Hey guys I need help in these. Thanks in advance^^
1) In which operations does the order of the numbers make a difference to the
final answer? Find out what this rule is called.
2) If evaluating the sum 2+3+4 does it make a difference which two numbers !
add first? Is the same true for the other operations? What's this rule called?

Recall that

cos(a + b) = cos(a) cos(b) - sin(a) sin(b)

cos(a - b) = cos(a) cos(b) + sin(a) sin(b)

and by subtracting the first equation from the second, we get

cos(a - b) - cos(a + b) = 2 sin(a) sin(b)

So, we can write

sin(t) sin(3t) = 1/2 (cos(2t) - cos(4t))

and expanding the left side in the original equation gives

sin(t) sin(3t) sin(5t) = 1/2 (cos(2t) - cos(4t)) sin(5t)

… = 1/2 cos(2t) sin(5t) - 1/2 cos(4t) sin(5t)

Similarly, recall that

sin(a + b) = sin(a) cos(b) + cos(a) sin(b)

sin(a - b) = sin(a) cos(b) - cos(a) sin(b)

===>   sin(a + b) + sin(a - b) = 2 sin(a) cos(b)

Then

cos(2t) sin(5t) = 1/2 (sin(7t) + sin(3t))

and

cos(4t) sin(5t) = 1/2 (sin(9t) + sin(t))

So we have

sin(t) sin(3t) sin(5t) = 1/2 cos(2t) sin(5t) - 1/2 cos(4t) sin(5t)

… = 1/2 (1/2 (sin(7t) + sin(3t))) - 1/2 (1/2 (sin(9t) + sin(t)))

… = 1/4 sin(7t) + 1/4 sin(3t) - 1/4 sin(9t) - 1/4 sin(t)

… = 1/4 (-sin(t) + sin(3t) + sin(7t) - sin(9t))

as required.

Answer:

a+b=2

Step-by-step explanation:

start by combining all the terms that are possible: (a+b)^2 - 4 = 0

move -4 to the other side:  (a+b)^2= 4

Find the square root of both sides: a+b=2

Answer:

6 centimeters

Step-by-step explanation:

Square E'F'G'H' is just square EFGH translated to the left.

It is still the same size, just in a different location.

Line segment EF is the same length as segment E'F'.

6 centimeters

The segment [tex]E'F'[/tex] is 6 centimeters long.

According to this question, Reynaldo created a new square with same dimensions of the former one by translating it 4 centimeters to the left, which means that line segments EF and E'F' have the same length. Let suppose that no further operations have been done.

If [tex]EF = 6\,cm[/tex], then [tex]E'F' = 6\,cm[/tex] because of translation. In other words, the segment [tex]E'F'[/tex] is 6 centimeters long.

We kindly invite you to check this question related to translation of squares: https://brainly.com/question/12891664

Answer:

12. (2, -3)

13. AH: +15   B: +721   CB: 0   N: +462   WB: -1200

Step-by-step explanation:

12.

When a point is reflected over the x-axis, the y coordinate becomes opposite because you are changing its y value, not its x-value. So (-2, 3) reflecting over the x-axis becomes (-2, -3).

The same concept goes for reflecting over the y-axis. The x coordinate becomes opposite because you are changing its x value. (It's like folding the graph in half and seeing where the point matches up with. So (-2, -3) reflecting over the y-axis becomes (2, -3).

13.

All you have to do is list each artifact and where they were found in relation the sea level (0). If it is above sea level then it is a positive number, below sea level is a negative number.

Arrow head: +15 (since it is 15 feet above sea level)

Woven basket: -1200 (since it is 1200 feet below sea level)

Answer:

brainliest is appreciated

Answer:

KY S

Step-by-step explanation:

Answer:

32 days

Step-by-step explanation:

2 days = 16km

1 day = 8km

256km÷8km=32 days

Answer:

(c) $75.37

Step-by-step explanation:

SStax = GrossPay * SSrate

SStax = 1215.60 * 6.2%

SStax = 1215.60 * 0.062

SStax = 75.37

Answer:

x=−2+2√6 or x=−2−2√6

Step-by-step explanation:

Let's solve your equation step-by-step.

x2+4x−20=0

For this equation: a=1, b=4, c=-20

1x2+4x+−20=0

Step 1: Use quadratic formula with a=1, b=4, c=-20.

x=

−b±√b2−4ac

2a

x=

−(4)±√(4)2−4(1)(−20)

2(1)

x=

−4±√96

2

x=−2+2√6 or x=−2−2√6

Answer:

191.829

Step-by-step explanation:

191.007+0.8215=191.8285. But since you want to round it to the nearest thousandths place, you have 191.829

Answer:

191.8290

Step-by-step explanation:

191.007 + 0.8215 = 191.8290

0.8215

0.0097

+______

0.8285

then add 191. to .8285, creating 191.8285, then rounding to the nearest thousandths, and in this case the thousandths is a 5, which means we always round up. That gives us 191.8290.

p.s. there's no need for the zero at the end

Answer:

By adding

please mark me brainliest

Answer:

8

Step-by-step explanation:

Answer:

3d - 4f

Step-by-step explanation:

(12d + 28f) - 5f - (27f + 9d)

12d + 28f - 5f - 27f - 9d

(12-9)d + (28-5-27)f

3d - 4f

don't forget to put bracket, it is fundamental

4(3d + 7f) – 5f – 3(9f + 3d)

Use the distributive properly:

12d + 28f - 5f -27f -9d

Combine like terms:

3d -4f

Answer:

polynomials are written in descending order.

Answer:

[tex] \frac{ - 3}{2} (4x + 2) + 2x = - 30 \\ \frac{ - 3 \times 4x}{2} + \frac{ - 3 \times 2}{2} + 2x = - 30 \\ - 6x + - 3 + 2x = - 30 \\ - 4x - 3 = -30 \\ - 4x = -27\\ x = \frac{-27}{ - 4} \\ = 6.75 = 7 \\ thank \: you[/tex]

Answer:

The correct answer is A.

Step-by-step explanation:

Answer:

$15.92

Step-by-step explanation:

3.98•4=15.92. You need 4 doxes so 5 students aren't left out.

Answer:

16

Step-by-step explanation:

A² for A = -4

= (-4)²

= (-4) × (-4)

= 16

Answer:

A² = 16

Step-by-step explanation:

Substitute A = - 4 into the expression

A² = (- 4)² = - 4 × - 4 = 16

Answer:

1/2 ÷1/6=1/2×6/1

=6/2=3.

the answer is 3

even though I didn't get the question I hope it helps

Answer:

The latest time she can leave is 6:56 A.M.

Step-by-step explanation:

Just trust me. :)

Step-by-step explanation:

it's an isosceles because it's has two vertices with the points -1

Answer:

Step-by-step explanation:

1 2/4

Well an easy way to solve this would be multiply it by 6. 1*6=6 and 4*6=24.

That would be enough for 6 people. Or you could do. 1/4+1/4+1/4+1/4+1/4+1/4 and get the same answer.

Hope this helps and if possible brainliest please?

Answer:

option a

Step-by-step explanation:

all positive real numbers

Answer:

C

Step-by-step explanation:

Factor: Something which is multiplied by something else. A factor can be a number, variable, term, or a longer expression. For example, the expression 7x(y+3) has three factors: 7 , x , and (y+3) .

Answer:

Five and six is the coefficient

Answer:

x=0, y=-2

Step-by-step explanation:

Let x=3y+6 be equation 1

and 2x-4y=8 be equation 2

sub equation 1 into equation2,

2(3y+6)-4y=8

6y+12-4y=8

2y=-4

y=-2

sub y=-2 into equation 1,

x=3(-2)+6

x=0

sub is an abbreviation for substitute