solving these quadratics for x using complete the square 3x^2-4x-1=0

Answer:

The absolute maximum and minimum of [tex]f(x) = 5 + 54\cdot x -2\cdot x^{3}[/tex] on [tex][0,4][/tex] are 113 and 5.

Step-by-step explanation:

Let be [tex]f(x) = 5 + 54\cdot x -2\cdot x^{3}[/tex], the first and second derivatives of the function are, respectively:

[tex]f'=54-6\cdot x^{2}[/tex]

[tex]f''=-12\cdot x[/tex]

Now, let equalize the first derivative to zero and solve the resulting expression:

[tex]54-6\cdot x^{2} = 0[/tex]

[tex]x^{2} = 9[/tex]

[tex]x =\pm 3[/tex]

According to the given interval, only [tex]x=3[/tex] is a valid outcome. Lastly, this is evaluated in the second derivative expression:

[tex]f''=-12\cdot(3)[/tex]

[tex]f'' = -36[/tex]

[tex]x = 3[/tex] leads to an absolute maximum.

[tex]f(3) = 5 + 54\cdot (3) -2\cdot (3)^{3}[/tex]

[tex]f(3) = 113[/tex]

The absolute minimum is determined by evaluating at each extreme of the interval:

[tex]x = 0[/tex]

[tex]f(0) = 5 + 54\cdot (0) -2\cdot (0)^{3}[/tex]

[tex]f(0) = 5[/tex]

[tex]x = 4[/tex]

[tex]f(4) = 5 + 54\cdot (4) -2\cdot (4)^{3}[/tex]

[tex]f(4) = 93[/tex]

The absolute maximum and minimum of [tex]f(x) = 5 + 54\cdot x -2\cdot x^{3}[/tex] on [tex][0,4][/tex] are 113 and 5.

Multiplication

2, 56, 0, 56, 18, 0, 3, 0, 20, 12

12, 54, 7, 64, 18, 25, 24, 0, 0, 28

14, 8, 6, 24, 35, 9, 27, 48, 40, 1

0, 3, 18, 16, 8, 7, 0, 0, 36, 48

49, 28, 40, 42, 15, 6, 27, 16, 36, 8

0, 32, 81, 4, 30, 0, 0, 9, 32, 10

30, 2, 45, 16, 5, 0, 0, 14, 35, 18

0, 54, 0, 12, 36, 24, 4, 8, 10, 18

72, 6, 63, 12, 0, 21, 0, 24, 63, 0

21, 20, 9, 15, 45, 0, 6, 72, 5, 4

don't give up you got it always stay positive

Answer:

θ = 5π/6 rad and 11π/6 rad

Step-by-step explanation:

Given the expression cotθ+√3=0

Subtract √3 from both sides

cotθ+√3-√3=0-√3

cotθ = -√3

Since cotθ = 1/tanθ

1/tanθ = -√3

Reciprocate both sides:

tanθ = -1/√3

θ = tan^-1(-1/√3)

θ = -30°

Since the angle is negative, and tanθ is negative in the second and fourth quadrant.

In the second quadrant;

θ = 180-30

θ = 150°

Since 180° = πrad

150° = 150π/180

150° = 5π/6 rad

In the fourth quadrant;

θ = 360-30

θ = 330°

Since 180° = πrad

330° = 330π/180

330° = 11π/6 rad

Hence the solutions are 5π/6 rad and 11π/6 rad.

Answer:

138

Step-by-step explanation:

f(x)= 18x + 12

Let x = 7

f(7) = 18*7 +12

     = 126+12

     = 138

Answer:

f(7) = 138

Step-by-step explanation:

[tex]f(x)= 18x + 12\\f(7) = ?\\\\f(7) = 18(7) +12\\f(7) = 126+12\\f(7)=138[/tex]

Answer:

[tex]4x^3-7x^2-23x-10[/tex]

Step-by-step explanation:

So we have the expression:

[tex](4x+5)(x^2-3x-2)[/tex]

Distribute. Multiply (4x+5) to each term:

[tex](x^2)(4x+5)+(-3x)(4x+5)+(-2)(4x+5)[/tex]

Distribute:

[tex]=(4x^3+5x^2)+(-12x^2-15x)+(-8x-10)[/tex]

Combine like terms:

[tex]=(4x^3)+(5x^2-12x^2)+(-15x-8x)+(-10)[/tex]

Add and simplify:

[tex]=4x^3-7x^2-23x-10[/tex]

And this is in descending order, so it's in standard form.

Answer:

find a shorter water-route to Asia.

Step-by-step explanation:

The Histogram is attached blow.

A histogram is a representation of statistical data that makes use of rectangles to illustrate the frequency of data items in a series of equal-sized numerical intervals. The independent variable is represented along the horizontal axis and the dependent variable is plotted along the vertical axis in the most popular type of histogram.

Given:

Data: 4,4,6, 11, 11, 12, 14, 14, 21, 21, 24, 26

So, Interval           Frequency

      0- 5                     4 , 4 (2)

       5-10                      6(1)

      10- 15                    11, 11, 12, 14, 14  

     15- 20                      _

     20- 25                  21, 21, 24

     25- 30                        26

Hence, the Histogram is attached blow.

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Answer:

  z = {1 +i, 1 -i, -1 +i, -1 -i}

Step-by-step explanation:

Using Euler's formula, you can write this as ...

  z^4 = 4e^(i(π+2kπ))

Then the 4th root is ...

  z = 4^(1/4)e^(i(π/4 +kπ/2)) = √2(cos(π/4+kπ/2) +i·sin(π/4+kπ/2))

for integers k in the range 0 to 3.

  z = √2(±1/√2 ±i·1/√2) . . . signs are independent

  z = ±1 ±i . . . . . . signs are independent; hence 4 solutions

  z = {1 +i, 1 -i, -1 +i, -1 -i}

_____

Comment on roots of complex numbers

In the complex domain, each number has a number of roots equal to the index of the root. That is, there are four 4th roots. They all have the same magnitude, but their angles are separated by 360°/(root index) = 90°. Here, the principal fourth root of 4∠180° is 4^(1/4)∠(180°/4) = √2∠45° = 1+i.

Adding 90° is equivalent to multiplying by i, so the other 3 roots are √2∠135° = -1+i, √2∠225° = -1 -i, and √2∠315° = 1 -i.

 z = {1 +i, 1 -i, -1 +i, -1 -i}

Answer:

Because the base of this expression is not same.

Answer:

In exponential form

3.2615 X 10¹

Answer:

5 + 4i

Step-by-step explanation:

In general, the conjugate of a + bi is a - bi

The answer can be seen on the attachment that I have given.

The two equations that represent the remaining angle relationships are (x = 60 - 2(y + z)) and (x = 2z + 20) and this can be determined by using the given data.

Given :

The linear equation that represents the situation "The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles" is:

x = 60 - 2(y + z)  --- (1)

The linear equation that represents the situation "The largest angle is twice the smaller angle plus 20 degrees" is:

x = 2z + 20  --- (2)

Therefore, the correct option is A) and E).

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Answer:

x < 6

Step-by-step explanation:

Given

5x - 9 < 21 ( add 9 to both sides )

5x < 30 ( divide both sides by 5 )

x < 6

Answer:

x < 6

Step-by-step explanation:

5x-9<21

Add 9 to each side

5x-9+9<21+9

5x < 30

Divide by 5

5x/5 < 30/5

x < 6

Answer:

C) 1 5/16

Step-by-step explanation:

(3/4)/(4/7)=(3/4)(7/4)=21/16=1 5/16

Answer:

B. (13-6) n - 55

Step-by-step explanation:

The number of shirts to be sold is n

The cost to purchase one shirt is $13

The cost of making each shirt is $6

Let's assume the shirt is one

Profit for a Shirt = (13-6)

But then there are no number of shirts

Profit= (13-6)n

But then also, an advert was run for the total shirts combined

Profit= (13-6)n -55

Answer:

b. (13-6)n-55

ap3x

Answer:

answer choice D

Step-by-step explanation:

CORRECT ANSWER IS D

i believe

Answer: Jenna did not multiply how much 4 goes into 14 which is 3.5 she should have multiplied 4*3.5=14 and 6*3.5=21

Step-by-step explanation:

so the answer should have been 4/6 is equivalent to 14/21

Answer:

32 miles per gallon

Step-by-step explanation:

351 divided by 11 = 31.90909090909090909090909090 e.t.c

Answer:

Find a number that can be divided by both 6 and 9, which is 18. That means they will do laundry on the same day every 18 days.

Answer: 18 Days

Step-by-step explanation:

Let's look at their indivigual schedules for hte nex little While

<-0------6------12---->

t=Tim does laundry every 9 days

<-0---------9---------->

They haven't done laundry on the same day again yet, so let's keep going!

When we keep goin, we see thar the multiple first meet at 18

Ronal

<-0----6----18----27---->

Tim

<-0----9----18----27--->

Mathematically, we say that 18 is the least common multiple of 6 and 9. in math notation this looks like:

lcm (6, 9) = 18

Answer:

the volume of the 2nd box is 1200 cubic inches

Step-by-step explanation:

Answer:

198

Step-by-step explanation:

Answer:6

Step-by-step explanation:

Answer:

Step-by-step explanation:

If A ⊂ B, that is, A is a subset of B

Also, B ⊂ A, that is, B is a subset A

Therefore, A = B in all respect.

A set is a mathematical model for a collection of items. If two sets are subsets of each other, the other relationship they must have is that they both are equal.

A set is a mathematical model for a collection of items; it comprises elements or members, which may be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.

If there exist two subsets such that A is a subset of B, also, B is the subset of A. Then the two sets are equal or the same.

Hence, If two sets are subsets of each other, the other relationship they must have is that they both are equal.

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Step-by-step explanation:

[tex]\huge{\purple{\underline{\underline{\bf{\pink{Answer}}}}}}[/tex]

[tex]\huge{\purple{\underline{\underline{\bf{\pink{Given}}}}}}[/tex]

It is a parrelogram

[tex]\huge\star{\underline{\mathtt{\red{To}\pink{f}\green{i}\blue{n}\purple{d}\orange{-:}}}}⋆[/tex]

X and Y

Solution

angle a = c. (opposite angles of 11gm is equal)

put the values of and c

x+45 = 3x-13

now take the variables to the l.H.S and number to R.H.S

x-3x = -13-45

-2x. = 58

x. = 58÷2

x. = 29

angle d + c = 180° (cointerior angle)

y + 3(29) + 13 =180°

y + 100 = 180°

y. = 80

Hope it helps

Answer:

B C D

Step-by-step explanation:

i did the assignment

Answer:

rectangle, triangle,trapezoid

Step-by-step explanation:

Answer: 16

Step-by-step explanation:

Answer:

10626 ways

Step-by-step explanation:

Given

Number of students = 23

Prizes = 3

Required

Number of different outcomes for the top 3

This question will be solved using permutation formula because it implies selection of 3 students from 23

[tex]^nP_r = \frac{n!}{(n-r)!}[/tex]

Where n = 23 and r = 3

The formula becomes

[tex]^{23}P_3 = \frac{23!}{(23-3)!}[/tex]

[tex]^{23}P_3 = \frac{23!}{(20)!}[/tex]

[tex]^{23}P_3 = \frac{23!}{20!}[/tex]

[tex]^{23}P_3 = \frac{23 * 22 * 21 * 20!}{20!}[/tex]

[tex]^{23}P_3 = 23 * 22 * 21[/tex]

[tex]^{23}P_3 = 10626[/tex]

Hence, there are 10626 ways

Answer:

Square Root 34

Step-by-step explanation:

Answer:

[tex]\sqrt{34}[/tex]

Explanation:

sub in the values for x1, x2, y1 and y2

[tex]\sqrt{(-2-3)^2+(2-(-1))^2}[/tex]

subtract and evaluate

= [tex]\sqrt{(-5)^2+3^2}[/tex]

= [tex]\sqrt{25+9}[/tex]

= [tex]\sqrt{34}[/tex]

Answer:

Two other names for WQ are QW and line g.

Step-by-step explanation:

A line can have as many points as possible. The two other names for WQ are QW and line g

From the given plane, we can observe the following:

This means that, we can rename WQ as

Hence, the two other names for WQ are QW and line g

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