One Step Trinomial, Two Step Factoring

Factor:

x^2 - 12x + 35

A) A polynomial function in factored form modeling the volume V of the box is; V(x) = x²(20 - x)

B) The maximum possible volume of the box is; 1185.19 in³

C) The way the maximum possible volume is found is by finding the derivative and equation to zero. Thereafter, we substitute the value into the first equation.

The formula for volume of a rectangular box is;

V =L * W * Height

Where;

L is length

W is width

H is height

We are given;

Height; h

Square base and so;

L = W = x

Thus, the volume is;

V = (x)(x)(h)

The combined length of a side of the square base and the height is 20 in. Thus; x + h = 20

h = 20 - x

Thus, volume is;

V(x) = x²(20 - x)

2) The expanded form of the volume is; V(x) = 20x² - x³

dV/dx = 40x - 3x²

The function has maxima and minima when dV/dx = 0. Thus;

40x - 3x² = 0

Solving for x gives;

x = 0 or 40/3

Maximum possible volume is;

V(40/3) = 20(40/3)² - (40/3)³

V(40/3) = 1185.19 in³

c) The way the maximum possible volume is found is by finding the derivative and equation to zero. Thereafter, we substitute the value into the first equation.

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Answer:

1.a)  Broken line.

1.b)  False.

2.a)  Solid line.

2.b)  True.

Step-by-step explanation:

When graphing inequalities:

Given inequality:

[tex]y > -2x+4[/tex]

a)  As the "<" sign has been used, the line will be a broken line.

b)  Substitute (0, 0) into the inequality:

[tex]\begin{aligned}\textsf{When $x=0$ and $y=0$}: \quad 0 & > -2(0)+4\\0 & > 0+4\\0 & > 4\end{aligned}[/tex]

As zero is not greater than 4, the solution at (0, 0) is false.

Graphing the inequality

Change the inequality sign to an equals sign, then substitute two values of x into the equation and solve for y to find two points on the line:

[tex]\begin{aligned}x=-2: \quad y & =-2(-2)+4\\y &=4+4\\y&=8\end{aligned}[/tex]

[tex]\begin{aligned}x=4: \quad y & =-2(4)+4\\y &=-8+4\\y&=-4\end{aligned}[/tex]

Plot the points (-2, 8) and (4, -4).

Draw a broken straight line through the points.

Shade above the line.

Given inequality:

[tex]3x+2y \leq 6[/tex]

a)  As the "≤" sign has been used, the line will be a solid line.

b)  Substitute (0, 0) into the inequality:

[tex]\begin{aligned}\textsf{When $x=0$ and $y=0$}: \quad 3(0)+2(0) & \leq 6\\0+0 & \leq 6\\0 & \leq 6\end{aligned}[/tex]

As zero is less than 6, the solution at (0, 0) is true.

Graphing the inequality

Change the inequality sign to an equals sign, then substitute two values of x into the equation and solve for y to find two points on the line:

[tex]\begin{aligned}x=-2: \quad 3(-2)+2y & =6\\-6+2y&=6\\2y&=12\\y&=6\end{aligned}[/tex]

[tex]\begin{aligned}x=4: \quad 3(4)+2y & =6\\12+2y&=6\\2y&=-6\\y&=-3\end{aligned}[/tex]

Plot the points (-2, 6) and (4, -3).

Draw a solid straight line through the points.

Shade below the line.

Answer:

  (a)  y -5= -2(x -2)

Step-by-step explanation:

You want the equation of the line perpendicular to y = (1/2)x - 2 that contains the point (2, 5).

Perpendicular lines have slopes that are opposite reciprocals of one another. The slope of the given line is the x-coefficient: 1/2. Its opposite reciprocal is ...

  -1/(1/2) = -2

The point-slope equation of a line is ...

  y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)

You want a line with slope -2 through point (2, 5), so its equation is ...

  y -5 = -2(x -2)

The regression equation for a scatterplot with these points  is y=13.4x-11.1

An equation is an expression that shows the relationship between two or more numbers and variables.

We have given the point (4, 35), (6.5, 92), (2, 10), (5, 50), (6, 85), (10, 110)

First we need to find the slope.

The formula to calculate the slope between two points is;

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Now substitute the values

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 92 - 35 ) / ( 6.5 - 4)

m = 13.4

Find the equation of the line in slope intercept form;

y = mx + c

we have

y = 13.4x + c

Then 35 = 13.4(4) + c

c = -11.1

therefore

y = 13.4x-11.1

The regression equation for a scatterplot with these points  is y=13.4x-11.1

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4.8 inches is the height of a trapezoid with an area of 24 square inches if the two bases measure 4 inches and 6 inches.

Using the formula for the area of a trapezoid, which is:

Area = (1/2)(b1 + b2)h

In this formula, b1 and b2 are the lengths of the two bases of the trapezoid, and h is the height of the trapezoid. In our problem, we know that the area is 24 square inches, and the lengths of the two bases are 4 inches and 6 inches. We want to solve for h, the height of the trapezoid.

Plugging in the known values, we get:

24 = (1/2)(4 + 6)h

24 = (1/2)(10)h

24 = 5h

4.8 = h

Therefore, the height of the trapezoid is 4.8 inches.

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a) The pie chart that represents this information is given at the end of the answer.

b) The amount that represents his savings is of: gh¢ 720.

A pie chart is a graph in which the values of each measure in the data-set assume a percentage equivalent to the percentage of these values in the circular graph.

In the context of this problem, these percentages are given as follows, as stated from the text:

All these percentages are inserted on the image given at the end of the answer, which represents the pie chart.

The percentage of savings is of:

12%.

Hence the amount of savings is given by the multiplication of 0.12 by 6,000. as follows:

0.12 x 6000 = gh¢ 720.

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Answer: SAS (Side angle side)

Rama had used 0.10 as an approximation for the length of each bead, the row would have been too short and would have dropped outside of the allowed length range.

Rama is stringing beads whose lengths are each 0.19 inches.

A bead's length is 0.19 inches, which is approximately 0.2 inches. If the row has 9 beads, we must double the length of each bead by the number of beads. Therefore

Because the beads are approximately 0.20 inches in length, the length of a row of 9 beads is

will be approximately 9 × 0.20 = 1.80 inches.

Thus, if she had used 0.10 as an approximation for the length of each bead, the row would have been too short and would have dropped outside of the allowed length range.

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The intermediate form for the limit , [tex]\lim_{x \to \infty}[/tex] e²ˣ/x⁵ is  ∞/∞

Given,

The limit ; [tex]\lim_{x \to \infty} \frac{e^{2x} }{x^{5} }[/tex]

L'Hospital's rule;

A general technique for assessing indeterminate forms like 0/0 or / is the L'Hospital rule. L'Hospital's rule is applied to calculate the limits of indeterminate forms for calculus derivatives. It is possible to use the L Hospital rule many times.

By using L'Hospital's rule the intermediate form is;

[tex]\lim_{x \to \infty} \frac{e^{2x} }{x^{5} }[/tex] = [tex]\lim_{x \to \infty}[/tex] e²∞/ ∞⁵

 [tex]\lim_{x \to \infty} \frac{e^{2x} }{x^{5} }[/tex] =  [tex]\lim_{x \to \infty}[/tex] e∞/∞

[tex]\lim_{x \to \infty}[/tex] e²ˣ/x⁵ = [tex]\lim_{x \to \infty}[/tex] 2e²ˣ / ∞

[tex]\lim_{x \to \infty}[/tex] e²ˣ/x⁵ = [tex]\lim_{x \to \infty}[/tex] 2e∞/∞ = ∞/∞

That is,

The intermediate form for the limit , [tex]\lim_{x \to \infty}[/tex] e²ˣ/x⁵ is  ∞/∞

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a) Karmila have 5 pieces of ribbon each 3/4 m long

b) the length of ribbon left over​ =   1 m

A roll of ribbon was 8m long.

Karmila cut 6 pieces of ribbon each length 2/3

Total length of 6 pieces of ribbon having length 2/3 would be,

6 * (2/3) = 4 m

This means, after cutting 6 pieces of ribbon, the length of the remaining ribbon = 4 m

Then we need to cut the remaining ribbon into some pieces each of length 3/4

Let t be the number of pieces.

So, we get an equation

(3/4) * t = 4

t = 4 * (4/3)

t = 16/3

t = 5 1/3

t ≈ 5

This means, Karmila have 5 pieces of ribbon each 3/4 m long and the length of ribbon left over​ =  1m

Therefore, a) Karmila have 5 pieces of ribbon each 3/4 m long

b) the length of ribbon left over​ =   1 m

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The amount that we have to increase the price to maintain your current dollar profit margin is  $2.04 , the correct option is (a) .

In the question ,

it is given that ,

there is a trucking strike that causes the increase in the price ,

the percent increase in the price of the ingredient = 17% .

the current cost of the package = $12 ,

the increases in price of the ingredient = 17% of 12

= 0.17 × 12            ......because 17% = 0.17

= 2.04

the increase is $2.04 .

Therefore , The amount that we have to increase the price to maintain your current dollar profit margin is  $2.04 , the correct option is (a) .

The given question is incomplete , the complete question is

There was a trucking strike that caused a prime ingredient in your menu item to shoot up 17%. You were paying $12 per package. How much will you have to increase the price of the menu item if you wish to maintain your current dollar profit margin on the menu item ?

(a) $ 2.04

(b) $6.37

(c) $7.15

(d) $9.44

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Answer: 1,500 people died and there names were. John Jacob Astor, Archibald Gracie IV, W. T. Stead, Noël Leslie, Thomas Andrews, Margaret Brown and John Thayer

Step-by-step explanation:

The Titanic — billed as an unsinkable ship — hit an iceberg and sank on April 15, 1912. Over 1,500 people died in the maritime disaster, while 705 individuals survived.

Answer:

Step-by-step explanation:

A septagon (7 sided polygon) adds up to 900 degrees. When adding up the given interior angle measures, you get 771. Subtract 771 from 900 and you get the answer of 129.

Answer:

x= 129°

Step-by-step explanation:

Interior angles: 180(n-2) where n=sides

=180(7-2)

=180(5)

=900°

130°+118°+135°+128°+126°+134°+x=900

771+x=900

x=900-771

x= 129°

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The front and side elevation diagram along with the diagram given in question is attached with the answer.

What is elevation?

A location's elevation can be defined as its height above or below a fixed reference point, most frequently a reference geoid, a mathematical representation of the Earth's sea level as an equipotential gravitational surface (see Geodetic datum Vertical datum). In most cases, elevation is used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying airplanes or orbiting satellites, and depth is used to describe locations below the surface.

Drawing the required Elevation Using the Construction Method

The scale is 2 squares to 1 meter.

16 squares total make up the plane on which the front elevation is to be drawn.

Front elevation: There are 4 squares across the front elevation's width.

4 + 1 squares make up the portion of the front closest to the observer.

The slant surface of the has a square count of 3 by 4 squares.

Side elevation: By following the same format as before, the side elevation is provided as follows;

The lower side of the side elevation's breadth is 2 meters wide, or 4 squares.

The side elevation's height is 2 meters, or 4 squares.

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The amount that the painter will charge is $519.75.

From the information illustrated, the painter can paint 175 square feet per hour and she charges $0.54 per square foot and then paints for 5.5 hours.

The amount that she will charge will be:

= Number of square foot × Amount charged × Number of hours

= 175 × $0.54 × 5.5

= $519.75

The amount is $519.75.

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In the provided problem of collection survay data the researchers use the Cluster Analysis data analysis techniques.

Cluster analysis is a statistical technique for processing data. It works by organizing items into groups or clusters based on how closely related they are.

Cluster analysis, similar to reduced-space analysis (factor analysis), deals with data matrices in which the variables have not been previously split into reference and prediction subsets. The goal of cluster analysis is to find similar groups of subjects. Here, “similarity” between each pair of subjects means a global measure of the entire set of traits.

The most common use of cluster analysis is classification. Subjects are divided into groups such that each subject is more similar to other subjects within that group than subjects outside the group.

Cluster analysis used in following areas

In the context of market research, this can be used to identify categories such as age ranges, income ranges, urban, rural, or suburban locations.

Marketing can use cluster analysis for audience segmentation to target different customer groups with the most relevant messages.

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When You fill up your car with 15 gallons of gasoline. then it weighs 90 pounds of weight.

the weight of an object is the force acting on the object due to gravity.

Given

A car with 15 gallons of gasoline is filled.

We need to find the weight of the gasoline

We know that 1 gallons of gasoline is 6 pounds

So now for 15 gallons will be fifteen times of 6 pounds

15×6

90 pounds

90 pounds is the weight of the gasoline.

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Answer:

100 square meters

Step-by-step explanation:

[tex] {x}^{2} + 6x + 8x = 240[/tex]

[tex] {x}^{2} + 14x = 240[/tex]

[tex] {x}^{2} + 14x - 240 = 0[/tex]

[tex](x - 10)(x + 24) = 0[/tex]

[tex]x = 10[/tex]

x = -24 will not work (it is extraneous).

[tex] {x}^{2} = 100[/tex]

So the area of the square region is 100 square meters.

The resulting dilation of the figure with the scale factor of 3/4 is given by the graph at the end of the answer.

Dilation on a image

Dilation in a image means multiply the coordinates of each vertex of the figure by the scale factors.

Given,

Here we have the triangle in the given figure.

Now, we have to find the dilation of the figure with the scale factor of 3/4.

Here from the original figure graph, the vertices are obtained as follows:

S(-8,-4), T(4, -4) and U(4,8)

Now we have to use the dilation scale factor of 3/4,

Which means that the coordinates are multiplied by 3/4,

Then the new coordinates of the resulting image are given as follows:

S(-8, -4) => ((-8 x 3/4), (-4,3/4)) => S'(-6, -3)

T(4, -4) => ((4 x 3/4), (-4,3/4)) => T'(3, -3)

U(8, 4) => ((8 x 3/4), (4,3/4)) => U'(6, 3)

Now, we have to plot these new coordinates on the graph, then we get,

the graph like the following.

Here the dilated figure is given by the graph at the end of the answer, having the same format as the original figure, just with smaller side lengths due to the dilation with a scale factor less than 1.

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Answer:

Step-by-step explanation:

The of miles the group walked in 3 weeks is 44 miles

What is proportion?

Proportion can be defined as the mathematical comparison of two elements or numbers.

From the information given, we have that;

• in 1 week people walked 62 miles

• in the second week reduced to 58 miles

• in week 3 they walked 14 fewer miles during week 2

to determine the many miles did the group walk in 3 weeks, we can reduce

58 miles - 14 miles less during week 2

=44 miles.

so, number of miles the group walked in 3 weeks is 44 miles.

the sampling distribution of the sample means is 0.03

According to the central limit theorem (n>= 30), the sampling distribution of the sample mean is approximately normal with a mean of 4.9 and a standard deviation of 3.

So:

x = standard dev/sample size

= 3 / 100

= 0.03; it is normal due to its large sample size.

Distribution is the technique of promoting and handing over services and products to clients. The term is related to marketing channels that are used to reach customers in special methods and exceptional areas. distribution characteristic, a mathematical expression that describes the chance that a machine will take on a particular value or set of values. The traditional examples are related to games of hazard.

distributing objects is an act of spreading them out similarly. Algebraic distribution method to multiply every one of the phrases inside the parentheses by way of another time period this is outside the parentheses. To distribute a term over several different terms, you multiply each of the alternative phrases by the primary term. the statistical distribution suggests which values are common and uncommon. there are numerous styles of statistical distributions, along with the bell-shaped everyday distribution.

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From the given statements it was found that statement p is false. So, -3x + 8x - 5x is equal to 0 not x.

In p statement,

-3x + 8x - 5x = x is given.

Let us check it.

-3x + 8x - 5x = 8x - 8x = 0

So, we can say statement p is false.

In q statement,

(3x)(5y) = 15xy is given.

Let us check it.

(3x)(5y) = 15xy

So, we can say statement is q is true.

Therefore, from the given statements it was found that statement p is false. So, -3x + 8x - 5x is equal to 0 not x.

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The number of days that it take Olivia to collect at least 54 1/3 cups of sugar is 12 days.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤.

In this case, Olivia needs to gather at least 54 1/3 cups of sugar.

The expression will be illustrated thus:

15 2/3 + 3 1/3d ≥ 54 1/3

Collect like terms

3 1/3d ≥ 54 1/3 - 15 2/3

3 1/3d ≥ 38 2/3

Divide

d ≥ 38 2/3 ÷ 3 1/3

d ≥ (116 / 3 × 3/10)

d ≥ 11 3/5

She needs 12 days.

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Exponential model representing the amount of Iodine-125 remaining in the tumor after t days is f(t) = 0.5 *[tex]e^{-0.0115t}[/tex] and number grams of Iodine-125 after 60 days is 0.2507 grams

Given:

A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day.

The formula for exponential decay is f(t)=a*e^kt where a is the original amount of the substance, k is the decay rate and t is the time elapsed. You are given the decay rate of 1.15% or -0.0115. For this problem t is left as is since we are creating a function of time.

f(t) = 0.5 *[tex]e^{-0.0115t}[/tex]

After 60 days

= 0.5 * [tex]e^{-0.0115*60}[/tex]

= 0.5*e^-0.69

= 0.5*0.50157

f(t) = 0.2507 grams

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Answer:

x=-20

y=10

z=-19

Step-by-step explanation:

It is given that the shape is a rhombus, which means all four sides are equal. This means we can set up the equations:

5y-4=46   --> 5y=50 --> y=10

-2x+6=46 --> -2x=40 --> x=-20

-2z+8=46 --> -2z=38 --> z=-19

The time taken to knit the scarf form start to finish is 10 hours .

In the question ,

it is given that ,

the total length of the scarf = 5 foot

After 4 hour, the volunteer still has to knit 3 feet, which means

time taken by volunteer to knit 2 feet scarf = 4 hours

So , the time taken by volunteer to knit 1 feet scarf = 4/2 = 2 hours .

hence , the the time taken by volunteer to knit the 5 feet scarf is calculated by using the formula

= 5 × (time taken to knit 1 feet)

= 5 × (2)

= 10 hours .

Therefore , The time taken to knit the scarf form start to finish is 10 hours .

The given question is incomplete , the complete question is

A volunteer knit a 5-foot long scarf at a constant rate. After 4 hour, the volunteer still has to knit 3 feet of the scarf. How much time does it take to knit the scarf from start to finish ?

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If you pick 25 fruits at random, then 15% of the time, their mean weight will be greater than 665 grams.

In statistics, mean is the ratio of sum of all the observations and total number of observations in a data set.

How to calculate their mean weight will be greater than how many grams?
Given that from the question

Mean = 641 grams

standard deviation 24 grams

If you pick 25 fruits at random, then 15% of the time, their mean weight will be greater than how many grams?

The formula for the calculating the x value in the normal distribution is,

x = μ + zσ

The level of significance is = 15% = 0.15

Therefore,

z = (=normsinv (1 - α))

= (=normsinv (1-0.15))

= (=normsinv(0.85))
= 1.036

The critical value of z is 1.036

z = 1.036

(x - μ) / σ = 1.036

x = μ + 1.036σ

= 641 + 1.036*23

= 641 + 23.828

= 664.828

= 665grams (rounded to the nearest gram)

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As the act of Texas Code of Judicial Conduct affect judicial campaigns, the correct statement is "Option D. It doesn't have much of an effect on political activity during judicial campaigns, since judges still discuss their political ideology.".

Texas code

Texas code refers the compilation of all state agency rules in Texas. In this one, there are 17 titles in the TAC. And each title represents a subject category and related agencies are assigned to the appropriate title.

Given,

Here we need to find how does the Texas Code of Judicial Conduct affect judicial campaigns.

According to the Andrew Cohen,

The correct statement in this one is,

Option D:

It doesn't have much of an effect on political activity during judicial campaigns, since judges still discuss their political ideology.

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