Answer:
Verified below
Step-by-step explanation:
We want to show that (Cos2θ)/(1 + sin2θ) = (cot θ - 1)/(cot θ + 1)
In trigonometric identities;
Cot θ = cos θ/sin θ
Thus;
(cot θ - 1)/(cot θ + 1) gives;
((cos θ/sin θ) - 1)/((cos θ/sin θ) + 1)
Simplifying numerator and denominator gives;
((cos θ - sin θ)/sin θ)/((cos θ + sin θ)/sin θ)
This reduces to;
>> (cos θ - sin θ)/(cos θ + sin θ)
Multiply top and bottom by ((cos θ + sin θ) to get;
>> (cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ)
In trigonometric identities, we know that;
cos 2θ = (cos² θ - sin²θ)
cos²θ + sin²θ = 1
sin 2θ = 2sinθcosθ
Thus;
(cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ) gives us:
>> cos 2θ/(1 + sin 2θ)
This is equal to the left hand side.
Thus, it is verified.
Find the value of each variable using sine and cosine. Round your answers to the nearest tenth.
Answer:
r = 19.0
s = 17.7
Step-by-step explanation:
In the given right triangle ABC,
Measure of Hypotenuse (AC) = 26
m(∠CAB) = 43°
By applying sine rule in the given triangle,
sin(43)° = [tex]\frac{\text{Opposite side}}{Hypotenuse}= \frac{BC}{AC}[/tex]
sin(43)° = [tex]\frac{s}{26}[/tex]
s = 26[sin(43)°]
s = 17.73
s ≈ 17.7
Similarly, by applying cosine rule in the given triangle,
cos(43)° = [tex]\frac{\text{Opposite side}}{Hypotenuse}= \frac{AB}{AC}[/tex]
= [tex]\frac{r}{26}[/tex]
r = 26[cos(43)°]
r = 19.02
r ≈`19.0
The perimeter of an isosceles triangle is 45 feet. The length of the shortest side is 11 feet. Find the length of the other two sides (in feet)
9514 1404 393
Answer:
17 feet
Step-by-step explanation:
The sum of the three side lengths is the perimeter.
s + s + 11 = 45
2s = 34 . . . . . . subtract 11
s = 17 . . . . . . . . divide by 2
Each of the other two sides is 17 feet.
Find the missing side length, 28,25 and x
Answer:
x
Step-by-step explanation:
if the sphere shown above has a radius of 15 units , then what is the volume of the sphere ?
Answer:
4,500 cubic units
Step-by-step explanation:
Answer:
4,500 cubic units
Have a good day.
Solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, or an infinite number of solutions. If the system has one solution, find the solution.
-4x+y=12
-8x+2y=14
Answer:
no solution
Step-by-step explanation:
4n = 2n+6 I really need help
jack surveyed students at his school about whether they use computers or cell phones more. He found that of the 74 seventh-graders he surveyed, 53 said they used their cell phones more. In the 8th grade, 59 students used their cell phone more, compared to 38 who used their computer more. What number should be placed in the orange box below?
Answer:
Number of student of 7th grade using computer = 21
Total number of 8th grader student surveyed = 97
Step-by-step explanation:
The complete question is attached herewith
Solution
As we can see in the table
Total number of 7th grader student = 74
Out of these 74 student, 53 use cell phone
Hence, the number of student of 7th grade using computer = 74-53 = 21
Like wise, total number of 8th grader student surveyed = 59 +38 = 97
Plsss help mark brainlist
Answer:
17
Step-by-step explanation:
34 / 2 = 17
Anyone know how to do this people are answering the question but aren’t choosing two anwsers
Answer:
Option B and Option D are the two answers
The probability of event A is 0.42, and the probability of event B is 0.39. If A and B are independent events, what is P(A and B)?
Answer:
0.1638
Step-by-step explanation:
P(A and B) or simply the probability of both events happening is the product of their individual probabilities.
P(A and B)= (0.42×0.39)= 0.1638
what is the markup percentage based on retail for an item with a dollar mark up of $70.00, cost of $30.00, and retail price of $100.00?
Answer:
70/100= 0.7= 70%
70%
Do you think the answer is A, B, C, or D.
Answer:
its A i guess
2(x+50)=16+4x
What is x?
Answer:
x=42
Step-by-step explanation:
Write the equation.
2(x+50)=16+4x
Spread the parentheses
2x+100=16+4x
Put variables on one side, numbers on the other.
2x-4x=16-100
Add/subtract/multiply/divide the variables with variables and numbers with numbers.
-2x=-84
Make x alone
-x=-42
Flip sides to make x positive
42=x
Solve the following word problem by creating and solving a system of linear equations. Rachel offers to go to the coffee shop to buy cappuccinos and lattes for her co-workers. She buys a total of nine drinks for $35.75. If cappuccinos cost $3.75 each and the lattes cost $4.25 each, how many of each drink did she buy? a 2 cappuccinos, 7 lattes b 6 cappuccinos, 3 lattes C 4 cappuccinos, 8 lattes d 5 cappuccinos, 4 lattes
Answer:
85
Step-by-step explanation:
$410 is invested in an account earning 4.2% interest (APR), compound quarterly. Write a function showing the value of the account after t years, where the annual growth rate can be found from constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
please help im stuck on this
Answer:
Slope = -8/5
Step-by-step explanation:
Use the slope formula:
m = y2 - y1 / x2 - x1
Plug in the numbers from the ordered pairs given in the graph: (-1, 4) and (4, -4).
m = -4 - 4 / 4 - - 1
m = -8 / 5
m = -8/5
m = rise/run, meaning verticl units/horizontal units
Check your work by counting it out on the graph:
From the first black dot at (-1, 4), count 8 units down and then 5 units to the right. After counting, I ended at the second ordered pair at (4, -4) which means my slope is correct.
Joseph drove to his grandmother's house which is 279 miles away in 4.5 hours. If he continues at the same speed, approximately how long will it take him to drive 325 miles?
Answer:
5.24 hours
Step-by-step explanation:
I like to set these up as ratios.
279 miles/4.5 hours = 325 miles/ x hours
Then cross multiply
279x = 4.5 x 325
279x = 1462.5
divide both sides by 279
x = 5.24 hours
You can also solve 279 miles/4.5 hours to get the miles per hour driven, then divide 325 by that number:
279/4.5 = 62mph
325/62 = 5.24
Find the value of x in each figure
Answer:
Value of variable 'x' is 18.
Step-by-step explanation:
From the picture attached,
In right triangle XYZ,
m(∠YXZ) = (3x + 11)°
m(∠XYZ) = 90°
m(∠XZY) = 25°
By applying triangle sum theorem in the given triangle,
m(∠YXZ) + m(XZY) + m(∠XYZ) = 180°
(3x + 11)° + (25)° + (90)° = 180°
3x + 126 = 180
3x = 54
x = 18
Therefore, value of variable 'x' is 18.
Select the statement that describes this expression: 5 x 3 − (2 x 4) + 5. (2 points)
a
5 more than 3 subtract the product of 2 and 4 plus 5
b
5 times the product of 2 and 4 times 3, then add 5
c
Subtract the product of 2 and 4 from the product of 5 and 3, then add 5
d
5 more than the product of 5 and 3 plus the 2 times 4
Answer:
I believe the answer is either going to be B or C
Step-by-step explanation:
Answer:
obviously C: Subtract the product of 2 and 4 from the product of 5 and 3, then add 5
Step-by-step explanation:
plz mark as brainliest!
(07.01)
What is the value of x in the equation x + 10 = 13? (4 points)
1-3
0 2 3
3) 13
4) 23
Answer:
x=3
Step-by-step explanation:
x+10=13
x=13-10
x=3
someone actually help me please :/ I REALLY NEED HELP AND NO ONES HELPING
Answer:
a) 8 m
Step-by-step explanation:
a) all sides of a square are equal - there's 4 sides.
4x = 32m
x = 32/4
x = 8 m
i like ur toga pfp besty :)
Please you guys I need help!!!! I'll mark branliest !!!!
1. In triangle ABC, Angle A = 2X + 7, Angle B = 5X-15, and Angle C = 6X. What is the value of X and what are the measures of angles A,B, and C?
2. In a triangle XYZ, Angle X= 37 degrees, Angle Y = 45 degrees and Angle Z = 3x + 6. What is the value of X and what is the measure of Angle Z?
Helppp plssssssssssss
Answer:
The answer is C
Step-by-step explanation:
If you plot them carefully.
What is the are of the triangle?
Answer:
48 units²
Step-by-step explanation:
Area=1/2 box=hight
area=1/2×12×8
area=48
hope it helps
have a great day
Answer:
48
Step-by-step explanation:
if x=49 and y=160 then what is the value of z?
9514 1404 393
Answer:
z = 62°
Step-by-step explanation:
You know that ...
x = (1/2)(y -z)
So ...
2x = y - z
z = y - 2x = 160 -2(49)
z = 62 . . . . degrees
HELP GIVING 20 POINTS
While on vacation in Belmont, Lara went out for a dinner that cost $75. If sales tax in Belmont is 8% and Lara left a 20% tip on $75, what was the total cost of her meal?
Answer:
The total cost as $96
Step-by-step explanation:
To find the total amount find the tax amount and the tip amount
75 * 8% = 6
75 * 20% = 15
add 6 and 15 to 75 to get 96
Answer:
ok
Step-by-step
ok
Classify the polyhedron. select all that apply-
•non-convex
•non-regular
•convex
•regular
convex
non-convex
regular
non-regular
y is directly proportional to the square root of (x+2). when x =7 y=2. find y when x =98
Answer:
98/7=14
14*2=28
y=28
Step-by-step explanation:
Someone please answer this
Answer:
8 m is the answer.
Step-by-step explanation:
a = ?
b (Brennan and Hannah) = 6 m
c (Jayce and Hannah) = 10 m
According to the Pythagoras theorem,
a² + b² = c²
a² + 6² = 10²
a² + 36 = 100
a² = 100 - 36
a² = 64
a = 8 m
∴ Jayce and Brennan are 8 m apart.
Which expression is equivalent to 5 (4x+3)-2
To simplify an expression means to write it in the simplest way possible. Ideally, there would be no parentheses and everything has been 'expanded'.
Solving the QuestionWe're given:
[tex]5 (4x+3)-2[/tex][tex]5 (4x+3)-2[/tex]
Open up the parentheses by multiplying each term by 5:
[tex]=5*4x+5*3-2\\=20x+15-2\\=20x+13[/tex]
Answer[tex]20x+13[/tex]