the expression $x^2 3x - 28$ can be written as $(x a)(x - b),$ and the expression $x^2 - 10x - 56$ written as $(x 2b)(x c)$, where $a$, $b$, and $c$ are integers such that $c > 0.$ what is the value of $2c - a$?

The expression of the given conditions is 8x - 12.

A sentence that contains a minimum of two numbers or variables and at least one operation is called an expression. These operations can be subtraction, addition, multiplication, or division. The structure of an expression is:

Expression is (Number/variable, Math Operator, Number/variable)

On the other hand, An algebraic expression consists of unknown variables, numbers and arithmetic operators. The algebraic expression does not contain any equality or inequality symbols.

Let's call the number you are thinking of as "x".

Multiplying it by 2:

2x

Subtracting 3:

2x - 3

Multiplying the result by 4:

4(2x - 3) = 8x - 12

So the final expression is:

8x - 12

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The equivalent expression of the perimeter of the regular hexagon is,

⇒ 42x + 24

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

A regular hexagon has six congruent sides.

And, The length of each side is represented by the expression (7x + 4).

Now, We know that;

The sum of all sides of a regular hexagon is called its perimeter.

Hence, We get;

Here, The length of each side is represented by the expression 7x + 4.

So, We get;

The perimeter of Hexagon = 6 × (7x + 4)

                                          = 42x + 24

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Solving the provided question we can say that as exponents because one bacteria can expand to two bacteria, which can then multiply to four bacteria, which can then multiply to eight bacteria. hence, answer  A.

what are exponents?

Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where

because one bacteria can expand to two bacteria, which can then multiply to four bacteria, which can then multiply to eight bacteria. hence,

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Question 9

[tex]\frac{\sin x}{23}=\frac{\sin 27^{\circ}}{11}\\\\\sin x=\frac{23\sin 27^{\circ}}{11}\\\\x \approx 71.7^{\circ}, 108.3^{\circ}[/tex]

Both of these cases satisfy the angle sum of a triangle.

Question 11

[tex]\frac{\sin x}{27}=\frac{\sin 74^{\circ}}{26}\\\\\sin x=\frac{27 \sin 74^{\circ}}{26}\\\\x \approx 86.6^{\circ}, 93.4^{\circ}[/tex]

Both of these cases satisfy the angle sum of a triangle.

Steve has three quarters, three nickels and three pennies. if Steve selects three coins at random and without replacement, then the probability  that the total value is exactly 35 cents is 0.107.

Probability:

Probability is the branch of mathematics that deals with numerical descriptions of the likelihood of an event occurring or the likelihood of a statement being true. Probability is a number between 0 and 1, with 0 generally indicating impossibility and 1 indicating certainty that an event will occur. A simple example is tossing a fair (unbiased) coin. Since the coin is fair, the two outcomes (heads and tails) are equally likely. The probability of heads is the same as the probability of tails. Since no other outcome is possible, the probability of heads or tails is 1/2.

Probability without Replacement:

Probability without replacement means that once you draw an item, you don't put it back into sample space before drawing a second item. In other words, an item cannot be drawn more than once. For example, if he takes one candy out of a box containing nine candies and does not replace the first one, he takes the second one. Of course, the rehearsal room for the second event no longer stays at 9 because we didn't replace the first candy. So the second event has a sample space of 8. That is, the sample space of the second event has changed.

According to the Question:

The only way you can get 35 cents is with 1 quarter and 2 nickels    

There are 3 ways to pick up a quarter  ³C₁

and there are 3 ways you can pick up 2 nickels : ³C₁

Thus,

There are  3× 3 = 9 ways to choose 1 quarters and 2 nickels.

That is 9 favorable outcome.

Now,

there are ⁹C₃ = 84 ways to choose 3 coins from 9  

Therefore,

the probability of picking up 35c is    

9/84

= 3/28

= 0.107  

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When we alter an expressions form but not its value, then these expression are called Equivalent expression.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

We alter an expressions form but not its value.

Now, Let an expression is,

⇒ (x + 2)²

And, We can change its form as;

⇒ x² + 4x + 4

Clearly, Both expression are equal but its form are change.

Hence, These expressions are equivalent.

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Analyzing the figure given in the question,

a.

  1. The corresponding sides are ,

  2. The scale factor ratio is , 2.5.

b. The height of the backhoe is 180''.

Corresponding sides of a triangle are the sides of a triangle that are in the same position relative to the vertices of the triangle. In other words, they are the sides of the triangle that are opposite to the same angles.

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

From the given figure,

length of base of the small triangle, let a = 52 inches

length of base of the bigger traingle, let b = 130 inches

height of the person , let c = 6ft = 6*12 inches = 72 inches

height of the backhoe, let d = ?

a.

Since the smaller and bigger traingles are similar triangles we can equate the proportion of corresponding sides ,

b/a = d/c = 130/52=2.5 -------- equation 1

Therefore the required scale factor is 2.5

b.

Using the 2nd ratio in equation 1,

d/c = 2.5

or, d/72 = 2.5

therefore, d = 180 inches

therefore the required height of the backhoe is 180 inches.

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0.6928 or 69.28% is the probability of at least one ace among five cards .

in order to get the probability that at least one of the five cards is an ace, then we implement the use of  complement rule.

as we know this rule states that the probability of an event happening  which is equal to 1 minus the probability of the event  which is not happening.

In this order of situation the event is drawing no aces from the five cards. hence the  probability of drawing no aces is (48/52)^5, as we are having   48 non-ace cards in the deck and the value of the  probability of drawing a non-ace is 48/52.

the calculation to get the probability of drawing at least one ace is:

1 - (48/52)^5 = 1 - (0.9231)^5 = 0.6928

hence  the probability value  of at least one ace among five cards is 0.6928 or 69.28%.  

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The equation for situation 1 is y = 3.5x

The equation for situation 2 is y = 3x

The equation for situation 3 is y = (5/2)x

The equation for situation 4 is  (1/2)x = y

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship. It is also known as unit rate and it is usually expressed by k. That is k = y/x

Situation1

A dump truck is hauling loads of dirt to a construction site. After 20 loads, there are 70 square feet of dirt.

k = y/x = 70/20 = 3.5

For every 70 square feet of dirt, there are 2 loads.

y = kx

y = 3.5x

Situation 2

I am making a water and salt mixture that has 2 cups of salt for every 6 cups.

k = 6/2 = 3

This means in every 3 cups there is 1 cup of salt

y = 3x

Situation 3

A store has a "4 for $10" sale on hats.

k = 10/4 = 5/2

This means $5 for 2 hats.

y = (5/2)x

Situation 4

For every 48 cookies I bake, my students get 24.

k = 24/48 = 1/2

This means 1 student gets 2 cookies

y = (1/2)x or (1/2)x = y

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Answer:

45 minutes

Step-by-step explanation:

I attached a pic of my work.

Integral = [tex]\int\limits \,[/tex] (V6+V5)/4 dv=(2to1) = 7.16

When infinitely small amounts of data are combined, notions like volume, area, and displacement are represented numerically by integrals. Locating integrals is the process of integration.

Definitive integrals can be represented by the signed area of the region in the plane that is bounded by the graph of a particular function between two points on the real line. Typically, areas above the horizontal axis of the plane are positive while areas below it are negative.

Determine the corresponding indefinite integral first.

[tex]\int\limits \,[/tex] v6(6v+7)/168 = (v6+v5)/4 dv

F(x)dx=f(b)f(a) according to the Fundamental Theorem of Calculus, so only assess the integral at the endpoints.

[tex]\int\limits \,[/tex] (v^6(6v+7)/168)at (v=2)=152/21.

[tex]\int\limits \,[/tex] (v^6(6v+7)/168)at (v=1)=13/168

[tex]\int\limits \,[/tex] (v6(6v+7)/168)at (v=2) - (v6(6v+7)/168)at (v=1) = 401/56 = 7.16

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If the mean of a population is 250 and the standard deviation is 20, we can say that approximately 68% of observations fall between 230 and 270, 95% of observations fall between 210 and 290, and 99.7% of observations fall between 190 and 310.

It's important to note that these percentages are approximate and based on the assumption that the population follows a normal distribution.

The normal distribution is a continuous probability distribution that is symmetric about the mean. The standard deviation (σ) is a measure of the spread of the data. Approximately 68% of the observations fall within one standard deviation of the mean, 95% of observations fall within two standard deviations of the mean, and 99.7% of observations fall within three standard deviations of the mean.

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The range of time values describes the entire interval over which Georgiana would be interpolating is 0 to 30 minutes.

Now, According to the question:

We know that:

Linear model regression is used to predict the relationship between 2 variables by fitting the observed data in a linear equation.

What is the domain and range of a function?

The domain of a function is the set of x values for which it is defined, whereas the range is the set of y values for which it is defined.

As in the table, the minimum time for which the distance is defined is 0 minutes while the maximum time is 30 minutes. Therefore, the range of time values describes the entire interval over which Georgiana would be interpolating is 0 to 30 minutes.

                                     Distance over time

          Time(min)                                              Distance (miles)

              0                                                                   0

              5                                                                   4

             10                                                                   9

             15                                                                   13

            30                                                                   18

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On solving the provided question, we can say that  the slope of the line measured is 33m/s

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).

rise of line = 600m

run of line = 3mins

Slope = rise/run

Slope = 600/180

Slope = 3.33 m/sec

, the slope of the line measured is 3.33

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The probability that a randomly selected family owns a dog or a cat is 0.61 and family owns a dog or doesn't own a cat is 0.39

AS we all know the rule of the probability is defined as the amalgamation of set theory and the probability theory yields some rules which form a part of the basic probability theory

Here we have listed down the rules as Multiplication Rule, Addition Rule and Complement Rule

Here we have given Information the following that is written as

=> Probability that a family can own a dog = 0.38.

=> Probability that a family can own a cat = 0.23.

Then the probability that a randomly selected family owns a dog or a cat is calculated as follows,

=> (0.38 + 0.23)

=> 0.61

And the the probability that a randomly selected family owns a dog or doesn't own a cat.

=> 1 - (0.38 + 0.23)

=> 1 - 0.61

=> 0.39

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Answer:

544

Step-by-step explanation:

34 * 2 = 68

68 *2 = 136

136 * 2 = 272

272 * 2 = 544 (month 12 = 1 year)

Both f(x) and g(x) have the same y-intercept of (0,0). So the answer is c) f(x) and g(x) have the same y-intercept.

What is the y-intercept?

The point where a graph completely lies on the y-axis is known as the y-intercept. Any point which lies only on the y-axis has an x-coordinate equal to 0, as is known y-intercept.

The y-intercept of a function is the point at which the graph of the function crosses the y-axis. To find the y-intercept of a function, we can set x = 0 and find the corresponding value of y.

For function f(x) = 5x^2, when x = 0, y = 5(0)^2 = 0.

For function g(x) = 3(2)x, when x = 0, y = 3(2)(0) = 0.

Therefore, both f(x) and g(x) have the same y-intercept of (0,0). So the answer is c) f(x) and g(x) have the same y-intercept.

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The probability of drawing three green marble, with replacing them, is 61/100.

Given,

A bag contains four red marbles, six green marbles, eight yellow marbles, and two blue marbles.

We need to find the probability of drawing three green marble and replacing them.

A combination is used to select required items from a set where the order of selection does not matter.

It is given by:

n^Cr = n! / r! (n-r)!

Where n = the number of elements present in a set.

Find the number of each marble.

Red marbles - 4

Green marbles - 6

Yellow marbles - 8

Blue marbles - 2

Find the probability of drawing a green marble

P (G) = ^6C_1 / ^20C_1

         = (6!/1!)/(20!/19! 1!)

        = 720 / 20

P(G)= 36

Find the probability of drawing a yellow marble

P ( Y ) = ^8C_1 / ^20C_1

         = (8! /1! 7!) / (20! / 191 1!)

         = 8 / 20

        P ( Y ) = 2 / 5

Find the probability of drawing a blue marble

P ( B ) = ^2C_1 / ^20C_1

         = (2! / 1!) / (20! / 19! 1!)

         = 2 / 20

  P ( B )= 1/10

Find the probability of drawing a blue marble

P ( R ) = ^4C_1 / ^20C_1

         = (4! / 1!) / (20! / 19! 1!)

         = 24 / 20

P ( R ) =6/5

Find the probability of drawing a green marble, replacing it, then drawing a yellow marble

Both the probability is independent so,

P = P ( G ) X P ( Y )+P ( G ) X P ( R )+P ( G ) X P ( B )

 = 36 X 2 / 5+36 X 6/5+36 X1/10

P= 61/100

Thus the probability of drawing three green marble, and replacing them, is 61/100.

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The total gross earnings are given as follows:

$360.

The total gross earnings are obtained applying the proportions in the context of this problem, first obtaining the total number of hours and then multiplying by the rate.

The hours are given as follows:

After November 14, the hours are given as follows:

Hence the total number of hours is obtained as follows:

3.5 + 2 + 3.5 + 4 + 5 + 5.5 + 4.5 + 4 = 32 hours.

The rate is of $11.25 per hour, hence the total earnings are given as follows:

11.25 x 32 = $360.

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We need to set the function equal to zero.

x² - 3x - 10 = 0

x = 5

x = -2

The answer is -2, 5

The answer consists of 10 examples of mathematical solutions: the Pythagorean Theorem, the Quadratic Formula, the Binomial Theorem, the Divergence Theorem, the Fundamental Theorem of Calculus, the Law of Cosines, the Law of Sines, the Triangle Inequality, the Extreme Value Theorem, and the Mean Value Theorem.

1. The Pythagorean Theorem states that for a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side.

2. The Quadratic Formula is used to calculate the roots of a quadratic equation.

3. The Binomial Theorem allows one to expand a binomial expression to any power.

4. The Divergence Theorem explains the relationship between a vector field and its associated flux.

5. The Fundamental Theorem of Calculus states the relationship between the derivative and integral of a function.

6. The Law of Cosines is used to calculate the length of a side of a triangle given the lengths of the other two sides and the angle between them.

7. The Law of Sines is used to calculate the length of a side of a triangle given the lengths of the other two sides and the angle between them.

8. The Triangle Inequality states that the sum of any two sides of a triangle must be greater than the third side.

9. The Extreme Value Theorem states that a continuous function on a closed interval has both a minimum and a maximum value.

10. The Mean Value Theorem states that for a given continuous function on a closed interval, there exists at least one point where the function's derivative equals the average rate of change over the interval.

The answer consists of 10 examples of mathematical solutions: the Pythagorean Theorem, the Quadratic Formula, the Binomial Theorem, the Divergence Theorem, the Fundamental Theorem of Calculus, the Law of Cosines, the Law of Sines, the Triangle Inequality, the Extreme Value Theorem, and the Mean Value Theorem. Each of these solutions explains a different mathematical concept or relationship.

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The highlights listed above indicate that: 35 - 5D reflects the quantity of postcards sold.

The highlights listed above indicate that: 35 - 5D reflects the quantity of postcards sold.

The examples include:

D indicates the cost of each postcard.

35 - 5D is the number of postcards that were sold.

D(35 - 5D) denotes the revenue resulting from the sales.

Describe phrases.

Mathematical assertions called expressions include all of the followings.

Mathematical operator variables for numbers

The phrase is given as follows:

The query leads us to believe that:

D indicates the cost of each postcard

D(35 - 5D) denotes the revenue resulting from the sales.

The highlights listed above indicate that: 35 - 5D reflects the quantity of postcards sold.

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According to the unitary method the smallest check they can receive so that both their earnings match is at the time of 2 or 3 hour.

Unitary method in math is known as in which the value of one article is first obtained to find out the value of any required articles

Here we have given that Jake makes $10 dollars an hour and Judy makes $15 dollars an hour.

Let us consider that x be the amount hour did they get the same amount.

Then it can be calculated as,

=> 15x = 10x

While we substitute the value on the x by finding the LCM for each of the  number than we get,

=> 15, 10 = 2,3

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An absolute value graph has one axis of symmetry that passes through the vertex.

From the preceding graph, it can be seen that when the coefficient of x increases, the v form moves closer to the line of symmetry and vice versa.

However, it is not always the case that the symmetry line and the y-axis coincide.

For instance:

A line of symmetry for the equation -y=|3x-6|-5 runs parallel to the y-axis and through the x-axis.

You must be aware of the location of the graph's vertex and the line of symmetry.

To obtain the value of x, which will be the x coordinate for the vertex of the graph, take the equation inside the absolute value and equal it with 0. Then, replace the value of x with the main equation to obtain the y coordinate for the vertex of the graph.

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In Korea, tofu is typically offered during breakfast.

Describe breakfast.

The first meal of the day, known as breakfast, is often had in the morning. After an overnight fast, it is a crucial meal that gives the body and brain fuel. Protein and carbs are generally found in breakfast foods such eggs, bacon, oatmeal, toast, pancakes, yoghurt, cereal, and fruits. A nutritious breakfast may boost energy levels, jump-start the metabolism, and enhance focus and memory. A nutritious breakfast can also aid in lowering mid-day snacking and preventing overeating in the evening. Make sure to incorporate breakfast in your daily schedule since eating breakfast is crucial to living a healthy lifestyle.

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The quadrilateral given is Parallelogram.

Quadrilaterals are four sided polygons which also have four vertices and four angles.

Sum of all the interior angles of a quadrilateral is 360 degrees.

(a) The quadrilateral is sketched as shown in the graph below.

(b) We have to write the equation of four lines AB, BC, CD and AD in the form y = mx + b. m is slope and b is intercept along Y axis.

Coordinates of vertices are A(-5, 2), B(-2, 6), C(3, 5) and D(0,1).

Equation of line AB :

Slope = (6 - 2) / (-2 - -5) = 4/3

Equation in point slope form is

(y - 2) = 4/3(x - -5)

y - 2 = 4/3 x + 20/3

y = 4/3 x + 26/3

Equation of line BC :

Slope = (5 - 6) / (3 - -2) = -1/5

Equation in point slope form is,

(y - 6) = -1/5 (x - -2)

y - 6 = -1/5 x - 2/5

y = -1/5 x + 28/5

Equation of line CD :

Slope = (1 - 5) / (0 - 3) = -4/-3 = 4/3

Equation in point slope form is,

y - 5 = 4/3 (x - 3)

y - 5 = 4/3 x - 4

y = 4/3x + 1

Equation of line AD :

Slope = (1 - 2) / (0 - -5) = -1/5

Equation in point slope form is,

y - 1 = -1/5 (x - 0)

y - 1 = -1/5 x

y = -1/5 x + 1

(c) Opposite sides are having the same slope.

From the sketch, opposite sides are equal.

So quadrilateral is either parallelogram or rectangle.

But if the figure is rectangle, adjacent sides are perpendicular and therefore the product of their slope is -1.

But it is not the case here.

So it is parallelogram.

Hence the given figure is a parallelogram.

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Vector w can be expressed as w=1u-2v as linear combination of vector u and v.

Vector equation would be w=Au + Bv

[1,1]=A[5,7] + B[2,3]

Here A and B are constants and we are trying to find their values.

We can split two equations as

1=5A+2B → equation a

1=7A+3B → equation b

Solving these equations by elimination method . Multiplying equation a with 3 and equation b with 2.

3=15A+6B

2=14A+6B

1=A → A=1

Putting value of A in equation b:

1=7+3B

1-7=3B

-6=3B

B=-6/3=-2

A = 1 and B = -2 . It means we can write w as 1u - 2v. We can recheck by plugging the values in any of the vector to confirm if the values are correct or not.

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Answer:

a) Let x be the number of bags of snacks supplied, and y be the number of beverages supplied.

b) We know that the total number of items supplied is the sum of the number of bags of snacks and the number of beverages, so we can write:

x + y = 400

We also know that the number of beverages supplied is 50 more than the number of bags of snacks, so we can write:

y = x + 50

Therefore, the system of equations for the situation is:

x + y = 400

y = x + 50

The difference in the account balance after 30 years is $345.31.

What is compounded continuously?

Theoretically, continuously compounded interest means that an account balance continuously earns interest as well as reinvesting that interest into the balance so that it too earns interest.

Given:

A business owner invested $7,000 in a treasury bond paying 4.3% compounded semiannually.

After 30 years, the value of the bond will be $25,084.20.

The business owner's investment was compounded continuously instead of twice per year.

We have to find the difference in the account balance after 30 years?

Consider, the compounded continuously formula,

[tex]A = Pe^r^t[/tex]

Plug p = 7000

r = 4.3% = 0.043

t = 30

⇒ [tex]A = 7000e^(^0^.^0^4^3^*^3^0^) = 25429.51[/tex]

A = $25429.51

So, the difference is, $25429.51 - $25084.20 = $345.31

Hence, the difference in the account balance after 30 years is $345.31.

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