Change 4 1/6to an improper fraction.

The sum form of the trigonometric function 2 · sin 2x · sin 2x by product-to-sum formula is 1 - cos 4x.

Herein we find the definition of a trigonometric function defined as a product of trigonometric function, this can be transformed into a sum of trigonometric functions by means of the following product-to-sum formula:

sin α · sin β = [cos (α - β) - cos (α + β)] / 2

First, write the trigonometric function defined in the statement:

2 · sin 2x · sin 2x

Second, use the product-to-sum formula by considering α = β = 2 · x:

2 · [[cos (2x - 2x) - cos (2x + 2x)] / 2]

cos 0 - cos 4x

1 - cos 4x

Third, write the resulting expression:

2 · sin 2x · sin 2x = 1 - cos 4x

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Answer:

The answer would be A. (Not sure if its A B C or D question but I will have picture below)

Step-by-step explanation:

Hope this helps you! :))

Answer: 13.9

Step-by-step explanation:

17.140 rounded to the nearest tenth is 17.1

03.179 rounded to the nearest tenth is 3.2

17.1 - 3.2 = 13.9

father age 46.5

daughter age 15.5

46.5 - 15.5 = 31

Answer:

1  :  4

Step-by-step explanation:

There are 4 squares and 16 triangles.

That is,

Squares : Triangles

          4  :  16

To write it in its simplest ratio, divide both by 4.

Squares : Triangles

         1  :  4

Step-by-step explanation:

9)=

By the question:-

x + y = 130-i

x - y = 34-ii

Now,

Add i and ii,

x + y + x -y = 164

or, 2x = 164

so, x = 82

Now,

x -y = 34

or, 82 - y = 34

so, y = 48

The numbers are 82 and 48.

10) =

Let adults ticket be x and childs ticket be y.

x + y = 800

x = 800 - y - eqn i

4.5x + 6y = 4500

Substituting x's value from eqn i,

4.5(800-y) + 6y = 4500

or, 3600 - 4.5y + 6y = 4500

or, 1.5y = 900

so, y = 600

Now,

x + y = 800

or, x + 600 = 800

so, x = 200

Hence, 600 adult tickets were sold and 200 child tickets were sold.

11)=

Let cost of one small box be x and one medium box be y.

So,

4x + 2y = 54-eqn i

x + 2y = 33-eqn ii

subtracting eqn i from ii,

x + 2y - 4x - 2y = - 21

or, -3x = - 21

so, x = 7

Now,

x + 2y = 33

or, 2y = 33 - 7

or, y = 26/2

so, y = 13

So, cost of one small box is $7 and medium box is $13.

Answer: 140 is the answer

Step-by-step explanation: Luis adds 100 to his account  so which makes the account balance 180 and then writes a check so he takes 40 out of his account which means he has 140 left in his account

Step-by-step explanation:

r - 535 = 175

r = 175 + 535 = 710

Answer:

take - 535 to the other side (over equal to side)

which makes it +535

r = 175 + 535

r = 710

Answer:

£27839

Step-by-step explanation:

O×M=N (original x multiplier = original value)

£28000×0.97%=£27160< 1st year decrease

£27160x1.025=£27839<2nd year increase

Answer:

  f(x) = x² -2x -35

Step-by-step explanation:

You want a quadratic function that has zeros 7 and -5.

Each zero (p) gives rise to a factor (x-p). The zeros 7 and -5 mean the quadratic has factors (x-7) and (x-(-5)).

  f(x) = (x -7)(x +5)

  f(x) = x² -2x -35

__

Additional comment

You may notice that the coefficient of the linear term is the opposite of the sum of the zeros. The constant term is the product of the zeros. Knowing this, we can write the quadratic without any concern for the factors.

  sum: 7-5 = 2

  product: (7)(-5) = -35

  quadratic: f(x) = x² -2x -35

Answer:

Step-by-step explanation:

domain: 1,2,3,4

Range: 8,6,4,2

D=-2

[tex]a_{n}=a_{1}+(n-1)-2[/tex] formula

By using the concept of set operation, the result obtained is

[tex]n(A \cap B) = 2[/tex]

What is a set?

Set is a well defined collection of distinct objects. The members of a set are called elements of a set. Set can be empty as well as non empty.

Set can be finite as well as infinite.

The number of elements inside a set is known as cardinal number of the set

Operations on set are union, intersection, set difference and symmetric difference

Concept of set operation has been used here

n(A)=5 n(B)=7 and n(AUB)= 10

[tex]n(A \cap B) = n(A) + n(B) - n(A \cup B)[/tex]

[tex]n (A \cap B) = 5 + 7 -10\\n(A \cap B ) =2[/tex]

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The equivalent equation to the given equation i.e, x = x² - 20  is   x² - x - 20 = 0

What is a Quadratic equation ?

A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.

The given expression is,

x = x² - 20

We have to make the equation in quadratic form i.e, ax² + bx + c = 0

so, first take x to the right side

0 = x² - 20 - x

Now swap the equation,

x² - 20 - x = 0

put 'x' term in middle and constant term at last like this,

x² - x - 20 = 0

Hence, The equivalent equation to the given equation i.e, x = x² - 20 is  x² - x - 20 = 0

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From the proportional relationship graphed, it is found that:

A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0, meaning that the relationship passes through the origin.

When the two variables x and y are direct proportional, the output variable y is obtained multiplying the input variable x by the constant of proportionality k, according to the rule presented follows:

y = kx.

From point (2,16) in this problem, the constant is given as follows:

k = 16/2 = 8.

Hence the equation is:

y = 8x.

Meaning that her rate is of:

8 miles per hour.

If she ran faster, the slope = constant would increase, as it represents the velocity.

The problem is given by the image at the end of the answer.

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The quotient of 5 divided by 3/10 is equal to 50/3

When we want to divide by a fraction, we just need to replace that division by the product with the inverse of the fraction.

So, if we want to divide A by the fraction (b/c), then we can write:

A÷(b/c)

That will be equal to A*(c/b), so:

A÷(b/c) =  A*(c/b)

Here we want to divide 5 by 3/10, then we need to solve:

5÷(3/10)

Using the above rule we will get:

5÷(3/10) = 5*(10/3) = 50/3

That is the quotient.

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The value of the translated function g(x) will be x²+1.

A function is defined as the expression that set up the relationship between the dependent variable and the independent variable.

Given that the function is f(x) = x². The function g(x) in the form of  a(x–h)²+k will be written as below,

The function is translated to the 1 unit up which means that the value of k will be equal to the positive 1.

The function is,

g(x) = a(x–h)²+k

g(x) = 1(x-0)² + 1

g(x) = x² + 1

Therefore, the value of the translated function g(x) will be x²+1.

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The maximum weight that could be supported by a beam that is 6 inches wide, 2 inches high, and 24 feet long is 3.33.

G = C×(w×h²/l)

Where,

C = constant

C = G×l/(w²h²)

Weight (w) = 6 in

Height (h) = 2 in

Length (l)= 10 ft

Maximum ton (G) = 8 t

C = 8×10/(6×2²)

C = 80/24

C = 10/3

G = (10/3)×(w×h²/l)

So, Maximum weight

G = (10/3)×(6×2²/24)

G = 10/3 t

G = 3.33 tones

The maximum weight is 3.33 tones.

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60 minutes will be taken by the older computer to send out the email on its own.

Two or more expressions with an Equal sign is called as Equation.

one computer takes x minutes and the other takes 3x minutes

in 1 minute, they send (1/x) and (1/3x) of the total message

together, (15/x)+(15/3x)=1, the full message

multiply by 3x to clear fractions

45+15=3x

60=3x

Divide both sides by 3

20=x

So for older computer  60 minutes  it take to send out the email on its own.

Hence, 60 minutes will be taken by the older computer to send out the email on its own.

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Answer:

(4)

Step-by-step explanation:

Let's make the smaller number equal to x. Since they are consecutive odd numbers, the larger number is x+2.

Twice the smaller number is 2x. Three times the larger number is 3(x+2). If twice the smaller is subtracted from three times the larger, then the expression should be: 3(x+2) - 2x

Then, since the result of this is four more than the smaller, this expression is x+4.

Finally, we put it all together, so we get: 3(x+2) - 2x = x + 4. Option 4 is our correct answer.

Hence, the option (4) is correct.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger, the result is four more than the smaller.

Let us assume the smaller number is [tex]x[/tex].

The larger number is  [tex](x+2)[/tex].

Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger than it is

[tex]3(x+2)-2x[/tex]

So, the result is four more than the smaller.

i.e., [tex]3(x+2)-2x=x+4[/tex]

Hence, the option (4) is correct.

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An inequality that can be solved to show the number of chairs c Mrs. Smith can buy 8c ≤ 56

In this question we have been given Mrs. Boyer is buying folding chairs that are on sale for $8.

She has $56

We need to find an inequality that can be solved to show the number of chairs c Mrs. Smith can buy.

A price of one chair is $8

So, the price of 'c' number of chairs would be 8c

But she has $56

So, to find the number of chairs she can buy, we need to divide 56 by 8

We can write is as 8c = 56

⇒ c = 7

But she might buy less that 7 chairs.

So, we write above relation in inequality form as,

8c ≤ 56

Therefore, an inequality that can be solved to show the number of chairs c Mrs. Smith can buy 8c ≤ 56

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Answer:

$208

Step-by-step explanation:

$79.50 x 24 = 1908

$1908 + 400 = 2308

$2100/2308 = 9%

Carey will pay a total interest of $1,508 over the course of the installment plan for the computer system.

Interest is a financial concept that represents the cost of borrowing money or the return on invested capital. It is a fee charged for the use of borrowed funds or the compensation received for lending money or investing in assets.

Total number of monthly payments

= 12 months/year x 2 years

= 24 months

and, Monthly payment amount = $79.50

Total amount paid in monthly installments

= Monthly payment amount x Total number of monthly payments

= $79.50 x 24

= $1,908

Next, we can subtract the initial down payment from the total amount paid to find the interest paid:

Total interest paid = Total amount paid - Down payment

= $1,908 - $400

= $1,508

Therefore, Carey will pay a total interest of $1,508 over the course of the installment plan for the computer system.

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on dividing 100 by 200 we get answer as 0.5 or we can also write it as 1/2 in fraction.

What is division?

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.

The fundamental goal of division is to produce equal groups or to ascertain how many individuals are in each category following a fair distribution.

To divide 12 donuts into three similar groups in the aforementioned case, you would need to put four doughnuts in each group. Consequently, 12 divided by 3 will equal 4.

We need to find 100/200,

on solving this division problem we get answer as 1/2 (in fraction) or 0.5 (in decimal).

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Answer:

instead of X, we replace 9.

So we have: f(9)=4*9^2-2*9+4.

Again, f(9)= 4*81-18+4=324-14=310.

The graph of the function g(x) = -2x - 3 is attached below.

Graph:

Graph refers a diagram that represents the variation of a variable in comparison with that of one or more other variables.

Given,

Here we have the function g(x) = -2x - 3

Now, we need to plot the graph of the function.

In order to plot the graph for the given function,

First we have to take some sample values for the given function and then apply it on the given function to generate the table to plot the graph.

Now, we have to take -2, -1, 0, 1, 2 are the samples value for x.

Then we get the value of the function as,

x = -2 => g(-2) = -2(-2) - 3 = 4 - 3 = 1

x = -1 => g(-1) = -2(-1) - 3 = 2 - 3 = -1

x = 0 => g(0) = -2(0) - 3 = 0 - 3 = -3

x = 1 => g(-2) = -2(1) - 3 = -2 - 3 = -5

x = 2 => g(2) = -2(2) - 3 = -4 - 3 = -7

Now, we can get the table like the below

Now, we have to plot the graph through this table, then we get the graph like the following.

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A graph of a quadratic function is a parabola, making an equation of a parabola with help of an x-intercept and vertex can be formed.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
With the help of the vertex and the x-intercept, the equation of the parabola can be formed which helps to graph a quadratic function because the equation of the parabola resembles the quadratic function,

Thus,  a graph of a quadratic function is a parabola, making an equation of a parabola with help of an x-intercept and vertex can be formed.

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Answer:

Step-by-step explanation:

The value of the side CB in the right angled triangle is found as 4√2 units.

For the given question,

The diagram is given;

AB = 7 units.

AG = 3 units.

GB = 7 - 3 = 4 units.

GC = 4 units.

In right angled triangle GCB, apply Pythagorean theorem.

CB² = GB² + GC²

CB² = 4² + 4²

CB² = 2(4)²

Taking square root both side.

CB = 4√2

Thus, the value of the side CB in the right angled triangle is found as 4√2 units.

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Answer: 584390

Step-by-step explanation: the r4u819