Given csc(A) = 60/16 and that angle A is in Quadrant I, find the exact value of sec A in simplest radical form using a rational denominator . Someone please help me!
Answer:
[tex] \frac{15 \sqrt{209} }{209} [/tex]
Step-by-step explanation:
Objective: Understand and work with trig identies.
Recall multiple trig identies and manipulate them to get from cosecant to secant.
Given
[tex] \csc(a) = \frac{60}{16} [/tex]
Apply reciprocal identity csc a = 1/sin a.
[tex] \sin(a) = \frac{16}{60} [/tex]
Apply pythagorean identity to find cos a.
[tex]( \frac{16}{60}) {}^{2} + \cos(x) {}^{2} = 1[/tex]
[tex] \frac{256}{3600} + \cos(x) {}^{2} = 1[/tex]
[tex] \cos(x) {}^{2} = \frac{3600}{3600} - \frac{256}{3600} [/tex]
We can simplify both expression
[tex] \cos(x) {}^{2} = \frac{225}{225} - \frac{16}{225} [/tex]
[tex] \cos(x) = \frac{ \sqrt{209} }{15} [/tex]
Cosine is positve on quadrant 1 so that cos(a)
Apply reciprocal identity sec a= 1/ cos a.
The answer is
[tex] \sec(a) = \frac{15}{ \sqrt{209} } [/tex]
Rationalize the denominator.
[tex] \frac{15}{ \sqrt{209} } \times \frac{ \sqrt{209} }{ \sqrt{209} } = \frac{15 \sqrt{209} }{209} [/tex]
Find the center and the radius of the circle with the equation:
x2 - 2x + y2 + 4y + 1 = 0
Complete the square:
x ^2 - 2x + y ^2 + 4y + 1 = 0
(x - 1)^2 + (y + 2)^2 + 1 = 1 + 4
(x - 1)^2 + (y + 2)^2 = 4 = 2^2
Hence the center is (1, -2) and the radius is 2. (D)
Graph the system below and write its solution.
2x+y=4
1
y =
2*-1
Note that you can also answer "No solution" or "Infinitely many" solutions.
.
Solution:
?
No
solution
Infinitely
many
(0,0)
0
5
?
Answer:
2x+y=4
2times-1 is -2
2x+-2=4
2x=4
x=2
can someone pls help for brainlest
Answer:
12.56 in ^2
Step-by-step explanation:
First find the area of a circle with radius 4
A = pi r^2
A = (3.14) 4^2
A =50.24
Since it is 1/4 of a circle, multiply by 1/4
1/4 ( 50.24)
12.56
Answer:
Quarter circle's area is 12.56 inches².
Step-by-step explanation:
Concept:- Firstly, we need to find the area of circle and Since, it is quarter of circle we need to multiply the area of circle by 1/4. and we get answer
✯ Solution ✯Finding area of circle
Using Formula
Area of circle = π × r ²
Where,
r ,is the radius of circleAnd we have given
Radius, r of circle is 4 in.Value of π is 3.14Substitute the value into the formula
Area of circle = 3.14 × ( 4 in. )/²
now,
Area of circle = 3.14 × 16 in ².
multiply , we get
Area of circle is 50.24 nches ²
As have to find the quarter circle's area ,
and we know that quarter is the one fourth of the circle .
Quarter circle's area = Area of circle × 1/4
Multiply , we get
Quarter circle's area = 50.24 × 1/4
Therefore, quarter circle's area is 12.56 inches².
helpppppppppppp!!!!!!!!!!!!!!
Answer:
480N
Step-by-step explanation:
answer is in photo above
Select the correct answer.
How would you write this expression as a sum or difference?
[tex]log_{3} (^{5\sqrt{x}} X y )[/tex]
Answer:
[tex]\log_{3} ({5\sqrt{x}} * y ) = \log_{3}({5) + \log_{3}(\sqrt{x}) +\log_{3}( y )[/tex]
Step-by-step explanation:
Given
[tex]\log_{3} ({5\sqrt{x}} * y )[/tex]
Required
Write as sum or difference
Using addition law of logarithm, the equation becomes:
[tex]\log_{3} ({5\sqrt{x}} * y ) = \log_{3}({5\sqrt{x}) +\log_{3}( y )[/tex]
Expand
[tex]\log_{3} ({5\sqrt{x}} * y ) = \log_{3}({5 * \sqrt{x}) +\log_{3}( y )[/tex]
Apply addition law
[tex]\log_{3} ({5\sqrt{x}} * y ) = \log_{3}({5) + \log_{3}(\sqrt{x}) +\log_{3}( y )[/tex]
True or False: in a table of a proportional relationship, the ratio or y/x is constant.
Answer:
true
Step-by-step explanation:
It is True that in a table of a proportional relationship, the ratio or y/x is constant.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
It is given that, y∝x
In order to eradicate the proportional sign introduces the constant as,
y=kx
k=y/x
k is the constant value.
Thus, it is True that in a table of a proportional relationship, the ratio or y/x is constant.
Learn more about the proportional here:
brainly.com/question/14263719
#SPJ2
ILL BRAINLIEST YOU IF YOU HELP ME PLEASE
option C is correct
b and c are parallel lines because they both are making equal angles at the point of intersection with line d
Answer:
the answer is c. because
95 plus 85 is equal to 180 mean its straight line
Step-by-step explanation:
please help me oh my lord
Answer:
A
Step-by-step explanation:
What is the value of c?
30°
с
Answer:
c = 60°
Step-by-step explanation:
Since the measures are among a 90° angle, we need to subtract 30° from 90° which equals 60°
c = 60°
45
24
K K
AM
51
이
15
17
15
이
8
15
O
8
17
음
Hope this help!!!
Have a nice day!!!!
What is the value of X in the figure below? In this diagram ∆ABD is similar to ∆CAD.
Answer:
F. 45/4Step-by-step explanation:
Corresponding sides have same ratio:
AB/AC = BD/ADFind AB:
AB = [tex]\sqrt{20^2-15^2} = 5\sqrt{7}[/tex]Find AD:
AD = √15²-x²Now the ratio:
5√7/15 = (20 - x)/√(15²-x²)√7 *√(225-x²)= 3(20 - x)7(225 - x²) = 9(20 -x)²7*225 - 7x² = 9(400 - 40x + x²)1575 - 7x² = 3600 - 360x + 9x²16x² - 360x + 2025 = 0(4x)² - 2*4x*45 + 45² = 0(4x - 45)² = 04x - 45 = 04x = 45x = 45/4Correct choice is F
Look at the number line below. Write the letter for each fraction in the correct box.
Answer:
DCAB
I arranged in increasing order
Answer:
DCAB
Step-by-step explanation:
[tex]A = \frac{2}{5} = 0.40\\\\B= \frac{2}{3} = 0.66\\\\C= \frac{1}{4} = 0.25\\\\D =\frac{1}{10} = 0.10[/tex]
So moving from least to highest DCAB
pleaseeee helpppp meee!!
Answer:
15 players on each team
Step-by-step explanation:
- 2 players from EACH team is subtracted= 2(players)x6(teams) = 12 players in total off the field
- now there are only 78 players on the field
(78+12)/6= 15
-Adding the amount of players on the feild and the players that were sent for equitment is 90. Then dividing 90 by the amount of teams there are, 6
lol it looks easy but everytime i submit my answer it ends up wrong sooo help pls
Answer:
(y+8)(y+2)
Step-by-step explanation:
y^2 + 10y + 16
What two numbers multiply to 16 and add to 10
8*2 = 16
8+2 =10
(y+8)(y+2)
What is cosθ = _____ based on this image
a)-3/5
b)-4/3
c)-4/5
d)-3/4
1.
Line RK
Line TY
Line RU
Line PQ
2. Pick three
- X
- T
- Q
- U
- Y
3. Pick three
- X
- s
- P
- R
- U
- T
4.
Plane QRP
Plane XUY
Plane s
Plane TRY
5. Show work if possible pls
(1/2, 4)
(4, 1/2)
(8, 1)
(1, 8)
6. Round to one decimal point
7-11. Show work if possible plz!
Answer:
the answer is plane try I'm pretty sure it's that.
b
144°
с
Help me please
Answer:
b=36 and c=144
Step-by-step explanation:
b+144=180, b=36
b+c=180, c=180-36=144
please help me answer this!!
Answer:
(x, y) = (10, 290)
Step-by-step explanation:
From the table
Total fees = fixed + variable
Fixed:
When number of times Ahmed mowed, x = 0
y = 40
When x = 2, y = 65
Rate of change = y2 - y1
= 65 - 40
= 25
y = 40 + 25x
Where,
y = total fees charged
40 = fixed fee
25x = variable fee
Total amount Ahmed will make for mowing 10 times
when x = 10
y = 40 + 25x
y = 40 + 25(10)
= 40 + 250
= 290
y = 290
(x, y) = (10, 290)
Victor must choose one pair of pants, one shirt, and one tie to wear to work. His possible choice combinations are shown in the tree diagram below.
If Victor chooses these work clothes at random, what is the probability that he will choose tan pants, a white shirt, and a red tie?
1/12
1/4
3/7
4/9
Answer:
should be 3/7 I think that's right
WORTH 25 POINTS!!!!
match the following
Answer:
Step-by-step explanation:
Domain of a function is defined by the set of x-values (input values) and Range is the set of y-values (output values) of the function.
1). The range and domain of P = {(x, y)| y = 3}
Domain: Set of all real numbers
Range: {y: y=3}
2). The domain set of C = {(2, 5), (2, 6), (2, 7)}
Domain: {2}
3). The range set of E = {(3, 3), (4, 4), (5, 5), (6, 6)}
Range: {3, 4, 5, 6}
4). The range and domain set of F = {(x, y)| x + y = 10}
Domain = Range = {All real numbers}
HELP ASAP!
The graphs below have the same shape. f(x) = x2.
What is the equation of the graph of g(x)?
Answer:
A
Step-by-step explanation:
Given the graph of f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift to the left of a units
• If a < 0 then a shift to the right of a units
Here g(x) is the graph of f(x) shifted 3 units to the left, then
g(x) = (x + 3)² → A
Answer:
A
Step-by-step explanation:
A bag of cereal contains 12 blue marsh mellows, 16 red marshmellows , and 8 orange marsh mellows.If a marshmellow is picked from the bag at random, what is the probability that it is a red marsh mellow? Answers have been rounded to the tenths place.
Answer:
0.4 (decimal)
4/9 (fraction)
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.
Probability a red marshmallow is picked = number of red marshmallows in the bag / sum of marshmallows in the bag
sum of marshmallows in the bag = 12 + 16 + 8 = 36
Probability a red marshmallow is picked = 16/36
To transform to the simplest form. divide both the numerator and the denominator by 4
= 4/9
to convert to decimal, divide 4 by 9 = 0.4444
0.4 to the nearest tenth
the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero
Find mZB.
Round to the nearest degree.
11
B В
7.
15
Answer:
m∠B = 111º
Step-by-step explanation:
use law of cosines
c² = a² + b² - 2ab*cosC
---------------------------------
15² = 7² + 11² - 2(7)(11)cosB
225 = 49 + 121 - 154cosB
225 = 170 - 154cosB
Subtract 170 form both sides
55 = -154cosB
Divide both sides by -154
-0.3571428571 = cosB
m∠B = arccos -0.3571428571
use calculator
m∠B = 110.924832425009406
Rounded
m∠B = 111º
find the measure of angle c
Answer:
add 7+5 and 3+9 and then subtract both answers together and the answer you get should be the answer if the degree
Mrs. Archer is doing a painting project with her art class. She uses a large jug with 28.5 ounces of blue paint to fill 6 smaller bottles. If she divides the paint evenly, how much paint will be in each bottle?
Answer:
4.75
Step-by-step explanation:
Divide 28.5 evenly with 6 because thee are 6 bottles. Then you receive 4.75
Hope this helps
Math question. Genius, please answer correctly.
Answer:
16-31 20, 18,25,28,31,23,19,27,22,25,20 11
32-47 33,42,36,41,47 5
48-65 65,52,61,50 4
Step-by-step explanation:
How many minutes will it take to bake 24 tortillas
Answer:
72 mins
Step-by-step explanation:
12 mins = 4 tortillas
1 tortilla = 3 mins
3x24=72
72 mins
Answer:
72 minutes
1 hour and 12 minutes
Step-by-step explanation:
[tex]\frac{4}{12}: \frac{24}{y}[/tex]
4 × y = 12 × 24
4y = 288
4y ÷ 4 = 288 ÷ 4
y = 72
Type the correct answer in each box. The reflection of point S across the y-axis is point . The reflection of point Q across the x-axis and the y-axis is point , whose coordinates are (, ).
Answer:
[tex]S' = (-5,-5)[/tex]
[tex]Q"=(-5,-5)[/tex]
Step-by-step explanation:
Given
[tex]S = (5,-5)[/tex]
[tex]Q= (5,5)[/tex]
Solving (a): Reflect S across y-axis
The rule to reflect across y-axis is:
[tex](x,y) \to (-x,y)[/tex]
So, we have:
[tex]S(5,-5) \to S'(-5,-5)[/tex]
Hence:
[tex]S' = (-5,-5)[/tex]
Solving (b): Reflect Q across x and y-axis
The rule to reflect across x-axis is:
[tex](x,y) \to (x,-y)[/tex]
So:
[tex]Q(5,5) \to Q'(5,-5)[/tex]
The rule to reflect across y-axis is:
[tex](x,y) \to (-x,y)[/tex]
So:
[tex]Q'(5,-5) \to Q"(-5,-5)[/tex]
Hence:
[tex]Q"=(-5,-5)[/tex]
i dont get it either
Step-by-step explanation:
十
139°
x° find the value of x.
Answer:
x = 139
Step-by-step explanation:
The angles are alternate exterior angles , and when the lines are parallel, alternate exterior angles are equal
x = 139
