Helpppppp ASAP !!!!!

The graphs below are both quadratic functions. The equation of the red graph is f(x)=x^2 . Which of these is the equation of the blue graph g(x)

Answer: B

Step-by-step explanation:

The line [tex]y=2x+3[/tex] is dotted and shaded above.

Similarly, the line [tex]y=\frac{1}{3}x+4[/tex] is also shaded above.

This leaves B as the correct answer.

Answer:

B.) addition property of equality; division property of equality

Answer:

A seems to be correct

Step-by-step explanation:

Answer:

0.7857

Step-by-step explanation:

Given :

Mean = 69 inches

Standard deviation, = 2.8 inches

The Zscore of a man who is 71.2 inches

The ZSCORE is obtained using the relation :

Zscore = (Score, x - mean) / standard deviation

Zscore = (71.2 - 69) / 2.8

Zscore = 2.2 / 2.8

Zscore = 0.7857

Answer:

p = 15/x

x= -3

Step-by-step explanation:

For the first problem, we can expand the equation to 4px+4=64

then simplify it to:

4px=60

then divide 4x from both sides of the equation

p=60/4x

then simplify:

p=15/x

For the second problem:

plug in -5 for p so the equation would look like

4(-5x +1)=64

simplify

-20x=60

x= -3

Answer:

$42.50

Step-by-step explanation:

All you have to do is simply multiply

170 x 0.25=$42.50

Answer:

156 degrees

Step-by-step explanation:

Bisects meand to cut into two equal halves.

That means 4x-2=3x+18.

Subtracting 3x on both sides gives x-2=18

Adding 2 on both sides gives x=20

If x=20, then 4x-2 equals 4(20)-2=78.

The other half is also 78 since the two angles were comgruent.

The whole angle is 78+78=156.

Answer:

24/25

Step-by-step explanation:

The sin value is the y coordinate of the exact value point.

24/25 is the y coordinate so 24/25 is the answer.

Answer:

24/25 is the correct answer

Answer:

The probability that Swallows will win the trophy is 0.8064

The probability that Rucks will win the trophy is 0.1936

Step-by-step explanation:

For each game, there are only two possible outcomes. Either the Swallows win, or they do not. The probability of them winning a game is independent of any other game, which means that the binomial probability distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Probability the Swallows wins is 0.56

This means that [tex]p = 0.56[/tex]

2 games:

This means that [tex]n = 2[/tex]

The probability that Swallows will win the trophy is

Probability they win at least one game, so:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{2,0}.(0.56)^{0}.(0.44)^{2} = 0.1936[/tex]

Then

[tex]P(X \geq 1) = 1 - 0.1936 = 0.8064[/tex]

0.8064 = 80.64% probability the Swallows win the trophy and 0.1936 probability that the Rucks win the trophy.

Hello!

237405 | 11 ?

237405 : 11 = 21582,(27)

Answer: false

Good luck! :)

Hello,

Is 237405 divisible by 11​?

a=sum of digits in rank odd : 5+4+3 = 12

b=sum of digits in rank even: 0+7+2=9

Calculate the difference: d=a-b=12-9 =3

d is not a multiple of 11 so, then number 237405 is not divisible by 11​.

Answer:

RA = 24

Step-by-step explanation:

Since the triangle is isosceles ( 2 equal sides ) , then LU is a perpendicular bisector , so

AU = RU , that is

4r = 18 - 2r ( add 2r to both sides )

6r = 18 ( divide both sides by 6 )

r = 3

Then

RA = 18 - 2r + 4r = 18 + 2r = 18 + 2(3) = 18 + 6 = 24

Answer:

how accurate the statistic is when using it to estimate the parameter.

Step-by-step explanation:

The margin of error may be referred to as a range or interval around a calculated statistic. The margin of error usually employed when calculating the confidence interval, will give a certain range of value within the sample statistic. This is sample statistic and margin is used to estimate the parameter albeit a certain percentage or proportion within the sample statistic. This provides the accuracy level at which the statistic will estimate the parameter.

Margin of Error :

Margin of Error = Zcritical * σ/√n ; OR

Margin of Error = Tcritical * s/√n

Where ;

σ = population standard deviation

s = sample standard deviation

Answer:

Step-by-step explanation:

Given that:

[tex]f_x = \dfrac{x^2}{a^7-x^7}[/tex]

[tex]= \dfrac{x^2}{a^7(1-\dfrac{x^7}{a^7})}[/tex]

[tex]= \dfrac{x^2}{a^7}\Big(1-\dfrac{x^7}{a^7} \Big)^{-1}[/tex]

since  [tex]\Big((1-x)^{-1}= 1+x+x^2+x^3+...=\sum \limits ^{\infty}_{n=0}x^n\Big)[/tex]

Then, it implies that:

[tex]\implies \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\Big(\dfrac{x}{a} \Big)^{^7} \Big)^n[/tex]

[tex]= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x}{a} \Big)^{^{7n}}[/tex]

[tex]= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x^{7n}}{a^{7n}} \Big)}[/tex]

[tex]\mathbf{= \sum \limits ^{\infty}_{n=0} \dfrac{x^{7n+2}}{a^{7n+7}} }}[/tex]

Answer:

[tex]14x cos(\frac{1}{15}x^{2})=14 \sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}[/tex]

Step-by-step explanation:

In order to find this Maclaurin series, we can start by using a known Maclaurin series and modify it according to our function. A pretty regular Maclaurin series is the cos series, where:

[tex]cos(x)=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{2k}}{(2k)!}[/tex]

So all we need to do is include the additional modifications to the series, for example, the angle of our current function is: [tex]\frac{1}{15}x^{2}[/tex] so for

[tex]cos(\frac{1}{15}x^{2})[/tex]

the modified series will look like this:

[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15}x^{2})^{2k}}{(2k)!}[/tex]

So we can use some algebra to simplify the series:

[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15^{2k}}x^{4k})}{(2k)!}[/tex]

which can be rewritten like this:

[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}[/tex]

So finally, we can multiply a 14x to the series so we get:

[tex]14xcos(\frac{1}{15}x^{2})=14x\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}[/tex]

We can input the x into the series by using power rules so we get:

[tex]14xcos(\frac{1}{15}x^{2})=14\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}[/tex]

And that will be our answer.

This is one single number slightly over 17 thousand.

You may need to erase the comma when typing the answer in.

=========================================================

Explanation:

Let's say that another person steps in for Joe, Susan, John, and Meredith. I'll refer to this person as the teacher (perhaps these 9 friends are students on a field trip).

The 9 friends drops to 9-4 = 5 people when those four named people leave the group temporarily. Then it bumps up to 5+1 = 6 people when the teacher steps in. Wherever the teacher is located, the four friends that left will replace the teacher. This guarantees that those four friends stick together.

There are 6! = 6*5*4*3*2*1 = 720 ways to arrange those 6 people. The exclamation mark is a factorial symbol.

Within any of those 720 permutations, we have 4! = 4*3*2*1 = 24 ways to arrange those group of named people when they come back to replace the teacher.

So overall the answer is 4!*6! = 24*720 = 17,280

You may need to erase the comma when typing the answer in.

-------------

Side note: There are 9! = 362,880 ways to arrange all nine friends regardless if those four mentioned people stick together or not. We see that they stick together roughly (17,280)/(362,880) = 0.0476 = 4.76% of the time.

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Answer:

  water

Step-by-step explanation:

Comparison of numbers can be done a couple of different ways. One way is to subtract one from the other. If the difference is positive, the minuend (first number) is the larger of the two.

Another way is to divide one number by the other. If the ratio is more than 1, then the numerator is the larger number.

For numbers in scientific notation, the division is perhaps the easiest. Here, that gives you ...

  [tex]\displaystyle\frac{\text{water mass}}{\text{oxygen mass}}=\frac{2.99\times10^{-26}\text{ kg}}{2.66\times10^{-26}\text{ kg}}=\frac{2.99}{2.66}\approx 1.12[/tex]

This value is greater than 1, so the mass of a water molecule is greater.

__

You will note that the multipliers (10^-26 kg) cancelled because they were equal. If they are unequal, the usual rules of exponents apply.

Answer:

Assuming you want better payment each week, any number of hours above 33.333 or 33 hours and 20 minutes per week

Step-by-step explanation:

There are several ways we could do this.  We could say we want to have Tim Hortons be the better employer on the first week, or after so many weeks by adjusting the hours.  I am going to assume we are saying we want it to be a better employer on the first week, so the profit will be the amount made every week plus the money made per hour times the number of hours.

Let's say number of hours is H

So Tim Hortons winds up as 200 + 5H for one week and  Mcdonalds will be 300 + 2H.

If you set the two expressions equal to each other you will find where they intersect, which means at that number of hours they will give the same amount of money while any amount before one of the companies will give more and after that many hours the other will.  Let's go ahead and solve.

200 + 5H = 300 + 2H

3H = 100

H = 100/3

So H is about 33.333.  let's check.

200 + 5(33.333) = 366.665 which rounds to 366.67 dollars

300 + 2(33.333) = 366.666 which also rounds to 366.67 dollars

So at 33.333 hours both give 366.67 dollars.  Let's look at a value below it, say 32.

200 + 5(32) = 360

300 + 2(32) = 364

So you can see here Tim Hortons  pays less.  Now we will try 34 as a value above 33.333

200 + 5(32) = 370

300 + 2(32) = 368

Here Mcdonalds pays less.  This was to show that values below 33.333 make Tim Hortonspay less and values above 33.333 make Mcdonalds pay less.  In other words any value above 33.333 hours will have Tim Hortons be the better employer.  And this is per week

I want to repeat, you can expand this to be multiple weeks and see which of the two becomes better in that epriod of time.  This was, I think, the simplest way to answer though.  

So the conditions where Tim Horton pays more isif you work more than 33.333 hours per week.  This will make them pay more every single week.  

9514 1404 393

Answer:

  x = 19

  A = 30°

  B = C = 75°

Step-by-step explanation:

In an isosceles triangle, the angles opposite the congruent sides have the same measures.

  A = B

  3x +18 = 7x -58

  76 = 4x . . . . . . . . add 58-4x

  19 = x . . . . . . . . . divide by 4

Then the equal angles measure ...

  A = B = 3(19) +18 = 75

  C = 2(19) -8 = 30

Angles A, B, C measure 75°, 75°, 30°, respectively.

_____

Alternate solution

The sum of angles in a triangle is 180°, so you could write ...

  (3x +18) +(7x -58) +(2x -8) = 180

  12x = 228 . . . . . add 48

  x = 19 . . . . . divide by 12

Answer:

0.0118 = 1.18% probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A telephone exchange operator assumes that 7% of the phone calls are wrong numbers.

This means that [tex]p = 0.07[/tex]

Sample of 459 phone calls:

This means that [tex]n = 459[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.07[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\sqrt{\frac{0.07*0.93}{459}}} = 0.0119[/tex]

What is the probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%?

Proportion below 0.07 - 0.03 = 0.04 or above 0.07 + 0.03 = 0.1. Since the normal distribution is symmetric, these probabilities are the same, which means that we find one of them and multiply by 2.

Probability the proportion is below 0.04.

p-value of Z when X = 0.04. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.04 - 0.07}{0.0119}[/tex]

[tex]Z = -2.52[/tex]

[tex]Z = -2.52[/tex] has a p-value of 0.0059

2*0.0059 = 0.0118

0.0118 = 1.18% probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%

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Answer:

  P' = (3, -5)

Step-by-step explanation:

Rotation 180° about the origin is the same as reflection across the origin. The transformation is given by ...

  (x, y) ⇒ (-x, -y) . . . . . . the signs of the coordinates are both changed

  P(-3, 5) ⇒ P'(3, -5)

Answer:

is it four I am not quite sure

Answer:

Solution given:

f(x)=x²

g(x)=x+5

h(x)=4x-6

now

23:

(fog)(x)=f(g(x))=f(x+5)=(x+5)²=x²+10x+25

24:

(gof)(x)=g(f(x))=g(x²)=x²+5

25:

(foh)(x)=f(h(x))=f(4x-6)=(4x-6)²=16x²-48x+36

26:

(hof)(x)=h(f(x))=h(x²)=4x²-6

27;

(goh)(x)=g(h(x))=g(4x-6)=4x-6+5=4x-1

28:

(hog)(x)=h(g(x))=h(x+5)=4(x+5)-6=4x+20-6=4x-14

Answer:

the answer is 4x - 4

Step-by-step explanation:

9514 1404 393

Answer:

  50.24 cm

Step-by-step explanation:

Fill in the given numbers and do the arithmetic.

  s = rθ

  s = (24 cm)(2/3π) = (24 cm)(2/3)(3.14) = 50.24 cm

Answer:

0.0070 = 0.70% probability that the proportion of smokers in a sample of 664 males would differ from the population proportion by greater than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A researcher believes that 9% of males smoke cigarettes.

This means that [tex]p = 0.09[/tex]

Sample of 664

This means that [tex]n = 664[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.09[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{664}} = 0.011[/tex]

What is the probability that the proportion of smokers in a sample of 664 males would differ from the population proportion by greater than 3%?

Proportion below 9 - 3 = 6% or above 9 + 3 = 12%. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Probability the proportion is below 6%

P-value of Z when X = 0.06. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.06 - 0.09}{0.011}[/tex]

[tex]Z = -2.7[/tex]

[tex]Z = -2.7[/tex] has a p-value of 0.0035

2*0.0035 = 0.0070

0.0070 = 0.70% probability that the proportion of smokers in a sample of 664 males would differ from the population proportion by greater than 3%

Answer:

D. y =

Step-by-step explanation:

The solutions to this graph (meaning when y equals 0 or when the graph crosses the x-axis) are 4 and 5.

The only answer choice that has the solutions 4 and 5 when you factor it out is D.

Here's the proof:

[tex]x^{2} -9x + 20[/tex]

Factors of 20: - 5 & -4

Sums that add up to -9: -5 + (-4)

[tex]x^{2} -4x-5x+20[/tex]

(factor the first two terms and the last two terms separately)

[tex](x^{2}-4x)(-5x+20)[/tex]

[tex]x(x-4) -5(x-4)[/tex]

(x - 5) (x - 4)

Hope it helps (●'◡'●)

Answers:

Choice 2) Angle ABC is bisected by ray BD.

Choice 3) BC = 1/2 AC

Choice 5) 2*(angle DBC) = angle ABC

================================================

Explanation:

Since B is the midpoint of AC, this means that AC is cut in half to form the smaller equal pieces AB and BC

We can then say

AB+BC = AC

BC+BC = AC

2BC = AC

BC = (1/2)*AC

which shows why choice 3 is one of the answers

----------------------

Angle ABD is shown to be 90 degrees. Let's say we didn't know angle DBC is also 90. Lets call it x

(angle ABD) + (angle DBC) = 180

90 + x = 180

x = 180 - 90

x = 90

So angle DBC is also 90.

We can see that the 180 degree angle (ABC) is cut in half into two smaller 90 degree angles (ABD and DBC). Therefore, angle ABC has been cut in half and that's why choice 2 is another answer.

------------------------

Using the angle addition postulate, we know that,

(angle ABD) + (angle DBC) = angle ABC

(angle DBC) + (angle DBC) = angle ABC

2*(angle DBC) = angle ABC

Showing why choice 5 is the third answer.

------------------------

Choice 1 isn't true since ray BD helps form angle DBC.

Choice 4 isn't true because there isn't a tickmark on segment BD to indicate it's the same length as BC.

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Explanation:

Your question covers a good bit of the material in an algebra course. The short answer is, "the same way you solve a numerical equation." The point of algebra is that literals can stand for numbers, and so be manipulated the same way numbers are.

Expressions are evaluated according to the Order of Operations. For equations involving a single variable, the equation specifies what operations are being performed on that variable. To find the vale of the variable (solve for that literal), you need to "undo" the operations that are performed on it. As with many problems that have layers, you work down through the layers from the outside in. Generally, that means working through the list of operations "backwards," undoing the last one first.

Simple example

  y = mx + b . . . . . . solve for x

In this equation, the operations performed on x are ...

In accordance with the above, the first thing we do is "undo" the addition of b. (Note that this could be a number or literal--or even a complicated expression--and the process would be exactly the same.) To "undo" addition, we add the opposite.

  y -b = mx +b -b   ⇒   y -b = mx

Next, we "undo" the multiplication by m. That is, we divide by m, or multiply by the reciprocal of m. Either is the same as the other.

  (y -b)(1/m) = (mx)(1/m)   ⇒   (y -b)/m = x

Now, we have solved this literal equation for x.

_____

Throughout this process you must adhere strictly to the properties of equality. That is, anything you do to one side of the equation must also be done to the other side.

The reason you study inverses and identity elements is so you understand that addition of an additive inverse produces the additive identity element:

  x + (-x) = 0

Similarly, multiplication by the multiplicative inverse (reciprocal) produces the multiplicative identity element.

  x · (1/x) = 1

When other operations are involved, such as raising to a power, trig functions, roots, logs, exponentiation, each of these has an associated inverse function that produces an identity:

  (x^a)^(1/a) = x^1 = x

  arcsin(sin(x)) = x

  (√x)^2 = x

  10^(log(x)) = x   or   log(10^x) = x

Some of these inverse functions have restricted domains, so care must be used when solving equations involving them.

When a variable of interest appears on both sides of the equal sign, then you must figure a way to rearrange the equation so the terms with the variable can be combined.

Example:

  ax + b = cx +d . . . . . solve for x

  ax -cx = d -b . . . . . . subtract (cx+b). (Of course, this is subtracted from both sides of the equation.)

  x(a -c) = d -b . . . . . combine x-terms

  x = (d -b)/(a -c) . . . . divide by the coefficient of x

Note that we had to divide the entire right-side expression by the x-coefficient, so had to enclose it in parentheses.

More Complicated Example:

A recent Brainly problem asked for the solution to ...

  T = 2π√(L/g) . . . . solve for L

Here, L is divided by g, a root taken, and that multiplied by 2π. Undoing these in reverse order, we first divide by 2π, square both sides to undo the root, then multiply by g to undo the division:

  [tex]T=2\pi\sqrt{\dfrac{L}{g}}\\\\\dfrac{T}{2\pi}=\sqrt{\dfrac{L}{g}}\\\\\left(\dfrac{T}{2\pi}\right)^2=\dfrac{L}{g}\\\\\boxed{L=g\left(\dfrac{T}{2\pi}\right)^2}[/tex]

The problem posted on Brainly had numbers where some of these variables are. That does not affect the solution method, except that sometimes numerical values can be combined where literal values cannot.

_____

Key Points

Answer:

[tex]m = 12[/tex]

[tex]n =3[/tex]

Step-by-step explanation:

Given

[tex]P(x) = x^3 + mx^2 - nx - 10[/tex]

Required

The values of m and n

For x - 1;

we have:

[tex]x - 1 = 0[/tex]

[tex]x=1[/tex]

So:

[tex]P(1) = (1)^3 + m*(1)^2 - n*(1) - 10[/tex]

[tex]P(1) = 1 + m*1 - n*1 - 10[/tex]

[tex]P(1) = 1 + m - n - 10[/tex]

Collect like terms

[tex]P(1) = m - n + 1 - 10[/tex]

[tex]P(1) = m - n -9[/tex]

Because x - 1 divides the polynomial, then P(1) = 0;

So, we have:

[tex]m - n -9 = 0[/tex]

Add 9 to both sides

[tex]m - n = 9[/tex] --- (1)

For x + 2;

we have:

[tex]x + 2 = 0[/tex]

[tex]x = -2[/tex]

So:

[tex]P(-2) = (-2)^3 + m*(-2)^2 - n*(-2) - 10[/tex]

[tex]P(-2) = -8 + 4m + 2n - 10[/tex]

Collect like terms

[tex]P(-2) = 4m + 2n - 10 - 8[/tex]

[tex]P(-2) = 4m + 2n - 18[/tex]

x + 2 leaves a remainder of 36, means that P(-2) = 36;

So, we have:

[tex]4m + 2n - 18 = 36[/tex]

Collect like terms

[tex]4m + 2n = 36+18[/tex]

[tex]4m + 2n = 54[/tex]

Divide through by 2

[tex]2m + n=27[/tex] --- (2)

Add (1) and (2)

[tex]m + 2m - n + n = 9 +27[/tex]

[tex]3m =36[/tex]

Divide by 3

[tex]m = 12[/tex]

Substitute [tex]m = 12[/tex] in (1)

[tex]m - n =9[/tex]

Make n the subject

[tex]n = m - 9[/tex]

[tex]n = 12 - 9[/tex]

[tex]n =3[/tex]

Answer:

a) month salary = RM(18×800+2000)

= RM 16400

b) his salary = RM(800n+2000)

Hope it helps