Expand and simplify (2x + 1)(x-2)(x + 3)
Optional working
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Answer
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since the border is 4 inches wide and there are 2 sides to the border , the expression in factored form that represents the area of border = 8 x (length of border)

The area of a rectangle is the amount of two-dimensional space that the rectangle occupies. It is calculated by multiplying the length of the rectangle by its width.

The perimeter of a rectangle is the distance around the outside of the rectangle.

(4 inches) * (2 sides) * (length of border) = 8 inches * (length of border)

To write this expression in factored form, we can factor out the 8 inches:

8 inches * (length of border) = 8 inches * (length of border)

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Hence, the slope of equation is [tex]f(x)=-0.25x+2[/tex].

What is the slope of the line?

The slope is always estimated by determining the ratio of the “vertical change” to the “horizontal change” between any two different points on a line.

Suppose that the amount of water in the tank after a certain number of minutes.

Let [tex]x[/tex] be any value. So, after the [tex]x[/tex] minutes the tank has lost [tex]0.25x[/tex] gallons from the original [tex]2[/tex] .

So, the [tex]f(x)=2-0.25x[/tex] where [tex]f(x)[/tex] is the number of gallons remaining after [tex]x[/tex] minutes and here [tex]x[/tex] is the number of minutes.

[tex]f(x)=2-0.25x\\\\f(x)=-0.25x+2[/tex]

Hence, the slope of equation is [tex]f(x)=-0.25x+2[/tex].

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The frequency distribution of the data from 103 to 107 is 2, from 108 to 112 is 4 and from 113 to 117 is 2.

Frequency distribution in a data set is the no. of times a certain data of an interval of grouped data occurs.

Temperature(°F)                              Frequency

103 to 107                                                2

108 to 112                                                4

113 to 117                                                  2

The class width of a data set is represented by the two consecutive lower limits.

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Answer: 2m-6+4m

Step-by-step explanation:

The statement that best describes the changes in air pressure and wind speed is C. When a high- and a low-pressure air mass are far apart, air moves slowly from high to low pressure.

The weight of air molecules pressing down on the Earth is referred to as air pressure. As you ascend from sea level into the atmosphere, the pressure of the air molecules changes. The greatest pressure exists at sea level, where the density of air molecules is greatest.

Atmospheric pressure, also known as barometric pressure, is the pressure that exists within Earth's atmosphere. The region with low pressure will always get winds from the high pressure. This means that the region of low will attract winds from the high pressure and vice versa.

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Equation of line in slope-intercept form is 3y-2x= -1.

Hence, Equation of line in slope-intercept form is 3y-2x= -1.

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Anserw:

Say the averge water a person uses a day is 90 gallons 30% of the water is used outside a day. So that would mean around 27 gallons.

hope that helps :)

Step-by-step explanation:

The order pair will be greater than (-2,5) because when substituted the value (-2,5) will give 11 that will be false.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence. In order to understand a point visually, it can be helpful to position it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers. Two variables are frequently represented by ordered pairs. (x, y) = (7, - 2) means that x = 7 and y = -2. The x-coordinate is the number that corresponds to the value of x, and the y-coordinate is the number that corresponds to the value of y.

Here,

The given inequality,

-3x+y<11

at (0,0)

0<11

it is true.

at (1,1)

-3+1<11

-2<11

it is true.

Because 11 will be false when the value (-2,5) is substituted, the order pair will be greater than (-2,5).

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The percentage increase in the population of the chilrden since past year is 11.96%.

What is Percentage ?

A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.

According to the question, the town's population of children increased from 376 to 421 during the past year.

So, the increase in the population of the children is-

Increase =421-376

Increase =45

Now, the percentage increase in population of the children per year is calculated as-

Percentage Increase [tex]$=\frac{\text { Increase }}{376} \times 100 \%$[/tex]

Percentage Increase [tex]$=\frac{45}{376} \times 100 \%$[/tex]

Percentage Increase [tex]$=0.1196 \times 100 \%$[/tex]

Percentage Increase [tex]$=11.96 \%$[/tex]

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Answer: y= -2/3x + 0

Explanation: y= mx +b

Y-intercept at (o,o), so b is 0

Let's pick 2 points (-3,2) ( 0,0), so the slope is -2/3

So the equation is y=-2/3x + 0

The correct integers are;

For first diver, the elevation = - 36 feet

For second diver , the elevation = - 44 feet

What is an 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;

One diver is 36 feet below the surface.

And, The other diver is 44 feet below the surface.

Now,

Since, One diver is 36 feet below the surface.

And, The other diver is 44 feet below the surface.

Hence, The correct integers to represent the surface are;

For first diver, the elevation = - 36 feet

For second diver , the elevation = - 44 feet

Thus, The correct integers are;

For first diver, the elevation = - 36 feet

For second diver , the elevation = - 44 feet

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Answer:

153

Step-by-step explanation:

Use long division on a piece of paper I can't show photo sorry.

Answer:

12

Step-by-step explanation:

3*4=12

In linear equation, The domain defines the values of numbers of flower arrangements that

can be expected from the florist.

The practical domain of the function is; All integers from 0 to 25, inclusive.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

The domain of the function = The possible number of flower arrangements

that can be sold

The possible number of flower arrangements that can be sold = Whole

numbers from 0 to 25

Therefore;

The possible number of flower arrangements that can be sold = 0 ≤ x ≤ 25

Where;

x = An integer

Which gives;

The domain of the function, D = {0 ≤ x ≤ 25 | x ∈ Z}

Therefore;

The practical domain of the function if the florist sells 25 flower

arrangements is D = All integers from 0 to 25, inclusive.

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(a) The joint probability distribution of the two points will be 1/x, 0<x<1, 0<y<1

(b) The expectation of the product of the two points will be 1/6

(c) The marginal distribution of the point your friend picks will be (-1/2) lny^2

We have, X=(0,1)

Y | X=X=(0, X)

a) Let f(x,y) be the joint probability distribution of the two points will be:

f(X)=1

f(Y|X)=1/x

[tex]$$\begin{aligned}& f(x, y)=f(X) f(Y \mid X=x)=1 / x, 0 < x < 1,0 < y < x\end{aligned}$$[/tex]

b) Let E(XY) be the expectation of the product of the two points.

[tex]$$\begin{aligned}E(XY)=& \int_0^1 \int_0^x \frac{x y}{x} d y d x=\frac{1}{6} \quad \text { (Decimal : } 0.16667 \ldots \text { ) }\end{aligned}$$[/tex]

c) Let f(y) be the marginal distribution of the point your friend picks.

So, the value of f(y) will be:

[tex]$$\begin{aligned}& \mathrm{f}(\mathrm{y})= \\& \int_y^1 \frac{1}{x} d x=-\frac{1}{2} \ln \left(y^2\right)\end{aligned}$$[/tex]

d)for 0<y<1

[tex]$$\begin{aligned}& f(y) > =0 \\& \int_0^1-\frac{1}{2} \ln \left(y^2\right) d y=1\end{aligned}$$[/tex]

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Option B is correct, Vincent will be able to buy the sneakers, while David will not be able to.

Because the shoe cost after including sales tax is

6% of 86$ is 5.16$

so, 86 + sales tax (which is 5.16) = 91.16$

David only has 90$ so he can't afford the sneakers. They are 1.16$ over his budget.

While for Vincent,

9% of 86$ is 7.74$

so, 86 + sales tax (which in this case is 7.74) = 93.74

Vincent has 95$ to spend so he can afford the shoes.

A sales tax is a tax paid to a governing body for the income of certain items and services. Typically, legal guidelines permit the seller to gather funds for the tax from the customer at the factor of purchase. While a tax on goods or services is paid to a governing body immediately by means of a patron, it also includes called a use tax. frequently legal guidelines offer for the exemption of positive goods or services from income and use tax, which includes food, schooling, and medicines. A fee-introduced tax (VAT) collected on goods and services is associated with a sales tax. See the contrast with income tax for key variations.

Traditional or retail income tax is levied at the sale of an amazing to its very last quit person and is charged whenever that item is sold retail. sales to corporations that later resell the products aren't charged the tax. A patron who isn't always an end-user is generally issued a "resale certificate" by way of the taxing authority and required to provide the certificate (or its identification variety) to a seller on the point of buy, at the side of an assertion that the object is for resale. The tax is otherwise charged on each item sold to clients without any such certificate and who are underneath the jurisdiction of the taxing authority.

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The vertices after reflection will be (-6, 1), (-3, 2), (-5, 7) and the vertices after rotation of 180° will be (6, 1), (3, 2), (5, 7).  

A form of Euclidean space isometry in geometry is called a point reflection, also known as a point inversion, center inversion, or asymmetry through a point.

An object is said to have point symmetry if it is unchanged under a point reflection, and central symmetry or being centrally symmetric if it is invariant below a point reflective thinking through its center.

As per the given information in the question,

The given vertices of the triangle are:

D(-6, -1), E(-3, -2), F(-5, -7).

a.

The equation towards reflection in the x-axis: (x, -y)

D = (-6, -1)

Reflected vertex = (-6, 1)

E = (-3, -2)

Reflected vertex = (-3, 2)

F = (-5, -7)

Reflected vertex = (-5, 7)

b.

Now let's find out the rotation of 180° of the given points,

As we can see that the vertices are in the third quadrant because both the points of each vertex are negative, so after rotation of 180° it will move to the 1st quadrant where all the points are positive.  

So,

D = (-6, -1)

After rotation, D = (6, 1)

E = (-3, -2)

After rotation, E = (3, 2)

F = (-5, -7)

After rotation, F= (5, 7)

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The equation of line of c and y intercept are y = 100x +400 and 400 respectively.

The equation, y = mx + b, is in slant capture structure for the situation of a line. At the point when a condition is here, the slant of the line is given by m and the y-capture is situated at b. For instance, a line with the situation y = 2x + 4 has a slant of 2 and a y-catch of 4.

Let take two random points lying on the line.

(0, 400) and (1, 500)

we know that,

Slope(m) = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = (500-400)/(1-0) = 100

And y-intersect from the graph is c = 400

Then,

Y = mx + c

y = 100x +400

Y-intercept represent the number of phones produce in a day.

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The solution set of the function based on the graph is (3, 1). Option D

We know that the solution set of a function would be obtained as the points where the graph cut the axes of the graph. The graph has to do with a system in which information is presented in the x, y coordinate system.

In this kind of system, the vertical axis is the y axis while the horizontal axis is the x axis, as such we would need to plot the data points of the graph and then try to obtain the points that would correspond to the solutions of the points on the graph.

We would now need to observe the graphs so as to be able to obtain the correct presentation of the data points that would serve as the solutions of the graph as we can see the function plotted completely here.

The line cut the y axis at y =1. If we trace this point to the point that it corresponds to in the x axis we have x = 3 and we have the required points as (3, 1).

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The monomial that we need to add to have a square of a difference is:

-2bc

Remember that the square of a difference is written as:

(a - b)^2 = a^2 - 2ab + b^2

Here we have the two  terms:

0.01*b^2 + ... + 100c^2

We can rewrite the known terms as:

0.01*b^2 = (0.1*b)^2

100*c^2 = (10c)^2

Then our expression becomes:

(0.1*b)^2 + ... + (10c)^2

And the missing term must be:

-2*(0.1b)*(10c) = -2bc

Then the complete expression is:

(0.1b)^2 - 2bc + (10c)^2 = (0.1b - 10c)^2

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Answer:

There was no data provided but due to simple research i have conducted the following data

Qualifiers are in bold, italics and underlined.

Step-by-step explanations:

Chio- 3 1/5

Kevin- 3.2

Ojas- 3 8/30

Sydney- 3 13/60

Qualifiers: Chico, Kevin

let me know if this is incorrect data

The length of side q to the nearest 10th of an inch is 4.1 inches.

The sine rule for a triangle ABC is a/sinA = b/sinB = c/sinC.

Given, In ΔPQR, p = 4.7 inches, ∠P=76°, and ∠Q=57°.

∴  the length of q can be obtained by,

p/sinP = 1/sinQ.

4.7/sin76° = q/sin57°.

4.7/0.97 = q/0.84.

q = (4.7×0.84)/0.97.

q = 4.1 inch.

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Hello,

I hope you and your family are doing well!

Part A)

The given expression is in the form y = -16t^2 + 441, which is a quadratic equation. A quadratic equation can be factored into the form (ax + b)(cx + d) = 0, where a, b, c, and d are constants.

To factor in the given expression, we can start by completing the square. To complete the square, we need to add and subtract the square of half of the coefficient of the x^2 term, which is (1/2)(-16) = -8. This gives us:

y = -16t^2 + 441 = (-16t^2 - 8t^2) + 441 = -24t^2 + 441

Now, we can rewrite the expression as follows:

y = -24t^2 + 441 = (-8t^2) + 441

To complete the square, we need to add and subtract (1/2)^2(-8)^2 = 16:

y = (-8t^2 + 16) + 425

This expression can be rewritten as:

y = (-8t^2 + 16) + (20t)^2

So the expression can be factored as:

y = (-8t + 4)(2t - 5) (this is the answer)

Part B)

To find the time it takes the object to fall to a height of 377 feet, we can set y equal to 377 and solve for t. Substituting the factored form of the expression into the equation and solving for t gives us:

377 = (-8t + 4)(2t - 5)

We can then solve this equation by setting each factor equal to 0 and solving for t. This gives us:

-8t + 4 = 0

2t - 5 = 0

Solving these equations separately gives us:

t = 1/2

t = 5/2

The time it takes the object to fall to a height of 377 feet is t = 1/2 seconds. (or 0.5 in decimal form)

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Happy Holidays & New Year!

Answer: -8

Step-by-step explanation:

We see on the graph that there are two points located y=4. They are (7,4) ( -8,4).

So the other value other than 7 is -8!

Answer: 13/15

Step-by-step explanation:

2/3 x 5 = 10/15

1/5 x 3 =3/15

3/15 + 10/15 =13/15

Answer:

13/15

Step-by-step explanation:

2/3 = 15/3 = 10 this is because 5 and three have common factors. So I now have 10/15.
1/5 = 3/15.

3/15 + 10/15 = 13/15.

Answer:

y = -4x-9

Step-by-step explanation:

The slope must stay the same for parallel lines, which is -4. Now we will plug the point into slope-intercept form(y=mx+b) where m is the slope and b is the y-intercept. Plugging in -4 for the slope and (-3, 3) for x and y, we get [tex]3=-4*13 + b[/tex], or [tex]3 = 12 + b[/tex]. Subtracting 12 from sides gives us that b = -9, which is the y-intercept! We know have both the slope and y-intercept, so we get that the equation is y = -4x - 9.

Hope this helps!

The correct answer is option B: "g(-4) = -11". This statement is consistent with the given information about the domain, range, and specific values of the function g. Since the domain of g is -20 ≤ x ≤ 5, the value x = -4 is within the domain of the function, and therefore we can evaluate g at this value. Similarly, since the range of g is -5 ≤ g(x) ≤ 45, the value g(-4) = -11 is within the range of the function. Furthermore, since g(0) = -2 and g(-9) = 6, we know that g takes on negative values, which is consistent with the fact that g(-4) = -11.

Option A, C, and D are all incorrect because they do not satisfy the conditions of the domain and range of the function g. For example, option A states that g(-13) = 20, but since the domain of g is -20 ≤ x ≤ 5, the value x = -13 is not within the domain of the function, and therefore it is not possible to evaluate g at this value. Similarly, option C states that g(7) = -1, but since the range of g is -5 ≤ g(x) ≤ 45, the value g(7) = -1 is not within the range of the function, and therefore this statement cannot be true for g. Option D states that g(0) = 2, but since we are given that g(0) = -2, this statement is not consistent with the given information about the function g.

For the mileage of 80 miles company A will charge less than company B.

So, the inequality is m≤80.

A variety of notations are available to denote different kinds of inequalities. An inequality in mathematics is a relationship between two expressions or values that is not equal. To resolve an inequality, follow these steps: First, multiply each term by the total of the least common denominators of all the fractions to be subtracted. Step 2: Combine similar terms on both sides to simplify the inequality. Step 3: Calculate the unknown by adding or subtracting the amounts from the numbers on either side.

Charge for company A=$131

Charge for company B=$75+0.70m

75+0.70m≤131

0.70m≤56

m≤(56/0.7)

m≤80

Therefore, for the mileage of 80 miles company A will charge less than company B.

So, the inequality is m≤80.

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The number of possible ways a person can order a two-course meal = 99

In this question, we have been given a restaurant offers 9 entrees and 11 desserts.

We need to find the number of possible combinations (ways) a person can order a two-course meal.

Here, the entrees = 9

and the desserts = 11

The entrees can be ordered in 9 ways

The desserts can be ordered in 11 ways.

a two-course meal = entrees * desserts

so,  the number of possible ways a person can order a two-course meal would be,

a two-course meal = 11 * 9

a two-course meal = 99

Therefore, in 99 ways a person can order a two-course meal.

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According to the given figure of triangle , f = 58 °

A linear pair of angles is formed when two lines intersect at a single point. The angles are said to be linear if they follow the point where the two lines intersect in a straight line.

The sum of the angles in a pair of linear equations is always 180°. These are also referred to as additional angles.

According to the given information

We are given that

a = 119°

Applying linear Pair of Angles

a + b = 180°

119° + b = 180°

b = 180° - 119°

b = 61 °

We know that

b = c = 61 °

According to Angle sum Property

b + c + f = 180°

61° + 61° + f = 180°

f = 180 - 61 -61

f = 58 °

According to the given figure of triangle , f = 58 °

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