c) tan²0 - cot²0 = sec²0 (1- cot²0)
Prove that LHS = RHS So that LHS will be the sec²0 (1- cot²0) ​

A graph of each of the exponential equation is shown in the image attached below.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = ab^x

Where:

Since Amber shared her photo with 3 people who continued to share it, an exponential function that models the situation is given by:

f(x) = 3(4)^x

Similarly, Ben's post was shared with 2 friends and each of them shared it with 3 more every day, tripling the number of shares every day, an exponential function that models the situation is given by:

g(x) = 2(3)^x

Lastly, an exponential function that represents the spread of Carter's social media post is given by:

h(x) = 10(2)^x

In this scenario, we would use an online graphing calculator to graph each function as shown in the image attached below.

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They continued to share it, so the number of shares increases every day, as shown by the function.

Social Media Post Shares f(x) = 3(4)x

Day Number of Shares

0 2

1 6

2 18 Carter shared his post with 10 friends, who each share with only 2 people each day.

Answer: 951 ft

Step-by-step explanation:

-230 + 602 - 183 + 762
= 951 ft

Answer: The statement that is true about the function f(x)=4x-4 is:

It is a linear function, as it is a straight line in the form of y=mx+b where m is 4 and b is -4

The y-intercept of this line is -4, which means when x=0, y=-4

The slope of this line is 4, which means for every 1 unit increase in x, y increases by 4 units

The domain of this function is all real numbers and the range is all real numbers except -4

The equation of the line is y = 4x - 4

The graph of this function is a line with a slope of 4 and y-intercept of -4.

Step-by-step explanation:

Answer:

See explanation below.

Step-by-step explanation:

2.3p – 10.1 = 6.5p – 4 – 0.01p?

2.3p -6.5p + 0.01p=  – 4 + 10.1

-4.19p = 6.1           [Combine like terms and moved from one side to the other]

p = -1.456

Select two options.

The options seem to run together.  Where does one equation stop and the other begin?

Are these the equation options?

2.3p – 10.1 = 6.4p – 4

2.3p – 10.1 = 6.49p – 4

230p – 1010 = 650p

– 400 – p 23p – 101 = 65p – 40

– p 2.3p – 14.1 = 6.4p – 4

These don't look correct.   Please review the derivation of p=-1.456 and find the option(s) that provide the same result.

By graphing a plot point using the x-intercept form, the function (x + 4)2 is shown to be x2 + 16 + 8x.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

(x + 4)²

= x2 + 16 + 8x

By graphing a plot point using the x-intercept form, the function (x + 4)2 is shown to be x2 + 16 + 8x.

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The four types of Sequence are Arithmetic Sequence , Geometric sequence , Harmonic Sequence and Fibonacci Sequence .

What is a Sequence ?

The Sequence is defined as an arrangement of objects or a set of numbers in a particular order which are followed by some rule .

The Four Types of Sequences are :

(i) Arithmetic Sequence : It is defined as a type of sequence in which  every term of the series is created by adding or subtracting a fixed number to preceding number .

(ii) Geometric Sequence : It is defined as a type of sequence in which  every term is obtained by multiplying or dividing a fixed number with the preceding number .

(iii) Harmonic Sequence : It is defined as a type of sequence in which the reciprocals of the terms follows the Arithmetic Progression .

(iv) Fibonacci Sequence : It is defined as a type of sequence in which every element is obtained by adding the two preceding elements and the sequence starts with 0 and 1 .

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So on solving the provided question, we can say that  y = a + xb is the necessary equation for the total fee the repairman charged, y = 260 + 6x

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

Here,

Let the total amount charged by the repairman be y and the total number of hours worked be x,

[tex]y = a + xb[/tex]

a is as  travel fee

b is as  hourly rate

Therefore, y = a + xb is the necessary equation for the total fee the repairman charged.

y = 260 + 6x

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Therefore , the solution of the given problem of trigonometry comes out to be we can find the sides of triangle by trigonometry ratios.

The area of mathematics known as trigonometry explores the correlation between square side length and As a result of the combination of astronomy and geometry studies, the field initially emerged inside the Nineteenth century, most likely there in third century BC. Precise methods of mathematics cover a number of geometric equations and possible applications to calculations.

Here,

To find the all sides of a triangle

By using trigonometry ,

We can:

Apply the law of sines or trigonometry to find the right triangle side lengths: a = c × sin(α) or

a = c × cos(β)

b = c × sin(β) or

b = c × cos(α)

Therefore , the solution of the given problem of trigonometry comes out to be we can find the sides of triangle by trigonometry ratios.

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The equations which are equivalent to -1/4(x) + 3/4 = 12 are -1(x/4) + 3/4 = 12 and -x/4 +3/4 = 12. Choose the 2nd and 5th options

Equivalent equations are equations that work the same way even though they look different

The given equation is -1/4(x) + 3/4 = 12 which can simplified as:

-1/4(x) + 3/4 = 12

(-x + 3)/4 = 12

Compare with options:

1. 4x/1 + 3/4 = 12

4x/1 + 3/4 = 12

This is not equivalent

2. -1(x/4) + 3/4 = 12

-1(x/4) + 3/4 = 12

-x/4 + 3/4 = 12

(-x + 3)/4 = 12

This is equivalent

3. -(x+3)/4 = 12

-(x+3)/4 = 12

This is not equivalent

4. 1/4(x+3) = 12

1/4(x+3) = 12

This is not equivalent

5. -x/4 +3/4 = 12

-x/4 +3/4 = 12

(-x+3)/4 = 12

This is equivalent

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Answer:it’s b and d

Step-by-step explanation:

The equation of the circle center, C(2, -3), with the point on the circle, P(-4, 5), is the option;

The standard form of the equation of a circle is presented as follows;

(x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The length of the radius of the circle

The location of the specified center of the circle, C = (2, -3)

The location of the point P = (-4, 5)

The radius of the circle found using the distance formula used for finding the distance between two points is therefore;

r = √((-4 - 2)² + (5 - (-3))²) = √((-6)² + (8)²) = 10

The radius of the circle, r = 10

Therefore;

The center of the circle, (h, k) = (2, -3)

The equation of the circle = (x - 2)² + (y - (-3))² = 10²

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The correct equation of step 2 is 16x = 14

from the question, we have the following parameters that can be used in our computation:

14 + 12x - 6 = 18 - 4x + 4

When the like terms on each side are Evaluated, we have

Step 1: 8 + 12x = 22 - 4x

When the like terms on all sides are Evaluated, we have

Step 2: 16x = 14

Hence, the correct equation is 16x = 14

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The value for constant of proportionality and inverse proportionality is k=12 and x=12/y respectively.

What is constant of proportionality and inverse proportionality?

The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship.

When the value of one item rises in relation to a fall in the other or vice versa, two values are said to be inversely proportionate. This indicates that the natural behaviour of these two quantities is contrary

In a bakery workers must make 12 batches of bagel dough an hour.

The number of batches of dough, y, that each worker needs to mix in one hour is inversely proportional to the number of workers, x.

Lets find the constant of proportionality first.

According to the graph -

The point given in the graph is (6,2).

x=6 and y=2

(where 'x' denotes  no of workers and 'y' denote no. of bagel dough batches).

Equation for constant of proportionality is -

x×y=k

6×2=k

k=12 is the constant of proportionality.

Now find the equation for inverse proportionality.

No. of workers (along x-axis) = x

No. of the bagel dough batches (along y-axis) = y

The algebraic equation relating both = x×y=k

The constant of proportionality is k=12.

x×y=12

xy=12

x=12/y

Therefore, the equation of inverse proportionality is x=12/y.

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The expression for the perimeter of the gardening area is 10x+16

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

The perimeter of the garden will be the sum of all the sides of the garden.

left side = x+3+x = 2x+3

right side = x+3x+x =2x+3

top side = x+3+x+3+x = 3x+6

bottom side = 3x+6

therefore this shot the garden as a rectangular shape.

The perimeter of a rectangle = 2(L+B)

= 2((2x+3)+3x+6)

= 2( 5x+8)

therefore the expression that best represents the perimeter of the garden is 10x+16

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The probability that on any one day, Heila will not be late for school is 0.69 or 69%.

We can use conditional probability to find the probability that Heila will not be late for school on any one day.

Let W be the event that Heila walks to school, and L be the event that Heila is late for school.

We know that:

P(W) = 0.65 (the probability that Heila walks to school)

P(L | W) = 0.4 (the probability that Heila is late for school given that he walks to school)

P(L | W') = 0.1 (the probability that Heila is late for school given that he cycles to school)

The probability that Heila is not late for school is the complement of the event that he is late for school. So:

P(L') = 1 - P(L)

We can use the formula for conditional probability to find the probability that Heila is not late for school:

P(L' | W) = 1 - P(L | W) = 1 - 0.4 = 0.6

P(L' | W') = 1 - P(L | W') = 1 - 0.1 = 0.9

We also know that the total probability of the outcomes must be equal to 1. Therefore, we can find the probability that Heila walks to school, P(W) by using the following equation:

P(W) + P(W') = 1

We know that P(W) = 0.65, so we can find P(W') by subtracting P(W) from 1:

P(W') = 1 - P(W) = 1 - 0.65 = 0.35

Now, we can use the formula of Total Probability to find the probability that Heila will not be late for school:

P(L') = P(L' | W) * P(W) + P(L' | W') * P(W')

P(L') = 0.6 * 0.65 + 0.9 * 0.35 = 0.69

Therefore, the probability that on any one day, Heila will not be late for school is 0.69 or 69%.

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Answer:

Step-by-step explanation:

1 you would pour the water in the cup and see what dash it lands on

let's say you pour the water and it lands on the 1/8 mark it would be one 1/8

Hope this help if not sorry

The coordinates of A'', B'' and C'' are (-1, 4), (-4, 3) and (-1, 2) respectively.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

Given triangle has coordinates,

A(2, -2), B(5, -3) and C(2, -4).

First the triangle is translated by the rule (x, y) → (x - 1, y + 6)

A(2, -2) becomes A'(2 - 1, -2 + 6) = A'(1, 4).

B(5, -3) becomes B'(5 - 1, -3 + 6) = B'(4, 3)

C(2, -4) becomes C'(2 - 1, -4 + 6) = C'(1, 2)

Then the translated triangle is reflected across the Y axis.

When reflected a point (x, y) across the Y axis, y coordinate remains same and x coordinate flips.

A'(1, 4) becomes A''(-1, 4)

B'(4, 3) becomes B''(-4, 3)

C'(1, 2) becomes C''(-1, 2)

Hence the vertices of the triangle after undergoes translation and reflection becomes A''(-1, 4), B''(-4, 3) and C''(-1, 2).

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The input variable is "Height," while the output variable is "Weight."

A variable that is independent is precisely what it sounds like. It is a stand-alone variable that is unaffected by the other variables you are attempting to assess. Age, for instance, could be an independent variable.

The cause is the independent variable. Its value is unaffected by the other study variables. Effect is the dependent variable. Changes in the independent variable affect its value.

When doing an experiment, the independent variable is what you alter, and the dependent variable is what changes as a result of that change. This is an easy way to conceive of independent and dependent variables. The independent variable can alternatively be viewed as the cause, and the dependent variable as the result.

The input and output variables are "Height" and "Weight," respectively.

Detailed explanation:

"Weight and height are related"

As we all know, the independent variable in a function of the form y=f(x) is x, and the dependent variable is y.

In other words, after substituting the values of "x," we are getting the values of the quantity "y."

As a result, we can infer from the assertion that,

We are getting the values of "Weight" after substituting the values of "Height."

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As per the given statement, the scuba diver's position means the distance he traveled is below 18 feet at the sea level.

Here we have given that a scuba diver starts at sea level and travels to a position that is a little lower than -18 feet.

Now, we need to find the scuba diver's position means the distance he traveled.

While we consider that the scuba driver travelled on -18 feet.

Here the negative term is defined that the the traveler goes on the bottom level.

Therefore, here we said that the person is going to below the sea level.

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So, on solving the provided question, we can say that coefficient of y² in the expression 3y² -  4x is 3

A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include:  The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example  Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.

here,

coefficient of y² in the expression 3y² -  4x is 3

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The number of pair of sunglasses that the company needs to sell in order to make profit is 80,000.

In economics, business, and especially cost accounting, the break-even point is the point at which total cost and total income are equal, i.e. "even". There is no net loss or gain, and one has "broken even," despite the fact that opportunity costs were incurred and capital got the risk-adjusted, expected return.

In order to make profit the organization needs to be at breakeven. Therefore, firstly they need to make profit that is equal to the refurbish cost.

The Profit on per pair of glass =  Selling price per pair - Labor and material cost per pair - marketing cost per pair

The Profit on per pair of glass =  $99 - $30 - $19

The Profit on per pair of glass =  $50

Now, the breakeven point can be found as,

Break even quantity = Refurbish Cost / Profit on a pair of sunglasses

                                  = $4,000,000 / $50

                                  = 80,000

Hence, the company needs to sell  80,000 pair of sunglasses.

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Answer:

Step-by-step explanation:

You want Lisa's and Myra's ages if the sum of their ages is 40 and in 10 years, Lisa will be 3 times as old as Myra.

The current sum of their ages is 40. In 10 years, 10 will be added to each of their ages, so the sum will be 60.

At that time Lisa's age is 3 times Myra's age, so will be 3/(3+1) = 3/4 of the total.

  Lisa's age in 10 years = (3/4)(60) = 45

Lisa is 35 now, and Myra is 5 now.

__

Additional comment

We could write some equations, but we find a mental solution based on ratios to be quick and easy. Here is a solution using equations:

  L + M = 40

  (L +10) = 3(M +10) . . . . . . age relation in 10 years

  (40 -M) +10 = 3M +30 . . . . substitute for L

  20 = 4M . . . . . . . . . add M-30

  M = 5; L = 40-M = 35

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An equation that represents the relationship between n and w is w = 10n + 8.

Mathematically, the slope-intercept form of a line can be represented by using this linear equation:

y = mx + c

Where:

Next, we would determine the slope of the data points in this table (see attachment) as follows;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (78 - 68)/(7 - 6)

Slope, m = 10/1

Slope, m = 10.

At point (6, 68), an equation of this line can be calculated in slope-intercept form as follows:

y - y₁ = m(x - x₁)

y - 68 = 10(x - 6)

y - 68 = 10x - 60

y = 10x - 60 + 68

y = 10x + 8 ≡ w = 10n + 8.

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Answer:

quartic trinomial : 3x4 – 2x3 + x2 + 8, a4 + 1, and m3n + m2n2 + mn.

quintic polynomial:  x5 – x3 + x, y5 + y4 + y3 + y2 + y + 1, and 42a3b2.

Step-by-step explanation:

Quartic Polynomial

A polynomial of degree 4.

Examples: 3x4 – 2x3 + x2 + 8, a4 + 1, and m3n + m2n2 + mn.

a quintic function is defined by a polynomial of degree five.

Because they have an odd degree, normal quintic functions appear similar to normal cubic functions when graphed, except they may possess one additional local maximum and one additional local minimum.

The quartic trinomial having a degree of 4 and the quintic polynomial having a degree of 5.

Quartic Trinomial:

A quartic trinomial is a polynomial expression of degree four that consists of three terms.

The general form of a quartic trinomial is:

[tex]ax^4 + bx^2 + c[/tex]

Example:

Let's consider the quartic trinomial:

[tex]2x^4 - 5x^2 + 3[/tex]

In this example, the term "[tex]2x^4[/tex]" is the highest degree term (degree 4), the term "-[tex]5x^2[/tex]" is the second highest degree term (degree 2), and the constant term "3" has no variable.

So, the quartic trinomial has three terms.

Quintic Polynomial:

A quintic polynomial is a polynomial expression of degree five that may contain multiple terms.

The general form of a quintic polynomial is:

[tex]ax^5 + bx^4 + cx^3 + dx^2 + ex + f[/tex]

Example:

Let's consider the quintic polynomial:

[tex]3x^5 - 2x^4 + 4x^3 + x^2 - 7x + 2[/tex]

In this example, the term "[tex]3x^5[/tex]" is the highest degree term (degree 5), the term "-[tex]2x^4[/tex]" is the second highest degree term (degree 4), and so on. The quintic polynomial has six terms, including the constant term "2".

Hence the quartic trinomial having a degree of 4 and the quintic polynomial having a degree of 5.

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For loop is a type of looping structure that is used in programming to repeat a sequence of codes until a certain condition is met.

In mathematics, a function is a relation between a set of inputs and a set of outputs, such that each input is related to exactly one output. Functions are often represented as mathematical expressions, or as a graph or table. The input to a function is known as the argument, while the output is known as the value. Functions are used to describe physical phenomena, and to model relationships between different variables.

It is commonly used to go through each element in an array or a list without having to write the same code multiple times. For example:

// Initialize array
int arr[] = {1, 2, 3, 4, 5};

// For loop to print out each element in the array
for (int i = 0; i < 5; i++) {
 System.out.println(arr[i]);
}
In this example, the for loop will print out each element of the array until it reaches the condition that i is less than 5, which is the length of the array.

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On solving the provided question, we can say that the provided slope is -2/3 equation of line 2x + 3y -7 = 0

A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

the provided slope is -2/3

let us assume x1 = 2 and y1 = 1

equation of line =>

y-1 = -2/3(x-2)

y-1 = -2x/3 + 4/3

3y-3 = -2x + 4

2x + 3y -7 = 0

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(C) x=-5, y=6 is the solution of the equation 2x+3y=8

To find out which among the following options are solutions of the equation 2x+3y=8, we can substitute the values of x and y in the equation and see if it holds true or not.

a) x=0, y=5 : 2(0) + 3(5) = 0 + 15 = 15 != 8

b) x=3, y=2 : 2(3) + 3(2) = 6 + 6 = 12 != 8

c) x=-5, y=6 : 2(-5) + 3(6) = -10 + 18 = 8 = 8

d) x=-1, y=-2 : 2(-1) + 3(-2) = -2 + -6 = -8 != 8

so the value of left hand side and right hand side of a), b) ,d) is not equals to each other and hence they won't be the equation solution .

So the correct answer is (c) x=-5, y=6

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The following actions must be taken in order to simplify the rational function f (x) = p (x) q (x): Where q (x) = 0, identify the values of x.

The study of mathematics include the study of numbers, formulas and related structures, forms and the environments in which they exist, quantities and their variations, and the environments in which they exist. A function is an association between a number of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs in which each input leads to a single, distinct result.  Usually, the letter f is used to denote functions (x). input consists of x. There are four different types of functions. based on the following elements: one-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

given

The following actions must be taken in order to simplify the rational function f (x) = p (x) q (x): Where q (x) = 0, identify the values of x.

If so, all real values, with the exception of these roots, are in the domain of f (x).

It may be necessary to factor by grouping or by applying the factor theorem in order to fully factor both p (x) and q (x).

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Answer:

There is no such set of two numbers that multiply to get 0 and add to get 7. Since any number multiplied by 0 is 0, it is impossible for two numbers to multiply to 0 and add to 7 as adding two numbers that multiply to 0 will always result in zero.

Answer:

Step-by-step explanation:

the numbers are 0 and 7 itself.

Multiply : 0*7 = 0

Add       : 0+7 = 7