
Answers
So the scale of the model is 1:18
now just multiply 7 by 18 to get-
126 inches, or 10.5 feet
If a road has a 4% grade and rises 200 feet, what is the run?
Answers
as an equation 4%=0.04
0.04*run=200
so run=200/0.04
run=5000feet
Answer:
5000
Step-by-step explanation:
400 ÷ 4% = 5000
Traveling at 45 miles per hour, how many minutes, rounded to the nearest whole number, does it take to drive 240 miles from Orlando to Miami?
a. 5
b. 195
c. 285
d. 320
Answers
D. 320 would be the correct answer.
Jen is making a frame to stretch a canvas over for a painting. She nailed four pieces of wood together at what she believes will be the four vertices of a square. How can she be sure that the canvas will be a square?
a. All four of the pieces of wood are the same length & at least two interior angles are congruent.
b. At least two pieces of wood are the same length & at least two interior angles are congruent.
c. At least two pieces of wood are the same length & all four interior angles are congruent.
d. All four of the pieces of wood are the same length & all four interior angles are congruent.
Answers
Hope you will find it helpful!
9 times as many as 457 is
Answers
Given F(x) = log8 x, find F(64). ...?
Answers
Below is the solution:
f(64) = log8 64
= log8 8^2
= 2 log8 8
= 2
Answer:
[tex]F(64)=2[/tex]
Step-by-step explanation:
Given the funtion:
[tex]F(x)=log_8(64)[/tex]
We need to find the value of the function at x=64:
[tex]F(64)=log_8(64)= z[/tex]
Where z is the value we are trying to find. In order to find z, let's use the definition of the base of a log:
[tex]log_xy=z\Rightarrow x^z=y[/tex]
So:
[tex]8^z=64[/tex]
Express [tex]8^z[/tex] as:
[tex]2^{3z}[/tex]
And express 64 as:
[tex]2^6[/tex]
Which leads to:
[tex]2^{3z}=2^6[/tex]
Equate exponents of 2 on both sides:
[tex]3z=6[/tex]
Solving for z:
[tex]z=\frac{6}{3} =2[/tex]
Therefore:
[tex]F(64)=log_8(64)= z=2[/tex]
Which of the points shown below are on the line given by the equation y = 5x? Check all that apply.
A. Point A: (5, -1)
B. Point B: (1, 5)
C. Point C: (0, 0)
D. Point D: (-3, 2)
Answers
The correct Options are B and C.
What is Function of graph ?The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We may alternatively say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function. Allow f(x) to equal x2 - 3.The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point.To solve y = 5x we check all options in equation by value putting.
let y = 5x .......................(1)
Put point A ( 5, -1) in equation (1)
So, x = 5 & y = -1
y = 5x ⇒ -1 = 5 ×5= 25
Put point B (1,5) in equation (1)
So, x = 1 & y = 5
y = 5x ⇒ 5 = 5 × 1 = 5
Put point C (0,0) in equation (1)
x = 0 & y = 0
y = 5x ⇒ 0 = 5 × 0 =0
Put point D ( -3 ,2) in equation (1)
x = -3 & y = 2
y = 5x ⇒ 2 = -3× 2 = -6
In all these points , B & C points are have same value on both side.
So, we can say that b&c are the points which are shown on the line.
Therefore, The correct Options are B and C.
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What is the value of x? 18-7x = -20.5
Answers
you have: 18-7x= -20.5
Isolate the variable x
18-7x= -20.5
18-7x= -20.5
-18 -18
-7x=-38.5
Now simply divide-->>
x=5.5
Thus, your answer.
Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is –99.
Which equation can be used to find m, the midpoint of the two numbers?
(m – 5)(m + 5) = 99
(m – 10)(m + 10) = 99
m2 – 25 = –99
m2 – 100 = –99
Answers
proof
m2 – 100 =(m – 10)(m + 10)
for eg. m=1, (-9)(11)= –99
The equation can be used to find m, is [tex]m^{2} -100 = -99[/tex].
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
According to the given question.
We have two numbers.
Both are 10 m away from their midpoint, m.
Therefore,
If the first number is ( m + 10).
Then the second number will (m-10).
Also it is given that the product of these two numbers is 99.
⇒ [tex]( m + 10)( m - 10) = -99[/tex]
⇒ [tex]m^{2} -10m + 10m -100 = -99[/tex]
⇒ [tex]m^{2} - 100 = -99[/tex]
Hence, the equation can be used to find m, is [tex]m^{2} -100 = -99[/tex].
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A square has an area of 80 square inches. What is the length of a side of the square, in inches?
Answers
To find the length of a side of a square with an area of 80 square inches, we take the square root of the area. This results in each side of the square being approximately 8.944 inches long.
Explanation:The question is asking to find the length of a side of a square that has an area of 80 square inches. In geometry, the area of a square is calculated by squaring the length of one side. Therefore, to find the length of a side when you know the area, you need to take the square root of the area.
So, in this case, we take the square root of 80. Using a calculator, this results in approximately 8.944 inches. Therefore, each side of the square is about 8.944 inches long.
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If a and b are positive numbers, find the maximum value of f(x)=x^a*(1-x)^b, 0 less than or equal to x less than or equal to 1.
Your answer may depend on a and b. What is the maximum value? ...?
Answers
If a < 1 or b < 1, this may not be defined at one or both of the end points. f '(x) = 0 if the right most term is zero.
a - ax - bx = 0 ==> x = a/(a + b).
Note that this number is both well define and is between 0 and 1.
f(0) = 0
f(1) = 0,
f(a/(a+b)) = a^ab^b/(a + b)^(a + b) <--- the maximum value.
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find (2 × 107) (3 × 104).
Answers
------------
(2 × 107) = 214
(3 × 104) = 312
------------------------------
312 x 214
---------------------------
= 66768
Which statement is correct?
A horizontal line has no slope.
A vertical line has a slope of zero.
A line that rises from left to right has a positive slope.
A line that falls from right to left has a negative slope.
Answers
Answer:
A line that rises from left to right has a positive slope
Step-by-step explanation:
Verify each statement
case A) A horizontal line has no slope
The statement is False
Because a horizontal line has a slope equal to zero
case B) A vertical line has a slope of zero
The statement is False
Because a vertical line has a undefined slope
case C) A line that rises from left to right has a positive slope
The statement is True
case D) A line that falls right to left has a negative slope
The statement is False
Because a is a positive slope
In the equation y = mx + b, b represents:
A. slope
B. rise
C. y - intercept
D. x - intercept
Answers
If you help, please finish the answer, because I really need help. Everyone disappears on me.
Answers
Hope this helps!!! :)
at her job, mary works 4 hours on monday, 3 hours on wednesday, and 6 hours on saturday. her boss adds a $10 bonus to her paycheck, which then totals $120.50. what is mary's hourly pay?
a. $8.50
b. $9.27
c. $5.24
d. $8.05
Answers
13x=110.50
x=8.5
so she makes $8.50 an hour which is A.
Which set of ordered pairs in the form (x,y) does not represent a function of x?
A {(-1,2),(3,-2),(0,1),(5,2)}
B. {(-1,2),(3,2),(-2,2),(0,2)}
C. {(-1,2),(3,-2),(0,1),(3,5)}
D. {(-1,2),(2,3),(3,-2),(-2,0)}
Answers
Answer:
Option C
Step-by-step explanation:
A function is a relation that does not contain two pairs with same first component.
Option A
{(-1,2),(3,-2),(0,1),(5,2)} is a function, since there are no two pairs with the same first component.
option B
{(-1,2),(3,2),(-2,2),(0,2)} is a function, since there are no two pairs with the same first component.
option C
{(-1,2),(3,-2),(0,1),(3,5)} is not a function, since there are two pairs with the same first component i.e, 3
OptionD
{(-1,2),(2,3),(3,-2),(-2,0)} is a function, since there are no two pairs with the same first component.
So, {(-1,2),(3,-2),(0,1),(3,5)} is the required answer.
What is the product of written in simplest form? 7/10 divided by 5/6
Answers
We can re-write it as:
7/10 * 6/5 = 42/50 = 21/25
So, your final answer is 21/25
Find the radius of a circle with an area of 90 cm^2
Answers
so 90=pi*r^2
r=square root(90/pi)
r=5.35
Find the values of x and y drawing not to scale
Answers
Part 1)
In this problem we know that
[tex]4y\°+112\°=180\°[/tex] ------> by supplementary angles
solve for y
[tex]4y\°=180\°-112\°[/tex]
[tex]y=68\°/4[/tex]
[tex]y=17\°[/tex]
Part 2)
In this problem we know that
[tex]7x+7=112\°[/tex] ------> by vertical angles
solve for x
[tex]7x=112\°-7\°[/tex]
[tex]x=105\°/7[/tex]
[tex]x=15\°[/tex]
therefore
the answer is the option A
[tex]x=15\°, y=17\°[/tex]
if you found 259 to the nearest hundreds,what is the answer
Answers
this is because the number in the tens column is 5 or above therefore you round up.
hope this helps you
Let U = {21, 22, 23, ..., 40}, A = {21, 22, 23, 24, 25}, B = {26, 27, 28, 29}, C = {21, 23, 25, 27, ..., 39}, and D = {22, 24, 26, 28, ..., 40}.
Use the roster method to write the following set.
11) Aʹ
Answers
The complement of set A with respect to the universal set U (A') is {26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}, which contains all elements in U that are not in set A.
Explanation:The student is asked to use the roster method to write the set A', which represents the complement of set A with respect to the universal set U. The set A' consists of all elements in the universal set U that are not in set A.
First, we list all the elements of the universal set U, which are {21, 22, 23, ..., 40}. Set A contains {21, 22, 23, 24, 25}. To find A', we remove the elements of A from U, resulting in A' = {26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}.
Final answer:
The set A' includes all numbers from 26 to 40 in the universal set U, which are not included in set A.
Explanation:
To find the set A' or the complement of set A in the universal set U, we need to list all the elements in U that are not in A. Given that the universal set U consists of the numbers 21 through 40, and the set A includes the numbers 21, 22, 23, 24, and 25, we can determine A' by subtracting these from U.
The roster method simply lists out all of the elements. Doing so for A' yields the following:
A' = {26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}
These are all the numbers in U that are not in A.
Absolute value?? |x+2|=10
Answers
Answer:
x=8 or just x+2=10
Step-by-step explanation:
if you wanted to know this without absolute value, its still x+2=10. if you wanna know what 'x' is, its 8.
what is 200 times 16?
Answers
You're welcome ;>
What is the absolute value of 6?
Answers
Answer:
absolute value is 6
is y = x an additive Relationship? Explain.
Answers
During the National Football League’s 1999 season, Troy Aikman, the quarterback for the Dallas Cowboys, earned $0.467 million more than Deion Sanders, the Cowboys cornerback. Together they cost the Cowboys $12.867 million. How much did each player make?
Answers
Troy Aikman make 6667000 and Deion Sanders makes 6200000 for the Cowboys cornerback.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Troy Aikman, the quarterback for the Dallas Cowboys, earned $0.467 million more than Deion Sanders
Let Deion Sanders earning is x.
Troy Aikman earning is x+467000
Together they cost the Cowboys $12.867 million
x+x+467000=12867000
2x+467000=12867000
Subtract 467000 on both sides
2x=12867000-467000
2x=12400000
Divide both sides by 2
x=6200000
So Troy Aikman make 6200000+467000=6667000 and
Deion Sanders makes 6200000
Hence Troy Aikman make 6667000 and Deion Sanders makes 6200000 for the Cowboys cornerback.
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simplest form for 21/49
Answers
=3/7(divide by 7 numerator and denominator)
PLs brainliest answer
They are offering chocolate, vanilla, strawbrry ice cream. and they ar also can choose from toppings chocolate syrup, sprinkles, caramel, or whipped cream. how many sundae combinations ar possible
Answers
V- CS,S,C,W
S- CS,S,C,W
12 combinations ( 4x3)
Final answer:
By using the counting principle and multiplying the choices for ice cream flavors (3) by the choices for toppings (4), we find there are 12 possible sundae combinations.
Explanation:
To determine the number of possible sundae combinations with the given choices, we can use the counting principle. We multiply the number of options for each category. In this case, there are three choices for ice cream flavors (chocolate, vanilla, and strawberry) and four choices for toppings (chocolate syrup, sprinkles, caramel, and whipped cream).
Since a sundae consists of one ice cream flavor and one topping, we simply multiply the number of options for ice cream by the number of options for toppings.
3 ice cream flavors × 4 toppings = 12 possible combinations.
Therefore, there are 12 unique sundae combinations a customer can choose from.
A survey by the state health department found that the average person ate 208 pounds of vegetables last year and 125 5/8 pounds of fruit.What fraction of the total pounds of fruit and vegetables do the pounds of fruits represent?
Answers
Answer: The fraction of pounds of fruits over total pounds of fruits and vegetables is given by
[tex]\frac{25125}{66724}[/tex]
Step-by-step explanation:
Since we have given that
Total amount of vegetables = 208 pounds
Total amount of fruits is given by
[tex]125\frac{5}{8}\text{ pounds}[/tex]
Total amount of fruits and vegetables is given by
[tex]208+125\frac{5}{8}\\\\=208+\frac{1005}{8}\\\\=\frac{1664+1005}{8}\\\\=\frac{2669}{8}\\\\=333.625\text{ pounds }[/tex]
So, we need to find the fraction of pounds of fruits over the total pounds of fruit and vegetables :
[tex]\frac{\text{Pounds of fruits }}{\text{ total pounds of fruits and vegetables}}\\\\=\frac{\frac{1005}{8}}{333.62}\\\\=\frac{1005}{8\times 333.62}\\\\=\frac{1005}{2668.96}=\frac{25125}{66724}[/tex]
The fraction of the total pounds of fruit and vegetables that fruits represent is approximately 0.377, or 37.7%.
Explanation:To find out what fraction the pounds of fruits represent out of the total pounds of fruits and vegetables, we first need to calculate the total pounds of fruits and vegetables consumed. This is found by adding the pounds of vegetables (208) to the pounds of fruits (125 5/8). So, 208 + 125 5/8 = 333 5/8 pounds.
Now, to determine the fraction, we take the pounds of fruits and divide by the total. Hence, the fraction is given by 125 5/8 ÷ 333 5/8. To divide fractions, we multiply by the reciprocal of the divisor, which gives us (125 5/8) * (8/333) = 0.377 (rounded to three decimal places).
Therefore, fruits represent approximately 0.377, or 37.7% of the total pounds of fruits and vegetables consumed.
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