An equivalent expression to (5x - 3x^2) (5x - 2) • ( 10x + 7x^2) in standard form

The solutions to the inequality -5 < 9 - 6x is x ≤ 7/3.

What is inequality?

In mathematics, the term 'inequality' is defined as a statement or equation with an ordered relationship like greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now the given inequality is,

-5 < 9- 6x

Adding 5 both the side we get,

5 - 5 < 9 - 6x + 5

⇒ 0 < 14 - 6x

⇒ 14 - 6x > 0

Dividing both the side by 6 we get,

⇒ 14 < 6x

⇒ x > 14/6 = 7/3

or, x ≤ 7/3

this is the required solution of the given inequality.

Thus, the solutions to the inequality -5 < 9 - 6x is x ≤ 7/3.

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Answer:

The answer is B

Step-by-step explanation:

This is because the smaller triangle has the same angles and scaled side lengths as the bigger one.

Answer:

60

Step-by-step explanation:

4 times 3 = 12     12 times 5 =60

Answer:

47cm²

Step-by-step explanation:

Answer:

log 8

Step-by-step explanation:

all the x number smaller than 1

Explanation

the symbol

represents an inequality, it means smaller than , this is Strict inequalities without the “or equal to” component are indicated with an open dot on the number line and a parenthesis using interval notation.so in thsi case 1 is not part of the solution set

so, as 1 is not part of the solution this is a open interval

all the x number smaller than 1

I hope this helps you

Answer:

4/100 = x/50

Step-by-step explanation:

inches on top miles on bottom

Answer:

7

Step-by-step explanation:

Answer:

The way you can find the cost of just one loaf of bread is by taking the amount charged and then dividing it by 4 and then you would get your answer of  $5.93

Step-by-step explanation:

Let me know if this is correct or not ok.

Step-by-step explanation:

the slope = (8-5)/(-6+2) = 3/-4 = -¾

Answer:

10÷250

= 0.04

Step-by-step explanation:

that's the answers

The differential equation "+ 4y + y = 0" actually corresponds to the simple harmonic oscillator equation, which has the form:

y'' + w^2 y = 0

where w is the angular frequency of the oscillator.

To find the first three nonzero terms of the series solution, we assume a power series solution of the form:

y(x) = Σ a_n x^n

where a_n are undetermined coefficients.

Substituting this into the differential equation and equating the coefficients of like powers of x, we get:

a_0 w^2 = 0

2a_2 + a_0 w^2 = 0

3a_3 + 2a_1 w^2 = 0

From the first equation, we get a_0 = 0 (since w is nonzero).

Substituting a_0=0 into the second equation, we get:

a_2 = 0

Substituting a_0=0 and a_2=0 into the third equation, we get:

a_3 = 0

Therefore, the first three nonzero terms of the series solution are:

y(x) = a_1 x + a_4 x^4 + a_5 x^5 + ...

where a_1 is an arbitrary constant and all coefficients a_n with n <= 3 are zero. Note that in this case, the series solution actually terminates since there are no nonzero terms beyond a_1x.

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The value illustrated by the weight of gravel in a pile is 120 lb. is a continuous data set.

It should be noted that a continuous data set is the quantitative data set that represents a scale of measurement which can consist of numbers other than whole numbers, like decimals and fractions.

It should be noted that continuous data sets would consist of values like height, weight, length, temperature, etc.

Therefore, the value illustrated by the weight of gravel in a pile is 120 lb. is a continuous data set.

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y = -1/3x + 1

y = -2x - 3

We can compare the equations to the graphs and see which graph represents the intersection point of the two equations.

The first equation, y = -1/3x + 1, has a negative slope (-1/3) and a y-intercept of 1.

The second equation, y = -2x - 3, also has a negative slope (-2) and a y-intercept of -3.

Based on the slopes and y-intercepts, we can identify the correct graph by finding the point where the two lines intersect.

Unfortunately, since the graphs are not provided, I am unable to determine which specific graph shows the solution to the system of linear equations. I recommend referring to the graph representation of the equations and identifying the intersection point to determine the correct graph.

The solution of each of the equations for the variable indicated in each case are as follows;

It follows from the task content that the equations given are to be solved for the variables indicated.

The equations can therefore be solved as follows;

11. u = vw + z

Isolate vw so that we have;

vw = u -z; Divide both sides by w;

v = (u - z)/w.

12. x = b - cd

Isolate cd so that we have;

cd = b -x; Divide both sides by d;

c = (b - x)/d.

13. fg - 9h = 10j

Isolate fg so that we have;

fg = 10j + 9h; Divide both sides by f;

g = (10j + 9h)/f.

14. m - p = -n

Isolate m; so that we have;

m = p - n.

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The independent variable in this study is the place of residence, specifically whether the participants live in Florida or Pennsylvania.

The researcher is interested in examining the relationship between the location of residence and the amount of money spent on clothes. By selecting participants from both Florida and Pennsylvania, the researcher can compare the spending habits of individuals from these two locations and determine if there is a significant difference. Thus, the independent variable is the categorical variable that defines the groups being compared, which in this case is the place of residence.

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Answer:

Richard is older

Step-by-step explanation:

We can set up an inequality for both statements.

Let r equal Richard's age and s equal Sylvia's age.

"I am older than my wife."

Since Richard is speaking, the inequality would look like this:

r > s

This means Richard is older than Sylvia.

"I am younger than my husband."

Since Sylvia is speaking, the inequality would look like this:

s < r

This means that Sylvia is younger than Richard.

We can flip one inequality to "see" them from the same perspective.

Let's use s < r

To make it so that we can see the relationship from Richard's perspective, flip the entire inequality.

s < r

to

r > s

The inequality from the first quote is identical to this one!

Therefore, Richard is older than Sylvia.

The graph of f(x) = -x² + 2x + 1 and g(x) = 2ˣ, have the same y-intercept of (0, 1)

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

Given the polynomial function f(x) = -x² + 2x + 1 and an exponential function g(x) = 2ˣ

From the graph of f(x) = -x² + 2x + 1 and g(x) = 2ˣ, have the same y-intercept of (0, 1)

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The justification of each step in solving the inequality is;

⇒ - 21 - 56x + 5x ≤ 1 − 62x    (Distributive property)

⇒ - 21 - 51x ≤ 1 − 62x            (Subtraction property of order)

⇒ - 21 + 11x ≤ 1                       (Addition property of order)

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

The inequality is given as;

−7 (3 + 8x) + 5x ≤ 1 − 62x

Now, Find the justification of each step in solving the inequality as;

The inequality is solve as,

−7 (3 + 8x) + 5x ≤ 1 − 62x

                                      (Given)

- 21 - 56x + 5x ≤ 1 − 62x

                                    (Distributive property)

- 21 - 51x ≤ 1 − 62x

                                    (Subtraction property of order)

- 21 + 11x ≤ 1

                                     (Addition property of order)

11x ≤ 22

                                     (Addition property of order)

x ≤ 2

                                     ( Division property of order )

Hence, The justification of each step in solving the inequality is;

⇒ - 21 - 56x + 5x ≤ 1 − 62x    (Distributive property)

⇒ - 21 - 51x ≤ 1 − 62x             (Subtraction property of order)

⇒ - 21 + 11x ≤ 1                        (Addition property of order)

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To find out after how many years the government's target will be reached, we can set up an equation and solve for the number of years.

Let P be the current public sector expenditure as a percentage of GDP, which is 8%.

Let G be the current GDP.

Let r be the annual growth rate of public sector expenditure, which is 7%.

Let g be the annual growth rate of GDP, which is 4%.

Let t be the number of years it will take to reach the target.

The government wants to increase the ratio of public sector expenditure to GDP from 8% to 11%. This means that the new public sector expenditure as a percentage of GDP should be 11%.

We can set up the equation:

P + rt = 11% * (G + gt)

Substituting the given values:

0.08 + 0.07t = 0.11 * (G + 0.04t)

To solve for t, we need the value of G. Assuming continuous growth, the new GDP after t years can be calculated using the formula:

G_new = G * e^(g*t)

Substituting the given values:

G_new = G * e^(0.04*t)

Now, substitute this value of G in the equation:

0.08 + 0.07t = 0.11 * (G * e^(0.04t) + 0.04*t)

Simplifying this equation may require numerical methods or approximation techniques to solve for t.

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To find out after how many years the government's target will be reached, we can set up an equation and solve for the number of years.

Let P be the current public sector expenditure as a percentage of GDP, which is 8%.

Let G be the current GDP.

Let r be the annual growth rate of public sector expenditure, which is 7%.

Let g be the annual growth rate of GDP, which is 4%.

Let t be the number of years it will take to reach the target.

The government wants to increase the ratio of public sector expenditure to GDP from 8% to 11%. This means that the new public sector expenditure as a percentage of GDP should be 11%.

We can set up the equation:

P + rt = 11% * (G + gt)

Substituting the given values:

0.08 + 0.07t = 0.11 * (G + 0.04t)

To solve for t, we need the value of G. Assuming continuous growth, the new GDP after t years can be calculated using the formula:

G_new = G * e^(g*t)

Substituting the given values:

G_new = G * e^(0.04*t)

Now, substitute this value of G in the equation:

0.08 + 0.07t = 0.11 * (G * e^(0.04t) + 0.04*t)

Simplifying this equation may require numerical methods or approximation techniques to solve for t.

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Answer:

97, 485, 197

Step-by-step explanation:

Given:

Then we have:

Substituting b and c in the third equation:

Answer:

x = 1

Step-by-step explanation:

\(\sqrt[3]{3x - 2} = 1\)        Cube both sides of the equation

3x - 2 = 1

3x = 3

x = 1

Check:  \(\sqrt[3]{3(1) - 2} = \sqrt[3]{3 - 2} = \sqrt[3]{1} = 1\)   Since x = 1 makes the original equation true, then x = 1 is the solution.

The correct solution for the given equation is x = 1.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given is a cubic equation, \(\sqrt[3]{3x-2}\) = 1

Solving for x,

\(\sqrt[3]{3x-2}\) = 1

Cubing both the sides,

(\(\sqrt[3]{3x-2}\))³ = 1

3x - 2 = 1

3x = 3

x = 1

Hence, the correct solution for the given equation is x = 1.

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Our final rational function becomes: g(x) =\([(x + 4)(ax + b)(x + 3)^2(x + 1)] / [(x + 4)(cx + d)(x - 1)^2]\)

To create a rational function g(x) that satisfies the given properties, we can start by considering the horizontal asymptote and the hole.

Given that the horizontal asymptote is y = 0, we know that the degree of the polynomial in the numerator is less than or equal to the degree of the polynomial in the denominator.

Considering the hole at (-4, -3/19), we can introduce a factor of (x + 4) in both the numerator and denominator to cancel out the common factor. This will create a hole at x = -4.

So far, we have:

g(x) = [(x + 4)(ax + b)] / [(x + 4)(cx + d)]

Next, let's consider the local minimum at (-3, -1/6) and the local maximum at (1, 1/2).

To ensure a local minimum at x = -3, we can make the factor (x + 3) squared in the denominator, so that it does not cancel out with the numerator. We can also choose a positive coefficient for the factor in the numerator to create a downward-facing parabola.

To ensure a local maximum at x = 1, we can make the factor (x - 1) squared in the denominator, and again choose a positive coefficient for the factor in the numerator.

Adding these factors, we have:

g(x) =\([(x + 4)(ax + b)(x + 3)^2] / [(x + 4)(cx + d)(x - 1)^2]\)

Finally, we consider the x-intercept at x = -1 and the y-intercept at y = 1/3.

To achieve an x-intercept at x = -1, we can set the factor (x + 1) in the numerator.

To achieve a y-intercept at y = 1/3, we set the numerator constant to 1/3.

Multiplying these factors, our final rational function becomes:

g(x) = \([(x + 4)(ax + b)(x + 3)^2(x + 1)] / [(x + 4)(cx + d)(x - 1)^2]\)

Where a, b, c, and d are coefficients that can be determined by solving a system of equations using the given properties.

Please note that without additional information or constraints, there are multiple possible rational functions that can satisfy these properties. The function provided above is one possible solution that meets the given conditions.

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Answer: x=3 , y=1

Step-by-step explanation:i good at that kind of thing

The population of birds to increase by 50% in 31.25 years.

The differential equation for the population of birds is:

dp/dt = 0.016P

where P is the population of birds and t is time in years.

To obtain the time it takes for the population to increase by 50%, we need to solve for t when P increases by 50%.

Let P0 be the initial population of birds, and P1 be the population after the increase of 50%.

Then we have:

P1 = 1.5P0 (since P increases by 50%)

We can solve for t by integrating the differential equation:

dp/P = 0.016 dt

Integrating both sides, we get:

ln(P) = 0.016t + C

where C is the constant of integration.

To obtain the value of C, we can use the initial condition that the population at t=0 is P0:

ln(P0) = C

Substituting this into the previous equation, we get:

ln(P) = 0.016t + ln(P0)

Taking the exponential of both sides, we get

:P = P0 * e^(0.016t)

Now we can substitute P1 = 1.5P0 and solve for t:

1.5P0 = P0 * e^(0.016t

Dividing both sides by P0, we get:

1.5 = e^(0.016t)

Taking the natural logarithm of both sides, we get:

ln(1.5) = 0.016t

Solving for t, we get:

t = ln(1.5)/0.016

Using a calculator, we get:

t ≈ 31.25 years

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The statement "f(n) equals O(g(n)) and g(n) equals O(f(n)) then f(n) equals Θ(g(n))" is true.

In computer science, the O-notation and Θ-notation are used to describe the upper and tight bounds, respectively, of the running time of an algorithm. O-notation provides an upper bound on the running time of an algorithm, while Θ-notation provides a tight bound, meaning that the running time of an algorithm is both upper-bounded and lower-bounded by a certain function.

When f(n) equals O(g(n)), it means that the growth rate of f(n) is upper-bounded by the growth rate of g(n). In other words, the running time of f(n) is no greater than that of g(n), multiplied by some constant factor.

When g(n) equals O(f(n)), it means that the growth rate of g(n) is upper-bounded by the growth rate of f(n). This implies that the running time of g(n) is no greater than that of f(n), multiplied by some constant factor.

If both f(n) equals O(g(n)) and g(n) equals O(f(n)), it can be concluded that the running time of f(n) and g(n) are asymptotically equivalent. This means that their growth rates are the same, and thus f(n) equals Θ(g(n)).

In conclusion, if f(n) equals O(g(n)) and g(n) equals O(f(n)), it is true that f(n) equals Θ(g(n)), which means that the two functions have the same growth rate. This property can be useful in comparing the running time of different algorithms or in analyzing the efficiency of algorithms.

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Answer:

slope = 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (- 6, - 3)

m = \(\frac{-3-5}{-6+2}\) = \(\frac{-8}{-4}\) = 2

Answer:

Step-by-step explanation:

Mean: 41+39+48+52+41+48+36+41+37+35/10

=41.8

Mode:41

Median:41

DSA is only used for signature purposes but RSA is used for cryptographic purposes.

But somehow DSA uses discrete logarithms for Encryption and in RSA long-term calculations are used which is more secure as compared to DSA.

Now while signing messages with DSA leads to a more time and more memory-consuming process because at every point the message is signed. So the verification of signatures gets complicated.

But in the case of RSA, the calculations are high, but they consume less memory and less need for verification. Because of large calculations, RSA is much slower than DSA.

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Answer:

\( \frac{x}{4} + \frac{1}{2} = \frac{1}{8} \)

\( \frac{x}{4} = - \frac{3}{8} \)

\(x = - \frac{3}{2} = - 1 \frac{1}{2} \)

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

Consider the equation, we have only one x term, so taking all the terms without x to the other side and terms with x on one side.

x/4 + 1/2 = 1/8

Take the 1/2 term on the other side,

x/4=1/8 - 1/2

Taking the LCM on the Right side,

x/4 = (1-4) / 8

x/4 = -3/8

Now, we have x/4 so what we can do is, shift the 4 to the other side too, we get,

x = ( -3/8) * 4

x = -3/2

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

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