Which function is shown on the graph?
of(x) = 1/2cos x
of(x) = -1/2cos x
Of(x) = -1/2sin x
Of(x) = 1/2sin x

The value of  expression - a² - 2bc - |c| if a = -2, b = 3, and c = -3, is 11.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given:

- a² - 2bc - |c|, a = -2, b = 3, and c = -3,

Plug the values of a, b, and c as shown below,

- a² - 2bc - |c|  = -(-2)² - 2 × (3) × (-3) - |-3|

- a² - 2bc - |c|  = - 4 - 6 × (-3) - 3

- a² - 2bc - |c|  = -4 + 18 - 3

- a² - 2bc - |c|  = 18 - 7

- a² - 2bc - |c|  = 11

Thus, the value of the expression is 11.

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The percentage of cars traveling east is 28% of the total number of cars.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, The commission counted 486 cars traveling east and 189 cars traveling west.

We know percentage change we'll divide the net amount change by the original amount and multiply it by 100%.

From this concept, the percentage of the cars were traveling east would be

The cars traveling east divided by the total numbers of cars time s100%.

= (189/486 + 189)×100%.

= (189/675)×100%.

= 0.28×100%.

= 28%.

So, 28% of the total cars traveling east.

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The number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.

An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.).

Given that n and (2n + 9) are the seeds that Frank will plant in various gardens, the total number of seeds that Frank will plant can be represented algebraically by combining the two formulas.

Like terms with the same variables are added together.

Let the equation be n + 2n + 9

simplifying the above equation, we get

3n + 9

Therefore, the number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.

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The number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.

An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.).

Given that n and (2n + 9) are the seeds that Frank will plant in various gardens, the total number of seeds that Frank will plant can be represented algebraically by combining the two formulas.

Like terms with the same variables are added together.

Let the equation be n + 2n + 9

simplifying the above equation, we get

3n + 9

Therefore, the number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.

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The algebraic expression to show Jill's age will be;

Jill = 1/3 x b

Algebraic expressions are the mathematical statements that are derived when operations such as addition, subtraction, multiplication, division, etc. are operated upon on variables and constants.

There are different parts of an algebraic expression and they are; Variables - a symbol that doesn't have a fixed value is called a variable. It can take any value assigned to it.

Constants - a symbol that has a fixed numerical value is called a constant. All numbers are constants.

Terms - A term is a variable alone (or) a constant alone (or) it can be a combination of variables and constants and the operation of multiplication or division with it.

Coefficients - the numbers that are multiplying the variables are called coefficients.

Beth's age = b

Jill's age = 1/3 of Beth's age

Jill's age = 1/3 x b

Jill's age = 1/3b

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Answer:

Yes, a(b)+a(c) is the same as a(b+c)

Step-by-step explanation:

a(b)+a(c) is the same as a(b+c). We call it distributive property in math.

Distance between first base to home plate and from home plate to third plate are equal.

Given : It is the same distance from second base to first base, and from second base to third base. The angle formed by first base, second base, and home plate has the same measure as the angle formed by the third base to home plate ,and from home plate to third base.

The given situation and distance between first base to home plate and from home plate to third plate are equal.

On Converting the given situation into a geometry problem. So we name the require points.

Let A be the home plate,

B is first base,

C is the second base,

And D is the third base.

Now, we can present a geometrical proof:

Statement and their reasons

(1) BC = CD - ( Given )

(2) AC = AC - ( Reflexive Property )

(3) Δ ACD = Δ ACB -  ( SAS Congruence - side angle side)

(4) AD = AB - ( CPCTC - Congruent Parts of Congruent Triangles are Congruent )

Therefore, the gap from 1st base to home plate, and from home plate to 3rd plate are equal.

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The factored quadratic functions with their equivalent standard form are given as follows:

1. e -> x² - 3x - 10 = (x - 5)(x + 2)

2. a -> x² + 7x - 10 = (x + 5)(x + 2).

3. c -> x² - 7x + 10 = (x - 5)(x - 2).

4. d -> x² - 2x - 63 = (x - 9)(x + 7)

5. f -> x² + 2x - 63 = (x + 9)(x - 7).

6. b -> x² + 16x + 63 = (x + 7)(x + 9).

A quadratic function is defined as follows:

y = ax² + bx + c.

A quadratic function can be factored as a function of it's roots x* and x**, as follows:

y = a(x - x*)(x - x**).

For item a, the function is given as follows:

y = x² + 7x + 10.

The coefficients are given as follows:

a = 1, b = 7, c = +10.

The discriminant is of:

D = 7² - 4(1)(10)

D = 49 - 40

D = 9.

Hence the first root is of:

x = (-7 - square root of 9)/2

x = -5.

The second root is of:

x = (-7 + square root of 9)/2

x = -2.

Meaning that the factored expression is given as follows:

y = (x + 5)(x - 2).

Matched with the second expression of column A.

The same procedure is followed for the remaining quadratic functions.

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Answer:

[B] 6²

Step-by-step explanation:

Given:

[tex]\frac{6^4\cdot \:6^3}{6^5}[/tex]

Solve:

Add the exponents - [tex]6^4 \times 6^3=6^7[/tex]

Now we have - [tex]\frac{6^7}{6^5}[/tex]

Exponent Rule: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

Which means - [tex]\frac{6^7}{6^5}=6^{7-5}[/tex]

Subtract the exponent - [tex]6^2[/tex]

Hence, the answer is [B] 6²

RevyBreeze

The cumulative total in Vietnam j(n) is 23(n-1),cumulative takes into account all data up to the present. In month four, j(n) will be worth more than v(n).

The distinction between total and cumulative is that total refers to the entirety of something, whereas cumulative takes into account all data up to the present.

When a new number is added to a series of numbers, the running total is updated by adding the new number's value to the previous running total. Partially sum is another name for it. Running totals serve two distinct objectives.

We take it for granted that you mean that vehicles delivered to Vietnam should be modeled by v(n) = 5 + 11 and those sent to Japan by j(n) = 23(n-1).

In month four, j(n) will be worth more than v(n).      

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Statement 1 is correct and Statement 2 is not correct.

As A, B and C represent distinct non-zero digits

For least value of x

Let A=1, B=2, C=3

The possible numbers that can be formed using 1,2,3 are 6 {using permutations}

123, 132, 213, 312, 231, 321

x is the sum of all possible 3-digit numbers formed by A, B and C without repetition so

x= 123+ 132+ 213+ 312+ 231+ 321

x=1332

So statement 1 is correct

statement 2 cannot be correct as least value of x is  4-digit so  greatest value of x cannot be a three digit number.

The 4-digit least value of x is 1332 so Statement 1 is correct and Statement cannot be correct.

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Answer:

81

Step-by-step explanation:

by corresponding angles from angle ABC

The smallest positive integer that is both multiple of 4 and 7 is 2

In mathematics, multiples are the results of multiplying an integer by a given number.

The given numbers for this problem are 4 and 7. The positive multiples of 4 and 7 will be listed and the first number that appeared in the both multiples s the smallest positive integer that is both a multiple of 7 and a multiple of 4.

The multiples of 4

4 8 12 16 20 24 28 32 36 .......

The multiples of 7:

7 14 21 28 35 42 49 56 63 70 77 84 91 98 .....

The smallest common multiple is 28

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AAA triangles are impossible to solve further since there is nothing to show us the size.

The AAA triangle is a triangle in which all three angles are given, and the triangle is said to be similar to another triangle if any two of its three angles are equal to any two of its three angles.

Knowing only angle-angle-angle (AAA) is insufficient because it can result in triangles that are similar but not congruent.

There are four shortcuts that can be used to check whether two triangles are congruent.

You don't need to be familiar with all of the six corresponding parts, which include three angles and three sides.

When a triangle's three angles are known but not its sides, the answer is "AAA."

Since there is no information to indicate size, AAA triangles are impossible to solve further. We know their shape but not their size.

Hence, the AAA triangles are not solvable or difficult to find angles.

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$855.78

Interest, in this context, is the amount of money a saving account can earn over time.

Compound Interest Formula

There are 2 types of interest: simple and compound. For this question, we are going to use the compound interest formula. This formula is [tex]A = P(1+\frac{r}{n})^{nt}[/tex]. As stated in the question, A is the total balance, P is the principal, r is the interest rate, n is how often the interest is compounded, and t is time.

Variables

The values of these variables for this question are as follows:

The principal is the initial amount, and the question states that the account starts at 300 dollars.

The question says the interest rate is 14%, so we can convert this to the decimal 0.14.

If something is compounded annually, it is compounded once a year, so n must be 1.

If we want to find the balance after 8 years, we should set t equal to 8.

Solving for A

To find A, all we have to do is plug the variables into the formula.

This can be rewritten as:

Solve this to find that A ≈ 855.78. After 8 years, the balance will be $855.78.

The explicit formula of the sequence is aₙ = -10 + 8n

From the question, we have the following sequence that can be used in our computation:

The first term and the common difference

These values of the first term and the common difference are given as

First term = -2

Common difference = 8

The interpretation of the above sequence is that the 8 is added to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

aₙ = aₙ₋₁ + 8

When represented explicitly, we have

aₙ = a + (n - 1) * d

Where

a = -2 and d = 8

Substitute the known values in the above equation, so, we have the following representation

aₙ = -2 + (n - 1) * 8

Evaluate the products

aₙ = -2 + 8n - 8

Evaluate the like terms

aₙ = -10 + 8n

Hence, the explicit formula is aₙ = -10 + 8n

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The binomial equation can be squared to provide an expression that is a perfect square trinomial.

Perfect squares result from squaring an integer. One such example is the number 81, which is a perfect square since it can be derived by squaring 9: 99=81. 144 is a perfect square since it can be generated by squaring the number 12, which results in 12. 169 is a perfect square since it can be squared to produce the number 13. mathematics-specific language Informally: When an integer (a "whole") number, whether positive, negative, or zero, is multiplied by itself, the result is referred to as a square number, a perfect square, or simply "a square". Accordingly, all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.

given

The binomial equation can be squared to provide an expression that is a perfect square trinomial.

If and only if a trinomial that takes the form ax 2 + bx + c satisfies the requirement b 2 = 4ac is considered to be a perfect square.

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To read a linear equation, first, identify the constants and the variable, then determine the coefficient of the variable.

A linear equation is an equation that contains two variables and can be written in the form of ax + b = 0, where 'a' and 'b' are constants and 'x' is the variable.  This coefficient will indicate how the variable is related to the constants. Then, solve the equation by isolating the variable to determine its value.

To read a linear equation, start by identifying the constants and the variable. The constant is the numerical value that is not connected to the variable. For example, in the equation "2x + 4 = 0", the constants are '2' and '4'. The variable is the letter that represents the values that can change. In this equation, the variable is 'x'.

Next, determine the coefficient of the variable. The coefficient is the numerical value in front of the variable. It represents how the variable is related to the constants. In this example, the coefficient of 'x' is '2'. This means that the value of 'x' will be twice as much as the constants.

Once the constants, variables, and coefficients have been identified, the equation can be solved.

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Plotting a graph step by step is mentioned below.

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.

Using rectangular bars with heights or lengths proportionate to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

There are a few steps to follow when plotting a graph:

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Answer: c = P - a - 5

Step-by-step explanation:

P= a + 5 + c

P - a - 5= c

The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.

To explain this using a formula, we can use the dilation formula. This formula states that for any point (x,y) on the original line (f), when dilated with a scale factor of k and the center of dilation is the origin (0,0), the coordinates of the point on the new line (f') would be (kx, ky).

For point A, which has coordinates (2,0) on line f, when dilated with a scale factor of 3 and the center of dilation being the origin, the coordinates of point A' on line f' would be (3 * 2, 3 * 0) = (6, 0).

Similarly, for point B, which has coordinates (0,2) on line f, when dilated with a scale factor of 3 and the center of dilation being the origin, the coordinates of point B' on line f' would be (3 * 0, 3 * 2) = (0, 6).

Since the two lines have the same slope, line f and line f' are parallel.

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Step-by-step explanation:

y varies inversely as x=

y= k/xz

-5= k(-5)/6

k= 6

y=6/xz

y=6/5×-8

y= -3/20

6b - 0.78b it will result after expanding the expression.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Any one of the following mathematical operations can be used i.e. addition, subtraction, multiplication, or division.

There are three different expression types:

Let, b represent the original price of a loaf of bread.

Given that,

A grocery store has 13%-off sale on all bread.

This means that the amount by which the price of bread was reduced would be

13/100 × b = 0.13 × b = 0.13b

The new price for the loaf of bread would be: b - 0.13b

you decide to purchase 6 loaves of bread. The expression would be:

6(b - 0.13b)

Expanding the expression, it becomes: 6b - 0.78b

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A line segment is merely a portion of a line, one with definite ends and a finite length.

A line segment is merely a portion of a line, one with definite ends and a finite length. An object with only one dimension, a line has length but no width. A line is made up of several points that are endlessly stretched in the opposing directions. In a two-dimensional plane, it is specified by two points. Collinear points are described as two points that are on the same line.

An endlessly long, two-directional line is referred to as a line. It just has one, and that is length. Collinear points are those that are situated along the same path. Two points make up a line, which is written as follows with an arrowhead: AB.

O is between M and P, and N is the midpoint of MO. IF NO=3 and MP = 10, find OP.

Given the following details as:

N is between M and O.

O is between N and P .

NO=6 and NP = 8.

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3 quarts is equal to approximately 285 centilitres.

To Calculate this we have:

3 quarts is equal to 3 x 0.95 liters = 2.85 liters.

1 litre is equal to 100 centilitres, so 2.85 litres is equal to 2.85 x 100 = 285 centilitres.

Therefore, 3 quarts is equal to approximately 285 centilitres.

In detail, a quart is a unit of measurement in the Customary System Units and is defined as a quarter of a gallon. 1 quart is equal to 0.95 litres. To find out how many centilitres are in 3 quarts, we need to multiply the number of quarts (3) by the conversion factor (0.95 litres per quart). This gives us 2.85 litres. Since 1 litre is equal to 100 centilitres, we can multiply 2.85 litres by 100 to get 285 centilitres. Therefore, 3 quarts is equal to approximately 285 centilitres.

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The use of if__name__ == '__main__' in python is to check whether the current script is being run on its own or being imported somewhere else by combining it with if statement.

Here we need to find the use of if __ name __ == '__ main __' in Python.

Basically, in python the term Allows You to Execute Code When the File Runs as a Script, but Not When It’s Imported as a Module

Here for most practical purposes, this is known as the conditional block that you open with if __name__ == "__main__" as a way to store code that should only run when your file is executed as a script.

Therefore, the function is used as  a variable defined for each script that defines whether the script is being run as the main module or it is being run as an imported module.

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[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 6}(x-\stackrel{x_1}{3}) \implies y +4= -6 (x -3) \\\\\\ y+4=-6x+18\implies {\Large \begin{array}{llll} y=-6x+14 \end{array}}[/tex]

Null hypothesis (H0): The proportion of newsletter readers who own a Rolls Royce is greater than or equal to 0.68.

Alternative hypothesis (H1): The proportion of newsletter readers who own a Rolls Royce is less than 0.68.

In statistics, hypothesis testing is the process by which an analyst tests an assumption about a population's parameter. Using sample data, hypothesis testing is performed to examine the plausibility of a theory.

In this scenario, we can set up the null and alternative hypotheses as follows:

Null hypothesis (H0): The proportion of newsletter readers who own a Rolls Royce is greater than or equal to 0.68.

Alternative hypothesis (H1): The proportion of newsletter readers who own a Rolls Royce is less than 0.68.

In order to determine if there is sufficient evidence to support the publisher's claim, we would need to conduct a statistical test to determine if the proportion of newsletter readers who own a Rolls-Royce is significantly less than 0.68. The significance level of 0.02 is used to determine the level of evidence required to reject the null hypothesis.

If we run a test, if the p-value is below 0.02, we can reject the Null hypothesis and conclude that the evidence is sufficient to show that the proportion of newsletter readers who own a Rolls Royce is less than 0.68, and thus the publisher's claim is substantiated.

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Answer:

y=2x-7

Step-by-step explanation:

y=mx+b  ==> m is the slope and b is the y-intercept

y=(2)x + (-7)  ==> plugin 2 for m=slope and -7 for b = y-intercept

y=2x-7 ==> simplify

Given that ON = [tex]x^{2}[/tex] - 10; LM = -2x + 5; NM = 3x + 21; and OL = 4y + 18; with x and y values of [tex]\sqrt{10}[/tex] and -4.5, respectively.

ON = [tex]x^{2}[/tex] - 10 ⇒  [tex]x^2[/tex] = 10 ⇒ x =[tex]\sqrt{10}[/tex]

OL = 4y + 18 ⇒ 4y =-18 ⇒ y = -18/4 ⇒ -4.5 .

The issue at hand is here A parallelogram of O N M L is nm. Suppose   ON = [tex]x^{2}[/tex] - 10 or LM = -2x + 5. Here, we must determine what X's value is. then look up N M N O L. Due to the parallelogram shape of ONA male, there are four.

Since N M is equal to the opposing sides of a parallelogram and an e parallelogram, we can express that as follows. due to the parallelogram's equal opposite sides. We can therefore write [tex]x^{2}[/tex] - 10 where N M = O L. that is four, -2x + 5, and. Change the two sides of the equation, then write four. Nine times X is equivalent to [tex]x^{2}[/tex] - 10.

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