the transformation shown is a rotation

true or false​

Answer:

-72 + 4 = -68

Answer:

She should cut 1.21 inches (or a square of area 1.46 inch²) from 4 corners to get the maximum volume

Step-by-step explanation:

Length = L = 10 inches

Width = W = 6 inches

Suppose x is cut from the 4 corners to make a box.

Dimensions of the Box:

L= 10 - 2x

W = 6 - 2x

H = x

Volume of the Box:

V = (L)(W)(H)

V = (10-2x)(6-2x)(x)

V = 4x³ -  32x² + 60x

For Maximum value:

[tex]\frac{dV}{dx}=0[/tex]

[tex]\frac{dV}{dx}=\frac{d}{dx}(4x^3-32x+60x)\\\frac{dV}{dx}=12x^2-64x+60\\12x^2-64x+60 = 0[/tex]

The values of x found are:

x= 4.12 , x = 1.21

If we put x= 4.12 in W= 6-2x , the value of width becomes negative, so that is not possible.

We discard 4.12. Now x=1.21

So,

If 1.21 inches are cut from 4 corners, or a square of 1.21*1.21 = 1.46 inch² is cut from 4 corners, we get the maximum value of V

Answer:

Step-by-step explanation:

Let the number be x

Take away 1: x -1

Then multiply the result by 3:  (x- 1) * 3 = (x-1)3 or 3x - 3

Answer:

The expression for the amount of wallpaper needed is [tex]20b^{2}- 2d[/tex]

Step-by-step explanation:

The necessary dimensions of the living room we need are the length and the height. We will not be needing the width because we will not be covering the floors with any wallpaper.

We will now assign variables to represent the surface areas of some features of the rooms.

Let the length of one wall of the living room be = l cm

Let the breadth of one wall of the living room be = b cm

Let the surface area of the doors be = d [tex]cm^{2}[/tex]

From the problem, we know that  l = 5b

The area to be covered on one wall of the living room will be = length X breadth.

l X b

recall l = 5b

[tex]5b \times b = 5b^{2}[/tex]

this is the area to be covered on one wall.

For the four walls, we would have [tex]4 \times 5b^{2}= 20b^{2}[/tex]

Let us remember that the living room has two doors each covering a surface area of [tex]d cm^{2}[/tex] we will have to subtract these out since hey won't be covered.

[tex]20b^{2}- 2d[/tex]

Therefore, the expression for the amount of wallpaper needed is [tex]20b^{2}- 2d[/tex]

Answer:

hope this helps you

Answer:

$27.83

Step-by-step explanation:

If Darrien spends 26.50, multiply that by 0.05 (26.50×0.05) which is 1.325 which rounds to 1.33. $1.33 is the amount of tax he has to add. For the full price you would do 26.50+1.33 to get 27.83.

Answer:

The answer is 27.83

Step-by-step explanation:

Thank the person above me.

Answer:

Expected Payoff ⇒ $ 1.50 ; Type in 1.50

Step-by-step explanation:

Considering that 1 out of the 100 tickets will have a probability of winning a 150 dollar prize, take a proportionality into account;

[tex]100 - Number of Tickets,\\1 - Number of Tickets You Can Enter,\\\\1 / 100 - Probability of Winning,\\$ 150 - Money Won,\\\\Proportionality - 1 / 100 = x / 150, where x - " Expected Payoff "\\\\1 / 100 = x / 150,\\100 * x = 150,\\\\Conclusion ; x = 1.5 dollars[/tex]

Thus, Solution ; Expected Payoff ⇒ $ 1.50

Answer:

functions f(x) and g(x) share one root in common that of x=2 and each have another different root

Step-by-step explanation:

Notice that function g(x) has for roots the values x = -1 and x = 2, (these are the crossings of the x axis that you see in the graph)

On the other hand, the function f(x) has two roots that are obtained by factoring it out:

[tex]f(x)=x^2+x-6\\f(x)= x^2-2x+3x-6\\f(x)=x(x-2)\,+\,3(x-2)\\f(x)=(x-2)\,(x+3)[/tex]

Therefore it has roots at x=2 and x= -3

So functions f(x) and g(x) share one root in common that of x=2 and each have another different root

Answer:

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

Step-by-step explanation:

Given

Line coordinates: (5,5)

Perpendicular slope = [tex]\frac{1}{4}[/tex]

Required

Find the point slope form of the line

First, the slope of the line has t be calculated;

Given that two lines are perpendicular;

The relationship between there slopes is given as [tex]m_1.m_2 = -1[/tex]

Let m_2 represent the slope of the second line;

such that [tex]m_2 = \frac{1}{4}[/tex]

So;

[tex]m_1 * \frac{1}{4} = -1[/tex]

Multiply both sides by 4

[tex]m_1 * \frac{1}{4} * 4 = -1 * 4[/tex]

[tex]m_1 = -1 * 4[/tex]

[tex]m_1 = -4[/tex]

Now, the equation of the line can be calculated using slope formula;

[tex]m = \frac{y - y_1}{x- x_1}[/tex]

Where

[tex](x_1,y_1) = (5,5)\\m_1 =m = -4[/tex]

So; [tex]m = \frac{y - y_1}{x- x_1}[/tex] becomes

[tex]-4 = \frac{y - 5}{x- 5}[/tex]

Multiply both sides by x - 5

[tex]-4(x-5) = \frac{y - 5}{x- 5} * (x-5)[/tex]

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

Reorder

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

Hence, the line in point-slope form is [tex]y - 5 = -4(x-5)[/tex]

Answer:

The Answer is: (-2,1)

Step-by-step explanation:

Answer:

John has 18 pieces of paper.

Larry has 32 pieces of paper.

Step-by-step explanation:

Let [tex]l[/tex] be how many pieces of paper Larry has and [tex]j[/tex] be how many pieces of paper John has.

We get:

[tex]j+14=l[/tex]

[tex]j+l=50[/tex]

[tex]j+j+14=50\\\\2j+14=50[/tex]

Subtract 14 from both sides

[tex]2j=36[/tex]

Divide both sides by 2

[tex]j=18[/tex]

John has 18 pieces of paper.

[tex]j+14=l\\\\18+14=l\\\\l=32[/tex]

Larry has 32 pieces of paper.

Answer:

You can also represent it as  [tex]\sqrt[3]{2}[/tex]

Step-by-step explanation:

[tex](\sqrt[3]{2})^{3} =2\\2^{\frac{1}{3} } =2[/tex]

Answer:

Step-by-step explanation:

You didn't give your options, but it doesn't matter. We'll find all the possibilities and then you can pick it from your list.

When I teach this in Algebra 2, I call it the "the c over d thing" and all my students know EXACTLY to what I am referring. "c" is the constant and "d" is the leading coefficient. The combination of c/d give you the possibilities of roots for the polynomial. There are no real roots that a polynomial can have other than the possibilities we find when we do the c/d thing.

Our c is a 20.  All the factors of 20 are as follows (notice that we have both the positive and negative factors):

20: ±1, ±2, ±4, ±5, ±10, ±20

Our d is a 3.  All the factors of 3 are as follows (again, both the + and the -):

3: ±1, ±3 and that's it for 3.

c/d is as follows. Make sure you put ever c over every d!!!:

c/d: ±[tex]\frac{1}{1}[/tex], ±[tex]\frac{2}{1}[/tex], ±[tex]\frac{4}{1}[/tex], ±[tex]\frac{5}{1}[/tex], ±[tex]\frac{10}{1}[/tex], ±[tex]\frac{20}{1}[/tex], ±[tex]\frac{1}{3}[/tex], ±[tex]\frac{2}{3}[/tex], ±[tex]\frac{4}{3}[/tex], ±[tex]\frac{5}{3}[/tex], ±[tex]\frac{10}{3}[/tex], ±[tex]\frac{20}{3}[/tex]

Those are all the possibilities for your roots for that polynomial. As long as the roots are real (and they won't always all be real!), there are no roots but these.

Answer:

its D on edge

Step-by-step explanation:

Answer:

2a+50=5a-4

5a-2a=50+4

3a=54

a=18

Answer:

[tex]a=18[/tex]

Step-by-step explanation:

[tex]2a+50=5a-4\\\mathrm{Subtract\:}50\mathrm{\:from\:both\:sides}\\2a+50-50=5a-4-50\\Simplify\\2a=5a-54\\\mathrm{Subtract\:}5a\mathrm{\:from\:both\:sides}\\2a-5a=5a-54-5a\\\mathrm{Simplify}\\-3a=-54\\\mathrm{Divide\:both\:sides\:by\:}-3\\\frac{-3a}{-3}=\frac{-54}{-3}\\Simplify\\\frac{-3a}{-3}=\frac{-54}{-3}\\\mathrm{Simplify\:}\frac{-3a}{-3}:\quad a\\\frac{-3a}{-3}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{3a}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1[/tex]

[tex]=a\\\mathrm{Simplify\:}\frac{-54}{-3}:\quad 18\\\frac{-54}{-3}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{54}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{54}{3}=18\\=18\\a=18[/tex]

Answer:

Brainliest here!

Step-by-step explanation:

3 dozen cookies = 1.5 cups

one dozen cookies= 0.5 cups

5 dozen cookies = 2.5 cups of sugar

Answer:

Step-by-step explanation:

-(x-2)(x+3)

Answer:

1/20

Step-by-step explanation:

5%

Percent means out of 100

5/100

Divide top and bottom by 5

1/20

Answer:

HI THERE,THE ANSWER IS

B

Step-by-step explanation:

[tex]\frac{1}{20} \\[/tex] X 100%=5%

Answer: The speed of the current is 3.5 km/h.

Step-by-step explanation:

When they move in the river, the speed of the canoe is:

Sc is the speed of the canoe and Sr is the speed of the current.

Sc + Sr (when they move in the same direction as the current)

Sc - Sr (when they move in the opposite direction as the current)

So we have that in one hour, they moved 2km and then they returned other 2km.

Now, using the relation:

Velocity*time = distance

we can write 1hour = T1 + T2 such that:

(Sc + Sr)*T1 = 2km

(Sc - Sr)*T2 = 2km

T1 + T2 = 1hour -------> T2 = 1h - T1

Sc = 6km/h.

So we can write this as two equations:

(6km/h + Sr)*T1 = 2km

(6km/h - Sr)*(1h - T1) = 2km.

Now, the first step will be isolate one of the variables in one equation, we can get:

T1 = 2km/(6km/h + Sr)

and replace it in the second equation:

(6km/h - Sr)*(1h -2km/(6km/h + Sr)) = 2km.

Now we solve this for Sr, i will ignore the units, so it is easier to read the math.

(6 - Sr) - 2*(6 - Sr)/(6 + Sr) = 2

(6 - Sr)*(6 + Sr) - 2*(6 - Sr) = 2*(6 + Sr)

6^2 - Sr^2 - 12 + 2*Sr - 12 - 2*Sr = 0

-Sr^2 + 36 -12 -12 = 0

-Sr^2 + 12 = 0

Sr = √12 = 3.5km/h

(where we take the positive value of the square root)

The speed of the current is 3.5 km/h

Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance / time

Let a represent the speed of the current and t₁ represent the time spent paddling up and t₂ represent the time spent paddling back. Hence:

(6 - a)(t₁) = 2 km

t₁ = 2 / (6 - a)      (1)

(6 + a)(t₂) = 2 km

t₂ = 2 / (6 + a)   (2)

t₁ + t₂ = 1 hour

[2 / (6 - a)] + [2 / (6 + a)] = 1

12 + 2a + 12 - 2a = 36 - a²

a² - 12 = 0

a = 3.5 km/h

The speed of the current is 3.5 km/h

Find out more at: https://brainly.com/question/22610586

Answer:

Barlow School has the greater number of boys by  178.

Answer:

Barlow school by 178

Step-by-step explanation:

→ First let's work out the number of boys at Barlow school

[tex]\frac{4}{9}[/tex]  of  [tex]873[/tex]  [tex]=[/tex]  [tex](873/9)*4[/tex]  [tex]=[/tex]  [tex]388[/tex]

→ There is 388 boys in Barlow school. Now let's work out the number of boys at Willow school. Since we know that  [tex]\frac{2}{3}[/tex]  of the school is girls, it must mean that the remaining part must be boys so the fraction of boys at Willow school is  [tex]\frac{1}{3}[/tex]

[tex]\frac{1}{3}[/tex]  of  [tex]630[/tex]  [tex]=[/tex]   [tex](630/3)*1[/tex]  [tex]=[/tex] 210

→ The question specifies to say which school has a greater number of boys and we can see Barlow school has more boys and the question says by how many so we take away the totals so 388 - 210 = 178

Answer:

s=5

Step-by-step explanation:

72=27+9s

Subtract 27 from both sides.

72-27=9s+27-27

45=9s

Divide 9 from both sides.

5=s

Answer:

C

Step-by-step explanation:

Constant means unchanging. You can see that there is a portion in the graph where the line is just flat. That means that the graph is constant in that interval. Find where the constant line starts and ends. Since the coordinates are increasing by 2, and the constant line starts between 0 and the first tick (2), the constant line starts at 1. Do the same thing to find where it ends(the last point where the line is flat). This should be 6.

That means the line is unchanging(constant) from 1 to 6, which can be represented by C.

Answer:

The answer is C 3- sqrt 11

Step-by-step explanation:

Answer:

Probability ≈ 0.0714

Step-by-step explanation:

Consider permutation and combination;

[tex]Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714[/tex]

Answer:

40 millimetres

Answer:

40

Step-by-step explanation:

Answer:

No solution!

Just turned it in <3

Answer:

tis indeed no solution your honor

Step-by-step explanation:

Answer:

[tex]p = 43 \: \: \: degrees[/tex]

Answer A is correct

Step-by-step explanation:

[tex]90 + p = 133[/tex]

the sum of the exterior angles in a triangle is equal to the sum of opposite interior angles.

[tex]p = 133 - 90 \\ p =4 3 \: \: \: degrees[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

A round plane figure whose boundary (the circumference)consists of points equidistant from a fixed point (the center)

Answer:

A round plane figure

Step-by-step explanation:

Answer:

a) 27 m/s

b) 30 m/s

c)   i) 3

     ii) Deceleration

Step-by-step explanation:

The question is not complete, the correct question is given as:

The graph shows information about the speed of a vehicle during the final 50 seconds of a journey.  At the start of the 50 seconds the speed is k metres per second.  The distance travelled during the 50 seconds is 1.35 kilometres.

(a) Work out the average speed of the vehicle during the 50 seconds

(b) Work out the value of k.

(c) (i) Calculate the gradient of the graph in the final 10 seconds of the journey

    (ii) Describe what this gradient represents

Answer:

The graph is attached. The total time = 50 seconds, total distance = 1.35 km = 1350 m  

a) The average speed is the ratio of the total distance traveled to the total time taken to cover this distance. The average speed is given by the formula:

[tex]Average \ speed=\frac{total\ distance}{total\ time}\\ Substituting: \\ Average \ speed=\frac{1350\ m}{50\ s} = 27\ m/s[/tex]

b) From the graph, the total distance covered is the area of the graph. The graph is made up of a rectangle and triangle, the area of the graph is equal to the sum of area of rectangle and area of triangle.

[tex]Total \ distance=Total\ area=Area\ of \ rectangle+Area\ of \ triangle\\Total \ distance=(length *breadth)+\frac{1}{2}base*height\\1350 \ m=(40*k)+0.5*10*k\\1350=40k+5k\\45k=1350\\k=1350/45\\k=30\ m/s[/tex]c) i) The gradient in the last 10 seconds is the ratio of change in speed to change in time

[tex]Gradient=\frac{change\ in\ speed }{change\ in\ time}=\frac{0-k}{50-40} \\ bt \ k=30\\Gradient=\frac{0-30}{50-40}= \frac{-30}{10} =-3[/tex]

ii) Since the gradient is negative it means it is deceleration. That is in the in the last 10 seconds the vehicle decelerates at a rate of 3 m/s²

Answer:

Step-by-step explanation:

a)34 m/s

b) 40k=34

k=34/40

k=0.85 m/s

Answer:

3383361889.8

Step-by-step explanation:

1 meter = 39.3701 inches

85937392 x 39.3701 = 3383361889.8

Answer:

3,383,361,889.76 inches

Step-by-step explanation:

1 meter = 39.37 inches

multiply 85937392 by 39.37

answer is 3383361889.76