Review the incomplete derivation of the cosine sum identity.
A 2-column table with 5 rows. Column 1 has entries step 1, step 2, step 3, step 4, step 5. Column 2 has entries cosine (x + y), sine (StartFraction pi Over 2 EndFraction minus (x + y) ), blank, sine (StartFraction pi Over 2 EndFraction minus x) cosine (negative y) + cosine (StartFraction pi Over 2 EndFraction minus x) sine (negative y), blank.
Which expressions for Step 3 and Step 5 complete the derivation?
Step 3: Sine ( (StartFraction pi over 2 EndFraction minus x) + y )
Step 5: cos(x)cos(y) + sin(x)sin(y)
Step 3: Sine ( (StartFraction pi over 2 EndFraction minus x) + y )
Step 5: cos(x)cos(y) – sin(x)sin(y)
Step 3: Sine ( (StartFraction pi over 2 EndFraction minus x) minus y )
Step 5: cos(x)cos(y) + sin(x)sin(y)
Step 3: Sine ( (StartFraction pi over 2 EndFraction minus x) minus y )
Step 5: cos(x)cos(y) – sin(x)sin(y)
Answer:
Option (4)
Step-by-step explanation:
STEP - 1
cos(x + y)
STEP - 2
[tex]\text{sin}[\frac{\pi}{2}-(x+y)][/tex]
STEP - 3
[tex]\text{sin}[(\frac{\pi}{2}-x)-y][/tex]
STEP - 4
[tex]\text{sin}(\frac{\pi}{2}-x)\text{cos}(-y)+\text{cos}(\frac{\pi}{2}-x)\text{sin}(-y)[/tex]
STEP - 5
cos(x)cos(y) - sin(x)sin(y)
[Since, [tex]\text{sin}(\frac{\pi}{2}-x)=cos(x)[/tex] and [tex]\text{cos}(\frac{\pi}{2}-x)=\text{sin}(x)[/tex]]
[Since, cos(-x) = cos(x) and sin(-x) = -sin(x)]
Therefore, Option (4) will be the correct option.
Answer:
D
Step-by-step explanation:
Top Answer was right, don't know why it was rated poorly
CAN SOMEONE PLZ HELP ME:))))))))
Emma jogs 2 miles along the beach in 1/3
of an hour. If she travels at a constant rate, how far will she jog in an hour?
1. Use the known information to write a rate.
Emma’s rate:
2 miles 1/3 hours
2. Write an equivalent rate with a denominator of 1.
2(3) miles / 1/3 (3) hours = ? /1 hour
Answer:
Step-by-step explanation:
6 miles
2 times 3 = 6
or
2 x 3/3 = 6
3 (4x - 2) - 30 = -6 (6 - 2x) - 20
A.Infinite Solutions/Identity
B.No Solution
C.x = 0
D.x = 1
show work please
Answer:
B.
Step-by-step explanation:
3(4x-2)-30=-6(6-2x)-20
12x-6-30=-36+12x-20
12x-36=12x-56
To quickly find the product of a whole number time 1000, add *Blank* Zeroes to the number
Answer:
Add three zeros to the end.
Step-by-step explanation:
When you add three zeros, the result is equivalent to when multiplying by 1000. For example, 20 times 1000 is 20,000.
Hi! I believe your answer is 3 zeros. For example, 7 × 1,000 = 7,000 (add 3 zeros). I hope this helps you! Good luck and have a great day/night. ❤️✨
Which expression represents the area of this figure in square feet
Answer: A im positive its A
Step-by-step explanation: 3 times 2 equals 6 and add that to 3 times 4 which is 12 and you get 18
Vance wants to determine if an old photo frame is still rectangular. The height of the frame is
8 inches, the base is 6 inches and the diagonal is 10 inches long. Is the old photo frame still
rectangular? How do you know?
Answer:
The old photo frame is still rectangular
Step-by-step explanation:
Rectangles
The rectangle shape can be identified because it has 4 internal angles of 90° each. The diagonal forms with two adjacent sides a right triangle where the Pythagora's Theorem must stand. Being a and b the length of the sides of the rectangle and d the diagonal, then:
[tex]d^2=a^2+b^2[/tex]
Vince's photo frame has dimensions of 8 inches and 6 inches, with a diagonal of 10 inches. If the above condition is met, then the frame is still rectangular.
Calculating:
[tex]10^2=6^2+8^2[/tex]
[tex]100=36+64[/tex]
[tex]100=100[/tex]
Since the condition is met, the old photo frame is still rectangular
HELPS ME SOLVE THIS PROBLEM PLEASE
Answer:
The third answer, y = 4x + 1
Step-by-step explanation:
Let's take the pair x = 2, and y = 9.
We know what x is, and what the result, y, is now.
Let's plug x into the third equation, y = 4x + 1
y = 4 * 2 + 1
y = 8 + 1
y = 9
We already know that y = 9, so this equation is correct.
Hope this helps!
(Let me know if you want to know why it's not any of the others.)
Help ASAP
Write the fraction [tex]\frac{45}{81}[/tex] in simplest form.
Answer:
[tex]\frac{5}{9}[/tex]
Step-by-step explanation:
Given
[tex]\frac{45}{81}[/tex] ( divide numerator and denominator by HCF of 9 )
= [tex]\frac{5}{9}[/tex] ← in simplest form
I need help a-sap! Please and thank you!!
Answer:
x = 80 degrees
Step-by-step explanation:
A straight line forms 180 degrees in total. It is given that the first angle is 100 degrees. 180 - 100 = 80, therefore x = 80 degrees
Ms. Rivera's class hoped to raise $135. They missed heir goal by $8.62. How ip much money did Ms. Rivera's class raise?
1. 144.42
2. 135
3. 126.38
4 127.28
Answer:
126.38
Step-by-step explanation:
$135.00-$8.62=$126.38
8x=-1/2 Whats the answer
How to solve 3(x + 1) − (3x + 2)
Answer:
Step-by-step explanation:
3(x + 1) − (3x + 2)
we will expand the first bracket:
3x+3-3x-2
3x and -3x cancels
3-2=1
Answer:
1
Step-by-step explanation:
3x+3+−3x+−2
=(3x+−3x)+(3+−2)
=1
When Rd 105 is divided into two parts in the ratio of2:5 how much money will be in first part
Answer:
30
Step-by-step explanation:
2x+5x= 105
7x= 105
x= 105/7
x= 15
First part= 2x= 2(15)= 30
Which graph below shows the solution set for the inequality b ≥ 5?
pls help meeeeeeeee
Answer: we can’t see graphs but I can help you if you show me them
Step-by-step explanation:
Any help and this please ??
2. Rena mixes i cup of blue paint for every cup of red paint to make purple paint.
Enter the number of cups of red paint Rena mixes with 1 cup of blue paint.
Jose paid 45.00$ for 5 movie tickets . EACH ticket cost the same amount . What was the cost of each movie ticket in dollars ?
Answer:
$9
Step-by-step explanation:
divide 45 and 5, you get 9
Answer:
45.00$ divided by 5.00$ is 9.00$
i hoped this helped!
Step-by-step explanation:
Absulate value of |-78|
Solve for h: A = (1/2)*b*h*
O h = 2*A*b
O h = A *(b/2)
O h = (2*A)/b
0 h = (2+b)/A
Step-by-step explanation:
The answer is the third option
which of the following expressions represents the product of a number and 8
Answer:
The answer is c. 8x
7) Cameron wants to buy new lacrosse equipment that costs $55.25. She plans to save $4.25 each
week. Write and solve an equation to determine how many weeks it will take her to save enough
money to buy the equipment. Define your variable and label your answer!
Answer:
13 weeks
Step-by-step explanation:
Let's say the number of weeks she will take is x. This would mean that 4.25 times the number of weeks(x) is equal to 55.25
Equation:
4.25x = 55.25
x=13
Yesenia swims laps at a pool. For every 10 laps she swims the backstroke, she swims 15 laps of freestyle. Which ratio shows the number of laps Yesenia swims the backstroke to the number of laps she swims freestyle?
Answer:
2 3
Step-by-step explanation:
Which ratio is NOT equivalent to 1:2
10:20
20:30
5:10
4:8
Answer:
The ratio 20:30 is not equivalent to 1:2.
someone please help me ASAP
Answer:
Step-by-step explanation:
1. 9.6x10^4
2. 7.2x10^8
3. 1.19x10^-7
4. 9.48x10^-3
5. 2.04x10^8
whats the capitol of Florida miaaaaaaa
Answer:
Tallahassee
Step-by-step explanation:
A chemist has three different acid solutions,
The first solution contains 20 % acid, the second contains 35 % acid, and the third contains 55%
acid.
She created 108 liters of a 40 % acid mixture, using all three solutions. The number of liters of
55 % solution used is 3 times the number of liters of 35 % solution used.
How many liters of each solution was used?
The chemist used
liters of 20% solution,
liters of 35 % solution, and
liters of 55 % solution.
Question Help: Message
instructor
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Answer:
36 liters of 20%18 liters of 35%54 liters of 55%Step-by-step explanation:
Let a, b, c represent the quantities of 20%, 35%, and 55% solutions, respectively. Then for the given mix, we have ...
a + b + c = 108 . . . . . total number of liters
.20a +.35b +.55c = 0.40·108 . . . . . liters of acid
0a - 3b + c = 0 . . . . . 55% solution was 3 times 35% solution
__
Solving these three equations by your favorite method gives ...
(a, b, c) = (36, 18, 54)
The chemist used 36 liters of 20%, 18 liters of 35%, and 54 liters of 55%.
_____
Comment on alternate approach
Since the ratio of 55% to 35% is 3 : 1, that mix will have an acid content of ...
(3(.55) +1(.35))/4 = 0.50 = 50%
So, the final mix is equivalent to some quantity of 50% mix being added to some quantity of 20% mix. The fraction that is 50% mix* will be (40-20)/(50-20) = 2/3 of the total, or (2/3)(108 L) = 72 L.
Now we know that (1/3)(108 L) = 36 L of 20% solution is needed and (1/4)(72 L) = 18 L of 35% solution is needed. 3 times that is 54 L of 55% solution.
__
* After you work a few mixture problems, you can see the pattern. If we start with an equation for x = fraction of 50% to use with 20% to make 40%, we get ...
x(50%) +(1 -x)(20%) = 40%
x(50% -20%) = 40% -20% . . . . . subtract 1(20%) and factor out x
x = (40% -20%)/(50% -20%)
The key here is to see where the numbers 20%, 40%, and 50% show up in the fraction.
Which statement is false A the inequality sign alwats opens up to the largers number. B the greater number in the equality is always above the number on the vertical number line. C the smaller number is inequality is always located to the left of the other number on the horizontal number line. D inequality sign always open up to a smaller number
Answer:
D inequality sign always open up to a smaller number
Step-by-step explanation:
Karen works at a car dealership. She makes only $5 an hour, but for every car she sells, she makes $1,000 in commission. If Karen worked 200 hours this month and made a total of $6,000, how many cars did Karen sell this month?
Answer:
4
Step-by-step explanation:
PLEEEEEEEEEEEEASE HELP ME WITH THIS! IT IS DUE TOMORROW!!!