❶ Find the values of x, y and z in each of the case given below ⟼
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❷ Prove that –
If Cos∅ + Sin∅ √2Cos∅, Show that Cos∅ - Sin∅ = √2 Sin∅
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– Kindly Don't Spamm⚠️
– No Copied answers⚠️
– Answer with full solution please
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Note (For 1st Question) :
• Figure is provided in the Attachment[tex].[/tex]
Answers
Answer:
1)
y = 45° (converse of alternate interior angle theorem)
z = 45° (alternate interior angle theorem)
k = 135° (exterior angle theorem)
2)
Cos θ + Sin θ = √2 Cos θ
(Cos θ + Sin θ)² = (√2 Cos θ)²
(Exponential property of equality)
Cos² θ + Sin² θ + 2 (Cos θ • Sin θ) = (√2 Cos θ)²
(Distributive property)
1 + 2(Cos θ • Sin θ) = (√2 Cos θ)²
(Definition of the pythagorean identity).
This identity is true because, if a² + b² = c². The triangle must be a right triangle, and a right triangle always has a 90° angle tangent to the triangle, and the tangent of 90° is 1, cos applied to the adjacent over hypotenuse, and sin applies to the opposite over hypotenuse, so this identity must work).
1 + 2(Cos θ • Sin θ) = 2 Cos² θ
(definition of an exponent)
1 + 2(Cos θ • Sin θ) – 1 = 2 Cos² θ – 1
(subtraction property of equality)
2(Cos θ • Sin θ) = 2 Cos² θ – 1
2(Sin θ • Cos θ) = 2 Cos² θ – 1
(Associative property of multiplication ; the input for both functions are θ so this rule works, this is an exception)
Sin (2x) = 2 Cos² θ – 1
(double angled identity of 2 sine and cos)
Related Questions
Find the slope of a line that passes through the points. (-2, 3) and (4,8).
Answers
m=8-3/4-(-2)
m=5/6
the slope of the line that passes through the points (-2,3) and (4,8), is 5/6
solve by substitution
y=x+7
2x+y=-5
Answers
Answer:
(-4,3) or X=-4, y=3
Step-by-step explanation:
when solving for the first variable once you have the result then substitute the result into the other equation.
Ramon would like to plant a garden where each row has the same combination of plants. If
Ramon has 27 tomato plants, 15 cucumber plants and 6 basil plants, what is the greatest number of rows the garden can have if Ramon uses all of the plants?
Answers
Answer:
48
Step-by-step explanation:
The greatest number of rows that can be formed in the garden will be 3.
What is the highest common factor?The Highest Common Factor (HCF) of two numbers is the highest possible number that is divisible by both numbers.
In other words, the highest common factor is the common factor between the two numbers but it should be the highest among all common factors.
As per the given,
Ramon has 27 tomato plants, 15 cucumber plants, and 6 basil plants.
Factors of 27 = 1, 3, 9, and 27.
Factors of 15 = 1, 3, 5 and 15
Factors of 6 = 1, 2, 3 and 6
The GCF of 27,15 and 6 is 3.
Thus, only three raws are possible.
Hence "The greatest number of rows that can be formed in the garden will be 3".
To learn more about the highest common factor,
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what is 3/4 ÷ 1/6 hlp
Answers
Answer:
The answer is 4.5
Step-by-step explanation:
.caculator.....hehe
Answer:
4.5
Step-by-step explanation:
If you divide 3/4 by 1/6 you will get 4.5. Hope this helps.
Find the zeros of each function. Part 2. Please show work.
1. f(x)=2x^3 - 3x^2 - 8x - 3
2. f(x)= x^3 + 3x^2 - 5x - 15
3. f(x)= 2x^4 - 3x^3 - 14x^2 + 18x + 12
4. f(x) = x^3 - 5x^2 + 5x - 1
Answers
9514 1404 393
Answer:
-1, -1/2, 3-3, -√5, √5-√6, -1/2, 2, √62-√3, 1, 2+√3Step-by-step explanation:
Personally, the "work" I like to do when finding higher-degree polynomial zeros is writing the equation into a graphing calculator. The rational zeros are usually fairly obvious (for school problems), and the irrational ones often can be arrived at without a lot of trouble.
__
1. The graph in the first attachment shows the zeros are -1, -1/2, 3. (You expect a zero with 2 in the denominator because of the leading coefficient.)
__
2. The graph in the first attachment shows the zeros are -3, -2.236, and +2.236. Factoring the function by grouping shows you the factors to be ...
f(x) = (x^3 +3x^2) -(5x +15) = x^2(x +3)-5(x +3) = (x +3)(x^2 -5)
The quadratic factor can be factored using the form for "difference of squares":
f(x) = (x +3)(x -√5)(x +√5)
The value of √5 is about 2.236, matching the numbers shown on the graph.
The zeros are -3, -√5, +√5.
__
3. The graph in the second attachment shows the zeros are -2.449, -1/2, 2, +2.449. (As in problem 1, you expect a zero with 2 in the denominator.) Factoring out the rational zeros* gives ...
f(x) = (2x +1)(x -2)(x^2 -6) = (2x +1)(x -2)(x -√6)(x +√6)
The zeros are -1/2, 2, -√6, +√6.
* The "work" of the synthetic division is shown in the third attachment. The coefficients of the quadratic are reduced by a factor of 2 from the result of division by (x+1/2) so they effectively show the quotient from division by (2x+1).
__
4. The graph in the fourth attachment shows the zeros are 0.268, 1, 3.732. Factoring out the rational zero gives ...
f(x) = (x -1)(x^2 -4x +1)
The zeros of the quadratic factor can be found any of several ways. One of my favorite is to use the graph to discover the vertex. For the vertex form ...
y = (x -h)^2 +k
the roots are h±√(-k). The vertex form of the quadratic term is
y = (x -2)^2 -3
so the roots are 2±√3.
The zeros are 1, 2-√3, 2+√3.
Which problem can be solved by division of decimals?
Danette needs 8 dozen eggs for her restaurant. How many eggs should she buy?
How much money does Dawna need to fill her 11.5 gallon gas tank if the price of gas is $3.59 a gallon?
How many more miles does Judy’s family have to drive to reach their destination if they have driven 45.4 miles of a 123.8 mile trip?
What is Jeremy’s average if he received a total of 323.7 points on 7 tests?
Answers
Answer:
What is Jeremy’s average if he received a total of 323.7 points on 7 tests?
Step-by-step explanation:
You have to divide 323.7 points by 7 tests so it is the only division problem out of all the problems.
It can be solved using division of decimals!!
if you know the answer to this PLEASE HELPPPP MEEE
Answers
Answer:
-2, -1, 1, 3
Step-by-step explanation:
Range is the amount so that is why it is the answer
Can someone help me solve all the questions in number 1?
Answers
Answer:
1 = 50⁰
2 = 130⁰
3 = 50⁰
4 = 85⁰
5 = 130⁰
6 = 50⁰
7 = 85⁰
8 = 45⁰
9 = 45⁰
10 = 135⁰
11 = 135⁰
12 = 45⁰
(√7)5=7n, what is n?
Answers
Answer:
n = 5/√7
Step-by-step explanation:
(√7) 5 = 7n
5√7 = 7n
7n = 5√7
n = 5√7/7
n = 5/√7
-TheUnknownScientist
(√7)5 = 7n
Divide both sides by n.
(√7)5/7 = n
What is the absolute magnitude of a star that has a period of 50 days?
Answers
Answer:
-6.07
Step-by-step explanation:
write an expression in simplest form 3x x+10 2x+2 and 5x
Answers
I'm not sure how many equations you are asking for, but hopefully, you can use what I wrote here to solve your actual question. Here is my go:
3x+10+2x+2+5x
First, add all the x's together:
3x+2x+5x=10x
Next, add all our numerals together:
10+2=12
Put it together!
10x+12
Predict the exam grade for a student who studies 10 hours per week.
hours studied 5 9 3 12 1
exam grade 80 95 75 98 70
Answers
Answer:
100
Step-by-step explanation:
100
Which of the following correctly shows the re-grouping strategy for solving 57 x 18?
50 x 10; 7 x 10; 10 x 8; 7 x 8
50 x 10; 7 x 10; 50 x 8; 7 x 8
50 x 10; 7 x 50; 50 x 8; 7 x 8
10 x 8; 7 x 10; 50 x 8; 7 x 8
Answers
Answer:
map
Step-by-step explanation:
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
With the regrouping strategy, we get,
50 x 10; 7 x 10; 50 x 8; 7 x 8
Option B is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
57 x 18
This can be written as,
(50 + 7) x (10 + 8)
Simplifying we get,
(50 x 10) + (50 x 8) + (7 x 10) + (7 x 8)
Now,
With the regrouping strategy, we get,
(50 x 10)
(50 x 8)
(7 x 10)
(7 x 8)
Thus,
With the regrouping strategy, we get,
50 x 10; 7 x 10; 50 x 8; 7 x 8
Option B is the correct answer.
Learn more about expressions here:
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Nicola is multiplying 1/6 by 3/2. Use the drop down menu to complete the statement
Answers
Answer:
Step-by-step explanation:
1/6 x 3/2 = 1/4
Hope it helps
Answer:
Greater than
Step-by-step explanation:
The product of z and 19 is represented by which of the following expressions?
A.
19 ÷ z
B.
19z
C.
19 + z
D.
19 – z
Answers
z times 19= 19z
Answer: B. 19z
Which problem can be shown using the equation 2 x 8 = 16 2
A rabbit jumps 2 feet. A kangaroo jumps 15 feet The kangaroo jumps 8 times as foros
the rabbit
O A rabbit jumps 2 feet A kangaroo jumps 15 feet The kangaroo jumps & more feet then
the rabbit
6) A rabbit jumps 2 feet A kangaroo jumps 8 feet. The kangaroo jumps 15 times as foros
the rabbit
A rabbit jumps 2 feet. A kangaroo jumps 8 feet. The animalis jump 15 feet in all
Answers
Answer:
C
Step-by-step explanation:
I need help understanding this-
Answers
Answer: B
Step-by-step explanation: So that inequality, basically means that x is less than -6. Because there is also a line under the less than sign, that means that x is less OR equal to 6. When x can also be equal to 6, the circle on the number line will be filled in (if x was just less than 6, WITHOUT also being equal to it, than the circle would be empty). And because x is less than -6, the arrow will be pointing to the left.
what is one thousandth less than 0.029
Answers
Answer:
0.0009
Step-by-step explanation:
-1 < 4x + 3 < 7
solve for x
Answers
Answer:
-1 <x< 1
Explanation:
Add -3 to both sides
Divide all parts by 4
Find the value of k. Then find the
angle measures of the triangle.
2k
45°
ko
Sum of angle
measures: 180°
Answers
k + 2k + 45 = 180
3k = 180-45
k = 135/3
k = 45
2k = 2* 45
90
WILL MARK BRAINIEST!!!
What is the best estimate for 38?
5.75
6.25
7.5
8.1
Answers
The answer is 6.25
Step-by-step explanation:
Root 38 is exactly 6.161441400297. That number estimated would be 6.20 sine 6.16 is close to 6.20. The closest number to 6.20 is 6.25.
The average age of 40 students of a class is 15 years. An 18 year-old student left the class and a new student was admitted. As a result the average age fell to 14.885 years. Find the age of the new student.
Answers
Answer:
Answer:age of new student is 13.4 years
Step-by-step explanation:
SUM of ages all 40 students =average age times 40
=15*40=600
after leaving 18 years old student
SUM of ages of 39 students will be 600-18=582
after adding new student with age x
SUM of ages of 40 students will become 582+x
and the average would be (582+x)/40
which is given as 14.885
so we get equation
(582+x)/40=14.885
582+x=14.885*40=595.4
x=595.4-582
x= 13.4
age of new student is 13.4 years
Hope it will help you
Please mark as brainliest answer
the sudent age is 13.4
Step-by-step explanation:
SUM of ages all 40 students =average age times 40
=15*40=600
after leaving 18 years old student
SUM of ages of 39 students will be 600-18=582
after adding new student with age x
SUM of ages of 40 students will become 582+x
and the average would be (582+x)/40
which is given as 14.885
so we get equation
(582+x)/40=14.885
582+x=14.885*40=595.4
x=595.4-582
x= 13.4
age of new student is 13.4 years
Kam can make 72 cookies in 3 hours, Madison can make 128 cookies in 4 hours. How many hours would it take them to make 200 cookies together?
Answers
Answer:
3.7 hours
Step-by-step explanation:
Answer:
3.7 hours
Step-by-step explanation
Kam
x = 72/3 . = 24 cookies/h
Madison
x = 120 / 4 = 30 cookies/hour
Now we write and equation where "t" will be time
24t + 30t = 200
54t = 200
t = 200/54
t = 3.7 hours
A, B & C form a triangle where
∠
BAC = 90°.
AB = 9.1 mm and CA = 12.5 mm.
Find the length of BC,
Answers
Answer:
15.5
Step-by-step explanation:
9.1^2 + 12.5^2 = 239.06
square root of 239.06 is 15.5
PLZZZZZZZZZZZZZZZZZ HELP!
Solve each equation for the variable. Show every step in your work
-5(x+12)=20
Answers
answer: -5x+12=20
-12 -12
-5x/-5= 8/-5
x= -1.6
Check: rewrite the orignal problem
plug your variable
Sierra wants to invest $5,000 at her local bank. She will receive an interest rate of 1%, compounded annually. What is the value of her investment after two years?
Answers
Answer:
Value of investment for Sierra after two years will be $5100.5
Step-by-step explanation:
Principal Amount P =$5000
Interest rate r = 1% = 0.01
Time t = 2 years
Compounded annually n = 1
We need to find future amount A
The formula used is: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Putting values and finding A
[tex]A=P(1+\frac{r}{n})^{nt}\\A=5000(1+\frac{0.01}{1})^{1*2}\\A=5000(1+0.01)^{2} \\A=5000(1.01)^{2}\\A=5000(1.0201)\\A=5100.5[/tex]
So, Value of investment for Sierra after two years will be $5100.5
Paul bought 1 1/3 pounds of bananas and apples. If he bought 1 4/5 pounds of apples, how many pounds of bananas did he buy
Answers
Answer:
that doesn't make sense. u cant buy more lbs of apples than apples and bananas combined
Step-by-step explanation:
Answer:
7/15
Step-by-step explanation:
Hope this helps!! :)
Halla tres enteros impares consecutivos tales que 3 veces el entero del medio es 5 mas que la suma del primero y el tercero.
Answers
Responder:
3, 5, 7
Explicación paso a paso:
Sean enteros impares consecutivos:
x, x + 2, x + 4
3 (x + 2) = (x + x + 4) + 5
3x + 6 = (2x + 4 + 5)
3x + 6 = 2x + 9
3x - 2x = 9 - 6
x = 3
Por lo tanto,
x = 3; (x + 2) = 3 +2 = 5; x + 4 = .3 + 4 = 7
(3, 5 y 7)
Nat’s grocery bill was $150, which included a 5% club discount. What was Nat’s bill before the discount? Write and solve an equation.
Please show work
Answers
A 5% discount is 0.05 then, you have to multiply 150 times 0.05 after, that you get 157.5.
HOPE THIS HELPS!!!!
Alana runs 4 laps around the track in 10 minutes. If Alana runs 17 laps at the same rate how long does it take her
Answers
Answer:
42 minues 5 seconds to do 17 laps.
Step-by-step explanation:
it takes her 2 minuetes and 50 seconds to do 1 lap if you multiply 2.5x17=
42 munites and 5 secondesto do 17 laps
Answer:
It would take 42.5 min
Step-by-step explanation:
4/10 = 2.5(unit rate for every lap it takes 2.5 min)
17 x 2.5 = 42.5