Amelia had 26 sea shells. Then, she collected 11 more sea shells. After that, she gave S sea shells to her little sister. Which of the following shows how many sea shells she has currently? A. 26 + S + 11 B. 26 - 11 - S C. 26 + 11 - S D. 26 + S - 11

Answer:

The amount off the original price is $3.6.

Step-by-step explanation:

The original price of the sweater = $18.00

Amount off on the sweater = 20% of the original price of the sweater

=[tex]18.00\times\frac{20}{100}=$3.6[/tex]

The cost of the sweater on the sale = $18.00 - $3.6 = $14.4

The amount off the original price is $3.6.

Attached pictures shows the answers in RED.

Answer:

9/10

Step-by-step explanation:

In ratio units, the relative lengths of the first, second, and third towels are ...

... 1 : 3/5 : (5/12)·(1 +3/5)

... = 1 : 3/5 : 2/3

Then the fraction the second towel is of the third towel is ...

... (3/5)/(2/3) = (3/5)·(3/2) = 9/10

answer:

the answer is 2/3

Answer:

Answer is: D. $40

Step-by-step explanation:

20+40=60

100-60=40

Answer:

A 48

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

These are generally easier to evaluate by hand if they are simplified first.

... (4a^2)b -ab^2 -(3a^2)b +ab^2 -ab +6

... = (a^2)b(4 -3) + ab^2(-1 +1) -ab +6

... = a^2·b -ab +6

... = ab(a -1) +6

... = (-3)(2)(-3-1) +6

... = (-6)(-4)+6

... = 24 +6 = 30

Put the values of a = -3 and b = 2 to the expression

[tex]4a^2b-ab^2-3a^2b+ab^2-ab+6[/tex]

[tex](4)(-3)^2(2)-(-3)(2)^2-(3)(-3)^2(2)+(-3)(2)^2-(-3)(2)+6\\\\=(4)(9)(2)+(3)(4)-(3)(9)(2)-(3)(4)-(-6)+6\\\\=72+12-54-12+6+6\\\\=\boxed{30}[/tex]

Answer:

The inequality [tex]f>40[/tex] represents the length of the femur for which the woman had a height greater than 160cm.

Step-by-step explanation:

The given equation is

[tex]h=60+2.5f[/tex]

Where, h is woman's height in centimeters and f is length of the femur in centimeters.

If woman's height is greater than 160cm, then

[tex]h>160[/tex]

[tex]60+2.5f>160[/tex]

Substract 60 from both sides.

[tex]2.5f>100[/tex]

Divide both sides by 2.5.

[tex]f>40[/tex]

Therefore the inequality  [tex]f>40[/tex] represents the lengths of the femur for which the woman had a height greater than 160cm.

Answer:

Total tax paid by Bruce = $2477.62

Step-by-step explanation:

Bruce banner taxable income last year = $43,467

State's income tax rate = 3.9%

State's income tax = 43467*3.9% = 43467*0.039 = $1695.21

City income tax rate is = 1.8

City income tax = 43467*1.8% = 43467*0.018 =$782.41

Total tax = $1695.21 + $782.41

= $2477.62

Thank you.

B. (5, -2)

Try the points in the inequalities and see what works. Here, we evaluate the point in the first inequality, and if that works, then the second inequality.

A. 2 ≤ -(-5) -5 . . . ⇒ . . . 2 ≤ 0 . . . false

B. -2 ≤ 5 -5 . . . true

... -2 ≥ -(5) -4 . . . true . . . . . . selection B is a viable choice

C. we know from A that the first inequality will be satisfied

... -2 ≥ -(-5) -4 . . . ⇒ . . . -2 ≥ 1 . . . false

D. 2 ≤ 5 -5 . . . . false

Answer:

Probability that a vehicle is white, given that the vehicle is a car :

0.2222

Step-by-step explanation:

A: vehicle is white

probability that a vehicle is white =P(A)= 0.25

B:vehicle is a car

probability that it is a car =P(B)= 0.36

A∩B:vehicle is a white car

P(A∩B)=probability that it is a white car = 0.08

A/B:vehicle is white,given that vehicle is a car

to find P(A/B)

baye's theorem says that

P(A∩B)=P(A/B)×P(B)

⇒   0.08=P(A/B)×0.36

⇒  P(A/B)=0.2222

Hence, probability that a vehicle is white, given that the vehicle is a car is :

0.2222

Answer: 0.22

Step-by-step explanation:

confirmed

Answer:

[-5/2, 1/2] is the correct answer

Step-by-step explanation:

Subtract the left side to compare to zero:

... 4x^2 +8x -5 ≤ 0

... (2x +5)(2x -1) ≤ 0 . . . . factor

... x = -5/2 . . . or . . . x = 1/2 . . . . are the zeros

The factors will differ in sign (the product will be negative) when x is between the zero values. Hence the solution set is ...

... x ∈ [-5/2, 1/2]

_____

Check

When you normalize the leading coefficient of the quadratic to 1, it becomes ...

... x² +2x -5/4 ≤ 0

Now, you know the sum of zeros must be -2 and the product of zeros must be -5/4. The zeros associated with the answer given in your key have a sum of -4.5 and a product of -5/2. It cannot be right.

B. 3x +y = 4

It is perhaps easiest to simply try the equations to see which one works.

For x=0, there are two different kinds of answers:

... A and C: -y = 4

... B and D: y = 4

Since we know y=4 when x=0 (from the point (0, 4)), we can eliminate choices A and C.

___

Using the point (1, 1), you can try choices B and D to see which works:

... B: 3·1 +1 = 4 . . . . true (put 1 where x and y are in the equation)

... D: -3·1 +1 = -2 = 4 . . . . false

The appropriate choice is the equation of B: 3x +y = 4.

_____

Derive the equation from the given points

There are several ways you can derive the equation. Since you have the y-intercept (the point with x=0), you can use the slope-intercept form to start.

The slope (m) is ...

... m = (change in y)/(change in x) = (4 -1)/(0 -1)

... m = -3

We know the y-intercept (b) is 4, so the slope-intercept form of the equation is ...

... y = mx +b

... y = -3x +4

Adding 3x puts this in standard form:

... 3x +y = 4

The equation of the line passing through points (1,1) and (0,4) is y = -3x + 4 or in standard form -3x + y = 4.

In the subject of mathematics, when it comes to identifying equations of the line in a graph, we consider the points it passes through. In this case, the line passes through the points (1, 1) and (0, 4). The equation of a line can be found using the formula: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. The slope m between two points can be found using the formula: m = (y2 - y1) / (x2 - x1).

Let's substitute the given points into the slope formula and find the slope: m = (4 - 1) / (0 - 1) = -3.  Now, using the slope and one of the points (let's use (0,4)), we substitute into the line formula: y - 4 = -3(x - 0). This simplifies to y = -3x + 4, which aligns with answer D: −3x + y = 4.

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Answer:

ave rate of change = (-6)^(2+2) +3 -  (-6)^(-1+2) +3

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

                                      2+1

Step-by-step explanation:

To find the average rate of change

ave rate of change = f(x2) - f(x1)

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

                                   x2-x1

We know that x2 = 2 and x1 = -1

ave rate of change = f(2) - f(-1)

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

                                   2--1

ave rate of change = (-6)^(2+2) +3 -  (-6)^(-1+2) +3

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

                                      2+1

Answer:

ave rate of change = (-6)^(2+2) +3 -  (-6)^(-1+2) +3

Step-by-step explanation:

Answer:

{x = 1/7 ,y = 1

Step-by-step explanation:

Solve the following system:

{-5 y = -5 | (equation 1)

{7 x + 6 y = 7 | (equation 2)

Swap equation 1 with equation 2:

{7 x + 6 y = 7 | (equation 1)

{0 x - 5 y = -5 | (equation 2)

Divide equation 2 by -5:

{7 x + 6 y = 7 | (equation 1)

{0 x+y = 1 | (equation 2)

Subtract 6 × (equation 2) from equation 1:

{7 x+0 y = 1 | (equation 1)

{0 x+y = 1 | (equation 2)

Divide equation 1 by 7:

{x+0 y = 1/7 | (equation 1)

{0 x+y = 1 | (equation 2)

Collect results:    Answer:    {x = 1/7 ,y = 1

Answer:

No

Step-by-step explanation:

Answer:

x = 2/5

Step-by-step explanation:

[tex]x^3=\dfrac{0.008}{0.125}=\dfrac{8}{125}=\dfrac{2^3}{5^3}\\\\x=\sqrt[3]{\dfrac{2^3}{5^3}}=\dfrac{\sqrt[3]{2^3}}{\sqrt[3]{5^3}}=\dfrac{2}{5}[/tex]

The value of x is 2/5.

Answer:

x = 2/5

Step-by-step explanation:

x^3 = .008/.125

Take the cubed root on each side

x^3 ^ (1/3)  = (.008/.125) ^ 1/3

Using ( a/b) ^c = a^c / b^c  and a^b^c = a^ (b*c)

x^(3 *(1/3))  = (.008) ^ 1/3 / (.125) ^ 1/3

x = (.008) ^ 1/3 / (.125) ^ 1/3

x = .2/.5

x = 2/5

QUESTION 1

a)

Let

[tex]s [/tex]

represent the amount Same earned and

[tex]k[/tex]

represent the amount Kevin earned.

We were told that, they earned $425 dollars together.

This implies that,

[tex]k+s= 425---eqn(1)[/tex]

It was also given that, Kevin earned $25 more than Same.

This implies,

[tex]k-s=25---eqn(2)[/tex]

For equation (1), when

[tex]s=0[/tex]

[tex]k=425[/tex]

We plot the point,

[tex](425,0)[/tex]

When

[tex]k=0[/tex]

[tex]s=425[/tex]

We plot the point,

[tex](0,425)[/tex]

Similarly for the second equation when

[tex]s=0[/tex]

[tex]k=25[/tex]

This gives the point,

[tex](25,0)[/tex]

When

[tex]k=0[/tex]

[tex]s=-25[/tex]

We plot

[tex](0,-25)[/tex]

and draw a straight line through them.

We can see from the graph that the two points intersect at  

[tex](225,200)[/tex]

This implies that

[tex]k=225\:and\:s=200[/tex]

Therefore Kevin earned $ 225

and Same earned $ 200

QUESTION 2

The given system is

[tex]6=-4x + y---eqn(1)[/tex]

and

[tex]-5x-y=21---eqn(2)[/tex]

From equation (2),

[tex]y=-5x-21---eqn(3)[/tex]

Put equation (3) into equation (1).

This implies that,

[tex]6=-4x-5x-21[/tex]

Group like terms,

[tex]6+21=-4x-5x[/tex]

Simplify, to get,

[tex]27=-9x[/tex]

[tex]x=-3[/tex]

We substitute this value into equation (3) to get,

[tex]y=-5(-3)-21[/tex]

[tex]y=15-21[/tex]

[tex]y=-6[/tex]

Therefore the solution is

[tex](-3,-6)[/tex]

QUESTION 3

We want to solve,

[tex]2x+y=20---(1)[/tex]

and

[tex]6x -5y=12---(2)[/tex]

We multiply equation (1) by 3 to get,

[tex]6x+3y=60---(3)[/tex]

Equation (3) minus equation (2) will give us,

[tex]8y=48[/tex]

This means

[tex]y=6[/tex]

Put this value into equation (1) to get,

[tex]2x+6=20[/tex]

[tex]2x=20-6[/tex]

[tex]2x=14[/tex]

[tex]x=7[/tex]

The solution is

[tex](7,6)[/tex]

Answer:

Sam earns $200 and Kevin earns $225.

x , y= -3 , -6 by substitution

x , y= 7, 6 by elimination

Step-by-step explanation:

a) Let the amount earned by Sam = s and the amount earned by Kevin = k

We are given, that they both earn total $425 i.e. s + k = 425

Also, Kevin earns $25 more than Sam i.e. k = s + 25

Hence, the system of equations comes out to be:

s + k = 425

-s + k = 25

b) Take s = x and k = y. See the graph plotted below

c) As the intersection point from the graph comes out to be (s,k) = (200,225)

Therefore, Sam earns $200 and Kevin earns $225.

Now, we have the system

-4x + y = 6

-5x - y = 21

We need to use substitution method.

Take y= -5x - 21 from the 2nd equation and put it in the 1st.

We get, -4x - 5x - 21 = 6  i.e.  -9x = 27  i.e.  x= -3

Now, substitute this value of x in any of the equation to find y.

We get, -5*(-3) - y = 21  i.e.  y = 15 - 21  i.e.  y = -6

Now, we are given the system,

2x + y = 20

6x - 5y = 12

We need to use elimination method.

Multiply 5 by equation 1. We get,

10x + 5y = 100

6x - 5y = 12

Adding the above equations, we get, 16x = 112  i.e. x = 7

Put this value in any of the equation to find the value of y.

We get, y = 20 - 2x  i.e.  y = 20 - 2*7  i.e.  y = 20 - 14  i.e. y = 6

The "rate of change" is presumed to refer to the rate at which the balance in the bank account changes as dues are collected from Art Club members. It increases by $15 for each new collection, so we can say ...

... the rate of change is $15 per member.

We further presume that the problem intends the "initial value" to refer to the fact that the 17 × $15 = $255 does not match the full amount of the current Art Club account balance ($300). So, there must have been some balance in the account before collection started. We can interpret that $45 "initial value" as ...

... the account balance before dues collection started is the initial value.

Answer:

The equation of the line would be y = -3/7x - 20/7

Step-by-step explanation:

To start finding the line of this equation, you need to find the slope. You can do this using the slope equation.

m(slope) = (y2 - y1)/(x2 - x1)

m = (-2 - -5)/(-2 - 5)

m = (-2 + 5)/(-2 - 5)

m = 3/-7

m = -3/7

Now that we have the slope, we can use that and either point in point-slope form to get the equation.

y - y1 = m(x - x1)

y + 5 = -3/7(x - 5)

y + 5 = -3/7x + 15/7

y = -3/7x - 20/7

To find the equation of the line that passes through (-2, -2) and (5, -5), calculate the slope, apply it to the point-slope form using one of the points, then simplify to slope-intercept form, resulting in y = (-3/7)x - 20/7.

To find the equation of the line that passes through the points (-2,-2) and (5,-5), we first need to calculate the slope of the line. The slope (m) can be found using the formula:

m = (y_{2} - y_{1}) / (x_{2}  - x_{1})

Substituting our points into the formula:

m = (-5 - (-2)) / (5 - (-2)) = (-5 + 2) / (5 + 2) = -3 / 7

Next, we use the point-slope form of a line's equation which is y - y1 = m(x - x1). Let's use the first point (-2, -2):

y - (-2) = (-3/7)(x - (-2))

Now we simplify and write the equation in slope-intercept form (y = mx + b):

y + 2 = (-3/7)x - 6/7

Subtract 2 from both sides of the equation to solve for y:

y = (-3/7)x - 6/7 - 14/7

y = (-3/7)x - 20/7

The equation of the line that passes through the points (-2,-2) and (5,-5) is y = (-3/7)x - 20/7.

3 seconds

For the given problem conditions, the parameters in your formula are ...

... h = 0

... r = 48

Putting these values into the equation, we can solve for t.

... 0 = 48t -16t²

... 0 = 16t(3 -t) . . . . . factored

This will be true for t=0 and for t=3

The ball will hit the ground after 3 seconds.

_____

Comment on answer choices

For the ball to take 456 seconds (more than 7 1/2 hours) to hit the ground, it would have to  be launched at 7296 ft/s, several times the speed of sound. Its maximum height would be over 157.5 miles, and all of the usual assumptions about a stationary flat Earth with a uniform gravity field and no air resistance could not apply.

So, we know that 456 seconds is an impossible choice (as are the higher values, such as 1863 seconds). Perhaps that should be 4 5/6 seconds. For that to be the answer, the launch speed would need to be 77 1/3 ft/s, not 48 ft/s.

___

If these are the actual answer choices associated with this problem, it would be a good idea to have your teacher show you how to work it.

Answer:

Step-by-step explanation:

I don't know how is to speak it English correctly but is the teoreme of whole probability

P(A1)=0.08*0.4=0,032 is probability to choose defective item line I

P(A2)=0.1*0.6=0.06  is probability to choose defective item line II

P(B)=P(A1)+P(A2)=0,032+0.06=0.092 probability to choose defective item

P(C)=1-P(B)=0.908 the probability that it is not defective

D. R(x) = 850x +9600

Selling 10 more machines increased revenue from $18100 to $26600, an increase of ...

... $26,600 -18,100 = $8,500

That is, the revenue increased by $8500/10 = $850 per machine.

Only one answer choice has this number in it:

... D. R(x) = 850x+9600

_____

Check

R(10) = 850·10 +9600 = 8500 +9600 = 18,100 . . . . OK

R(20) = 850·20 +9600 = 17000 +9600 = 26,600 . . . . OK

_____

Comment on answer selection

On multiple-choice questions, it is rarely necessary to work out the solution to the problem completely. Usually, it is sufficient to find the one number that discriminates between correct and incorrect answers.

In real life, answers are rarely multiple-choice. You are required to work the problem completely and to figure out how to tell if your answer is correct.

Here, we have worked the problem far enough to find the slope, the amount by which revenue increases when sales increases by 1 unit. The intercept can be found different ways. One of them is to see what number makes the revenue match for one of the "x" values:

... R(10) = 850·10 +b = 18100

... b = 18100 -8500 = 9600

so ...

... R(x) = 850x +9600

We can check this answer by computing R(20), as we have above.

Answer:

R(x)=850x+9600

Step-by-step explanation:

:⊃

Answer:

The answer is: 8km - 4

Step-by-step explanation:

Given: (4k4m - 8)1/2 =

Simplify then multiply 1/2 by each term:

4k4m/2 - 8*1/2 =

16km/2 - 4

8km - 4

Hope this helps! Have an Awesome day!! :-)

Answer:

(A) y - 7 = 2(x -2)

(B) y = -x + 6; y - 5 = -1(x + 1)

(C) Consistent independent

(D) (1, 5)

Step-by-step explanation:

(A) Road 1

(a) Slope

The point-slope formula for a straight line is

y₂ - y₁ = m(x₂ - x₁)     Insert the points  

 3 - 7 = m(0 - 2)

     -4 = m(-2)           Divide each side by -2

     m = -4/(-2)          Divide numerator and denominator by-2,

      m = 2

=====

(b) y-intercept

y₂ - y₁ = m(x₂ - x₁)

y₂ - 7 = 2(x₂ -2)

y - 7 = 2(x -2)

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

(B) Road 2

(a) Slope

y = mx + b

Choose point (3,3)

m = (3 - 5)/(3 - 1)

m = -2/2

m = -1

=====

(b) y-intercept

y = mx +b

Choose point (3,3).

3 = -3 + b      Add 3 to each side

b = 6

=====

(c) Equation of line (point-slope form)

y = mx + b

y = -x + 6

=====

(d) Equation of line (slope-intercept form)

y - 5 = -1(x - 1)

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

(C) Consistency

The two roads intersect.

There is only one point of intersection, so this is a consistent, independent system of equations

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

(D) Point of intersection

(1)      y - 7 = 2(x -  2)

(2)          y =   -x + 6     Substitute (2) into (1)

-x + 6 – 7 = 2(x – 2)    Remove parentheses

       -x - 1 = 2x – 4      Add 4 to each side

       -x +3 = 2x            Add x to each side

             3 = 3x            Divide each side by 3

             x = 1               Substitute into 2

=====

            y = -1 + 6

           y = 5

The point of intersection is (1, 5).

Answer:

Length of Charlie's brother's room  = 8 2/5 feet

Area of Charlie's brother's room  = 60 9/10 feet²

Step-by-step explanation:

Width Charlie's room = 7 1/4 = (7 x 4 +1)/4 = 29/4  feet

Length Charlie's room =  10 1/2 = (10 x 2 +1)/2 = 21/2 feet

Length brother's room = 4/5 x 21/2 = (4 x 21)/(5 x 2) = 84/10 = 8 2/5 feet

Area = Length x Width = (42/5 x 29/4) feet² = 1218/20 feet² = 60 9/10 feet²

[tex]\textit{\textbf{Spymore}}[/tex]

Answer:

77° or 103°

Step-by-step explanation:

All of the angles are either the given angle or its supplement. Corresponding angles are congruent, as are vertical angles. Any linear pair of angles will add to 180°.

Answer:

77° and 103°

Step-by-step explanation:

77° because it says one of the angles is 77°

103° because two parallel lines are equal to 180°

180°-77° is 103°

Answer:

7:10 (boys to girls)

10:7 (girls to boys)

7:17 (boys to everyone combined)

10:17 (girls to everyone combined)

~

Answer:

Point (1,8)  

Step-by-step explanation:

We will use segment formula to find the coordinates of point that will partition our line segment PQ in a ratio 3:1.

When a point divides any segment internally in the ratio m:n, the formula is:

[tex][x=\frac{mx_2+nx_1}{m+n},y= \frac{my_2+ny_1}{m+n}][/tex]

Let us substitute coordinates of point P and Q as:

[tex]x_1=-8[/tex],

[tex]y_1=-4[/tex]

[tex]x_2=4[/tex]

[tex]y_2=12[/tex]

[tex]m=3[/tex]

[tex]n=1[/tex]

[tex][x=\frac{(3*4)+(1*-8)}{3+1},y=\frac{(3*12)+(1*-4)}{3+1}][/tex]

[tex][x=\frac{12-8}{4},y=\frac{36-4}{4}][/tex]

[tex][x=\frac{4}{4},y=\frac{32}{4}][/tex]

[tex][x=1,y=8][/tex]

Therefore, point (1,8) will partition the directed line segment PQ in a ratio 3:1.

Answer:

Step-by-step explanation:

1,8

The simplest form of 38 multiplied by 45 equals  to 1710.

To multiply 38 and 45, we'll use the long multiplication method:

  38

x 45

------

 190   (38 * 5)

+1520  (38 * 40, shift one position to the left)

------

1710

So, 38 multiplied by 45 equals 1710.

Another method is to break down 38 into its factors to simplify the multiplication:

38 = 2 * 19

Now, we can rewrite 38 * 45 as (2 * 19) * 45:

(2 * 19) * 45 = (2 * 45) * 19

             = 90 * 19

Now, we can multiply 90 by 19:

90

x 19

-----

180  (90 * 9, shift one position to the left)

+ 0   (90 * 1, with a zero placeholder)

-----

1710

Again, we get the result as 1710.

So, whether we use long multiplication directly or break down the numbers into factors, the result remains the same: 38 * 45 = 1710.

c - the number

The sum of 7 times a number and 9 is 5:

[tex]7c+9=5[/tex]     subtract 9 from both sides

[tex]7c=-4[/tex]          divide both sides by 7

[tex]\boxed{c=-\dfrac{4}{7}}[/tex]

Answer:

Step-by-step explanation:

We have been given an equation:

[tex]x-3=2\frac{1}{2}[/tex]

(a) Related equation means the equation that are equivalent to the given equation.

We can shift 3 on the right hand side of the equation:

(1)[tex]x=3+2\frac{1}{2}[/tex]

We can solve the mixed fraction [tex]2\frac{1}{2}=\frac{5}{2}[/tex] we get.

(2)[tex]x=3+\frac{5}{2}[/tex]  

We can solve the right hand side of the equation [tex]x=3+\frac{5}{2}[/tex]    we get:

(3)[tex]x=\frac{11}{2}[/tex]

Hence, above three expressions are the related equations of the given equation.

(b) We have to find the related equations that isolates the variable and simplify.

So, basically we can solve for x.

[tex]x=2\frac{1}{2}+3[/tex]

[tex]x=1+3[/tex]

[tex]x=4[/tex].

Answer:

-x^3+5x^2-8x+1, which is choice A

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Work Shown:

f(x) = x^3 - x^2 - 3

f(x) = (x)^3 - (x)^2 - 3

f(2-x) = (2-x)^3 - (2-x)^2 - 3 ................ see note 1 (below)

f(2-x) = (2-x)(2-x)^2 - (2-x)^2 - 3 ........... see note 2

f(2-x) = (2-x)(4-4x+x^2) - (4-4x+x^2) - 3 ..... see note 3

f(2-x) = -x^3+6x^2-12x+8 - (4-4x+x^2) - 3 ..... see note 4

f(2-x) = -x^3+6x^2-12x+8 - 4+4x-x^2 - 3 ....... see note 5

f(2-x) = -x^3+5x^2-8x+1

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note1: I replaced every copy of x with 2-x. Be careful to use parenthesis so that you go from x^3 to (2-x)^3, same for the x^2 term as well.

note2: The (2-x)^3 is like y^3 with y = 2-x. We can break up y^3 into y*y^2, so that means (2-x)^3 = (2-x)(2-x)^2

note3: (2-x)^2 expands out into 4-4x+x^2 as shown in figure 1 (attached image below). I used the box method for this and for note 4 as well. Each inner box or cell is the result of multiplying the outside terms. Example: in row1, column1 we have 2 times 2 = 4. You could use the FOIL rule or distribution property, but the box method is ideal so you don't lose track of terms.

note4: (2-x)(4-4x+x^2) turns into -x^3+6x^2-12x+8 when expanding everything out. See figure 2 (attached image below). Same story as note 3, but it's a bit more complicated.

note5: distribute the negative through to ALL the terms inside the parenthesis of (4-4x+x^2) to end up with -4+4x-x^2

Answer:

–x3 + 5x2 – 8x + 1

–x3 + 7x2 – 16x – 15

x3 + 5x2 + 8x + 1

x3 – 7x2 + 16x – 15

Step-by-step explanation:

–x3 + 5x2 – 8x + 1

–x3 + 7x2 – 16x – 15

x3 + 5x2 + 8x + 1

x3 – 7x2 + 16x – 15