In your opinion, which is the best and simplest way to factor polynomials (including quadratics)? Explain why you chose this method compared to other methods. Are there some exceptions to this, maybe a polynomial that might factor better with another method?

Answer:

x = 8

Step-by-step explanation:

Every angle in an EQUILATERAL triangle = 60°

so   9x -12 = 60

       9x = 72

         x = 8  

Step-by-step explanation:

[tex]9x - 12 = \frac{180}{3} = 60 \\ [/tex]

[tex]9x = 60 + 12[/tex]

[tex]9x = 72[/tex]

[tex]x = \frac{72}{9} \\ [/tex]

[tex]x = 8[/tex]

hence the value of x is 8...

[tex]|\Omega|=8\cdot7=56\\|A|=2\cdot1=2\\\\P(A)=\dfrac{2}{56}=\dfrac{1}{28}[/tex]

n^3 + 6

I'll make n stand for the number

Six more means adding extra 6 onto our number cubed.

So, n x n x n = n^3

(n^3 means n cubed)

Thus, answer is n^3 + 6

Hope this helps!

68% of the data lies within one standard deviation from the mean

95% of the data lies within two standard deviation from the mean

99.7% of the data lies within three standard deviation from the mean

The empirical rule states that for a normal distribution, 68% of the data lies within one standard deviation from the mean, 95% of the data lies within two standard deviation from the mean and 99.7% of the data lies within three standard deviation from the mean

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Answer:

66.4 in^2

Step-by-step explanation:

Surface area is defined as the area around the surface of a 3-dimensional solid. The shape we are given here is a triangular prism with a square base. This means it contains one square and 4 triangles on the surface. To find the surface area, we just need to find the areas of all 5 surface shapes and add them up. We have been given that the square has a side length of 4 inches, meaning the area is 4^2 or 16. The area of a triangle is (1/2)base*height. The base length is 4 inches and the height is 6.3, and (1/2)*4*6.3 is 12.6. Note that, since there are four triangles, we have to multiply this value by 4 (12.6*4 = 50.4). Now we have the area of the square and the area of all the triangles put together, so we can just add them up:

16 + 50.4 = 66.4

The solution of the linear equation is a = 11/4.

Here we have the linear equation:

9 = 4a - 2

We want to solve this for a, so we need to isolate a on one side of the equation.

First, we can add 2 on both sides to get:

9 + 2 = 4a

11 = 4a

Now we can divide both sides by 4 to get:

11/4 = a

The solution of the linear equation is a = 11/4.

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By combining the equations we can found that the number of impulse clothing and Opal essence stores by equations be C (3x+5)/2 where x is the number of years after the brand's founding.

Given The equation showing number of impulse clothing stores is C=2x. The equation showing number of clothing stores be C=x+5.

We have to first plot both the equations on the graph.

For plotting we need points which can be calculated as

C=2x

when x=1 ,C or y=2

when x=3 , C or y=6

C=x+5

when x=0 ,C or y=5

when x=1 ,C or y=6

By combining both equations we get

C=(3x+5)/2

Plot this also and finding points

when x=0  , C=5/2

when x=1 , C=4

Hence the combination of both statements which shows the total stores owned is C=(3x+5)/2

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Answer:

So, after

3

years, Impulse Clothing and Opal Essence will own the same number of clothing stores.

The total number of stores during that year will be 8.

Answer:

1960

Step-by-step explanation:

1960

times 56 times 7 time 5 = 1960

The measure of the ∠Q = 41°

By law of cosines:

a law in trigonometry: the square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.

Which can we stated as:

[tex]{q}^2 = {p}^2 + {r}^2 - 2prcos(Q)\\{4}^2 = {6}^2 + {5}^2 - 2*6*5*cos(Q)\\\\[/tex]

solving equation using normal algebra:

60cos(Q) = 36 + 25 - 16

60 cos(Q) = 45

cos(Q) = 45/60

cos(Q) = 3/4

[tex]Q = {cos}^{-1} (\frac{3}{4})\\[/tex]

Thus, Q = 41°

Hence, the measure of the smallest angle in a triangle whose sides have lengths 4, 5, and 6. ∠Q is 41°.

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On the given graph, we can see that we have:

The correct option would be a in both cases.

We want to study the asymptotes of the graph

If we look at the graph, we can see that the horizontal asymptote (denoted by the horizontal dashed line) is at y = 3.

the graph has a horizontal asymptote (or two actually) at y = 3.

For the vertical asymptote we just look at the vertical dashed line, it is at x = -2

Notice that none of these coincides with the options, so the only options that can be correct (depending on the graph of g(x), which is not shown) are option "a" in both cases.

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Answer:

1/6

Explanation:

$36 in 1:5

so, the total amount of shares is 6 (1+5)

36 / 6 = 6

$6 per share

shared in the ratio of 1:5

5 x 6 = 30

1:5

M:A

$6:$30

Madison gets $6. Or, 6/36 of the total (which, simplified, is 1/6)

Hope this makes sense!

The weight of James cake in ounces is 52 ounces and the Pint of water dispensed in 20 seconds is 24 pints

1 pound = 16 ounces

Number of ounces the cake weigh = 3 1/4 pounds × 16 ounces

= 13/4 × 16

= (208) / 4

= 52 ounces

1 gallon = 4 quarts

0.15 gallon = 0.6 quarts

1 quart = 2 pints

0.6 quart = 1.2 pints

Pint of water dispensed in 20 seconds = 1.2 × 20

= 24 pints of water

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Applying the triangle inequality theorem, the best representation for the third side is: A. 2 < s < 18.

According to the triangle inequality theorem, the sum of any two sides of a given triangle must be greater than the length of the measure of the third side of the triangle.

Thus, given an acute triangle has sides, 8 cm and 10 cm, applying the triangle inequality theorem, the range of sides would be calculated as shown below:

10 - 8 < s > 8 + 10

2 < s > 18

The range of values for the third side is: A. 2 < s < 18.

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Answer: A. 2 < s < 18.

Step-by-step explanation:

Applying the triangle inequality theorem, the best representation for the third side is: A. 2 < s < 18.

Answer:

2x+7

Step-by-step explanation:

To Simplify an Expression , we combine Like-Terms

So for our Question , we have Terms with x and Constant Term

Combine Terms with x : 5x-2x-x=2x

Constant Term : 7

Then 5x-2x+7-x = 2x+7

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation: }[/tex]

[tex]\mathbf{5x - 2x + 7 - x = }[/tex] ________[tex]\mathbf{\ x \ + }[/tex]________

[tex]\huge\textbf{Simplify the left side of the equation, to}\\\huge\textbf{get the result of the right side of the}\\\huge\textbf{equation.}[/tex]

[tex]\huge\textbf{Simplifying the LEFT side:}[/tex]

[tex]\mathbf{5x - 2x + 7 - x}[/tex]

[tex]\mathbf{= 5x - 2x + 7 - 1x}[/tex]

[tex]\huge\textbf{Combine the like terms:}[/tex]

[tex]\mathbf{= (5x - 2x - 1x) + (7)}[/tex]

[tex]\mathbf{= 5x - 2x - 1x + 7}[/tex]

[tex]\mathbf{= 3x - 1x + 7}[/tex]

[tex]\mathbf{= 2x + 7}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{2\mathsf{x} + 7}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Steve is 1.2 times faster than Paul.

The quantitative relationship between two values indicating how frequently one value is contained within the other.

For example: Speed = Distance / Time

Total distance covered by both Steve and Paul = 100m

Total time taken by Steve = 10s

Steve's speed = 100 / 10 = 10m/s

Total time taken by Paul = 12s

Paul's speed = 100 / 12 = 8.33m/s

Ratio of Steve's speed to Paul's speed = 10 / 8.33 = 1.2

Hence we can say that Steve is 1.2 times faster than Paul.

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A radius and diameter are parts of a circle. Thus the reasons required in the question are given as;

i. A tangent is always perpendicular to the radius of a circle because they are always at a right angle.

ii. A line that is drawn from the end of a diameter of a circle to its circumference form a right angle because they are always perpendicular.

A circle is a figure that is bounded by a curved line which is called its circumference. Some of its parts are radius, diameter, chord, sector, etc.

Thus the reasons required in the question are given as;

i. A tangent is always perpendicular to the radius of a circle because they are always at a right angle.

ii. A line that is drawn from the end of a diameter of a circle to its circumference form a right angle because they are always perpendicular.

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Answer:

Eli is incorrect. He added the exponents even though the bases are not the same.

Step-by-step explanation:

6^5 * 5^-3 = 6^2

5^-3 = 1/5^3 = 1/125

6^5 = 7776

7776*1/125 = 7776/125 = 62.2 approximately

Answer:

Eli is incorrect. He added the exponents even though the bases are not the same.

Step-by-step explanation:

Edge

The age that has the maximum number of arrest is 25 years

The equation of the function is given as:

[tex]f\left(x\right)\ =\ \frac{27725\left(x\ -\ 14\right)}{x^{2\ }+\ 9}-5x[/tex]

See attachment for the graph of the function.

The end behavior of the graph is

[tex]\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:-\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty \:[/tex]

This means that:

As the age of the driver increases, arrested drivers decreases and as the age of the driver decreases, arrested drivers increases

From the graph, the maximum is:

Maximum = (25.388, 356.166)

Remove the y values

Maximum = 25.388

Approximate

Maximum = 25

Hence, the age that has the maximum arrest is 25

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Stratified sampling is used by Made Eyewear

Stratified sampling is is where we divide the population into groups by some characteristic such as age or occupation or gender. Then make sure our survey includes people from each group in proportion to how many there are in the whole population.

Example of this sampling is A stratified sample is one that ensures that subgroups (strata) of a given population are each adequately represented within the whole sample population of a research study. For example, one might divide a sample of adults into subgroups by age and use of eyeglasses, like 18–29, 30–39, 40–49, 50–59, and 60 and above

So, Stratified sampling is used by Made Eyewear

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The standard deviation is a measure of dispersion that is used in constructing confidence intervals for the mean and in evaluating research hypotheses.

In statistics, the same old deviation is a degree of the amount of variation or dispersion of a hard and fast of values. A low well-known deviation suggests that the values tend to be close to the suggested of the set, while an excessive widespread deviation shows that the values are spread out over a much broader range.

It tells you, in common, how some distance every rating lies from the suggestion. In everyday distributions, a high well-known deviation approach that values are typically far from the implied, while a low popular deviation suggests that values are clustered close to the mean.

Fashionable deviation tells you ways to unfold out the statistics is. It is a degree of the way some distance each location cost is from the suggest. In any distribution, about ninety-five% of values may be inside 2 preferred deviations of the suggested.

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Answer:

x = - 3

Step-by-step explanation:

A vertical line parallel to the y- axis has equation

x = c

where c is the value of the x- coordinates the line passes through

the line passes through (- 3, 0 ) and (- 3, 3 ) with x- coordinates - 3 , then

x = - 3 ← equation of vertical line

Answer: 65

Step-by-step explanation:

By the geometric mean theorem, the length of the altitude to the hypotenuse has length [tex]\sqrt{25 \cdot 144}=60[/tex]

So, by the Pythagorean theorem,

[tex]x=\sqrt{60^2 + 25^2}=65[/tex]

The polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4

Given the polynomial function below

F(x)=x³-x² + 4x-4

Group

F(x)=(x³-x²) + (4x-4)

f(x) = x²(x-1)+4(x-1)

f(x) = (x²+4)(x-1)

If f(x) = 0

x²+4 = 0 and x -1. = 0

x² = -4 and x = 1

x = ±2i and -1

Hence polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4

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The root of the polynomial equation x (x-2) (x + 3) = 18 is x = 3.

Concept: An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

Given:

x (x-2) (x + 3) = 18

Divide both sides of the equation by x:

x (x-2) (x + 3) / x = 18 / x

(x-2) (x) + 3) = 18 / x

You can use the following simultaneous equations.

(1) y = (x-2) (x + 3)

(2) y = 18 / x

Using a graphing calculator, we get:

x = 3, y = 6 → point = (x, y) = (3,6)

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Step-by-step explanation:

First, there is a vertical stretch by a factor of 3,

Next, there is a horizontal compression by a factor of 2.

Reflect about the y axis.

After, shift to the right 3 units horizontally,

Finally , shift upwards 7 units

Answer:

22.470

Step-by-step explanation:

In this example you have to use the trigonometric function sine which is defined as [tex]sin(\theta) = \frac{opposite}{hypotenuse}[/tex]

Plug in known values:

[tex]sin(64) = \frac{x}{25}[/tex]

Multiply both sides by 25

[tex]sin(64) * 25 = x[/tex]

Approximate sin(64) using a calculator:

[tex]0.89879 * 25 = x[/tex]

Simplify

[tex]22.470 \approx x[/tex]

Answer:20ft

Step-by-step explanation:Because you add the numbers up 9 and 6 you get 15 so 300/15=20

20x15 equals 300 so it goes both ways

Answer:

The answers are:
(i) 108.33%
(ii) 93.75%

Step-by-step explanation:

The original area and perimeter are as follow:

Perimeter = 2l + 2w
                = 2(2p) + 2(p)
                = 4p + 2p
                = 6p cm

Area = l * w
        = 2p * p
        = 2p^2 cm^2

A 25% increase of the length is = 2p * (1 + 25%) = 2p * 1.25 = 2.5p cm

A 25% decrease of the breadth is = p * (1 - 25%) = p * 0.75 = 0.75p cm

Perimeter = 2l + 2w
                 = 2(2.5p) + 2(0.75p)
                 = 5p + 1.5p
                 = 6.5p cm

Area = l * w
        = 2.5p * 0.75p
        = 1.875p^2 cm^2

Now that we have found the changes, let's calculate the percentage changes

Percentage change of perimeter:

x% * 6p = 6.5p
x/100 * 6p = 6.5p
x * 6p = 6.5p * 100
x = 650p/6p
x = 108.33

Percentage change of area:

x% * 2p^2 cm^2 = 1.875p^2 cm^2
x/100 * 2p^2 cm^2 = 1.875p^2 cm^2
x * 2p^2 cm^2 = 1.875p^2 cm^2 * 100
x = 187.5p^2 cm^2 / 2p^2 cm^2
x = 93.75

Answer:

i = 8 1/3%

ii = -6 1/4%

Step-by-step explanation:

The previous answer is wrong this is the correct one:

Because they are using the same variable P let's assume P = 10
Length increase 25% = 10 + (10 x 25%) = 10 + 2,5 = 12,5 cm
Breath decreased 25% = 10 - (10 x 25%) = 10 - 2,5 = 7,5 cm

i. Original Perimeter : 2(L) + 2(B) = 2(2p) + 2(p) = 2(2x10) + 2(10) = 2(20) + 2(10) = 60cm
Modified Perimeter : 2(L) + 2(B) = 2(2p) + 2(p) = 2(2x12,5) + 2(7,5) = 2(25) + 2(7,5) = 65cm

The percentage change is

65-60/60 x 100

= 5/60 x 100

= 500/60

= 8 2/6% simplified 8 1/3%

ii. Original Area: L x B = 2p x p = 2(10) x 10 = 20 x 10 = 200 cm^2
Modified Area: L x B = 2p x p = 2(12,5) x 7,5 = 25 x 7,5 = 187,5 cm^2

The percentage change is

187,5-200/200x 100

= - 12,5/200 x 100

= - 1250/200 = - 6 1/4 %

That is the Correct answer. Hope that help

[tex]\huge\boxed{25\%}[/tex]

We need to find the number of students that study art first. This includes the students who study both art and biology (4) and the students who study art but not biology.

We know the counts for every category except for "art but not biology", so we can use subtraction.

[tex]26-4-5-5=12[/tex]

This means that 12 students study art but not biology, which combines with the 4 who study both subjects to give us 16 art-studying students.

Now, we just need to find the probability that a student studies both subjects (4 students) given that they study art (16 students).

This is simple division.

[tex]4/16=0.25=25\%[/tex]