hey guys I need help again!

Answer:

Step-by-step explanation:

How can we solve equations such as the cubic equation shown here?

   x3 − x2 – 4x + 4 = 0

There is an extremely complicated formula for solving cubic equations. Some calculators have this formula built in and therefore can be used to solve cubic equations.

We are going to learn how these equations can be solved by factorising. If the equation has solutions that are integers  a, b and c then we can factorise the equation as follows:

   x3 − x2 – 4x + 4 = (x − a)(x − b)(x − c) = 0

Multiplying the brackets together we see that the constant term, 4, must be the number we get when we multiply a, b and c together.

   abc = 4

All the solutions a, b and c must be factors of 4 so there are not many whole numbers that we need to consider.

We have only the following possibilities:

   ±1, ±2 and ±4

We’ll examine each of these numbers to find which ones are solutions of the equation.

   f(1) = 13 − 12 – 4×1 + 4 = 0                        1 is a solution

   f(−1) = (−1)3 − (−1)2 – 4×(−1) + 4 = 6    

   f(2) = 23 − 22 – 4×2 + 4 = 0                         2 is a solution

  f(−2) = (−2)3 − (−2)2 – 4×(−2) + 4 = 0        −2 is a solution

We have now found three solutions so we don’t need to try  4 and −4 as a cubic equation has a maximum of three solutions.

These three numbers give us the values of a, b and c and we can  factorise the equation.

   x3 − x2 – 4x + 4 = (x − 1)(x − 2)(x + 2) = 0

This method involves finding integers that are factors of ( can be divided into ) the constant term and then testing whether these integers are solutions of the equation.

Unfortunately we cannot assume that the solutions of a third degree equation are all integers.

However, if we can find one integer solution, lets say it is x = a then, by the remainder theorem , we know that (x − a) is a factor of the equation. We can find another factor, a quadratic factor,  by division. We can then solve the quadratic equation by using the formula for solving quadratics.

Example 1

Solve the equation x3 − 3x2 – 2x + 4 = 0

We put the numbers that are factors of 4 into the equation to see if any of them are correct.

   f(1) = 13 − 3×12 – 2×1 + 4 = 0                        1 is a solution

   f(−1) = (−1)3 − 3×(−1)2 – 2×(−1) + 4 = 2    

   f(2) = 23 − 3×22 – 2×2 + 4 = −4

   f(−2) = (−2)3 − 3×(−2)2 – 2×(−2) + 4 = −12

   f(4) = 43 − 3×42 – 2×4 + 4 = 12

   f(−4) = (−4)3 − 3×(−4)2 – 2×(−4) + 4 = −100

The only integer solution is x = 1. When we have found one solution we don’t really need to test any other numbers because we can now solve the equation by dividing by (x − 1) and trying to solve the quadratic we get from the division.

Now we can factorise our expression as follows:  

   x3 − 3x2 – 2x + 4 = (x − 1)(x2 − 2x − 4) = 0

It now remains for us to solve the quadratic equation.  

   x2 − 2x − 4 = 0

We use the formula for quadratics with a = 1, b = −2 and c = −4.

We have now found all three solutions of the equation x3 − 3x2 – 2x + 4 = 0. They are: eftirfarandi:

   x = 1

   x = 1 + Ö5

   x = 1 − Ö5

Example 2

We can easily use the same method to solve a fourth degree equation or equations of a still higher degree. Solve the equation f(x) = x4 − x3 − 5x2 + 3x + 2 = 0.

First we find the integer factors of the constant term, 2. The integer factors of 2 are ±1 and ±2.

   f(1) = 14 − 13 − 5×12 + 3×1 + 2 = 0                       1 is  a  solution

   f(−1) = (−1)4 − (−1)3 − 5×(−1)2 + 3×(−1) + 2 = −4

   f(2) = 24 − 23 − 5×22 + 3×2 + 2 = −4

   f(−2) = (−2)4 − (−2)3 − 5×(−2)2 + 3×(−2) + 2 = 0   we have found a second solution.

The two solutions we have found 1 and −2  mean that we can divide by x − 1 and x + 2 and there will be no remainder. We’ll do this in two steps.

First divide by x + 2

Now divide the resulting cubic factor by    x − 1.

We have now factorised

f(x) = x4 − x3 − 5x2 + 3x + 2 into

f(x) = (x + 2)(x − 1)(x2 − 2x − 1)  and it only remains to solve the quadratic equation

x2 − 2x − 1 = 0.  We use the formula with a = 1, b = −2 and c = −1.

Now we have found a total of four solutions. They are:

   x = 1

  x = −2

  x = 1 +

  x = 1 −

hopefully this helps!:)

Answer:

Which two equations represent the same function?

A) y = 2x – 7  and f(x) = 7 – 2x

B) 3x = y – 2  and f(x) = 3x – 2

C) f(x) = 3x2 + 5 and y = 3x2 + 5

D) None of the above

Show/Hide Answer

A) y = 2x – 7  and f(x) = 7 – 2x

Incorrect. These equations look similar but are not the same. The first has a slope of 2 and a y-intercept of −7. The second function has a slope of −2 and a y-intercept of 7. It slopes in the opposite direction. They do not produce the same graph, so they are not the same function. The correct answer is f(x) = 3x2 + 5 and y = 3x2 + 5.

B) 3x = y – 2  and f(x) = 3x – 2

Incorrect. These equations represent two different functions. If you rewrite the first equation in terms of y, you’ll find the equation of the function is y = 3x + 2. The correct answer is f(x) = 3x2 + 5 and y = 3x2 + 5.

C) f(x) = 3x2 + 5 and y = 3x2 + 5

Correct. The expressions that follow f(x) = and y = are the same, so these are two different ways to write the same function: f(x) = 3x2 + 5 and y = 3x2 + 5.

D) None of the above

Incorrect. Look at the expressions that follow f(x) = and y =. If the expressions are the same, then the equations represent the same exact function. The correct answer is f(x) = 3x2 + 5 and y = 3x2 +

Step-by-step explanation:

Answer:

36% ÷2 =18%

25%

18%+25%=43%

Answer:

Calculator soup has a calculator that can do that

Step-by-step explanation:

Answer:

I believe the answer is B

Step-by-step explanation:

PLZ MARK BRAINLIEST

Answer:

6.5 $

Step-by-step explanation:

by simply adding the different items that were bought you get the result

Answer: b) exponential.

Step-by-step explanation: the picture shows that the line is not going in a straight line. so it cant be linear.  

Answer: Choice D

Natural Numbers, Whole Numbers, Integers, Rational Numbers

Step-by-step explanation:

As a positive whole number, it is a Natural Number.

Integers include all the positive and negative whole numbers, and zero.

It can be written as 1972/1 As such it is a rational number. (irrational are values like pi, √3, ∛4 which cannot be expressed as fractions where the numerator and denominator must be integers.

Answer:

d looks like the best answer

Step-by-step explanation:

Answer: For a translation, you need a distance and a direction.

For a rotation, you need a point that is the center of the rotation and the degree (and sometimes direction) of rotation.

For reflection you need the axis or a defined line that the triangle is reflected across.

Step-by-step explanation:

Answer:

C) 67%

Step-by-step explanation:

In Mr. Changs class

there are 28 students in total

4 over 7 = 4/7 = out of every 7 students 4 are girls.

2 - Use mathematical reasoning

To figure out how many girls;

Out of the for every 7 students of the 28 total 4 are girls

With that in mind we'll need to know how many groups of 7 there are which is 28/7

We know now that there are 4 groups of 7 students, so with there being 4 girls in each group, we multiple 4 girls across each group which is 4 x 4

This equals 16

To summarize what I did, I divided 28 by 7 and multiplied that by 4 (How many girls per) which is the same as multiplying 28*4 and dividing that by 7

which is the same as 28 x 4/7

Reasoning

[tex]\frac{28~students}{1~class} * \frac{4~girls}{7~students} = \frac{28~students~*~4~girls}{7~students} = \frac{28~*~4}{7} = 16[/tex]

Answer:28 times 4 over 7 = 16

Step-by-step explanation:now mark the outher person as brainlyest its the little cronw

Answer:

Step-by-step explanation:

Answer:

the guy one the top is the answer

Step-by-step explanation:

Answer:

x = 7.5

Step-by-step explanation:

Step 1: Create a fraction with the known sides

[tex]\frac{x}{10}[/tex]

Step 2: Set the fraction equal to the scale factor

[tex]\frac{x}{10}= \frac{0.75}{1}[/tex]

Cross multiple to solve for x

[tex]x=7.5[/tex]

Therefore x is equal to 7.5

Answer: all of them are equivalent to the ratio 3:4 so they're all correct.

Answer:

It would be mg, so the last option, I believe

Answer:

mg

Step-by-step explanation:

I just know it no explanation

Step-by-step explanation:

The expression is: 7 × -5 - 7

The value of the expression is: -42

-35 - 7 = -42

Answer:

Expression: (7*-5) - 7

= -35 - 7

Value = -42

Step-by-step explanation:

When using "less than", the problem is asking for you to subtract a value from something. "Product" means to multiply, therefore we multiply negative 5 and 7 to get negative 35, then subract 7 to get negative 42.

Answer:

756723

Step-by-step explanation:

bc its right

Answer:

A. $232.85

B. No

Step-by-step explanation:

A.  $87 + $48 + $35 + $26 + $37 = $233

$233 - 0.15 (sign they saw spend $200, Save 15%) = $232.85

(Got 0.15 from the picture below)            

B.  No, Waylon shouldn't spend more to qualify for a higher discount because the price will be more higher.

Answer:

Depends

Step-by-step explanation:

Well first to get to fraction multiply 3/4 by two = so there is 6 /8 of a cup of sugar for every 1/8 of butter so  8X6 = 48 so for every full cup like 8/8 there would be 48/8 cups of sugar or 6 full cups

Answer:

the answer is 3 im like 50 50 with that but i tried

hope this helped

Step-by-step explanation:

Step 1 - Find Whole Number

Calculate out how many times the denominator goes into the numerator. To do that, divide 7 by 3 and keep only what is to the left of the decimal point:

7 / 3 = 2.3333 = 2

Step 2 - Find New Numerator

Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.

 7 - (3 x 2) = 1

Step 3 - Get Solution

Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer. 7/3 as a mixed number is:

2 1  

       3   well 2 and 1/3rd

Answer:

A

Step-by-step explanation:

Kirk:

5' 4" tall

Joey

4' 8" tall

1.1 - Convert to inches

Kirk: 5' = (12*5) inches (Every foot is 12 inches) = 60 inches + 4 = 64 inches

Joey: 4' = (12*4) inches = 48 inches + 8 = 56 inches

1.2 - Find the difference

64 - 56 = 8 inches (Since its not divisible by 12 we leave it as is.)

Because I was able to solve this without trouble there is no missing info. Letter A

Answer:

W=249.45x-31.75

Step-by-step explanation:

I can't really explain but I'm pretty sure this is the answer

Answer: To find the y-intercept, begin at the origin and move vertically to the graphed line.

To find the x-intercept, begin at the origin and move horizontally to the graphed line.

Step-by-step explanation:

There seems to be a typographical error in the answer choices.

To find the y-intercept you move vertically, up or down the y-axis.

To find the x-intercept you move horizontally, right or left the x-axis.

I made the corrections in my answer.

The description of the equation in the answers, "m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction." looks like

[tex]m=\frac{{y_{2-y_{1} } } }{x_{2-x_{1} } }[/tex]  It means to put the difference in y-values 0 -(-6) in the numerator

and put the difference in the x-values in the denominator 3 - 0.  Simplify, Then divide.

I hope this helps!

Answer:

answer is C.

Step-by-step explanation:

Answer:

it's Zac Efron for sure, Leonardo DiCaprio is just not the same...

Answer:

no

Step-by-step explanation:

the x axis (the nubers on the right side) cannot be stacted on the same number while being on the x axis so the anser id no