L) simplify
cos²x - sin²x

The company is likely to sell 3,120 copies of rock music per week.

If the company estimates sales of 6,000 copies a week at its online store, it is likely that 78/150 x 6,000 = 3,120 copies will be from the rock genre.

To find this, we first need to calculate the proportion of visitors that preferred rock music by dividing the number of visitors who preferred rock (78) by the total number of visitors surveyed (150). This gives us 78/150 = 0.52.

Next, we multiply this proportion by the estimated number of weekly sales at the online store (6,000) to find the number of sales that are likely to be from the rock genre. 0.52 x 6,000 = 3,120.

So, the company is likely to sell 3,120 copies of rock music per week.

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In mathematics, a plane is a two-dimensional surface that can be enlarged indefinitely. In order to make a plane we need at least 3 points.

In order to make a plane we need at least 3 points. Let A, B and C are three points which can be defined by two particular vector AB and AC.

As the two vectors is located on the plane, we can use their cross product to define a normal vector on the plane.

As we see a triangle which is a two-dimensional geometric figure that is developed based on 3 points. Triangle is the smallest polygon. The other polygon needs more point for creation.

Therefore, it is proved that minimum three points is mandatory for plane formation.

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Answer:

x = 5/3, y = 2/3

Step-by-step explanation:

x + 1/3 = 2 equ 2

The triangle LJK is congruent to the triangle RTS.

What do congruent triangles mean?

Triangles that are congruent share the same matching side lengths and angle measurements. The conditions for triangle congruence are: SSS, SAS (Side, Side, Side) (Side-Angle-Side)

According to the given image of triangles,

We can observe that:

∠L=∠R, ∠T=∠J, ∠S=∠K.

We can also observe that TS=JK, LK=RS, RT=LJ.

Therefore according to SSS congruency ΔLJK ≅ ΔRTS.

According to SAS congruency ΔLJK ≅ ΔRTS.

According to ASA congruency ΔLJK ≅ ΔRTS.

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Since points D and F are the intersections of sides AC and AE, In triangle respectively, DF is parallel to EC and so EC is twice as long as DF. Thus, the value of side EC is 32.

Given that it has 3 components and three vertices, a triangle qualifies as a polygon. It has a fundamental geometric form. Triangle ABC is the name given to a triangular with the corners A, B, and C. When the three aspects are not collinear, Euclidean geometry yields a single plane and triangle. Triangles are regarded as polygons since they have 3 components and three corners. The points where a triangle's three sides meet are referred to as its corners. Three triangle angles are multiplied to get 180 degrees.

Given :

Triangle ACE

The midpoint of EC is side, where AC = 38 B.

D sits in the middle of EC.

The center of AE is F.

DF = 16.

Given that D is the midpoint of EC and that F is the midpoint of AE, it follows that DF is parallel to AC.

If DF and AC are parallel, then DF and AC are equal to twice each other and DF equals 16. Thus, EC equals 32.

=>EC = 2*DF

=>EC = 2*16

=>EC = 32

It follows that if points B, D, and F are the midpoints of the sides of the triangle ACE, then DF is parallel to AC and EC = 2 x DF = 32.

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The total amount in the bank after the specific number of years is;

9.  $476. 1

11. $7, 128. 8

The formula for calculating simple interest is expressed as;

I = PRT/100

Where;

From the information given, we have that;

9.Principal amount = $450

Interest rate = 1.45

Time = 5

Substitute the values into the formula

SImple interest = $450 ×1. 45× 5/100

Multiply the values, we get;

Simple interest, I = 2610/100

Divide through

Simple interest = $26. 1

Total amount = $450 + $26.1 = $476. 1

11. Principal amount = $5600

Interest rate = 3.9

Time = 7 years

Substitute the values

Simple interest = $5600× 3. 9 × 7/100

Multiply the values

Simple interest = 152,880/100

Simple interest = $1528. 8

Total amount = $7, 128. 8

Hence, the values are $476. 1 and  $7, 128. 8

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Answer:10

Step-by-step explanation: Because negative 40 equals -50 + x equals 10

The following presumption has to be verified in order to establish whether the collection of ordered pairs fulfills an exponential function: The x-coordinates must have the same increment or a consistent difference.

A mathematical function of form f (x) = aˣ is an exponential function. "x" is a variable, while "a" is a constant that serves as the function's basis and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the foundation for exponential functions that are most frequently utilized.

Characteristics are:

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Answer:

62 candies can fit into each box

Step-by-step explanation:

We know

A small box can hold 94.24 g of candy

Each candy has a mass of 1.52 g

How many candies can fit into each box?​

To find it we take

94.24 divided 1.52 = 62 candies

So, 62 candies can fit into each box

Answer: not enough to answer

The range of the accidents reported from the grouped frequency table is 22.

The range is the difference between the highest value and the lowest value of a given set of data.

We have,

The number of accidents reported from the grouped frequency table.

The largest number of accidents = (19 - 25)

The smallest number of accident = (3 - 7)

Now,

Range.

= 25 - 3

= 22

Thus,

The range of the reported accidents is 22.

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The domain and range of function Y = 4x² are:

Domain: (-∞, ∞) {x | x ∈ R}

Range: [0, ∞) {y | y ≥ 0}

Now, According to the question:

What are the domain and range?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

We have,

Y = 4x²

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation: (-∞, ∞)

Set-Builder Notation:  {x | x ∈ R}

The range is the set of all valid y values: [0, ∞)

Set-Builder Notation: {y | y ≥ 0}

Hence, the domain and range of function Y = 4x² are:

Domain: (-∞, ∞) {x | x ∈ R}

Range: [0, ∞) {y | y ≥ 0}

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The complete question is this:

What is the domain of the function Y = 4x²

Answer:

[tex]13^{\circ}[/tex]

Step-by-step explanation:

Consider the smaller of the two triangles with angle [tex]x[/tex].

Using vertically opposite angles, one of the angles of this triangle is [tex]85^{\circ}[/tex].

Using corresponding angles combined with angles on a straight line, one of the angles is [tex]82^{\circ}[/tex].

Angles in a triangle add to [tex]180^{\circ}[/tex], so [tex]x=13[/tex].

The solution to the system of equations is x = 4 and y = 2.

We would use the elimination method to solve the system of equations:

Let's eliminate the variable y by adding equations 1 and 2:

4x + 8y = 24

2x + y = 19

.

.

.,

6x + 9y = 43

Now we can eliminate the variable x by subtracting equation 3 from the above equation:

6x + 9y = 43

3x + y = 15

.

.

.

3x + 8y = 28

We now have an equation with one variable: 3x + 8y = 28. We can solve for x by dividing both sides by 3:

x = (28 - 8y) / 3

Now we can substitute this expression for x into one of the original equations and solve for y. Let's use equation 4:

4x + 2y = 12

Substituting x = (28 - 8y) / 3:

4((28 - 8y) / 3) + 2y = 12

If we simplify:

Finally, we can use this value of y to find x by plugging it into the expression we found earlier:

x = (28 - 8(2)) / 3

x = (28 - 16) / 3

x = 12 / 3

x = 4.

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Answer:

she has rode 16 miles this week

Step-by-step explanation:

3 miles on monday 3 times that many on tuesday plus 4 miles one wensaday add them all up

3 times 3 is 9 plus 3 is 12 plus 4 is 16 there fore 16 miles in totale

sorry for my speling erros

She rode a total distance of 16 miles this week.

An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -

2x + 3y + 5

2z + y

x + 3y

The distance rode by Lexi per day is mentioned below -

Monday - Lexi rode 3 miles on a bike.

Tuesday - Lexi rode 3 times more than she did Monday.

Wednesday - Lexi rode an additional 4 miles.

We can write the expression to find the total distance in miles covered by Lexi as -

d = d{M} + d{T} + d{W}

d = 3 + (3 + 3) + 4

d = 3 + 6 + 4

d = 13 miles

Therefore, she rode a total distance of 16 miles this week.

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Answer: 11, 23, 166

Step-by-step explanation:

Hiya! From the drawings, I'm assuming all of the triangles are right-angled triangles. If they aren't though, tell me and I'll tell you how to solve them.

Anyways, assuming they are right angled-triangles, you can use Pythagoras' Theorem (aka a² + b² = c²)

c is the hypotenuse or the side opposite the right angle.

a and b are just the other two sides (doesn't really matter which is which)

Question 7:

c² = a² + b²

12² = a² + 5²

144 = a² + 25

144 - 25 = a²

119 = a²

a = 10.908712114635714411502154487373

(To the nearest whole number: 11)

Question 8:

c² = a² + b²

24² = 7² + b²

576 = 49 + b²

576 - 49 = b²

527 = b²

b = 22.956480566497992703585747092065

(To the nearest whole number: 23)

Question 9:

c² = a² + b²

c² = 90² + 140²

c² = 8,100 + 19,600

c² = 27,700

c = 166.43316977093238068928214785346

(To the nearest whole number: 166)

Hoped this helped! Tell me if there's something you don't understand. :)

A linear equation in two variables has only 1 solution.

Now, According to the question:

Let's know:

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2. Whereas if we speak about linear equation in two variables, it has two solutions.

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0.

A linear equation in two variables has only 1 solution.

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Answer: No, it is not a solution.

Step-by-step explanation:

   We will substitute the point given, and if the inequality is true after simplifying then it is a solution.

 Given:

3x + 11y ≤ 8

 Substitue:

3(1) + 11(7) ≤ 8

 Multiply:

3 + 77 ≤ 8

 Add:

80 ≤ 8 ✗

Answer:

PF = 9

Step-by-step explanation:

the incentre of a triangle is equally distant from the triangle's 3 sides, that is

PD = PE = PF

using PD = PE to solve for x

5x - 6 = 3x ( subtract 3x from both sides )

2x - 6 = 0 ( add 6 to both sides )

2x = 6 ( divide both sides by 2 )

x = 3

then

PE = 3x = 3 × 3 = 9

PF = PE = 9

Answer:

10.5 inches, 14 inches, 7 inches

Step-by-step explanation:

Let's say x is the multiplier of the ratio value and the actual length of the sides:

1/4 * x = side 1

1/3 * x = side 2

1/6 * x = side 3

Since the perimeter is the sum of all sides, the perimeter is equal to:

31.5 = 1/4 * x + 1/3 * x + 1/6 * x  ==> 31.5 inches is the perimeter

(31.5 = x/4 + x/3 + x/6)*12  ==> multiply the equation by 12 since 12 is the

                                           LCM (Least Common Multiple) of 4, 3, and 6

12 * 31.5 = 12 * x/4 + 12 * x/3 + 12 * x/6  ==> multiply each term by 12

378 = 12x/4 + 12x/3 + 12x/6 ==> simplify

378 = 3x + 4x + 2x

378 = 9x

x = 378/9 ==> divide both sides by 9

x = 42

Now find each side length [Refer to the first three equations] :

Side length 1: 1/4 * 42 = 42/4 = 10.5 inches

Side length 2: 1/3 * 42 = 42/3 = 14 inches

Side length 3: 1/6 * 42 = 42/6 = 7 inches

Answer: 10.5 inches, 14 inches, 7 inches

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The area of the figure given is 49 square feet's.

       ∫dA = ∫∫F(x, y) dx dy

       A =  ∫∫F(x, y) dx dy

Given is a figure as shown in the image attached.

We can write the area of the figure as -

A = A{T} + A{R}

A = (4 x 10) + (1/2 x 6 x 3)

A = 40 + 9

A = 49 square feet's

Therefore, the area of the figure given is 49 square feet's.

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I think it's answer this .

Answer:

hectogon or hecatontagon or 100-gon

Step-by-step explanation:

It is a hundred - sided polygon ( shape ). The sum of all hectogon's interior angles are 17640 degrees.

Answer:

Regular exercise has been shown to aid in the prevention and management of noncommunicable illnesses such as diabetes, heart disease, stroke, and a number of malignancies. Additionally, it lowers blood pressure, supports healthy body weight, and enhances well-being through enhancing mental health.

Step-by-step explanation:

The table representing the given absolute function should be completed as follows;

x          f(x)

6          8

-1          6

4          4

9         14

Based on the information provided, we have the following absolute function:

f(x) = |-2x + 4|

When x = 6, the value of the absolute function is given by;

f(6) = |-2(6) + 4|

f(6) = |-12 + 4|

f(6) = |-8|

f(6) = 8

When x = -1, the value of the absolute function is given by;

f(-1) = |-2(-1) + 4|

f(-1) = |2 + 4|

f(-1) = |6|

f(-1) = -6.

When the value of the absolute function y = 4 is given by;

4 = |-2x + 4|

±4 = -2x + 4

2x = 4 ± 4

2x = 8

x = 4 or 0.

When the value of the absolute function y = 14 is given by;

14 = |-2x + 4|

±14 = -2x + 4

2x = 4 ± 14

2x = 18

x = 9 or 5.

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The value of StartFraction P (t) Over A EndFraction for this problem will be 20

Take the value of x that they provide you and plug it into the problem for these kinds of difficulties.

The fraction's numerator is the highest number. It stands in for the entire thing that must be divided.

A fraction's denominator is the value at the bottom. It shows how many equally sized pieces are divided up in the object.

adding 3 to the formula:

6/(3) + 2(3)^2 —> use PEMDAS. Apply the 32 exponents first, followed by left-to-right multiplication and division, and finally addition.

6/x + 2x^2,

when x = 3

=20

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The question the incomplete the full question:

What is the value of StartFraction 6 Over x EndFraction + 2x2, when x = 3?

Answer:

The second part is 0.8 and B. About 1,845 years.

Step-by-step explanation:

:)

A one million sided shape called as Megagon.

We know that a polygon is noting but a closed two-dimensional figure which is enclosed by line segments.

These line segments are known as sides.

A polygon has at least three straight sides and angles.

Polygons are classified mainly into four categories. Regular polygon, Irregular polygon, Convex polygon and Concave polygon

We know that a polygon with n sides is called n-gon.

For n = 1000000, i.e., a polygon with one million sides is called as Megagon.

A number of edges and vertices = 1000000

And the internal angle of megagon is about 179.99 degrees.

Therefore, a shape with  1 million sides is known as a Megagon

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Step-by-step explanation:

(1). x-intercept: Put y = 0 in the equation y = 2x - 6 and solve for x. The x-intercept is 3.

y-intercept: Put x = 0 in the equation y = 2x - 6 and solve for y. The y-intercept is -6.

(2). x-intercept: Put y = 0 in the equation y = x - 7 and solve for x. The x-intercept is 7.

y-intercept: Put x = 0 in the equation y = x - 7 and solve for y. The y-intercept is -7

(3). x-intercept: Put y = 0 in the equation y = (3/2)x - 9 and solve for x. The x-intercept is -6.

y-intercept: Put x = 0 in the equation y = (3/2)x -9 and solve for y. The y-intercept is -9.

(4). x-intercept: Put y = 0 in the equation y = (-1/4)x + 1 and solve for x. The x-intercept is -4.

y-intercept: Put x = 0 in the equation y = (-1/4)x + 1 and solve for y. The y-intercept is 1.

(5). x-intercept: Put y = 0 in the equation -x + y = -5 and solve for x. The x-intercept is 5.

y-intercept: Put x = 0 in the equation -x + y = -5 and solve for y. The y-intercept is -5.

(6). x-intercept: Put y = 0 in the equation x + 2y = -14 and solve for x. The x-intercept is -14.

y-intercept: Put x = 0 in the equation x + 2y = -14 and solve for y. The y-intercept is -7.

(7). x-intercept: Put y = 0 in the equation 3x - y = -3 and solve for x. The x-intercept is -1.

y-intercept: Put x = 0 in the equation 3x - y = -3 and solve for y. The y-intercept is 3.

(8). x-intercept: Put y = 0 in the equation 5x + 3y = 15 and solve for x. The x-intercept is 3.

y-intercept: Put x = 0 in the equation 5x + 3y = 15 and solve for y. The y-intercept is 5.

The similar photo should be 4.5 inches wide.

Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -

y = Kx

K = y/x

where -

{K} is scale factor. It also tells by how many times is {y} greater than {x}.

Given is that Gwen scans a photo that is 4 inches wide by 6 inches long into her computer. Now, she scales the length down to 3 inches.

We can write -

y₁/x₁ = y₂/x₂

6/4 = 3/x₂

x₂ = 6 x 3/4

x₂ = 6 x 0.75

x₂ = 4.5

Therefore, the similar photo should be 4.5 inches wide.

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Answer: standard form of (6.31×10⁵ ) + (2.6×10⁴) is 65.7 × 10⁴.

What is a simplification of an expression?

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

As given,

(6.31×10⁵ ) + (2.6×10⁴) = ( 6.31× 10⁴ ×10 ) + (2.6 × 10⁴ )

                                   =  ( 6.31 × 10 + 2.6 )

                                   =  ( 63.1 + 2.6 )

                                   =  ( 65.7 )

                                   = 65.7 × 10⁴

Hence, the standard form of ( 6.31× 10⁵) + (2.6 × 10⁴) = 65.7 × 10⁴.

[tex](6.31\times 10^{5})+(2.6\times 10^{4})\implies 6\underline{31000}+2\underline{6000} \implies \text{\LARGE 657000}[/tex]

x2 - 3x - 5 = 0 has a unique solution of type -11, which is what the equation entails.

The "discriminant" is the value that aids in identifying the many types of solutions when using the quadratic formula to solve a problem. It is a unique function of a co-efficient in a mathematical equation (a quadratic equation), and the value it yields provides details about the roots of the equation. Calculating the discriminant involves square rooting the "b" term and subtracting four times the "a" term from the "c" term. Alongside "D," there is a (delta) that represents discrimination. A quadratic equation with two distinct real number solutions is said to have a positive discriminant. A quadratic equation with a discriminant of zero has repeated real number solutions. Both of the solutions are not real numbers, as indicated by a negative discriminant.

given

x2 - 3x - 5 = 0

D=b2−4ac

D= −32−4×1×5

D=92−20

D= −11

x2 - 3x - 5 = 0 has a unique solution of type -11, which is what the equation entails.

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