please answer all 3 questions thank you~!!!!

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so hmmm we look at hmm x³ + x² - 8x - 6 so how do squeak out a factor out of it, well, using the rational root test and using our p/q checking for factors, we find that likely factors can be ± 6/1 and ±(3, 2, 1) / 1, anyhow so we check some of those and hopefully without boring you to death we find that -3 works, we can always use the remainder theorem to check if that's true, by simply plugin in f(-3) and if it's indeed a factor, that'd give us 0, well, f(-3) = -27 + 9 +24 +6 = 0, holly smokes!! is a factor.

well, all that jazz means that -3 is a factor, namely the factor is really x = -3 or x + 3 = 0 so the factor is (x+3) and for our synthetic division we'll use the -3 version, Check the picture below.

so we end up with the factors of (x+3)(x²-2x-2), now for the 2nd factor what we can do to break it up is use the quadratic formula

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-2}x\stackrel{\stackrel{c}{\downarrow }}{-2} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]

[tex]x= \cfrac{ - (-2) \pm \sqrt { (-2)^2 -4(1)(-2)}}{2(1)} \implies x = \cfrac{ 2 \pm \sqrt { 4 +8}}{ 2 } \\\\\\ x= \cfrac{ 2 \pm \sqrt { 12 }}{ 2 }\implies x=\cfrac{2\pm\sqrt{2^2\cdot 3}}{2}\implies x=\cfrac{2\pm 2\sqrt{3}}{2}\implies x=1\pm\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} (x+3)(x-1+\sqrt{3})(x-1-\sqrt{3}) \end{array}}~\hfill[/tex]

now, just to clarify, all those are real roots, and the last two come from simply setting x = 1 ± √3 to 0 to get the factors.

Answer:

4 pounds of cheese

Step-by-step explanation:

4/5*5=4

Hello there!

Answer:

$400'000

Step-by-step explanation:

Estate -- $2.4 million or $2'400'000

Springfield University will receive: 10% * $2'400'000 = 0.1 * $2'400'000 = $240'000

First Church of Springfield will receive: 15% * $2'400'000 = 0.15 * $2'400'000 = $360'000

Wife will receive $600'000

Total: $240'000 + $360'000 + $600'000 = $1'200'000

Children will receive at total: $2'400'000 - $1'200'000 = $1'200'000

So each child will receive: $1'200'000 / 3 = $400'000

Answer: Each child of Homer Simpson gets $400000.

Step-by-step explanation:

Homer Simpson left 10% of his estate, or (10/100)  x $2.4 million

= $ (10/100)x2400000= $240000

$240,000 to Springfield University.

He left 15% of his estate, or (15/100) x $2.4 million = $(15/100)2400000

= $360000

So 360,000 to the First Church of Springfield.

So in total, he left $240,000 + $360,000 + $600,000 = $(240000+360000+600000)

=$1200000

 $1,200,000 to organizations and his wife.

That means the remainder of the estate, $2.4 million - $1,200,000

= $2400000-1200000

= $1200000

1,200,000, was divided among his three children. So each child received $1,200,000 / 3 = $1200000/3

=$400000

Answer: $400000.

The expanded form in terms of the sums of powers to tens of 237.45 is [tex]2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}[/tex]

As per the given data the given decimal number is 237.45.

Here we have to determine the expanded form in terms of the sums of powers to tens.

Expanded Form: In its extended sense, A number is divided up into its place values, then expanded to represent the value of each digit.

Then N can be written in expanded in for terms of 10 is

[tex]$$\Rightarrow N=a \times 10^2+b \times 10^1 + c \times 10^0+d \times 10^{-1}+e \times 10^{-2}$$[/tex]

Let the given number 237.45 is denoted by N.

N = 237.45

First, write the expanded form of a number before the decimal place.

Then using [tex]$\circledast$[/tex], we have

[tex]& N=2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times \frac{1}{10}+5 \times \frac{1}{10^2} \\[/tex]

[tex]& N=2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2} \\[/tex]

237.45 = [tex]2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}[/tex]

Therefore the expanded form of 237.45 is [tex]2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}[/tex].

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Which of the following expressions represents 237.45 written in expanded form in terms of the sums of powers to tens

A. [tex]$2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}$[/tex]

B. [tex]$237 \times 100+45 \times 1 / 1000$[/tex]

C. [tex]$2 \times 10^2+3 \times 10^1+7 \times 10^0-4 \times 10^1-5 \times 10^2$[/tex]

D. 200+30+7+0.4+0.05

Answer:

x=0

Step-by-step explanation:

The general form of the equation of y-axis is x = 0. hence, the equation of line parallel to the y-axis is given by the equation: x = k.

The solution for the rational equation (1/(x + 1)) - (1/(x + 2)) = 1/5 is specified by the option C.

C. x = -3.79, x = 0.79

A rational equation consists of a fraction that has a polynomial numerator denominator.

The specified equation can be expressed as follows;

[tex]\dfrac{1}{x + 1} - \dfrac{1}{x+2} = \dfrac{1}{5}[/tex]

Finding the common denominator for the right hand side expression, we get;

[tex]\dfrac{ (x + 2) - (x + 1)}{(x + 1) \times (x + 2)} = \dfrac{1}{5}[/tex]

[tex]\dfrac{1}{(x + 1) \times (x + 2)} = \dfrac{1}{5}[/tex]

[tex]\dfrac{1}{x^2+ 3\cdot x+ 2} = \dfrac{1}{5}[/tex]

Inverting both sides of the above equation, we get the following quadratic equation;

x² + 3·x + 2 = 5

x² + 3·x + 2 - 5 = 0

x² + 3·x - 3 = 0

The quadratic formula indicates that we get;

x = (-3 ± √(3² - 4×1×(-3))) ÷ (2 × 1)

x = (-3 + √(21)) ÷ 2 and x = (-3 - √(21)) ÷ 2

x ≈ 0.79 and x ≈ -3.79

The correct option is option C

C. x = -3.79, x = 0.79

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The exact value of secθ in simplest radical for is 1.083

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We are Given θ is an angle in standard position.

Its terminal side passes through the point (12, -5).

To find the exact value of secθ in simplest radical form.

When θ is an angle in standard position and its terminal side passes through the point (x,y), then the exact value of secθ is:

So, we have x = 12 and y = -5 which is in the first quadrant.

Therefore,

r² = x² + y²

r² = ( 12 )² + ( -5 )²

r² = 144 + 25

r² = 169

r = 13

Then,

sec θ = 1/cosθ

sec θ = [ 1/(x/r) ]

sec θ = r/x

sec θ = 13/12

sec θ = 1.083

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The degree of a constant polynomial (such as 7) is zero.

The variable's highest power in a polynomial expression is the polynomial's degree.

A polynomial is a mathematical expression made up of more than two algebraic terms, particularly the sum (or difference) of several terms that each contain a different power of a single or several variables (s).

It is a monomial combination that is linear. Since the polynomial can be conceived of as 7x0, the degree of a constant polynomial (such as 7) is zero.

Normally, the degree of the zero polynomial (zero) is regarded as being undefinable.

A polynomial function with a degree of 7 is known as a septic function (also known as a 7th degree polynomial). 

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The area of square 1 is 180 sq cm

The area of a square is calculated with the help of the formula: Area = s × s, where, 's' is one side of the square. Since the area of a square is a two-dimensional quantity, it is always expressed in square units

Square 1 formed on hypotenuse of the triangle, squares 2 and 3 are formed on the perpendicular legs of the triangle. Thus, by Pythagoras Theorem, A(square 1) will be equal to the sum of the areas of (square 2) and (square 3).

Area of square 1 = Area of square 2 + Area of square 3

Area of square 1 = 100 + 80

Area of square 1 = 180cm^2

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Answer:

Step-by-step explanation: first we have to solve the bracket both side of equal to.

1/6(3x-6)=1/8(4x+)

x/2-1 = x/2+1

-2

There are 15 different books and 3 each can be arranged on a shelf i.e., there are 15/3 i.e., 5 shelves to arrange the book in the the display case.

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By using the triangular inequality, we will get the possible lengths:

a) 6km < x < 16km

b) 0mi < x < 24mi

c) 15yd < x < 30yd

If A, C, and D are the lengths of the sides of a triangle, then the triangular inequality says that:

A + C > D

A + D > C

C + D > a

Now, if the two sides are 5km and 11 km, and the other side is x, then we can write:

x + 5km > 11km

x + 11km > 5km

11 km + 5 km > x

From these inequalities we can get:

16km > x

x > 11km - 5km

x > 6km

Then the possible lengths of the third side are:

6km < x < 16km

b) Now the sides are 12 mi and 12mi, then the inequalities are:

x + 12mi  > 12mi

12mi + 12mi > x

The first one gives:

x > 0mi

The second:

24mi > x

The possible lenghts are 0mi < x < 24mi

c) 25 yd and 10 yd

Here we will get:

25yd + 10yd > x  ----- >  30yd > x

x + 10 yd > 25yd -------> x > 15yd

The possible lengths are:

15yd < x < 30yd

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The volume of the pyramid as calculated from the data given is found to be as 21.33 cubic units .

The distance from a corner to the center is 8 , and from the corner to the top of the pyramid is 8, because it is given that the tringles are equilateral.

so the height becomes,

√3a/2 = 4√3

The area of the hexagon is calculated using the formula ,

=3√3/2 x a²

=3√3/2 x 64

= 963√3

=332.553 square units.

Volume of a pyramid is calculated as ,

1/3 x base x height

= 1/ 3 x 8 x 8

= 1/3 x 64

=21.33 cubic units answer.

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Answer:

y = 2x

Step-by-step explanation:

y = mx + b

m = 2

y-intercept = b = 0

y = 2x + 0

y = 2x

This is how you construct a parent graph - it is the simplest form of the function, and has a basic shape.

The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.

For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.

We can take a few examples to understand this concept further.

Hence, this is how you construct a parent graph - it is the simplest form of the function, and has a basic shape.

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The value of next two terms are,

⇒ 0 and - 60

A relation between a set of inputs having one output each is called a function.

Given that;

The values are,

⇒ f (1) = 120,

⇒ f (2) = 60

And, The function is,

⇒ f (n) = f (n - 1) + ___

For n ≥ 2

Now,

Since, The values are,

⇒ f (1) = 120,

⇒ f (2) = 60

And, The recursive formula is,

⇒ f (n) = f (n - 1) + b

For n ≥ 2

Substitute n = 2;

⇒ f (2) = f (2 - 1) + b

⇒ 60 = f (1) + b

⇒ 60 = 120 + b

⇒ b = 60 - 120

⇒ b = - 60

So, The recursive formula is,

⇒ f (n) = f (n - 1) - 60

Substitute n = 3;

⇒ f (3) = f (3 - 1) - 60

⇒ f (3) = f (2) - 60

⇒ f (3) = 60 - 60

⇒ f (3) = 0

Substitute n = 4;

⇒ f (4) = f (4 - 1) - 60

⇒ f (4) = f (3) - 60

⇒ f (4) = 0 - 60

⇒ f (4) = - 60

Thus, The next two term are 0 and - 60.

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The circumference of the base of figure 2 is 5π inches, and the area of the base of figure 2 is 6.25π square inches

You can presume that the cylinders are proportionate because they are comparable.

9/5 = 4.5/x would be the equation to be used for the calculation.

The radius of 2.5 is obtained by dividing and multiplying by crosses.

Figure 1's circumference will be:

Circumference = 2 * 2.5 = 5π

The area for figure 2 is as follows:

Area = (2.5)² = 2.5 * 2.5 = 6.25π

As a result, the base of figure 1 has a 5π inches circumference.

The base of figure 2 has a 6.25π square inch area.

The base of figure 1 has a 5π inch circumference.

The base of figure 2 has a 6.25π square inch area.

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Answer:

1376x-736

Step-by-step explanation:

Take 32 and multiply it by 43. By multiplying vertically, distribute the multiplication of 3 (from 43) times both the 2 and 3 of 32 (right to left)

3 x 2=6; 3 x 3=9:

32

x

43

--------

96

Then, distribute the multiplication of 4 (from 43) times both the 2 and 3 of 32 (right to left) and leave a zero under the last number of your previous answer while moving the distribution of numbers forward.

4 x 2=8; 4 x 3=12

32

x

43

--------

   96

+

1280   <----(this is the zero you must leave under your previous set)

After distributing each number of 43 to each number of 32 while multiplying, add your answers together vertically from right to left and bring down the x:

  96

+

1280

----------

1376x

Now do the same for 32 x -23 after learning vertical multiplication to get -736

Your final answer put together is 1376x-736

To translate a triangle with vector (-5/2), you need to subtract 5/2 from the x-coordinate and add 2 to the y-coordinate of each vertex of the triangle. This will move the triangle 5 units to the right and 2 units up.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

To translate a triangle with a vector, you can use the vector to adjust the coordinates of the triangle's vertices.

For example, if the triangle has vertices at (x1, y1), (x2, y2), and (x3, y3), you can translate it by the vector (-5/2) by subtracting 5/2 to the x-coordinates of the vertices. The new coordinates of the translated triangle would be (x1-5/2, y1), (x2-5/2, y2), and (x3-5/2, y3).

This will move the triangle 5/2 units to the left along the x-axis.

It is important to note that the translation vector you provided only has one component, which is -5/2. Since the vector only has x component, the translation will only occur along the x-axis and the y-coordinate of the vertices will not change.

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Therefore , the solution of the given problem of function comes out to be  f(x) = 2871 thousands.

A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is a collection of inputs that together produce a single, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function. Usually, the letter f is used to represent functions (x). The input has an x in it.

Here,

Given :

=>  f(x) = 225(1.29)×

After 10 year number of years x =10

=> f(x) = 225(1.29)¹⁰

=> f(x) = 12.76 * 225

=>  f(x) = 2871 thousands.

Therefore , the solution of the given problem of function comes out to be  f(x) = 2871 thousands.

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Parallelogram M'N'P'Q' is larger than parallelogram MNPQ because MN and M'N' have lengths of 2 and 5 respectively, and parallelogram MNPQ is dilated by a factor of 5/2 to give parallelogram M'N'P'Q'.

A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two sets of parallel sides. In a particular kind of quadrilateral known as a parallelogram, both sets of opposite sides are parallel and equal. There are four different kinds of parallelograms, including three unique kinds. Parallelograms, squares, rectangles, and rhombuses are the four different shapes. Having two sets of parallel sides makes a quadrilateral a parallelogram. In a parallelogram, the opposing sides and angles are both the same length. On the same side of the horizontal line, the interior angles are additional angles as well. 360 degrees is the total number of interior angles.

To make parallelogram M'N'P'Q, parallelogram MNPQ was enlarged.

Points include M(2, 2), N(4, 2), P(3, 3), and Q. (1,-3)

M'(5, 5), N'(10, 5), P'(8, 7), and Q' (3,-7)

A) First, determine Minnesota's length:

|MN| = 2

|M'N'| = 4

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Answer:

+ - × ÷

Step-by-step explanation:

addition, subtraction, multiplication and division

The correct answer is option A: the optimal corner point won't change.

The optimal corner point is the point where the objective function reaches its maximum value, with the constraints of the problem being satisfied. If the slope of the objective function stays between the slopes of the binding constraints, it means that the current optimal corner point will remain unchanged.

This is because if the objective function's slope is within the slopes of the binding constraints, then the set of points where the objective function reaches its maximum value will be the same. Therefore, the optimal corner point will not change.

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The system of equations, in standard form, modeling the relationship between cost of gespils (x) and cost of alabers (y) is -

8x + 9y = 117

3x + 8y = 67

Given is that Farmers Lirn and Rew both bought gespils and alabers for their farms. Lirn bought 8 gespils and 9 alabers for $117. Rew bought 3 gespils and 8 alabers for $67.

We can write the system of equations as -

8x + 9y = 117

3x + 8y = 67

Where -

cost of gespils → (x)

cost of alabers → (y).

Therefore, the system of equations, in standard form, modeling the relationship between cost of gespils (x) and cost of alabers (y) is -

8x + 9y = 117

3x + 8y = 67

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The first blank is skewed left, the second blank is median, and the third blank is 9 is correct options.

A distribution that is left-skewing has a lengthy left tail.

Distributions that are negatively skewed are also known as left-skewed distributions.

This is due to the number line having a significant negative tail.

Additionally, the peak is to the left of the mean.

The right tail of a right-skewed distribution is lengthy.

It's a widespread misperception that "peakness" is defined by the distribution's peak.

To put it another way, a peak that leans left indicates a left-skewed distribution.

Hence, The first blank is skewed left, the second blank is median, and the third blank is 9 is correct options.

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The inverse of a quadratic graph is a square root function. To graph the inverse, we reverse the domain and range.

The curve-shaped graph of a quadratic function is known as a parabola. The vertex of a parabola is one of its focal points.

On the graph, it is either the highest or lowest point.

We can imagine it as the parabola's endpoint.

A square root function is the inverse of a quadratic function.

We switch the domain and range in order to graph the inverse.

The graph has the same structure but has been rotated to have the original function's domain and range switched.

Therefore, the inverse of a quadratic function is a square root function. To graph the inverse, we reverse the domain and range.

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Wilbur drove for 5 hours before Jack caught up with him.

Based on the information, the distance = (Wilbur's speed) x (time) = (Jack's speed) x (time + (time Wilbur drove))

We know that Jack's speed is 75 mph, and that he caught up with Wilbur after 2 hours. We also know that the distance covered by Jack is the same as the distance covered by Wilbur.

So we can write:

distance = (Wilbur's speed) x (time) = (Jack's speed) x (2 hours)

We are given that the Wilbur's speed is 30 mph, so we can substitute that in the above equation:

distance = 30 mph x (time) = 75 mph x 2 hours

Then we can solve for time by dividing both sides of the equation by 30:

time:

= (75 mph x 2 hours) / 30 mph

= 5 hours

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The answer is $112.70  The Question is a simple Sales tax rate calculating problem.

Multiplying the purchase price by the sales tax rate will provide the sales tax. Don't forget to round the sales tax rate from percent to decimal. The price of the purchase is increased after the sales tax has been calculated. The entire cost is what the client pays as a result.

Sales tax rate = Sales tax percent / 100.

Sales tax = List price x Sales tax rate.

Given,

Rate of sandwich is = $4. 00

Rate of drink is = 94$

The rate of a meal that Her grandson ordered is =$6. 35.

What was the total price of all three items when 8% sales tax was added?

Total price of all three items without tax = 4 + 94 + 6.35

= $104.35

Total price of all three items with tax = (100% + tax) * Price

= (100% + 8%) * 104.35 = 108% * 104.35

= 1.08 * 104.35 = 112.698

≅ $112.70

The estimation to check if the result is reasonable by putting the answer in the original equation.

E.g. x + 4 = 10; x = 10 - 4

We get that x = 6

Plug in x = 6 in x + 4 = 10.

6 + 4 = 10.

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Due to the fact that they obscure bimodality or any multimodality, boxplots are best reserved for distributions with a single mode.

The distribution is said to be symmetrical when the box's whiskers are roughly the same on both sides and the median is in the centre of the box. The distribution is positively skewed if the whisker is shorter on the lower end of the box and the median is closer to the bottom of the box (skewed right).

Due to the fact that they obscure bimodality or any multimodality, boxplots are best reserved for distributions with a single mode.

There is just one peak in a unimodal distribution, two peaks in a bimodal distribution, and three or more peaks in a multimodal distribution. If the data is skewed or symmetric, such information can also be used to characterise the histogram's structure.

Therefore, the correct answer is option b) Unimodal.

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The required correct option for the given question is uni-modal.

The distribution is said to be symmetrical when the box's whiskers are roughly the same on both sides and the median is in the center of the box. The distribution is positively skewed if the whisker is shorter on the lower end of the box and the median is closer to the bottom of the box (skewed right).

Due to the fact that they obscure bi-modality or any multi-modality, box-plots are best reserved for distributions with a single mode.

There is just one peak in a uni-modal distribution, two peaks in a bimodal distribution, and three or more peaks in a multi-modal distribution. If the data is skewed or symmetric, such information can also be used to characterize the histogram's structure.

Therefore, the correct answer is option b) Uni-modal.

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