The trigonometry identity sin(x + y) = sinx cosy + cosx siny.
What is sin(x + y) identity in trigonometry?sin(x + y) is one of the identities in trigonometry for compound angles.
The angle (x + y) represents the compound angles.
sin(x + y) = sinx cosy + cosx siny
To prove sin(x + y) = sinx cosy + cosx siny
Consider OX as a rotating line anti-clockwise. Let angle XOY = a
the making of an acute angle b the rotation in the same direction is
angleYOZ = b , angle XOZ = a + b
From triangle PTR,
∠TPR = 90 - ∠PRT , ∠ROX = a
From the right-angled triangle PQO
sin(a + b) = PQ/OP
= (PT + TQ) / OP
= PT/OP + TQ/OP
= PT/PR × PR/OP + RS/OR × OR/OP
= cos (∠TPR ) sinb + sina cosb
= sina cosb + cosa sinb
if we replace a=x and b=y
Therefore, sin(x + y) = sinx cosy + cosx siny.
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PLS HELP ASAP FIRST CORRECT ANSWER GETS BRAINLEIST
Answer:
b ≈ 18.3303
[tex]b = \sqrt{{c}^{2} - {a}^{2} } [/tex]
[tex]b = \sqrt{ {19}^{2} - {5}^{2} } [/tex]
[tex]b = 18.3303[/tex]
An integer is chosen at random from 1 to 50 inclusive. Find the probability that the chosen integer is divisible by 3. 8/25 3/10 3/50
How many numbers from 1 to 50 are multiples of 3?
3, 6, 9, 12, 15, 18 .......
Let's change the start and end value of the array and find the number of terms
Start at 3 and go all the way to 48 because those are the first and last multiples of 3 in this array.
There is a formula that allows us to quickly find the number of terms
We subtract the first term from the last term and divide by the amount of increase, then we add 1.
(48 - 3) / 3 + 1 = 16 numbers are exactly divisible by 3.
We have 50 numbers and 16 of them divisible by 3
16 / 50 = 8 / 25 probability
The probability that the chosen integer is divisible by 3 is 8/25 if an integer is chosen at random from 1 to 50 inclusive option first is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
We have the number from 1 to 50.
Total numbers between 1 to 50 or total outcomes = 50
Total favorable outcomes = total number which is divisible by 3
[tex]=\frac{48-3}{3} +1[/tex]
= 15 + 1
= 16
Now probability will be:
= 16/50
= 8/25
Thus, the probability that the chosen integer is divisible by 3 is 8/25 if an integer is chosen at random from 1 to 50 inclusive option first is correct.
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A cube is sliced as shown. Find the area of the cross section formed by the slice.
Answer: 5√(50) = 35.36 m^2
Step-by-step explanation:
The cross section is a rectangle, so its area formula is: Area = length * width.
If you look, the width is the diagonal of the side of the cube; thus, you can use Pythagorean theorem to find its measurement: a^2 + b^2 = c^2 → 5^2 + 5^2 = c^2 →
50 = c^2 → c = √(50)
Now, use the area formula and get: Area = 5 * √(50) = 5√(50) = 35.36 m^2 :)
help me please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Febuary 10th because on the left colom it showss the dates just look for the 10
Jen bought a cinnamon bun for $3. 42 and a giant candy cane for $5. 76. She then used the rest of her money to buy a notebook. She spent a total of $12. 83. How much money did Jen spend on the notebook? (5 points)
$9. 41
$7. 07
$3. 65
$2. 34
Answer:
She spent $3.65 on the notebook
Step-by-step explanation:
5.76 + 3.42 = $9.18
12.83 - 9.18 = $3.65
its literally 15 points
How do i find lateral area?
dont answer in a confusing way please i just need to understand this :(
Answer:
There are many areas but
Step-by-step explanation:
Area of square is L × W
where you multiply both length × width you get the answers squared
Area of a cube is L × W × H
this is where you multiply all length × width × height and get the answer cube
please help? , no decimals please,please explain to see picture.
Answer:
[tex]8x\sqrt{3xy[/tex]
Step-by-step explanation:
6 cm
6cm
6 cm
5 cm
4 cm
8cm
Solid B
Solid A
Which of the above solids has the larger surface area?
O O A. Solid A
O
B. Solid B
C. They have the same surface area.
Answer:
Solid A
Step-by-step explanation:
Surface area of a cube: 6 x a², where a is the side.
= 6 x 6²
= 6 x 36
= 216 cm²
Surface area of the cuboid/rectangular prism: 2(lw + wh + lh), where l is the length, w is the width, h is height.
= 2((5 x 4) + (4 x 8) + (5 x 8))
= 2(20 + 32 + 40)
= 2(92)
= 184 cm²
Therefore, Solid A has the larger surface area compared to Solid B.
select all fo the expressions that are equivilent to 6x + 1 -(3x-1)
6x+1-(3x-1)
6x+1-3x+16x-3x+1+1=3x+2
There are 221 students on a field trip.
. Five students ride in a van.
. The rest of the students fill 6 buses.
Enter an equation that can be solved to find the number of students, s, that are on each bus. Enter your response in
the first response box.
Enter the number of students that are on each bus. Enter your response in the second response box.
The equation that models the students is a linear equation
The equation that models the number of students in each bus is 6x = 216, and the number of students in each bus is 36
How to determine the equation?The given parameters are:
Students = 221
Van = 5
The rest students = 6 buses
Start by calculating the number of students remaining:
Remaining students = 221 - 5
Remaining students = 216
Represent the number of students in each bus with x.
So, we have:
6 buses * x = Remaining students
This gives
6x = 216
Divide both sides by 6
x = 36
Hence, the equation that models the number of students in each bus is 6x = 216, and the number of students in each bus is 36
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Knowing that ΔBIG ≅ ΔFNS, an angle pair that is NOT necessarily congruent is:
Knowing that ΔDAL ≅ ΔEKS, a side pair that is NOT necessarily congruent is:
solutions:
1) G ≅ F
2) DA ≅ ES
Explanation:
Q)1
ΔBIG ≅ ΔFNS
pairs that are congruent:
B ≅ FI ≅ NG ≅ SFrom the list given,
→ G ≅ F is not necessarily congruent.
Q)2
ΔDAL ≅ ΔEKS
pairs that are congruent:
DA ≅ EKAL ≅ KSDL ≅ ESFrom the list given,
DA ≅ ES is not necessarily congruent.
Usually the congruence is done according to naming
So
∆BIG≅∆FNS<B=F
<I=<N
<G=<S
Option A#2
Check the naming
∆DAL≅∆EKSSo
DA=EK
And DA may not be equal to ESSo option D
What is the domain of the following {(1,3),(2,7),(3,-1)
Answer: this is a function.
f(x)=y
Step-by-step explanation:
domain -> 1,2,3
values: 3,7,-1
-12 = -3y
How to Solve?
Answer:
y = 4
Step-by-step explanation:
Given:
[tex]-12=-3y[/tex]
Solve:
[tex]\mathrm{Divide\:both\:sides\:by\:}-3[/tex]
[tex]\frac{-3y}{-3}=\frac{-12}{-3}[/tex]
[tex]\mathrm{Simplify}[/tex]
Note: Negative + Negative = positive
y = 4
~lenvy~
each team in a youth soccer league pays $784 to join the league. if a team consists of 12 players and the fee is divided equally among the players, how much does each player pay?
Answer:
$65.33
Step-by-step explanation:
12x = 784
÷12 ÷12
x = 65.33
They would each have to pay $65.33.
I hope this helps!
a rectangular painting is 24 inches wide and 20 inches tall without the frame. With the frame, it is 28 inches wide and 24 inches tall. What is the area of the frame not covered by the painting?
Answer:
191
Step-by-step explanation:
do the frame with the pic first that is
28*24=672
next just the pic
24*20=480
next subtract the pic from the frame
672-480=191
Actually help PLSS
(will give brainliest)
Let's see point E in its original position: (3.-4)
Now lets transform the point (x,y) --> (x + 8, y +5)
(3, -4) --> (3 + 8, -4 + 5) --> (11, 1)
Therefore coordinate E's new position is (11, 1)
Hope that helps!
what is the slope of the line on the graph need answer ASAP please thank you I'm in k-12
I have 936 pencil . A box holds a dozen pencil . How many boxes will I be able to fill
Answer:
you will fill 78 boxes
Step-by-step explanation:
dozen = 12
936 divided by 12=78
explain how you know whether or not the point (0.75, 0.25) is on the unit circle.
Answer:
The point (0.75, 0.25) is not on the unit circle.
Step-by-step explanation:
The unit circle has radius 1, so:
[tex] {.75}^{2} + {.25}^{2} = .5625 + .0625 = .625 [/tex]
help me on both questions as attached below.
Also it's workings on how to get that if possible
Answer:
a) 160km
b) it will take 3.2 hours or 192 minutes or 3 hours and 12 minutes
Step-by-step explanation:
a) d=speedxtime
so, 64x2. 5=160km
b) time=d/s
so, 160/50
it will take 3.2 hours or 192 minutes or 3 hours and 12 minutes
Felipe is making triangles for a stained glass window, he made the design shown but wants to change it. Felipe wants to move the purple triangle to the corner. The purple piece has side lengths of 4.5 inches, 6 inches, and 7 inches. Can the purple piece be moved to the corner?
We have sides of triangle as [tex]4.5[/tex] inches, [tex]6[/tex] inches and [tex]7[/tex] inches.
So the sum of square of two smallest side is-
[tex]=4.5^2+6^2[/tex]
[tex]=20.25+36[/tex]
[tex]=56.25[/tex]
Now lets find the value of square of longest side of triangle-
[tex]=7^2[/tex]
[tex]=49[/tex]
Now from both value
[tex]49[/tex] [tex]\neq[/tex] [tex]56.25[/tex]
[tex]7^2[/tex] [tex]\neq[/tex] [tex]4.5^2+6^2[/tex]
So from Pythagoras theorem the given triangle is not a right triangle so it can not moved to the corner.
Thus, Since the triangle is not a right triangle therefore it can not moved to the corner.
What is the measure of <1?
Answer:
the measure of ∠1 is 92 degrees
Step-by-step explanation:
Can someone please answer the attachment
Step-by-step explanation:
linear pair
linear pair
alternate angles.
alternate angles
cointerior angles
I will hope that you like my answer
Help me with this question on congruent triangles? 20 points
Answer:
a) 5.7 cm
b) 3.05 cm
Step-by-step explanation:
a)
Since BE is parallel to CD,
Then AB/AC = BE/CD
So Length of CD = 12.3/8.2 x 3.8 = 5.7 cm
b)
AB/AC = AE/AD
So length of AE = 8.2/12/3 x 9.15 = 6.1 cm
ED = AD - AE = 9.15 - 6.1 = 3.05 cm
I need help this is so confusing
so point C would be on Quadrant I
T on Quadrant II, H on Quadrant III and R is not really on a quadrant, the coordinate is on the X axis.
Please Hurry! I will award the first person right the brainlyest award
Answer:
y = -3
Step-by-step explanation:
When you graph it on a graphing calculator or on desmos, it appears to be at y = -3
$400 interest is earned on a principal of $2000 at a simple interest rat 5% interest per year.for how many year was the principal invested
Answer:
4 Years.
Step-by-step explanation:
Given:Principle ⇒ 2000
Interest ⇒ 400
Rate ⇒ 5%
To Find:Time ⇒ _
Solution:Simple interest ⇒ p * x * t / 100
⇒ 400 = 2000 * 5 * t / 100
⇒ 400 = 200 * 5 * t / 10
⇒ 400 = 20 * 5 * t
⇒ t = 400 / 20 * 5
⇒ t = 40 / 2 * 5
⇒ t = 20 / 5
⇒ t = 4
Find a solution to the linear equation –7x+y= –28.
a
Answer:
x=4 + y/7
y= -28 + 7x
Step-by-step explanation:
Find x y and z.
please give answer as fast as possible to get marked BRAINLIEST
Answer:
X = 64
Y = 18
Z = 98
Step-by-step explanation:
Angles on a straight line always add up to 180 Degrees
Vertical Opposite Angles are equal to each other
X = 64
Y = 18
Z = 180 - 64 - 18 = 98
Find the probability of throwing a sum of 10 at least 7 times in 9 throws of a pair of fair dice
Answer:
19.308
Step-by-step explanation:
The probability of throwing a sum of 10 at least 7 times in 9 throws of a pair of fair dice is 0.083
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
We assume that the probability of throwing a sum of 10 in a pair of fair dice is
[tex]\frac{n(5,5)(6,4)(4,6)}{n\: all\: events}[/tex]
= 3/36
= 0.083
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