Sherri solved the equatjon 1/5(x-20)=45. For each step, write the name of the property sherri used

Answer:

  cylinder, has the least surface area

Step-by-step explanation:

We are to choose the shape that has the least surface area for the approximate volume desired. In general, the least area for the volume will be provided by a sphere, a "square" cylinder with height equal to diameter, and a cube, in order of increasing area.

__

We are asked to find the area and volume of two rectangular prisms, a cylinder, and a square pyramid. Then, we are to identify the shape with the least surface area. Volume and area formulas will be used for the purpose.

The relevant formulas are ...

  V = LWH

  A = 2(LW +H(L +W))

for length L, width W, and height H.

a) prism 1

The given dimensions are L = W = 8 in, H = 5 in. Then the volume and area are ...

  V = (8 in)(8 in)(5 in) = 320 in³

  A = 2((8 in)(8 in) +(5 in)(8 in +8 in)) = 2(64 in² +80 in²) = 288 in²

b) prism 2

The given dimensions are L = 10 in, W = 8 in, H = 4 in. Then the volume and area are ...

  V = (10 in)(8 in)(4 in) = 320 in³

  A = 2((10 in)(8 in) +(4 in)(10 in +8 in)) = 2(80 in² +72 in²) = 304 in²

__

The relevant formulas are ...

  V = πr²h

  A = 2πr(r +h)

for radius r and height h.

c) The given dimensions are r = 5 in, h = 4 in. Then the volume and area are ...

  V = π(5 in)²(4 in) = 100π in³ ≈ 314 in³

  A = 2π(5 in)(5 in +4 in) = 90π in² ≈ 283 in²

__

The relevant formulas are ...

  V = 1/3s²h

  A = s(s +2H)

for base side dimension s, vertical height h, and slant height H.

d) The given dimensions are s = 10 in, h = 10 in, H = 14 in. Then the volume and area are ...

  V = 1/3(10 in)²(10 in) = 1000/3 in³ ≈ 333 in³

  A = (10 in)(10 in + 2×14 in) = 380 in²

__

The proposed figures have volume and area (rounded to the nearest unit) as follows:

  [tex]\begin{tabular}{|c|c|c|c|}\cline{1-4}&shape&V (in^3)&A (in^2)\\\cline{1-4}a&rect prism&320&288\\b&rect prism&320&304\\c&cylinder&314&\bf283\\d&pyramid&333&380\\\cline{1-4}\end{tabular}[/tex]

The proposed cylinder requires the least amount of sheet metal for its construction. It has the least surface area of all of the shape choices offered.

_____

Additional comment

For a volume of 320 in³, a cube would have a surface area of 280.7 in². A "square" cylinder would have an area of 260.0 in². A sphere would have an area of 226.2 in². The above areas are somewhat larger because the shapes depart from the ideal aspect ratio.

The area of the rectangle is 31.937 cm².

A rectangle is a 2-dimensional quadrilateral with four right angles.  A rectangle has two diagonals of equal length which bisect each other

Area of a rectangle = length x width

9.64 x 3.313 = 31.937 cm²

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The probability that he does not wait for more than five minutes all 5 days this week is 0.16807

The probability that he waits for more than 5 minutes is:

p = 30%

This means that the probability that he does not wait for more than 5 minutes is

q = 70%

If he does not wait for more than five minutes all 5 days this week, the probability is:

P = q^5

This gives

P = (70%)^5

Evaluate

P = 0.16807

Hence, the probability that he does not wait for more than five minutes all 5 days this week is 0.16807

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Answer:

X=1 and Y=4

By counting eacht vetmrtical divided units

Applying the inscribed angle theorem, the measure of the arc from A to B is: 100 degrees.

The inscribed angle theorem states that an inscribed angle in a circle is half the central angle.

Angle BAC = 40 degrees, so, central angle = 80 degrees. Arc BC would also be 80 degrees.

Measure of arc AC through point B = 180 degrees.

Arc AB = 180 - 80 = 100 degrees.

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Answer:

because 3 and 5 the answer is 17

Answer:

9x - 3

Step-by-step explanation:

Hello!

A square has 4 sides.

We can factor out 4 from the expression to find the value of one side.

Factor:

This means that each side of the square is 9x - 3 units long.

Answer:

x = 18

Step-by-step explanation:

the 2 angles are alternate exterior angles and are congruent, then

7x - 7 = 6x + 11 ( subtract 6x from both sides )

x - 7 = 11 ( add 7 to both sides )

x = 18

Answer:

18

Step-by-step explanation:

(7x-7)° = (6x+11)°------ (alternate exterior angles are equal)

therefore,

7x-7= 6x+11

collect like terms

7x-6x = 11+7

x = 18

The completely factored expression of 2x^2 + 4x + 3xy + 6y is (2x + 3y)(x + 2)

The expression is given as:

2x^2 + 4x + 3xy + 6y

Group the expression into two

[2x^2 + 4x] + [3xy + 6y]

Factor out each group

2x(x + 2) + 3y(x + 2)

Factor out x + 2

(2x + 3y)(x + 2)

Hence, the completely factored expression of 2x^2 + 4x + 3xy + 6y is (2x + 3y)(x + 2)

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Answer:

Step-by-step explanation:

ans in picture

Answer:

140

Step-by-step explanation:

To solve this, we must reverse all the steps Adnan took to get the final number of 3.

If the last thing he did was take the square root, we need to square 3 to get the result. [tex]3x^{2} =9[/tex], so the sum they are referring to in the prompt is 9.

Before that, it says he added 1, so we need to subtract 9-1=8 to get the previous number.

It says that he took the square root before that, so we need to square 8 to get [tex]8x^{2} =64[/tex].

It says that he subtracted 6 to get this number, so we have to add 6 to get[tex]64+6=70[/tex].

Since the first thing Adnan did was divide his number by 2, we must multiply 70 by 2 to get Adnan's original number: [tex]70*2=140.[/tex]

Adnan's original number was 140.

Hope this helps! :)

Answer:

(1, - 7 )

Step-by-step explanation:

using the midpoint formula

given endpoints (x₁, y₁ ) and (x₂, y₂ ) , then

midpoint = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = A (3, - 12 ) and (x₂, y₂ ) = B (- 1, - 2 )

midpoint = ( [tex]\frac{3-1}{2}[/tex] , [tex]\frac{-12-2}{2}[/tex] ) = ( [tex]\frac{2}{2}[/tex] , [tex]\frac{-14}{2}[/tex] ) = (1, - 7 )

Step-by-step explanation:

[tex] x_{m} , y_{m} \: = ( \frac{x _{1} + x_{2} }{2} ,\frac{y _{1} + y_{2} }{2}) \\ [/tex]

x1 = 3, x2 = (-1)

y1 = (-12), y2 = (-2)

[tex] x_{m} , y_{m} \: = ( \frac{3+ ( - 1) }{2} ,\frac{( - 12)+ ( - 2) }{2}) \\ [/tex]

[tex]x_{m} , y_{m} \: = ( \frac{3 - 1 }{2} ,\frac{( - 12) - 2 }{2}) \\ [/tex]

[tex]x_{m} , y_{m} \: = ( \frac{2 }{2} ,\frac{- 14 }{2}) \\ [/tex]

[tex]x_{m} , y_{m} \: = 1 ,( - 7)[/tex]

Answer:

78

Step-by-step explanation:

QT is a 180 straight line so 180-55-47

Hope its right!

Answer:

U-60

S-90

Q-80

ur welcome

Answer:

Step-by-step explanation:

30 divided by 5 - 2 + 7 = 3

Then , write down the correct equation.

30 : (5 - 2 + 7) = 3

30 : (3 + 7) = 3

30 : 10 = 3

3 = 3

Answer:

8 - 4x^2y - 6y^6

Step-by-step explanation:

The range exist on all real values. This can be written as (-infty, infty)

The range is the value of the dependent variable for which it exists. Given the following functions

f(x) = |x| + 9 and;

g(x) = -6

Determine the sum

(f+g)(x) =  |x| + 9 + (-6)

(f+g)(x) = |x| + 9 -6

(f+g)(x) = |x| + 3

Determine the range of the function

The range exist on all real values. This can be written as (-infty, infty)

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Answer:

Answer:1296π

Step-by-step explanation:

As we know,

Area of cicle=πr^2

= π(36)^2

=1296π

Answer:

see the attachment photo!

just comment here if you need help

The best description about the line AD is,

⇒ Perpendicular bisector

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Triangle ABC is shown in figure.

Now, We have by figure;

BD = 17

DC = 17

Hence, We can say that;

Line AD is Perpendicular bisector of line BC.

Thus, The best description about the line AD is,

⇒ Perpendicular bisector

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The quadratic equation that has a root of 6 and 2 is x^2 - 8x + 12 = 0

The roots are given as:

x = 6 and x = 2

Rewrite as:

x - 6 = 0 and x - 2 = 0

Multiply both equations

(x - 6)(x - 2) = 0 * 0

Evaluate the product

x^2 - 6x - 2x + 12 = 0

Evaluate the difference

x^2 - 8x + 12 = 0

Hence, the equation that has a root of 6 and 2 is x^2 - 8x + 12 = 0

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3200\\ r=rate\to 7.75\%\to \frac{7.75}{100}\dotfill &0.0775\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &13 \end{cases} \\\\\\ A=3200\left(1+\frac{0.0775}{1}\right)^{1\cdot 13}\implies A=3200(1.0775)^{13}\implies A\approx 8444.51[/tex]

The phrase best describes the range of the function h(x) is option A: all real numbers.

The range is the set of all values which the given function can output.

A step function h(x) is represented by y = -2|x|.

The mode of x gives the real number every time by putting the values.

The phrase best describes the range of the function h(x) is option A: all real numbers.

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Answer:

[tex]n=-12[/tex]

Step-by-step explanation:

[tex]\text{When}~ n = -12,\\\\~~~~~-2(6x+2) = -12x-4\\\\\implies -12x -4 = -12x -4 \\\\\text{Since both sides are equal for all values of x, there are infinitely many solutions.}[/tex]

Using the cosine ratio formula, the length of RQ to the nearest tenth is: 13.2.

The cosine ratio formula is given as, cos ∅ = length of adjacent side / length of hypotenuse.

Find m∠PRT in ΔPRT using the cosine ratio formula:

cos(m∠PRT) = 15/17

m∠PRT = cos^(-1)(15/17)

m∠PRT ≈ 28.07°

Find RQ in ΔPRQ using the cosine ratio formula:

cos(28.07) = RQ/15

RQ = cos(28.07) × 15

RQ ≈ 13.2

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Answer:

60

Step-by-step explanation:

Answer:

a) 15:7

b) 1950 ml

c) There were 10 people in the group

Step-by-step explanation:

a) In its basic form, the ratio would be 750:350. However, to get it to it's most basic form, we must find the greatest common factor (GCF) of 750 and 350, which is 50. Then, we divide both numbers by the GCF so that 750 is 15 and 350 is 7. Therefore, the basic form of the ratio is 15:7.

b) First, we can find the amount of chicken stock needed for 12 people, which is just double of the recipe since the recipe is for 6 people. (900 * 2 = 1800). Then, we need to figure out how much chicken stock is required for one person since there are 13 and not 12. We can do this by multiplying 900 by 1/6 (since it's for 1 person out of the 6 people recipe) to get 150. Then, add the amount of chicken stock needed for 12 people and 1 person together. 1800 + 150 = 1950.

c) First, we must figure out how many grams of leeks are required for just one person. We can do this by taking the amount needed in the recipe (for 6 people) and dividing it by 6 to get the amount needed for 1 person. 750 divide by 6 is 125, so 125 g of leeks are required to make soup for 1 person. Then, we take the total amount of leeks that Delia used (1250) and divide that by 125 to get 10.

Answer:

27.72 cm^2

Step-by-step explanation:

Parallelogram's area = base x height

= 3.3 x 8.4

= 27.72 cm^2

Answer:

1% given away means 1/100 × 3= 0.03

therfore what is left is : 3-0.03= 0.97

Answer:

1% means 1/100, so 1% of 3 acres of land = 1/100×3 = 3/100 or 0.03 acres of land. Since he gave 0.03 acres of land away, Mr A has 3-0.03 = 2.97 acres of land

Answer:

3200

Step-by-step explanation:

Simple interest = PRT/100

= (16000 × 5 × 4%\)/100

= 320000/100

= 3200

The five-number summary as displayed in a box plot attached below, from the least to the greatest is: Minimum < Q1 < Median < Q3 < Maximum

The five-number summary can be described as a set of data points or values that summarizes the distribution of a data.

The diagram attached below shows the five-number summary as displayed by a box plot.

From the least to the greatest, the five-number summary consist of:

Minimum < Q1 < Median < Q3 < Maximum

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