Which set of steps can be used to prove the sine sum identity, sin(x y) = sin(x)cos(y) cos(x)sin(y)?

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

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

Read more about linear equations at:

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Answer:

4 Years.

Step-by-step explanation:

Principle ⇒ 2000

Interest ⇒ 400

Rate ⇒ 5%

Time ⇒ _

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

Answer: this is a function.

f(x)=y

Step-by-step explanation:

domain -> 1,2,3

values: 3,7,-1

Answer:

She spent $3.65 on the notebook

Step-by-step explanation:

5.76 + 3.42 = $9.18

12.83 - 9.18 = $3.65

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.

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

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.

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.

Learn more about the probability here:

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#SPJ4

6x+1-(3x-1)

=3x+2

Answer:

x=4 + y/7

y= -28 + 7x

Step-by-step explanation:

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

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~

solutions:

1) G ≅ F

2) DA ≅  ES

Explanation:

Q)1

ΔBIG ≅ ΔFNS

pairs that are congruent:

From the list given,

→ G ≅ F is not necessarily congruent.

Q)2

ΔDAL ≅ ΔEKS

pairs that are congruent:

From the list given,

DA ≅  ES  is not necessarily congruent.

Usually the congruence is done according to naming

So

<B=F

<I=<N

<G=<S

#2

Check the naming

So

DA=EK

So option D

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

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

Step-by-step explanation:

linear pair

linear pair

alternate angles.

alternate angles

cointerior angles

I will hope that you like my answer

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

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

Learn more about probability here;

https://brainly.com/question/11234923

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.

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 :)

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

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

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]

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!

Answer:

the measure of ∠1 is 92 degrees

Step-by-step explanation:

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]

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!

Febuary 10th because on the left colom it showss the dates just look for the 10

Answer:

you will fill 78 boxes

Step-by-step explanation:

dozen = 12

936 divided by 12=78

Answer:

[tex]8x\sqrt{3xy[/tex]

Step-by-step explanation:

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.