x2+6x-40 factored form

The order of the graphs from the narrowest to the widest would be:

f(x) = ax², where |a| < |b| < |c|

f(x) = ax² + bx, where |a| < |b|

f(x) = ax² + bx + c, where |a| < |b| < |c|

Quadratic functions are mathematical functions that have a specific shape when plotted on a coordinate plane. The shape of a quadratic function is called a parabola and it opens either upwards or downwards.

When we compare the width of different parabolas, we can arrange them from the narrowest graph to the widest graph. The order is determined by the value of the coefficient in front of the x-squared term in the equation of the quadratic function. If the coefficient is positive, the parabola opens upwards, and if the coefficient is negative, the parabola opens downwards.

The width of the parabola can be calculated using the equation,

=> f(x) = ax² + bx + c,

where a is the coefficient in front of x-squared, b is the coefficient in front of x and c is the constant term. If the absolute value of the coefficient a is smaller, the graph will be narrower. If the absolute value of the coefficient a is larger, the graph will be wider.

Complete Question:

What would be the order of these quadratic functions when they are arranged from the narrowest graph to the widest graph?

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Answer:

Step-by-step explanation:

(i) We know that more is the number of workers to do a job, less is the time taken to finish the job.

So, it is a case of inverse proportion.

(ii) Considering uniform speed, as the distance to be travelled increases, the time taken to cover it will also increase.

So, this is a case of direct variation.

(iii) Clearly, more is the area of cultivated land, more is the crop harvested.

So, it is a case of direct proportion.

(iv) We know that the more will be the speed of the vehicle, the distance will be covered in lesser time.

So, it is a case of inverse proportion.

(v) Clearly, more is the population, less is the area of land per person in a country.

So, it is a case of inverse proportion.

Answer:

Step-by-step explanation:

If y = 27 when x = 6, write the direct variation equation. If y = -7 when x = -14, write the direct variation equation and find y when x = 20. If x = 8 when y = 4, write the direct variation equation and find y when x = 5. y = 1/6x; If x = 36 when y = 6, find x when y = 42. If y = -16 when x = 4, find x when y = 20.

Answer:

Bank Of Trust

Step-by-step explanation:

So, value of when y is 51, x is -17.

When y varies directly as x, the relationship between y and x can be expressed as y = kx, where k is the constant of proportionality. In this case, we know that y = 27 when x = -9, so we can use this information to find k:

27 = k * -9

27/-9 = k

-3 = k

Now that we have found the value of k, we can use it to find x when y is 51:

y = kx

51 = -3x

x = 51/-3

x = -17

So, when y is 51, x is -17.

A linear equation is an equation that represents a straight line when plotted on a graph. It has the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of y with respect to x, and the y-intercept represents the point at which the line intersects the y-axis. Linear equations can be used to model real-world situations that exhibit a constant rate of change, such as the relationship between time and distance traveled, or the cost of a product and the number sold.

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Answer:

20%

Step-by-step explanation:

the question for this problem is basically 32/160*100

32/160=1/5=0.2. We need to make it into a percent so 0.2*100= 20%

Quantitative research is defined as research that quantifies observations and makes population predictions based on samples.

a research method that entails measuring variables with a numerical system, analysing these measurements with any of a number of statistical models, and reporting relationships and associations between the variables studied.
There are four main types of Quantitative research: Descriptive, Correlational, Causal-Comparative/Quasi-Experimental, and Experimental Research. attempts to establish cause- effect relationships among the variables. These designs are very similar to true experiments, but there are some significant differences.
The overarching goal of quantitative research is to investigate a specific topic or activity using quantitative methods.

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Answer:

1 and 2: Vertical angles

5 and 6: Adjacent angles

Step-by-step explanation:

In the first image, the two angles are opposite from each other and formed by the intersection of two lines, making 1 and 2 vertical angles.

In the second image, the two angles are right next to each other making 5 and 6 adjacent angles.

Vertical angles: opposite angles formed by the intersection of two lines

Adjacent angles: two angles that share a common vertex and a common side, but do not overlap

Answer:

Variable

Step-by-step explanation:

The number of sticks of cotton candy Team B needs to sell to reach their goal is 125.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Two teams need to raise $100 each for their end-of-the-year field trips. Team A wants to sell popcorn at the Spring Fling Carnival,

and Team B wants to sell cotton candy.

It costs $15 to rent a popcorn machine,

whereas it costs $25 to rent a cotton candy maker.

The cost of additional supplies for the popcorn is $0.05 per bag,

and the additional cost for the cotton candy is $0.10 per stick.

Team A will sell the bags of popcorn for $0.75 each.

Team B will sell the cotton candy for $0.80 per stick.

The number of sticks of cotton candy Team B needs to sell to reach their goal is,

= 100/0.80

= 125

Therefore, the required number is 125.

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Answer: 6x=37

Step-by-step explanation: Because it is.

Answer: 3

Step-by-step explanation:

Subtract the cost of paperback books from Jonelle's total amount.

(22.50 - 4.50)

Then, you'll get ($18).

Divide (18) by the number of hardcover books.

(18/6)

Finally, you'll get $3 for the cost of each hardcover book.

Quantitative measurement, as it involves counting or measuring numerical values

Quantitative measurement involves collecting and analyzing data that is expressed in numerical form. This type of measurement is often used to measure physical or behavioral characteristics, such as the number of completed written homework assignments, the number of completed arithmetic problems, or the number of thrown pencils. Quantitative measurement involves quantifying or assigning numerical values to certain characteristics. These numerical values are then used to compare different individuals or groups, or to measure changes over time. This type of measurement allows for reliable and valid data to be collected, which can be used to draw valid conclusions about the characteristics being measured.

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The equation of the line passing through the given points  y=3-(x-3)

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: The point (3,3) and (4,2)

Using the two point form to construct the line that passes through both the points by following the standard equation. Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).

Thus

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

y-3=-1(x-3)

y-3=-x+3

y+x=6

or it can also be rearranged as y=3-(x-3)

Thus the equation of the line that passes through the two given points is y=3-(x-3)

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The probability that each player receives an ace is: 0.1055

let us consider they are  52 open spots in a row. We should divide the cards by placing them on these spots. This is the understanding that the cards on spots  1,2,…, and 13 are for a player, and the cards on spots  14,15,…, and 26 are for another player.

Then there are  134 ways to place the aces in such a way that each player will get an ace. This is the understanding that we do not discern suits. Next to that, there are 524 ways in total to place the aces.

So the probability that each player receives an ace is:

134(524)=28561270725=219720825≈0.1055

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LHL is equal to RHL then limit exist

LHL is not equal to RHL then limit does not exist.

As per the given data the graph of the function is given

Here we have to determine the limit at the indicated value of a, if it was exists.

You may have found the limit from one side instead of from both sides as notated.

Now we have to find:

[tex]$\lim _{x \rightarrow a} f(x)$[/tex] when a = 1

We find the left hand side limit and the right hand side limit at a = 1

So,

The Left hand limit is [tex]$\lim _{\mathrm{x} \rightarrow 1^{-}} \mathrm{f}(\mathrm{x})=\frac{3}{2}$[/tex]

The Right hand limit is [tex]$\lim _{x \rightarrow 1^{+}}[/tex] f(x) = 3

Here [tex]$\lim _{x \rightarrow 1^{-}} f(x) \neq \lim _{x \rightarrow 1^{+}} f(x)$[/tex]

Hence [tex]$\lim _{x \rightarrow a}[/tex] f(x) = DNE

From the graph we find the left hand limit and the right hand limit:

If Left hand limit = Right hand limit then limit exist

If then Left hand limit ≠ Right hand limit then limit does not exist.

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Use the graph of the given function f to determine the limit at the indicated value of a, if it exists.(If an answer does not exist, enter DNE.)

Graph attached at the end of solution

you may have found the limit from one side instead of from both sides as notated. how might you consider the limit as x approaches a from both sides?

23. g(x)=3(2x+3) has a slope of 6 and y-intercept of 9.

24. g(x)=2(0.5x) +3 has a slope of 1 and y-intercept of 3.

25. g(x)=1(2x+3) has a slope of 2 and y-intercept of 3.

26. g(x)=2(1)x+3 has a slope of 2 and y-intercept of 3.

The value of k in the linear function g(x)=k(mx+b) affects the slope of the function by multiplying the slope of the original function m by k. The y-intercept of the function remains unchanged.

23. g(x)=3(2x+3) can be written as g(x)=6x + 9. This shows that the slope of the function is 6 and the y-intercept is 9.

24. g(x)=2(0.5x) +3 can be written as g(x)=x + 3. This shows that the slope of the function is 1 and the y-intercept is 3.

25. g(x)=1(2x+3) can be written as g(x)=2x + 3. This shows that the slope of the function is 2 and the y-intercept is 3.

26. g(x)=2(1)x + 3 can be written as g(x)=2x + 3. This shows that the slope of the function is 2 and the y-intercept is 3.

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a) Every Engineer loves to solve some problem.

x ∀ y(E(x) ∧ A(y) → ~L(x, y))

b) There is a smallest positive integer.

∀ x   y(N(x) ∧ M(y) → x < y)

c) All obtuse triangles have one angle that measures larger than 90°.

x(A(x)  → ~B(x) ∨ ~E(x))

d) There is a student in the class who helps all classmates.

∀x ∀y(C(x) ∧ A(y, x) → ~B(x, y))

a) Every Engineer loves to solve some problem.

The statement using multiple quantifiers and variables.

Let E(x) = x is an engineer

A(x) = x is a problem.

L(x, y) = x loves to solve probability

The negation of the given statement in words.

Negation: There exists at least one engineer who does not love to solve any problem.

The negation using multiple quantifiers and variables.

x ∀ y(E(x) ∧ A(y) → ~L(x, y))

b) There is a smallest positive integer.

The statement using multiple quantifiers and variables.

Let M(x) = x is a negative integer.

x ∀ y(M(x)  ∧ M(y) → x ≥ y)

The negation of the given statement in words.

There exists no longer negative integer.

The negation using multiple quantifiers and variables.

∀ x   y(N(x) ∧ M(y) → x < y)

c) All obtuse triangles have one angle that measures larger than 90°.

The statement using multiple quantifiers and variables.

Let A(x) = x is healthy.

B(x) = x follow diet plan.

C(x) = x follows exercise plan.

∀ x (A(x) → B(X) ∧ C(x))

The negation of the given statement in words.

There exists at least one healthy man who does not follow either diet plan or exercise plan.

The negation using multiple quantifiers and variables.

x(A(x)  → ~B(x) ∨ ~E(x))

d) There is a student in the class who helps all classmates.

The statement using multiple quantifiers and variables.

Let A(y, x) = y is classmate of x.

B(x, y) = x helps y.

C(x) = x is a student in the class.

x ∀ y (C(x) ∧ A(y, x) → B(x, y))

The negation of the given statement in words.

There is no student in the class who helps all classmates.

The negation using multiple quantifiers and variables.

∀x ∀y(C(x) ∧ A(y, x) → ~B(x, y))

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The complete question is:

For each of the statements in a, b, c, and d do the following:

(i) Rewrite the statement using multiple quantifiers and variables.

(ii) Write the negation of the given statement in words.

(iii) Rewrite the negation using multiple quantifiers and variables.

a) Every Engineer loves to solve some problem.

b) There is a smallest positive integer.

c) All obtuse triangles have one angle that measures larger than 90°

d) There is a student in the class who helps all classmates.

The inequality equation is 10x + 9y ≥ 180 and the y-intercept is y ≥ 20 and the x-intercept is x ≥ 18

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

10x + 9y ≥ 180   be equation (1)

On simplifying the equation , we get

To calculate the y-intercept , substitute the value of x = 0

when x = 0

9y ≥ 180

Divide by 9 on both sides of the equation , we get

y ≥ 20

To calculate the x-intercept , substitute the value of y = 0

when y = 0

10x ≥ 180

Divide by 10 on both sides of the equation , we get

x ≥ 18

Hence , the x and y intercepts are x ≥ 18 and y ≥ 20 respectively

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Answer:By solving a system of equations, we will see that the function is continuous for all values of x

Step-by-step explanation:

The plots provides the strongest evidence that its regression line is an appropriate model for the data and is consistent with the assumptions required for inference for regression is image 3.

Regression is one of the methods for determining cause-and-effect relationships between variables and other variables. In simple regression analysis, the relationship between variables is linear, where changes in variable X will be followed by changes in variables permanently. Whereas in a nonlinear relationship, changes in X are not followed by changes in variable Y proportionally.

The regression analysis method is used to produce a relationship between two or more variables in numerical form. The regression equation is the line equation that best represents the relationship between the two variables. Regression is divided into several types, namely simple regression, nonlinear regression, and multiple regression.

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She sold $8,811 worth of cleaning contracts in total, rounded to the nearest dollar.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given, Linda receives a 14% commission for every office that signs a contract for the cleaning services.

Here, we are interested in calculating the value of the cleaning contracts sold.

Let the total value of the cleaning contracts sold to be $x

Mathematically;

14% of x = 1233.60

14/100 * x = 1233.60

14x = 100 * 1233.60

x = 123360/14

x= 8,811.43

Therefore,  the total value of the cleaning contracts she sold, rounded to the nearest dollar will be $8,811.

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Answer:

360

Step-by-step explanation:

The formula for volume is length times width times height

so our equations is 3*12*10=360

Summary statistics, especially the mean and covariance of the two variables, can be used to find the regression equation.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

In simple linear regression with one independent variable (x) and one dependent variable (y), the regression equation can be expressed as:

y = β0 + β1x

where β0 and β1 are the regression coefficients. The coefficients can be estimated using the following formulas:

β1 = covariance(x, y) / variance(x)

β0 = mean(y) - β1 * mean(x)

Here, covariance(x, y) is the covariance between the two variables, variance(x) is the variance of the independent variable x, mean(x) and mean(y) are the means of x and y, respectively.

These formulas assume that the data has been standardized (mean = 0, variance = 1) for convenience, but the results can be easily transformed back to the original scale by using the actual mean and variance of the data.

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If the mode is 1 , the largest number of x is 11

If the mode is 2, the smallest number of x is 13

The mode of a set of data is the most frequent item in the set. For example , The mode of {4 , 2, 4, 3, 2, 2} is 2 because it occurs three times, which is more than any other number.

Therefore the mode of a set is the item that appeared most in the set.

In the table above , the table shows the number of students that read books

4 students reads 0 and 12 reads 1.

If 1 is the mode of the data, it means the highest possible value of x should be less than 12 l, which is 11.

If the mode is 2, the smallest number of x, should be greater than x which is 13

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North and end up at the starting point. The unique geographic properties of the North Pole allow you to travel one mile south, then one mile east, and then one mile north, and end up back at thepo starting point. This property is unique to the North Pole and cannot be found anywhere else on the planet.

The only place on earth where you can travel one mile south, then one mile east, and then one mile north and end up at the starting point is the North Pole. This is because at the North Pole, all directions are north, and so no matter which direction you travel, you will always be moving away from the equator and towards the North Pole. Additionally, since all longitudes converge at the North Pole, traveling one mile in any direction will not change your latitude or longitude, meaning that you will end up back at the North Pole after traveling one mile south, then one mile east, and then one mile north.

At the North Pole, there is no concept of east and west as all lines of longitude converge at the pole. Hence, traveling one mile east or west will bring you back to the same location. The same applies to traveling one mile north or south as all directions at the North Pole are north.

It's important to note that the North Pole is a remote and inhospitable environment, with temperatures that remain below freezing throughout the year. As a result, there are no permanent settlements at the North Pole, and accessing the area requires specialized equipment and training.

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Answer:

f(x) = [tex]\frac{1}{2}[/tex] x

Step-by-step explanation:

a linear function has the form

f(x) = ax + b

to find a and b substitute ordered pairs from the table into f(x)

using (0, 0 )

0 = a(0) + b

0 = b

then

f(x) = ax + 0

using (- 4, - 2 )

- 2 = a(- 4) = - 4a ( divide both sides by - 4 )

[tex]\frac{-2}{-4}[/tex] = a , that is

a = [tex]\frac{1}{2}[/tex]

Then

f(x) = [tex]\frac{1}{2}[/tex] x

or

f(x) = 0.5x

The inverses of the functions f(x) = x + 3 and f(x) = 2x + 4 are

y = x - 3 and x = (y + 4)/2.

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

The first graph y = x + 3.

To find the inverse we'll solve for 'x'.

y = x + 3.

x = y - 3.

y = x - 3.

f⁻¹(x) = x - 3.

And,

y = 2x - 4.

2x = y + 4.

x = (y + 4)/2.

f⁻¹(x) = (x + 4)/2.

The graph of the function y = x + 3 is shifted 3 units up to y = x.

And the graph y = 2x - 4 is shifted 4 units down and is steeper than y = x.

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296 hot lunches were sold on Friday.

The number of hot lunches sold on Friday can be calculated by multiplying the total number of hot lunches by the relative frequency on Friday:

Hot lunches sold on Friday = 1,350 * 0.22 = 296

Relative frequency is a measure of the number of times an event occurs in a sample, expressed as a proportion of the total number of events. To find the number of hot lunches sold on Friday, we multiply the total number of hot lunches sold in the week by the relative frequency of Friday. This gives us the number of hot lunches sold on Friday, which is 296 in this case. Understanding relative frequency is important in statistics as it helps to summarize data and understand the distribution of events.

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