solve f(x)=−3(x+1)(x−5)

In the given question, 1 British pound will be equal to AU$2.00.

Algebra is a common thread that runs through almost all of mathematics. It is the study of variables and the principles for manipulating them in formulas. Since all mathematical uses involve manipulating variables as though they were numbers, elementary algebra is a prerequisite.

The area of mathematics known as algebra aids in the representation of situations or issues as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z along with mathematical processes like addition, subtraction, multiplication, and division.

A homogeneous relation R over the set A, which includes the elements x, y, and z, is what mathematicians refer to as a transitive relation. If R relates x to y and y to z, then R also relates x to z.

In this question,

1£ = US$1.40             (Equation 1)

AU$1 = US$0.70      (Equation 2)

Multiplying equation 2 by 2, we get

AU$2 = US$1.40

Using equation 1, we can say that,

1£ = AU$2

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The Glasgow Coma Scale (GCS) is a neurological assessment tool used to measure a patient's level of consciousness after an injury or illness.

It consists of three components: eye opening, verbal response, and motor response. Each component is assigned a score ranging from 1 to 6, with a higher score indicating a better neurological status. The maximum score a patient can achieve is 15, with 5 being the minimum score for a patient to be considered conscious.

Regarding the highest numerical value assigned to eye opening, the answer is A. 6 points. Eye opening is one of the three components of the GCS, and it measures the patient's ability to open their eyes spontaneously, in response to verbal stimuli, or in response to painful stimuli.

A score of 6 is given when the patient opens their eyes spontaneously, which is the highest score for this component. A score of 5 is given when the patient opens their eyes in response to verbal stimuli, and a score of 4 is given when the patient opens their eyes in response to painful stimuli. Scores lower than 4 indicate a severe neurological impairment.

In summary, the highest numerical value assigned to eye opening when computing the GCS is 6 points, which is given when the patient opens their eyes spontaneously.

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Answer:

Here is the answer

BRAINLIEST ME PLEASE

CORRECT me if I am wrong

Answer:

m = - 1

Step-by-step explanation:

Given

- 9m - 86 = - 75 + 2m ( subtract 2m from both sides )

- 11m - 86 = - 75 ( add 86 to both sides )

- 11m = 11 ( divide both sides by - 11 )

m = - 1

We will compare the t-value to the critical value for a two-tailed test with a=.05 and degrees of freedom = n - 1 = 36 - 1 = 35. The critical value for this test is +/- 2.03.
Since the t-value (-1.08) is not greater than or less than the critical value (+/- 2.03), we cannot conclude that the students in the new program are significantly different from the rest of the freshman class.

The college can use a two-tailed test to determine if the students in the new program are significantly different from the rest of the freshman class. A two-tailed test is used when we are interested in determining if there is a difference between two groups, but we are not concerned with the direction of the difference.

To conduct the two-tailed test, we will first need to calculate the standard error of the difference between the two means. The standard error is given by:

SE = sqrt[(s^2/n) + (s^2/n)]

Where s is the standard deviation of the sample and n is the sample size. Plugging in the values from the question, we get:

SE = sqrt[(18^2/36) + (18^2/36)] = sqrt[9 + 9] = sqrt[18] = 4.24

Next, we will calculate the t-value for the difference between the two means. The t-value is given by:

t = (M - u) / SE

Where M is the mean of the sample, u is the mean of the population, and SE is the standard error. Plugging in the values from the question, we get:

t = (79.4 - 84) / 4.24 = -4.6 / 4.24 = -1.08

Finally, we will compare the t-value to the critical value for a two-tailed test with a=.05 and degrees of freedom = n - 1 = 36 - 1 = 35. The critical value for this test is +/- 2.03.

Since the t-value (-1.08) is not greater than or less than the critical value (+/- 2.03), we cannot conclude that the students in the new program are significantly different from the rest of the freshman class.

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Answer:

B. 2/5 barrel/hour

Step-by-step explanation:

cross multiply 1/5 and 2/1

=2/5

Answer:

Step-by-step explanation:

1)Since he can lose 5 pounds per week, this is a linear rate. The weight is decreasing in arithmetic progression. The formula for determining the nth term of an arithmetic progression is expressed as

Tn = a + (n - 1)d

n = number of terms(weeks)

d = common difference(5 pounds)

a= first term(300 pounds)

The equation that could be used to find how many weeks, w, it would take for him to weigh 150 pounds would be

150 = 300 + (w - 1)5

150 - 300 = 5w - 5

- 150 + 5 = 5w

w = 145/5 = 29 weeks

2) t represents the number of hours used to fix the car. The cost of t hours is 52t. Total amount paid is 210 + 52t. The equation that could be used to find, t, the length of time it took to fix the car is

210 + 52t = 527.23

3) 52t = 527.23 - 210 = 317.23

t = 317.23/52

t = 6 hours

3) Let x represent the time it will take before you and your sister have the same amount of money. The amount that you would have in x weeks is 60 + 7x

The amount that you sister will have in x weeks is 120 + 5x. The equation would be

60 + 7x = 120 + 5x

7x - 5x = 120 - 60

2x = 60

x = 60/2 = 30 weeks

4) let L represent the length of the parking lot.

let W represent the width of the parking lot.

If the length of a rectangular parking lot is 3 times its width, it means that

L = 3W

Its perimeter is 840 yards. It means that

2(L + W) = 840

L + W = 840/2 = 420

Substituting, it becomes

3W + W = 420

4W = 420

W = 420/4 = 105

L = 3 × 105 = 315

Length = 315 yards

The value of the constant m for which the area between the parabolas is 1/2 is m = 1/(12a^2), where a represents the x-coordinate of the point where the two curves intersect.

To find the value of the constant m for which the area between the parabolas y = 2x^2 and y = -x^2 + 6mx is 1/2, we need to set up an integral and solve for m.

The area between the two curves can be found by integrating the difference between the upper and lower curves with respect to x over the interval where they intersect.

First, let's find the x-values where the two curves intersect:

2x^2 = -x^2 + 6mx

Combining like terms:

3x^2 = 6mx

Dividing both sides by 3x^2 (assuming x ≠ 0):

1 = 2m

Therefore, the two curves intersect at m = 1/2.

Now, we can set up the integral to find the area between the curves:

A = ∫[a, b] [(upper curve) - (lower curve)] dx

Using the x-values where the curves intersect, the integral becomes:

A = ∫[-a, a] [(-x^2 + 6mx) - 2x^2] dx

Simplifying:

A = ∫[-a, a] [-3x^2 + 6mx] dx

Integrating:

A = [-x^3 + 3mx^2] |[-a, a]

Substituting the limits of integration:

A = [-(a)^3 + 3ma^2] - [-(−a)^3 + 3m(−a)^2]

Simplifying further:

A = -a^3 + 3ma^2 + a^3 - 3ma^2

A = 6ma^2

We want this area to be equal to 1/2, so we can set up the equation:

6ma^2 = 1/2

Simplifying and solving for m:

m = 1/(12a^2)

Therefore, the value of the constant m for which the area between the parabolas is 1/2 is m = 1/(12a^2), where a represents the x-coordinate of the point where the two curves intersect.

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The sum of the first 100 terms of the sequence is $620$.

\($s_3 = 4 + 7 = 11$\)

\($s_4 = 11 + 1 = 12$\)

\($s_5 = 12 + 8 = 20$\)

\($s_6 = 20 + 9 = 29$\)

\($s_7 = 29 + 7 = 36$\)

\($s_8 = 36 + 6 = 42$\)

\($s_9 = 42 + 4 = 46$\)

\($s_{10} = 46 + 7 = 53$\)

\($s_{100} = 620$\)

The given sequence is 4, 7, 1, 8, 9, 7, 6 and so on. The nth term of the sequence is the units digit of the sum of the two previous terms. To find the sum of the first 100 terms, we need to calculate the sum of the first two terms, 4 and 7. This is 11. The next term is the units digit of 11, 1. The sum of the first three terms is 12. The next term is the units digit of 12, which is 2. This process is repeated until we reach the 100th term. The sum of the first 100 terms is 620.

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The linear approximation of F at (Pi, 0) is \(-Pi^2cos^2(Pi).\)

To discover the linear approximation of the given function at (Pi, 0), we need to first discover the partial derivatives of the function with respect to x and y evaluated at (Pi, zero).

Partial derivative of F with recognize to x:

∂F/∂x = -2sin(x)cos(x)

evaluated at (Pi, 0):

∂F/∂x(Pi, 0) = -2sin(Pi)cos(Pi) = 0

Partial derivative of F with recognize to y:

∂F/∂y = 1/(2√y)

evaluated at (Pi, 0):

∂F/∂y(Pi, 0) = 1/(2√0) = undefined

For the reason that partial derivative of F with respect to y is undefined at (Pi, 0), we can't use the multivariable Taylor collection to discover the linear approximation. as an alternative, we will use the formula for the linear approximation:

\(L(x,y) = f(a,b) + ∂f/∂x(a,b)(x-a) + ∂f/∂y(a,b)(y-b)\)

Wherein (a,b) is the factor at which we want to find the linear approximation.

In this case, a = Pi and b = 0. So, the linear approximation is:

\(L(x,y) = F(Pi, 0) + ∂F/∂x(Pi, 0)(x - Pi)\)

\(L(x,y) = sqrt(0) + (cos(Pi))^2(0 - Pi)\)

\(L(x,y) = -Pi^2cos^2(Pi)\)

Consequently, the linear approximation of F at (Pi, 0) is \(-Pi^2cos^2(Pi).\)

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#a

\(\\ \rm\Rrightarrow f(-4)\)

\(\\ \rm\Rrightarrow 3(-4)+2\)

\(\\ \rm\Rrightarrow -12+2\)

\(\\ \rm\Rrightarrow -10\)

#b

#1

\(\\ \rm\Rrightarrow y=\dfrac{2x-1}{3}\)

\(\\ \rm\Rrightarrow x=\dfrac{2y-1}{3}\)

Find y

\(\\ \rm\Rrightarrow y=\dfrac{3x+1}{2}\)

Inverse is

\(\\ \rm\Rrightarrow g^{-1}(x)=\dfrac{3x+1}{2}\)

#2

\(\\ \rm\Rrightarrow gof(x)\)

\(\\ \rm\Rrightarrow g(f(x))\)

\(\\ \rm\Rrightarrow g(3x+2)\)

\(\\ \rm\Rrightarrow \dfrac{2(3x+2)-1}{3}\)

\(\\ \rm\Rrightarrow \dfrac{6x+4-1}{3}\)

\(\\ \rm\Rrightarrow \dfrac{6x+3}{3}\)

If we factor out

\(\\ \rm\Rrightarrow \dfrac{2x+1}{1}\)

\(\\ \rm\Rrightarrow 2x+1\)

#c

\(\\ \rm\Rrightarrow f(x)=g(x)\)

\(\\ \rm\Rrightarrow 3x+2=\dfrac{2x-1}{3}\)

\(\\ \rm\Rrightarrow 3(3x+2)=2x-1\)

\(\\ \rm\Rrightarrow 9x+6=2x-1\)

\(\\ \rm\Rrightarrow 7x=-7\)

\(\\ \rm\Rrightarrow x=-1\)

Answer:

Given functions:

\(f(x)=3x+2\)

\(g(x)=\left(\dfrac{2x-1}{3}\right)\)

Part (a)

\(\begin{aligned}\implies f(-4) & = 3(-4)+2\\& = -12+2\\ & = -10\end{aligned}\)

Part (b)(i)

\(\begin{aligned}g(x) & =\left(\dfrac{2x-1}{3}\right)\\\\\textsf{Swap }g(x) \textsf{ for }y : \\\implies y & = \left(\dfrac{2x-1}{3}\right)\\\\\textsf{Make } x \textsf{ the subject}: \\\implies 3y & = 2x-1\\3y+1 & = 2x\\x & = \dfrac{3y+1}{2}\\\\\textsf{Swap }x \textsf{ for }g^{-1}(x) \textsf{ and }y \textsf{ for }x:\\\implies g^{-1}(x) & = \dfrac{3x+1}{2}\end{aligned}\)

Part (b)(ii)

\(\begin{aligned}gf(x) & = \dfrac{2[f(x)]-1}{3}\\\\& = \dfrac{2(3x+2)-1}{3}\\\\& = \dfrac{6x+4-1}{3}\\\\& = \dfrac{6x+3}{3}\\\\& = \dfrac{6x}{3}+\dfrac{3}{3}\\\\& = 2x+1\end{aligned}\)

Part (c)

\(\begin{aligned}f(x) & = g(x)\\\\\implies 3x+2 & = \dfrac{2x-1}{3}\\\\3(3x+2) & = 2x-1\\\\9x+6 & = 2x-1\\\\7x & = -7\\\\\implies x & = -1\end{aligned}\)

Answer:

2

Step-by-step explanation:

Answer:

461 Hot Dogs.

Step-by-step explanation:

263+198=461 Hot dogs.

For the line maybe you can start at 0 then jump 200 then 60 then 3 then jump another 100 then 90 then 8 to get 461 Hot Dogs.
I hope this helps!

The high category cost in Spain is 57.8% lower than the high category cost in the United States, while the medium category cost in Spain is 61.0% lower than the medium category cost in the United States.

We can use the following calculations to determine the percentage by which Spain's high category and medium category costs are less than those of the United States' categories:

(High in the US - High in Spain)/High in the US * 100%

Spanish medium/US medium * 100% for the medium division.

 The first formula determines the percentage difference between the high category costs in the United States and Spain. The second calculation determines the percentage difference between the medium category costs in the United States and Spain.

 Calculate, for instance, the percentage difference between the high category costs in Spain and the United States. The values can be entered into the formula in the following way:

High category: (19.97)/(34.48 - 14.51)/(34.48 * 100%) = 57.8%

This indicates that the high category cost in Spain is 57.8% cheaper than the high category cost in the United States.

The similar method can be used to determine how much less Spain's medium category cost is than America's medium category cost:

(22.46 - 8.79)/22.46 * 100% = (13.67)/22.46 * 100% = 61.0% for the medium group.

   As a result, the medium category cost in Spain is 61.0% cheaper than the medium category cost in the United States.

.

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Answer:

High category = 58%

Medium category = 61%

Step-by-step explanation:

Corrected what he said. Brainliest?

Answer:

i think its 22 and 4idk

Step-by-step explanation:

Answer:

the blank space for -11 is 22 and the blank space for 8 is -16

Answer:

115

Step-by-step explanation:

Answer:

HEY IMAGE IS BLUR

Step-by-step explanation:

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

The relation S={(a,b)∈R×R:a²+b²=1} is not an equivalence relation on the set of real numbers R.

To show that S is not an equivalence relation, we need to demonstrate that it fails to satisfy one or more of the properties of an equivalence relation: reflexivity, symmetry, and transitivity.

Reflexivity: For a relation to be reflexive, every element of the set should be related to itself. However, in the case of S, there are no real numbers (a, b) that satisfy the equation a² + b² = 1 for both a and b being the same number. Therefore, S is not reflexive.

Symmetry: For a relation to be symmetric, if (a, b) is related to (c, d), then (c, d) must also be related to (a, b). However, in S, if (a, b) satisfies a² + b² = 1, it does not necessarily mean that (b, a) also satisfies the equation. Thus, S is not symmetric.

Transitivity: For a relation to be transitive, if (a, b) is related to (c, d), and (c, d) is related to (e, f), then (a, b) must also be related to (e, f). However, in S, it is not true that if (a, b) and (c, d) satisfy a² + b² = 1 and c² + d² = 1 respectively, then (a, b) and (e, f) satisfy a² + b² = 1. Hence, S is not transitive.

Since S fails to satisfy the properties of reflexivity, symmetry, and transitivity, it is not an equivalence relation on the set of real numbers R.

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Answer:x − x^{2} − 1.

Step-by-step explanation:

.

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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Jennifer needs to sample at least 151 vets to achieve a standard error of the mean of 3.42 years or less.

The variability or uncertainty of a sample statistic, like the mean or proportion, is measured by standard error. It represents the sample distribution's standard deviation for that statistic. In other words, it calculates the amount by which chance is likely to cause the sample statistic to deviate from the actual population parameter.

The calculation of the standard error is based on the particular statistic being produced as well as the characteristics of the sampled population. For instance, the population's standard deviation is divided by the square root of the sample size to determine the standard error of the mean. If p is the estimated proportion based on the sample, then the standard error of a proportion is determined as (p * (1 - p)) divided by the square root of the sample size.

A population parameter estimate that has a lower standard error is more accurate. Inferential statistics frequently employ the standard error to compute confidence intervals and test population parameter-related hypotheses.

The formula for the standard error of the mean can be used to get the approximate number of veterans Jennifer needs to sample:

\(SE = / \sqrt{n}\)

where n: sample size, delta: age standard deviation, and SE: standard error of the mean.

In this instance, we are aware that = 22 years and SE = 3.42 years. As we solve for n, we obtain:

\(n = (delta / SE)^2 n = (22 / 3.42)^2 \sn = 150.39\)

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Answer:

Hi,

Step-by-step explanation:

\(\left\{\begin {array} {ccc}x&=&2*cos(t)-1\\y&=&3*sin(t)+4\\\end{array}\right.\\\\\\\left\{\begin {array} {ccc}\dfrac{x+1}{2}&=&cos(t\\\dfrac{y-4}{3}&=&sin(t)\\\end{array}\right.\\\\Squaring\\\\\boxed{(\dfrac{x+1}{2})^2+(\dfrac{y-4}{3})^2&=1}\\\)

The curve is an ellipse having (-1,4) as center and half-axis (2 and 6)

Answer:

See below

Step-by-step explanation:

Slope-intercept form    ( or  slope -  y-axis intercept form)

 is   y = mx + b      where m = slope and   b is the y-axis intercept

so arrange each equation into this form

First one     y +3 = x        re-arrange to y = (1) x -3     slope =1  intercept = -3

Second one    2y-10 = -4x

                         2y = -4x +10

                           y = -2x+5           slope = -2    intercept = 5

I think you should try the rest of them....they are similar  (14 is already done)

9514 1404 393

Answer:

  see attached for the drawing

  slope = -1/2

Step-by-step explanation:

For the rise of -1 and the run of 2, the slope is ...

  m = rise/run = -1/2 . . . . slope in simplest form

__

Additional comments

It usually works best if you can identify points on the graph where the line crosses grid intersections. Then the number of squares in each direction can be counted easily. If you work with two grid intersections that are closest together, then the ratio of rise to run will already be in reduced form.

On this graph, there are other grid crossing points that are 4, 6, 8 units to the right or left of the one where we started. You need to remember that "run" is positive in the "right" direction, and "rise" is positive in the "up" direction.

We have shown the "rise" and "run" lines above the graphed line. They can also be shown below the graphed line.

Here, the grid squares are 1 unit in each direction. You need to pay attention to the scale, because some graphs have different numbering vertically than horizontally. The values for "rise" and "run" need to be figured using the appropriate scale.

Answer:

a is correct

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Because -4 4/5 is FAR below 4 2/5

The subtended arc along the circle is 79/360 of the circle's circumference. Therefore, the subtended arc is approximately 0.2194 times as long as 1/360 of the circle's circumference.


To find the length of the subtended arc along the circle, we need to know what fraction of the circle's circumference it represents.

The angle measures 79 degrees, which is a little over 1/5 of a full circle (which measures 360 degrees). Therefore, the subtended arc represents a little over 1/5 of the circle's circumference. More precisely, it represents 79/360 of the circle's circumference.

To find out how many times as long the subtended arc is as 1/360 of the circle's circumference, we can divide the length of the subtended arc by the length of 1/360 of the circle's circumference. This gives us:

(79/360) / (1/360) = 79

So the subtended arc is 79 times as long as 1/360 of the circle's circumference. Alternatively, we can express this as a decimal by dividing the subtended arc by 1/360:

(79/360) ÷ (1/360) = 0.2194

So the subtended arc is approximately 0.2194 times as long as 1/360 of the circle's circumference.

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According to the empirical rule, the observations in a data set that can be reasonably approximated by a normal curve lie within two standard deviations of the mean is 95% .

The empirical rule, also known as the 68-95-99.7 rule or the three-sigma rule, is a statistical guideline that describes the approximate distribution of data that can be reasonably approximated by a normal curve. The rule states that:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

In other words, if a set of data is normally distributed (meaning it follows a bell-shaped curve), we can use the empirical rule to estimate the proportion of the data that falls within a certain range of values.

For example, let's say we have a data set that has a mean of 50 and a standard deviation of 10. Using the empirical rule, we can estimate that approximately:

68% of the data falls between 40 and 60 (one standard deviation from the mean)

95% of the data falls between 30 and 70 (two standard deviations from the mean)

99.7% of the data falls between 20 and 80 (three standard deviations from the mean)

It's important to note that the empirical rule is only an approximation, and it only applies to data that is approximately normally distributed. In some cases, the actual distribution

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