The value of 2 in 2,783 and in 7,283

the expression cos(x − y) − cos(x + y) simplifies to 2sin(x)sin(y).

what is  expression ?

In mathematics, an expression is a combination of mathematical symbols (such as numbers, variables, and operators) that represents a mathematical object or relationship.

In the given question,

We can use the trigonometric identity cos(a - b) = cos(a)cos(b) + sin(a)sin(b) to simplify cos(x - y), and cos(a + b) = cos(a)cos(b) - sin(a)sin(b) to simplify cos(x + y).

cos(x - y) = cos(x)cos(y) + sin(x)sin(y)

cos(x + y) = cos(x)cos(y) - sin(x)sin(y)

Therefore,

cos(x - y) - cos(x + y) = (cos(x)cos(y) + sin(x)sin(y)) - (cos(x)cos(y) - sin(x)sin(y))

= cos(x)cos(y) + sin(x)sin(y) - cos(x)cos(y) + sin(x)sin(y)

= 2sin(x)sin(y)

So, the expression cos(x − y) − cos(x + y) simplifies to 2sin(x)sin(y).

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simplify the expressions  cos(x − y) − cos(x + y) ?

Answer:

Aircraft A: 403 seats

Aircraft B: 298 seats

Step-by-step explanation:

Let's x represent the seats in Aircraft B

We have the equations:

Aircraft A: (x + 105)

Aircraft B: x

We Know

Their total number of seats is 701; find the number of seats for each aircraft.

We Take

x + (x + 105) = 701

2x + 105 = 701

2x = 596

x = 298 seats

So, there are 298 seats in Aircraft B

Aircraft A has how many seats?

We Take

701 - 298 = 403 seats

So, there are 403 seats in Aircraft A

Final Answers:

Aircraft A: 403 seats

Aircraft B: 298 seats

The vertex of the graphed function f(x) = [x - 4] + 3 is (4, 3).

The function f(x) = [x - 4] + 3 is in the form of an absolute value function, where the expression inside the absolute value brackets represents the input value shifted horizontally by 4 units to the right.

The constant term of 3 represents a vertical shift upwards by 3 units.

To find the vertex of this function, we need to determine the x-coordinate that corresponds to the minimum value of the absolute value function.

In this case, since the absolute value function is within brackets and not being multiplied or divided by a coefficient, the minimum value occurs at the point where the expression inside the brackets equals zero.

Therefore, setting x - 4 = 0, we find x = 4.

Substituting this x-value into the function, we find f(4) = [4 - 4] + 3 = 3. So the vertex of the graphed function is located at the point (4, 3), where x = 4 and y = 3. This means that the graph is shifted 4 units to the right and 3 units upward from the origin.

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The monthly cell phone bill when shared data equals zero is given as follows:

$26.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

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The Reflexive Property is a property of equality that states that anything is equal to itself. This property is true for numbers, shapes, angles, and more.

In the context of geometry, the Reflexive Property of Congruence states that any geometric figure is congruent to itself. This includes angles, segments, triangles, and other polygons.

So, when you see "<J ≅ <J", it's saying that angle J is congruent to angle J, which is an application of the Reflexive Property. In other words, any angle is congruent (equal in measure) to itself.

The pencil is 15cm long and the ruler is shorter than the pencil by 5cm. So, the pencil is 5cm longer than the 10cm ruler.

The pencil is 15cm long. The ruler is 5cm shorter than the pencil. So, to find the length of the ruler, subtract 5cm from the length of the pencil:

15cm (pencil length) - 5cm (difference) = 10cm

Therefore, the pencil is 5cm longer than the 10cm ruler.

So, the filled sentence would be:

The pencil is 15cm long and the ruler is shorter than the pencil by 5cm. So, the pencil is 5cm longer than the 10cm ruler.

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The pencil is 15cm long and the ruler is shorter than the pencil by 5cm. So, the pencil is _____ than the ruler.

Answer:

5/18

Step-by-step explanation:

We assume they share equally.

5/6 ÷ 3 = 5/6 × 1/3 = 5/18

Answer:

H0 : μ = 60000

H1 : μ ≠ 60000

Test statistic = 3.464

Step-by-step explanation:

Given :

Sample mean salary, xbar = 80000

Sample standard deviation, s = 10000

Population mean salary , μ = 60000

Sample size, n = 3

Hypothesis :

H0 : μ = 60000

H1 : μ ≠ 60000

The test statistic :

T = (xbar - μ) ÷ (s/√(n))

T = (80000 - 60000) ÷ (10000/√(3))

T = 20000 / 5773.5026

T = 3.464

The Decison region :

If Tstatistic >Tcritical

Tcritical at 10%, df = 2 ; two - tailed = 2.9199

Tstatistic > Tcritical ; He

The area of a circle is 1017.36 miles².

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

Radius = 18 miles

Now,

The area of a circle = πr²

So,

= πr²

= 3.14 x 18 x 18

= 1017.36 miles²

Thus,

1017.36 miles².

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Answer:

216.1.4 is 4325÷20 so yup that's what I think

The result of converting 4325 to base 20 is 5

Therefore,

Converting 4325 to base 20.

4 × 20³ = 32,000

3 × 20² = 1,200

2 × \(20^{1}\) = 40

5 × \($20^{0}\) = 5

Adding all to get Ans = \($4325_{20}\)

Hence, The result of converting 4325 to base 20 is 5

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Answer:

Step-by-step explanation:

4/mx

Answer:

i d k there's no question to answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

B?

Answer:

71. 19  72. 100  73. 9  74.1  75. 90  76. 4

Step-by-step explanation:

#71.

Start with 2b-a

Plug in the given numbers where the variables are.

Now the equation is 2(12) - 5

Solve 2(12) - 5

2(12) = 24      24 - 5 = 19

#72.

Start with d(ab-c)

Plug in the given numbers where the variables are.

Now the equation is 2((5×12) - 10)

Solve in the parenthesis first.

5×12= 60    60-10=50    2(50)= 100

#73.

Start with 3+ \(\frac{b}{d}\)

Plug in the given numbers where the variables are.

Now the equation is 3+ \(\frac{12}{2}\)

Solve.

\(\frac{12}{2}\) = 6    3+6 = 9

#74.

Start with \(\frac{4a}{b+4d}\)

Plug in the given numbers where the variables are.

Now the equation is \(\frac{4(5)}{12+(4x2)}\)

Solve.

4(5)= 20    

(4×2)= 8    12+8= 20

Now the fraction is  \(\frac{20}{20}\) = 1

#75.

Start with 2a² - c

Plug in the given numbers where the variables are.

Now the equation is 2(5)² - 10

Solve 2(5) = 10      10² = 100  100-10= 90

#76.

Start with b - c + d

Plug in the given numbers where the variables are.

Now the equation is 12 - 10 + 2

Solve.

12 - 10 = 2     2 + 2 = 4

The gardner is correct Because the total distance traveled by the roller is greater than the length of the bowling green.

A diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.

For the gardener to be correct,

8×Perimeter of the roller = Length of the bowling green

Therefore,

Let use first find the perimeter of the roller

Where:

Substitute these values into equation 1

For 8 full rotation,

Comparing the distance for 8 revolution of the roller with the length of the bowling green,

Therefore, the gardner is correct

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Answer:

15

Step-by-step explanation:

a square root multiplied by itself equals the number inside the box, right?

(/~15~)2 = 15

Answer:

15

Step-by-step explanation:

Squaring a square root of a number will just give you back the number since the square and the square root will cancel each other.

Answer: 1017.88

Step-by-step explanation:

Hope it is right

The joint relative frequency is calculated by dividing the frequency of a specific subset (in this case, the number of adults who prefer watermelon) by the total number of data points.

Here, the specific subset is adults who prefer watermelon, which is 111. The total number of data points is the sum of all children and adults, regardless of fruit preference, which is 445.

So, to find the joint relative frequency of being an adult who prefers watermelon, you would divide 111 by 445.

Hence, the correct answer is:

C. Divide 111 by 445.

Answer:

\(\boxed{\sf \ \ \ answer \ b. \ \ +5 \ \ \ }\)

Step-by-step explanation:

Hello

let's assume that we are looking for x >=0

\(4x^2=100 <=> \dfrac{4x^2}{4}=x^2=\dfrac{100}{4}=25\\<=>\sqrt{x^2}=25\\<=> |x| = 5 <=> x = 5 \ or \ x=-5\)

Let's assume that we are looking for x>=0

so the correct answer is 5

Answer:

Linearly independent, x = 0

Step-by-step explanation:

- We are given three functions as follows:

                           \(f ( x ) = e^4^x\\\\g ( x ) = xe^4^x\\\\h( x ) = x^2e^4^x\)

- We are to determine the linear - independence of the given functions. We will use the theorem of linear independence which states that:

                           \(c_1*f(x) + c_2*g(x) + c_3*h(x) = 0\)

Where,

                       c1 , c2 , c3 are all zeroes then for all values of (x),

- The system of function is said to be linearly independent

- We will express are system of equations as such:

                           \(c_1*e^4^x + c_2*xe^4^x + c_3*x^2e^4^x = 0\\\\\)

- To express our system of linear equations we will choose three arbitrary  values of ( x ). We will choose, x = 0. then we have:

                          \(c_1*( 1 ) + c_2*(0) + c_3*(0 ) = 0\\\\c_1 = 0\)

- Next choose x = 1:

                          \(c_2*e^4 + c_3*e^4 = 0\\\\c_2 + c_3 = 0\)

- Next choose x = 2:

                          \(2*c_2*e^8 + 4*c_3*e^8 = 0\\\\c_2 + 2c_3 = 0\)

- Solve the last two equations simultaneously we have:

                          \(c_1 = c_2 = c_3 = 0\)     .... ( Only trivial solution exist )

Answer: The functions are linearly independent

- The only zero exist is x = 0.

Answer:

4778.4

Step-by-step explanation:

The volume of a cone is given by:

(π•r²•h)/3

(π•13²•27)/3

(π•169•27)/3

(4,563•π)/3

14,334.66/3=4778.4

C. 8

8/3 = g/3

, x3 both side

8/3 x 3 = g

8/3 x 3/1 = g

24/ 3 = g

8 = g

Hope this helps!

Answer:

Step-by-step explanation:

You want to identify the given shapes as a regular or irregular polygon, or neither.

A regular polygon is one that has all sides congruent, and all interior angles congruent. Polygon E is marked as having congruent sides and congruent angles.

Polygon E is a regular polygon.

A polygon is a closed figure formed by line segments connected end-to-end. A simple polygon is one that has no intersecting line segments. A convex polygon is one that has all interior angles measuring 180° or less.

Any simple polygon that is not a regular polygon is an irregular polygon.

Polygons A, B, D are irregular polygons.

A circle is not a polygon. Figure C is neither a regular polygon nor an irregular polygon.

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Answer:

15d10mo

Step-by-step explanation:

Simplify:

(9+6)(mod10)

=15d10mo

Step-by-step explanation:

To compare the two amounts of fabric, we need to express them with a common denominator:

15/2 = 30/4

7 1/2 = 15/2

Now we can compare the two amounts:

30/4 > 15/2

This is true because 30/4 is equal to 7.5 yards, which is greater than 7.5 yards (or 15/2 yards) of silver fabric.

Therefore, Ms. Thompson needs more red fabric than silver fabric.

Answer:

Step-by-step explanation:

Let h(x) = y

The exponentail function is of the form :

\(y = ab^x\)

We have :

\(y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}\)

Given points : (4, 9) and (5, 34.2)

We have:

\(\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b\)

Writing the equation with x, y and b:

\(y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043\)

a = 0.043

b = 3.8

When x = 6, y will be:

\(y = (0.043)(3.8^6)\\\\y = 128.47\)

This is not the y value in the question y = 59.4

Therefore (6, 59.4) does not lie on the graph h(x)

Differentiate both sides of

xy ³ - 2x ²y ² = 0

with respect to x :

d(xy ³ - 2x ²y ²)/dx = d(0)/dx

d(xy ³)/dx - 2 d(x ²y ²)/dx = 0

By the product rule,

d(x)/dx y ³ + x d(y ³)/dx - 2 (d(x ²)/dx y ² + x ² d(y ²)/dx) = 0

By the chain rule,

y ³ + 3xy ² dy/dx - 2 (2xy ² + 2x ²y dy/dx) = 0

y ³ + 3xy ² dy/dx - 4xy ² - 4x ²y dy/dx = 0

y ³ - 4xy ² + (3xy ² - 4x ²y) dy/dx = 0

(3xy ² - 4x ²y) dy/dx = 4xy ² - y ³

dy/dx = (4xy ² - y ³) / (3xy ² - 4x ²y)

dy/dx = (4xy - y ²) / (3xy - 4x ²)

At the point (1, 2), the gradient is

dy/dx (1, 2) = (4×1×2 - 2²) / (3×1×2 - 4×1²) = 4/2 = 2

Answer:

0.22

Step-by-step explanation:

Hope this helps!!!

Answer:

It is .22! :D

Step-by-step explanation: