Find the local and global extrema for the graph of ƒ(x) = x3 – 6x2.

Answer:

The answer in the procedure

Step-by-step explanation:

Let

A1 ------> the area of the first square painting

A2 ---->  the area of the second square painting

D -----> the difference of the areas

we have

[tex]A1=81x^{2}-90x-25[/tex]

[tex]A2=25x^{2}+30x+9[/tex]

case 1) The area of the second square painting is greater than the area of the first square painting

The difference of the area of the paintings is equal to subtract the area of the first square painting from the area of the second square painting

D=A2-A1

[tex]D=(25x^{2}+30x+9)-(81x^{2}-90x-25)[/tex]

[tex]D=(-56x^{2}+120x+34)[/tex]

case 2) The area of the first square painting is greater than the area of the second square painting

The difference of the area of the paintings is equal to subtract the area of the second square painting from the area of the first square painting

D=A1-A2

[tex]D=(81x^{2}-90x-25)-(25x^{2}+30x+9)[/tex]

[tex]D=(56x^{2}-120x-34)[/tex]

Final answer:

To find the difference between the areas of two square paintings, subtract the second area from the first to get an expression. By direct subtraction and using the distributive property, both methods yield the expression[tex]56x^2 - 120x - 34[/tex].

Explanation:

To find an expression that represents the difference between the areas of two square paintings, we simply subtract the area of the second painting from the area of the first painting.

The area of the first painting is [tex]81x^2 - 90x - 25,[/tex] and the area of the second painting is [tex]25x^2 + 30x + 9.[/tex]To find the difference, calculate [tex](81x^2 - 90x - 25) - (25x^2 + 30x + 9).[/tex]

Here's the direct subtraction method:

Subtract the [tex]x^2[/tex] terms: [tex]81x^2 - 25x^2 = 56x^2[/tex].

Subtract the x terms: -90x - 30x = -120x.

Subtract the constant terms: -25 - 9 = -34.

Combining these, we get the expression representing the difference in areas:[tex]56x^2 - 120x - 34.[/tex]

Another way to find the solution is using the distributive property to first factor out a negative from the second polynomial, making it easier to subtract:

Rewrite as[tex]: (81x^2 - 90x - 25) - 1*(25x^2 + 30x + 9).[/tex]

Distribute the negative sign:: [tex](81x^2 - 90x - 25) - 1*(25x^2 + 30x + 9)..[/tex]

Now proceed as in the direct subtraction method above.

The final result is the same: [tex]56x^2 - 120x - 34.[/tex]

To get the length of AC, you would add AB to BC

AB = 3x

BC = 2x +3

Add together:

3x + 2x +3 = 5x +3

The answer is A.

Answer:

6x=90

Divide by 6 for 6x and 90

6x/6=90/6

x=15

Check answer by using substitution method

6x=90

6(15)=90

90=90

Answer is x=15

Answer:

Step-by-step explanation:

6x = 90                  Divide by 6

6x/6 = 90/6

x = 15

Answer:

1436.03 units³

Step-by-step explanation:

The formula for the volume of a sphere of radius r is

V = (4/3)πr³.  We'll use 3.14 for π.

Then:

V = (4/3)(3.14)(7 units)³.  To the nearest hundredth:  1436.03 units³

Answer:

Step-by-step explanation:

Given

r = 7

pi = 3.14

Formula

V = (4/3) pi * r^3

Solution

V = (4/3) * pi * 343

V = (1.3333) * 3.14 * 343

V = 1435.99 You are going to get a lot of variation in this question: Everything depends on what value you use for 4/3. I used 1.3333 but it does go on. I would try this yourself. Whatever you get, enter it.

You are better off using 3.14 than using pi. You are still going to have to problem of how to represent 4/3

Answer:

A motor-powered bike has wheels that travel a linear distance of approximately 62.8 inches in one

revolution. What is the central angle the bike wheels turn through, in degrees, when the bike travels 2

inches?​

Step-by-step explanation:

PLEASE HELP!!

A motor-powered bike has wheels that travel a linear distance of approximately 62.8 inches in one

revolution. What is the central angle the bike wheels turn through, in degrees, when the bike travels 2

inches?​

The central angle the bike wheels turn through, in degrees when the bike travels 2 inches will be 11.46°.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

Area of the circle = πr² and the perimeter of the circle = 2πr where r is the radius of the circle.

The linear distance in one revolution = perimeter of a circle or wheel

Perimeter = 2πR

R = 62.8/(2π)

R = 9.99 = 10 inches.

When L = 2 inches the center angle will be as,

Ф = L/R

Ф = 2/10 = 0.2 radian

In degree → 0.2 × 180/π = 11.46°

Hence "The central angle the bike wheels turn through, in degrees when the bike travels 2 inches will be 11.46°".

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5 weeks

8×2.5=20

2×2.5=5

ANSWER

$28

EXPLANATION

The profit function is given as:

[tex]p(x) = - 2 {(x - 9)}^{2} + 100[/tex]

where x is the price of the T-shirt in dollars.

To find the profit on a T-shirt whose price is $15, we substitute x=15 into the function and simplify.

[tex]p(15) = - 2 {(15 - 9)}^{2} + 100[/tex]

We simplify to get:

[tex]p(15) = - 2 {(6)}^{2} + 100[/tex]

[tex]p(15) = -72+ 100[/tex]

[tex]p(15) = 28[/tex]

Answer:

$2

Step-by-step explanation:

Answer:$2.04

Step-by-step explanation:

Answer:

x >  2

Step-by-step explanation:

Given

- 8x + 2x - 16 < - 5x + 7x ← simplify both sides

- 6x - 16 < 2x ( subtract 2x from both sides )

- 8x - 16 < 0 ( add 16 to both sides )

- 8x < - 16 ( divide both sides by - 8 )

Remembering to reverse the symbol as a consequence of dividing by a negative value.

x > 2

Answer:

n = - 3

Step-by-step explanation:

It's not cheating unless this question is from a quiz or test.

5+0.5(6n+14)=3                Subtract 5 from both sides.

5-5 + 0.5(6n+14) = 3 - 5   Combine

0.5(6n+14) = - 2                There are two ways to go. I prefer dividing by 0.5

0.5(6n+14)/0.5 = -2/0.5    Do the division

6n + 14 = - 4                      Subtract 14

6n+14-14= -4-14                 Combine

6n = - 18                             Divide both sides by 6

6n/6 = - 18/6                      Combine

n = - 3      

The solution to the equation 5+0.5(6n+14)=3 will be n = - 3      

WE are given the equation as;

5+0.5(6n+14)=3                

We need to find the value of n here;

Subtract 5 from both sides.

5-5 + 0.5(6n+14) = 3 - 5  

Combine

0.5(6n+14) = - 2                

0.5(6n+14)/0.5 = -2/0.5    

6n + 14 = - 4                      

6n+14-14= -4-14                

6n = - 18                            

Divide both sides by 6

6n/6 = - 18/6                      

n = - 3      

Therefore, the solution to the equation 5+0.5(6n+14)=3 is n = - 3      

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Answer:

Check attached graph

Step-by-step explanation:

Given equation is [tex]y=x-2[/tex].

Now we need to graph the given equation [tex]y=x-2[/tex].

To graph that we can find two points then join them by a straight line.

We are free to plug any number for x say x=0 and x=2

plug x=0

[tex]y=x-2=0-2=-2[/tex]

Hence first point is (0,-2).

plug x=2

[tex]y=x-2=2-2=0[/tex]

Hence first point is (2,0).

Now graph both points and joint them to get final graph as shown below.

let's firstly convert the mixed fractions to improper fractions and then divide.

[tex]\bf \stackrel{mixed}{-4\frac{3}{5}}\implies \cfrac{-4\cdot 5+3}{5}\implies \stackrel{improper}{\cfrac{-23}{5}}~\hfill \stackrel{mixed}{1\frac{1}{5}}\implies \cfrac{1\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{6}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{-23}{5}\div \cfrac{6}{5}\implies \cfrac{-23}{\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\cdot \cfrac{\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{6}\implies \cfrac{-23}{6}\implies -3\frac{5}{6}[/tex]

Okay I'm assuming this is a mixed fraction -4 ⅗ ÷ 11/5

First step get rid of the mixed fraction.

4 multiplied by 5 is 20 then you add 3 and you get 23

Next step cross cancel

-23     times    11     equals   -23

 5                    5                     11

improper fraction so convert to mixed number

answer is -2 1/11    

if you're still confused lemme know

Answer:

a. 6km

b. 6.185 km

c. 18.37 km

Step-by-step explanation:

The question is on finding the distance of between two points

The general formulae is given by;

[tex]d= \sqrt{(X2-X1)^2+(Y2-Y1)^2}[/tex]

Where d is the distance

Given that;

1 unit on grid = 1.5 km

a. Finding distance between the library and Town A

A (-2,3)  and library (2,3)

[tex]d= \sqrt{(2- -2)^2  + (3-3)^2} \\\\= \sqrt{4^2} \\= 4[/tex]

Actual distance = 4 × 1.5 = 6 km

b. Distance between the library and Town B is

library (2,3)  and town B (1, -1)

[tex]d=\sqrt{(1-2)^2+ (-1-3)^2} \\\\\\d=\sqrt{-1^2 +-4^2}\\ \\\\d=\sqrt{1+16} \\\\\\d=\sqrt{17}  = 4.123[/tex]

Actual distance = 4.123×1.5 =6.185 km

c. First find the distance between Town B and Town C

Town B (1, -1) and Town C (-3,-2)

[tex]d=\sqrt{(-3-1)^2 + (-2--1)^2} \\\\d=\sqrt{-4^2 + -1^2} \\\\d=\sqrt{16+1} \\\\d=\sqrt{17} \\\\d=4.123[/tex]

Actual distance= 4.123×1.5 =6.185 km

Total distance traveled by Amelia = 6 +6.185 +6.185 =18.37 km

Answer:

1 whole and 1 over 12

Step-by-step explanation:

Answer:

Step-by-step explanation:

7

12

+

3

6

=

7

12

+

3

6

=

7

12

+

1

2

=

7

12

+

6

12

=

7+6

12

=

13

12

(Decimal: 1.083333)

Answer:

x = 3

Step-by-step explanation:

Only one of the choices matches the given points:

x = 3

Answer:

See below.

Step-by-step explanation:

Either 3 packets of 6 pens  or

2 packets of 9 pens.

he could buy 3 packs of 6

or 2 packs of 9

Answer:

Step-by-step explanation:

(6x - y)(2x - y + 2)=

= 12x^2 - 6xy + 12x - 2xy + y^2 - 2y

= 12x^2 - 8xy + 12x + y^2 - 2y

Answer:

B 12x2 – 8xy + 12x + y2 – 2y

Step-by-step explanation:

Answer: 1/16

Step-by-step explanation:

1/2 would become 8/16 so 9-8 equals 1 and then just add the denominator so 1/16

Answer:

8) h = 30

r = 16

l= 34

Surface Area= 2514.28

Volume= 8045.71

9) r = 12

h = 2

l = 5/2

Surface Area= 908.08

Volume= 298.42

Step-by-step explanation:

8)

h = 30

r = 16

l=?

Since its is right angled triangle, using pythogras theorem we can find the length of cone

l^2 = h^2 + r^2

l^2 = (30)^2 + (16)^2

l^2  = 900 + 256

l^2 = 1156

Taking square root on both sides

√l^2 = √1156

l = 34

Surface Area = [tex] [tex]\pi r(r+\sqrt{h^2+r^2} )[/tex][/tex]

π = 22/7, r = 16, h=30

Surface Area = [tex]=\frac{22}{7}* 16(16+\sqrt{(30)^2+(16)^2})\\=\frac{22}{7}* 16(16+34)\\=\frac{22}{7}* 800\\=2514.28[/tex]

Volume = [tex]\pi r^2\frac{h}{3}[/tex]

π = 22/7, r = 16, h= 30

Volume = [tex]\frac{22}{7} * (16)^2 *\frac{30}{3}\\=\frac{22}{7} * 256 *10\\= 8045.71[/tex]

9)

r = ?

h = 2

l = 5/2

Since its is right angled triangle, using pythogras theorem we can find the radius of cone

l^2 = h^2 + r^2

(5/2)^2 = (30)^2 + (r)^2

25/4  = 900 + r^2

r^2 = 900 * 4/25

Taking square root on both sides

√r^2 = √144

r = 12

Surface Area = [tex] [tex]\pi r(r+\sqrt{h^2+r^2} )[/tex][/tex]

π = 3.14, r = 12, h=2

Surface Area = [tex]=3.14* 12(12+\sqrt{(12)^2+(2)^2})\\=3.14* 12(12+12.1)\\=3.14* 289.2\\=908.08[/tex]

Volume = [tex]\pi r^2\frac{h}{3}[/tex]

π = 22/7, r = 12, h= 2

Volume = [tex]3.14 * (12)^2 *\frac{2}{3}\\=3.14 * 144 *0.66\\= 298.42[/tex]

Answer:

8) h = 30

Step-by-step explanation:

Answer:

See below in bold.

Step-by-step explanation:

Arrange in order first:

1 1 2 3 4 6 8 9 15

Median ( middle number) = 4.

Mode ( the number which occurs most) = 1.

Mean =  (1+1+2+3+4+6+8+9+15) = 49/9 = 5.4.

Range = 15 - 1 = 14.

List the numbers in order from smallest to largest:

1, 1 , 2, 3, 4, 6, 8, 9, 15

Median is the Middle value of the set = 4

Mode is  the number that appears the most = 1

Mean is the average add the numbers together and divide by the quantity of numbers:

1 + 1 +2 + 3+ 4+ 6 +8 + 9+15 = 49 / 9 = 5.44

Range is the difference between the largest number and smallest number: 15 -1 = 14

Answer:

a)

x≥3

b)

[tex]t<-\frac{7}{3}[/tex]

c)

y < 28

d)

x > 5/2

Step-by-step explanation:

a)

We have been given the following inequality;

4x-3≥9

add 3 to both sides of the equation,

4x-3+3≥9+3

4x≥12

divide both sides by 4,

x≥3

b)

We have been given the following inequality;

3(t+4)<5

we open the brackets on the left hand side,

3t + 12 <5

subtract 12 on both sides of the equation,

3t + 12 -12 <5-12

3t < -7

divide both sides by 3,

[tex]t<-\frac{7}{3}[/tex]

c)

We have been given the following inequality;

[tex]\frac{2y}{7}<8[/tex]

multiply both sides by 7,

2y < 56

divide both sides by 2,

y < 28

d)

5x + 4 > -3(x-8)

we open the brackets on the right hand side,

5x + 4 > -3x + 24

add 3x to both sides of the inequality,

5x + 4 + 3x > -3x + 24 + 3x

8x + 4 > 24

subtract 4 on both sides,

8x + 4 - 4 > 24 - 4

8x > 20

divide by 8 on both sides,

x > 5/2

The area of the rectangular field given the dimensions of the field is 5000m^2.

a + b = 150 equation 1

a = 2b equation 2

Where:

a = length

b = width

Subsiture for b in equation 1 using equation 2

2b + b = 150

3b = 150

b = 50m

a = 2 x 50

q = 100m

Area = length x width

100 x 50 = 5000 m^2

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The rectangular field is found to be 5000 square meters. Option (1) 5000 m² is the correct answer.

To find the area of a rectangular field given its perimeter and that the length is twice the width, follow these steps:

Answer:

by substitution

Step-by-step explanation:

To check if the solution to an equation is valid

Substitute the solution into the equation and if both sides agree then the solution is correct.

left side = z + 22 = 42 + 22 = 64 = right side

Hence z = 42 is the correct solution

The equation is given as:

  [tex]z+22=64[/tex]

⇒[tex]z+22-22=64-22[/tex]

⇒[tex]z=42[/tex]

So, we have to put the value of z in the 1st equation then we can say whether Frieda's work is correct or not.

⇒[tex]42+22=64[/tex]

[tex]=RHS[/tex]

Hence, Frieda's work is correct.

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in maths when you do not know the exact number in a calculation.

What is an equation example?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

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In Bar Graphs;

- Bars have equal space

- One the y-axis, we have numbers & on the x-axis, we have data which can be anything.

In Histograms;

- Bars are fixed

- On the y-axis, we have numbers & and on the x-axis, we have data which in continuous & will always be number.

An easy way you can remember the difference is looking at the spaces of the bars.

A bar graph has gaps

A histogram has no gaps.

If the parabola looks like an “n,” your vertex will be a maximum. If the parabola looks like a “u,” the vertex will be a minimum.

To determine if a vertex is a minimum or maximum, evaluate the behavior of the function at that point. If the function is increasing before the vertex and decreasing after, it is a minimum point. If the function is decreasing before the vertex and increasing after, it is a maximum point.

In mathematics, a vertex is a point where two or more lines, curves, or edges meet. When determining if a vertex is a minimum or maximum, we need to look at the behavior of the function or equation at that point.

If the function is increasing before the vertex and decreasing after the vertex, then the vertex is a minimum point. Conversely, if the function is decreasing before the vertex and increasing after the vertex, then the vertex is a maximum point.

For example, consider the parabola y = x^2. The vertex of this parabola is at (0, 0).

Since the parabola opens upwards and the function values increase on either side, the vertex is a minimum point.

ANSWER

1. No real roots

2. [tex] \frac{ 7\pm \: \sqrt{33} }{ - 4}[/tex]

3. The discriminant is negative.

EXPLANATION

1. The given equation is

[tex] - 2 {x}^{2} - 9x - 5 = 0[/tex]

We have a=-2,b=-9 and c=-5.

The discriminant is given by:

[tex]D= {b}^{2} - 4ac[/tex]

[tex]D= {( - 9)}^{2} - 4( - 2)( - 5)[/tex]

This simplifies to:

[tex]D= 36 - 40 = - 4[/tex]

Since the discriminant is less than zero, the quadratic equation has no real roots.

2. The given equation is:

[tex] - 2 {x}^{2} - 7x - 2= 0[/tex]

We have a =-2, b=-7 and c=-2.

The roots of this equation are given by;

[tex]x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

We plug in the values to get;

[tex]x = \frac{ - - 7\pm \: \sqrt{ {( - 7)}^{2} - 4( - 2)( - 2) } }{2( - 2)} [/tex]

[tex]x = \frac{ 7\pm \: \sqrt{33} }{ - 4} [/tex]

3. The given graph is hanging downwards. This means that it doesn't have x-intercepts.

Therefore the roots are complex or imaginary.

This implies that, the discriminant of the corresponding equation is negative.

Answer: You should use dot plot.

Step-by-step explanation:

1. you should use a dot plot

(correct dot plot)

Its C

How many friends has three pencils?

3

20. dot plot, box plot, and histogram.

L=4 and s=5 I’m to lazy to type it out

Answer:

L= 4

S= 5

Step-by-step explanation:

Given in the question, L+s = 9

So

L= 9-s

Substituting the value of L in the following equation

1.5L + 0.9s = 10.5

1.5 (9-s) + 0.9s = 10.5

13.5 - 1.5s +0.9s = 10.5

13.5 - 10.5 = 1.5s - 0.9s

3= 0.6s

s= 5

Now substituting the value of s in the equation L+s=9, we get the following

L= 9-5

L=4

Answer:

What's your question?

Lets do the math together.

3.5/2 to find the weight loss per week= 1.75.

We know that every week the friend will reduce her goal by 1.75.

15/1.75= 8.6.

This means that in 8.6 weeks the friend will lose 15 pounds.

I hope this Helps! :)

Hello there! It should take her 8.6 weeks.

Well, the question doesn't specify whether it wants how long it'll take her in weeks, months, or days, so let's go with weeks. To do this, find the unit rate by dividing the amount she lost by the number of weeks it took.

3.5 pounds ÷ 2 weeks = 1.75 pounds lost a week.

Now, divide the total she wants to loose (15 pounds) by the 1.75 pounds a week to see how many she looses in total.

15/1.75 = 8.57142... Which is a little over 8.5 weeks, so we can round up to 8.6 weeks.