Can you pease help me find all the zeroes of the polynomial function f(x)=x^3-5x^2+6x-30 using synthetic devision?
thank you!

An absolute value inequality is solved by re-writing it as compound inequality. For example.

|x+1| < 5

Since the value inside the absolute value brackets: (x+1) can be positive or negative, it is re-written as a compound inequality as the example below.

x+1 < 5

x+1 > - 5

solve for the range of values x can be

-6 < x < 4

Solving absolute value inequalities yields compound inequalities. Absolute value cases create intervals, linking the processes in algebraic solutions.

Solving absolute value inequalities and compound inequalities are related concepts in algebra, both involving multiple solutions and a range of possible values. Absolute value inequalities often result in compound inequalities due to the nature of the absolute value function.

When solving an absolute value inequality, such as [tex]\(|x - a| < b\), where \(a\)[/tex]and[tex]\(b\)[/tex] are constants, it generally leads to two separate cases: [tex]\(x - a < b\)[/tex] and [tex]\(x - a > -b\).[/tex] These cases represent the intervals where the expression inside the absolute value is less than [tex]\(b\)[/tex] and greater than its negative counterpart.

This process connects with solving compound inequalities, which involve combining two or more inequalities using logical connectors like "and" or "or." The solutions to the individual inequalities are then used to determine the overall solution to the compound inequality.

For instance, in the absolute value inequality[tex]\(|x - a| < b\)[/tex], the resulting compound inequality might be [tex]\(a - b < x < a + b\)[/tex]. This demonstrates that the solutions lie within the interval \((a - b, a + b)\), illustrating the linkage between solving absolute value inequalities and dealing with compound inequalities. Both concepts require careful consideration of multiple scenarios and the integration of solutions to find the overall solution set.

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The growth factor of g is given by [tex]A = e^{0.6t}.[/tex]

The function exhibits exponential growth.

We have,

(a)

Let's denote the growth factor as A(t), where t is the independent variable representing time.

The rate of change of g at any time t is proportional to g itself, with a constant of proportionality of 0.6.

This can be expressed as:

dA/dt = 0.6A

This is a separable differential equation, which we can solve by separating the variables and integrating them:

1/A dA = 0.6 dt

Integrating both sides,

ln|A| = 0.6t + C

Here, C is the constant of integration.

Exponentiating both sides:

[tex]|A| = e^{0.6t + C}[/tex]

Since the growth factor A is always positive, we can drop the absolute value:

[tex]A = e^{0.6t + C}[/tex]

We can do this by considering the initial condition.

Let's assume that at t = 0, the growth factor A is 1 (no growth). Substituting these values into the equation:

[tex]1 = e^{0.6(0) + C}\\1 = e^C[/tex]

Taking the natural logarithm of both sides:

[tex]ln(1) = ln{e^C}[/tex]

0 = C

So,

[tex]A = e^{0.6t}[/tex]

(b)

The function g exhibits exponential growth, as the value of g increases exponentially with time.

Thus,

The growth factor of g is given by [tex]A = e^{0.6t}.[/tex]

The function exhibits exponential growth.

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The growth factor of gg is 0.6. The function exhibits exponential growth.

(a) The growth factor of an exponential function is the base of the exponent. In this case, the growth factor is 0.6.

(b) The function gg exhibits exponential growth, meaning that as the input increases, the output increases at a proportional rate.

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Answer:

(m-n)(r-s)

Step-by-step explanation:

We will factor this by grouping.  First we rearrange the terms so the m's are together and the n's are together:

mr-ms+ns-nr

Next we group the first two and the last two:

(mr-ms)+(ns-nr)

The GCF of the first group is m; factor this out:

m(r-s)+(ns-nr)

The GCF of the second group is n; factor this out:

m(r-s)+n(s-r)

We want to have the same thing in both sets of parentheses; to do this, we will multiply the second factor by -1:

m(r-s)+-n(r-s)

Factoring out the term now in common, r-s, we have

(r-s)(m-n) = (m-n)(r-s)

The solution to the first algebraic equation is x = 7, and the solution to the second equation is x = -3. Both problems involve setting up and solving algebraic equations to find the value of the unknown number.

To solve the problems stated, we need to set up algebraic equations and solve for the unknown number x.

For the first one:

Fourteen less than five times a number is three times the number: 5x - 14 = 3x.

After simplifying, we get 2x = 14.

Divide both sides by 2 to find x = 7.

For the second one:

Twelve more than seven times a number equals the number less six: 7x + 12 = x - 6.

Rearrange to find 6x = -18.

Divide both sides by 6 to find x = -3.

We have found that the unknown number in the first equation is 7 and in the second equation, it is -3.

To solve this problem, we use the z statistic.  The z formula is:

z = (x – u) / s

where x is lakers score = 101.7, u is Celtics score = 99.2, s is standard dev = 10.5

z = (101.7 – 99.2) / 10.5 = 0.24

using the normal distribution table at z = 0.24, the P value is:

P (z = 0.24) = 0.5984 = 59.84% 

To find the proportion of games in which the Boston Celtics scored more than the Los Angeles Lakers' mean score, we need to standardize the Lakers' mean score, find the z-score, and then find the proportion from the standard normal distribution table.

To find the proportion of games in which the Boston Celtics scored more than the Los Angeles Lakers' mean score, we need to find the area under the normal distribution curve to the right of the Lakers' mean. First, we need to standardize the Lakers' mean score by finding the z-score using the formula:

z = (x - μ) / σ

where x is the mean score, μ is the mean of the Celtics' scores, and σ is the standard deviation of the Celtics' scores. Substituting the given values, we have:

z = (101.7 - 99.2) / 10.5 = 0.2381

Next, we find the proportion of scores greater than the Lakers' mean in the standard normal distribution table or using a calculator. Looking up the z-score of 0.2381 in the table, we find the proportion to be approximately 0.4069, or 40.69%.

[tex] p\%=\dfrac{p}{100}=p:100\\\\21\dfrac{1}{4}\%=\dfrac{21\cdot4+1}{4}=\dfrac{85}{4}\%=\dfrac{85}{4}:100=\dfrac{85}{4}\cdot\dfrac{1}{100}=\dfrac{85}{400}=\dfrac{85:5}{400:5}=\dfrac{17}{80} [/tex]

Answer:

the answer is 17/80 hope this helps

Answer:

288 hours.

Step-by-step explanation:

You exercise 24 hours in 1 month.

There are 12 months in one year.

24 * 12 = 288

Therefore, you exercised 288 hours in one year.

Answer:

Calculation with Distribution

24 (1+1+1+1+1+1+1+1+1+1+1+1)

24*1+24*1+24*1+24*1+24*1+24*1+24*1+24*1+24*1+24*1+24*1+24*1

24+24+24+24+24+24+24+24+24+24+24+24

288 hours

You did 288 hours of exercise.

Calculation without Distribution

24(1+1+1+1+1+1+1+1+1+1+1+1)

24(12)

288 hours

You did 288 hours of exercise.

Step-by-step explanation:

Answer-

The best-fit quadratic equation is  [tex]y=14.9786x^2+3.1057x+56.2771[/tex] and the game cost in 2010 will be $1586

Solution-

Plotting a table taking year as input variable and cost as output variable.

X= year - 2000    

Y= cost in dollar.

Quadratic equation formula,

[tex]y=ax^2+bx+c[/tex]

[tex]a=\frac{(\sum x^2y\sum xx)-(\sum xy\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex]

[tex]b=\frac{(\sum xy\sum x^2x^2)-(\sum x^2y\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex]

[tex]c=\frac{\sum y}{n}-b\frac{\sum x}{n}-a\frac{\sum x^2}{n}[/tex]

Where,

[tex]\sum xx=\sum x^2-\frac{(\sum x)^2}{n}[/tex]

[tex]\sum xy=\sum xy-\frac{\sum x\sum y}{n}[/tex]

[tex]\sum xx^2=\sum x^3-\frac{\sum x\sum x^2}{n}[/tex]

[tex]\sum x^2y=\sum x^2y-\frac{\sum x^2\sum y}{n}[/tex]

[tex]\sum x^2x^2=\sum x^4-\frac{(\sum x^2)^2}{n}[/tex]

Putting the values, we get

[tex]a=14.9786,b=3.1057,c=56.2771[/tex]

Putting these in the quadratic equation,

[tex]y=14.9786x^2+3.1057x+56.2771[/tex]

In order to  get the cost of game in 2010, we can put x=10 to get the value of y or the cost of game.

[tex]y(10)=14.9786(10)^2+3.1057(10)+56.2771=1585.1941 \approx 1586[/tex]

False, the given equation of hyperbola is vertical hyperbola.

What is hyperbola?

Hyperbola is defined as a conic section, two-branched open curve, produced by the intersection of a circular cone.

[tex]\frac{(y-2)^2}{16} -\frac{(x+1)^2}{144}=1[/tex]

Simplify each term in the equation in order to set the right side equal to 1

The standard form of an ellipse or hyperbola requires the right side of the equation be 1

This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.

[tex]\frac{(y-k)^2}{a^2} -\frac{(x-h)^2}{b^2}=1[/tex]

Match the values in this hyperbola to those of the standard form. The variable

h represents the x-offset from the origin,

k represents the y-offset from origin, a.

a=4

b=12

k=2

h=−1

c, the distance from the center to a focus  4√10

The foci is (−1,2+4√10),(−1,2−4√10)

Hence, the hyperbola is vertical.

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Answer:

PANCKACKES

Step-by-step explanation:

b. The slope is  - 400. This means that the helicopter descends 400 ft each minute. The slope is 400. This means that the helicopter ascends 400 ft each minute.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

This situation is mathematically represented as a line and slope.

Points  (0, 10,000) and (15, 4000).

We know slope(m) = (y₂ - y₁)/(x₂ - x₁).

Slope(m) = (4000 - 10000)/(15 - 0).

Slope(m) = - 6000/15.

Slope(m) = - 400.

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