a rectangular tank that is 6912 ft3 with a square base and open top is to be constructed of sheet steel of a given thickness. find the dimensions of the tank with minimum weight.

The answer is 10(t-1) (5t+3).

An algebraic equation of the second degree in x is a quadratic equation. Typically, a quadratic equation is expressed in standard form as,[tex]ax^2 + bx + c = 0[/tex].

And the factor is a number or algebraic expression that divides another number evenly without leaving any remainder.

To factor the given quadratic equation, first, take the common factor of the equation. Therefore,

[tex]50t^2-20t-30=10(5t^2-2t-3)[/tex]

Using the sum-product pattern, we can write 2t as 3t-5t. Therefore,

[tex]50t^2-20t-30=10(5t^2+3t-5t-3)[/tex]

Now, find the common factor between the pairs within the bracket. We get,

[tex]50t^2-20t-30=10(t(5t+3)-1(5t+3))[/tex]

Finally, rewriting the above terms by factoring out the greatest common factor, we get,

[tex]50t^2-20t-30=10(t-1)(5t+3)[/tex]

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Answer: 10 (5t+3) (t-1)

Step-by-step explanation:

Given, 50t²-20t-30

Here we take 10 as the common factor:

⇒ 10(5t²-2t-3)

Then, we use the sum-product pattern to divide the 2t into two parts:

⇒ 10(5t²-5t+3t-3)

Taking the common factor from the two pairs, we get:

⇒ 10 [5t(t-1) + 3(t-1)]

⇒ 10 (5t+3) (t-1)

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The polar form of the complex number z = - 2√3 - i 6 is z = (4√3) · (cos 4π / 3 + i sin 4π / 3). (Correct choice: D)

Complex numbers are numbers of the form z = a + i b, where a and b are real numbers. This form is known as rectangular form. The polar form equivalent to that number is:

z = r · (cos θ + i sin θ)

Where:

The norm and the direction of the complex number are, respectively:

r = √(a² + b²)

θ = tan⁻¹ (b / a)

If we know that a = - 2√3 and b = - 6, then the polar form of the complex number is:

r = √[(- 2√3)² + (- 6)²]

r = 4√3

θ = tan⁻¹ [(- 6) / (- 2√3)]

θ = 4π / 3

z = (4√3) · (cos 4π / 3 + i sin 4π / 3)

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Using Euler'formula, the difference between maximum and minimum possible numbers of faces is 96.

A polyhedron is a 3D shape with flat faces, straight edges, and sharp vertices (corners). "polyhedron" meaning "many" and "polyhedron" meaning "area". Therefore, when many planes are joined, they form a polyhedron.

Because all faces are triangles. So on a triangular base with triangular faces on both sides that meet at the vertex.

Therefore, the minimum number of triangular faces of a regular polyhedron is = 4

Next, the double pyramid has "2n" triangular faces. where n is a natural number greater than 2 and 'n' represents the number of sides of the base of the pyramid.

A polyhedron having equal quadrilateral faces is known as regular hexahedron.

quadrilateral faced polyhedron with total sides 100 and vertices 6 , then using Euler's formula

F + V-E = 2

=> F + 6- 100= 2 => F = 96 maximum faces possible = 96

Now the difference between maximum and minimum number of faces = 100 - 4 = 96

So the difference between maximum and minimum faces is 96.

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The AER on the savings account, based on the interest rate and the period it is paid is 8.16%

The AER stands for Annual Equivalent Rate which shows the periodic rate of an interest rate, based on the number of compounding periods of the savings account or investment.

The formula for Annual Equivalent Rate (AER) is:

= ( 1 + interest rate / number of payment or compounding periods) ^ number of payment or compounding periods - 1

The AER on the savings account is therefore:

= ( 1 + 8% / 2 semi annual periods) ² - 1

= 0.0816

= 8.16%

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Probability of chosen the acre of land as per given conditions are as follow:

a. Probability of chosen the acre of land not forested is 0.62.

b. Probability of chosen the acre of land either forest or agriculture is 0.45.

c. Probability of chosen the acre of land other than forest or agriculture is non-forested which is equal to 0.62.

As given in the question,

Given probability are:

Probability of chosen the acre of land is forest is equal to 0.38.

Probability of chosen the acre of land is agriculture is equal to 0.07.

Probability of chosen the acre of land as per given conditions are as follow:

a. Let P(A) represents the probability of chosen the acre of land is forest.

Then P(A') is the probability of not forested.

P(A) + P(A') = 1

⇒0.38 + P(A') = 1

⇒ P(A') = 1 - 0.38

⇒ P(A') = 0.62

b. Let P(G) is the probability of chosen acre of land agricultural.

No common land given for forest or agriculture, they are independent events.

P(A∩G) = 0

Probability of chosen the acre of land either forest or agriculture

= P( A or G)

= P(A) + P(G) - P(A∩G)

= 0.38 + 0.07 -0

= 0.45

c. Probability of chosen the acre of land other than forest or agriculture is non-forested which is equal to 0.62.

Therefore, probability of chosen the acre of land as per given conditions are as follow:

a. Probability of chosen the acre of land not forested is 0.62.

b. Probability of chosen the acre of land either forest or agriculture is 0.45.

c. Probability of chosen the acre of land other than forest or agriculture is non-forested which is equal to 0.62.

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Answer:

∠DEA
I think, adjacent means "next to, or adjoining something else."
Since ∠BEC, and ∠DEA are sharing point E, I think they are adjacent.

(I haven't done this kind of math in forever..)

Answer:

5.267

Step-by-step explanation:

Let's do long division to figure this out.

Answer: 5.26666666667

Step-by-step explanation:

If your asking for the decimal answer, than it is 5.26666666667, or you can round it to 5.3. :)

The complex number in rectangular form is 17√2 / 2 - i 17√2 / 2. (Correct choice: A)

In this problem we have a complex number in polar form, whose formula is described below:

z = r · (cos θ + i sin θ)

Where:

And the rectangular form of the complex number is represented by:

z = a + i b, where a = r · cos θ and b = r · sin θ.

If we know that r = 17 and θ = 315°, then the rectangular form of the complex number is:

a = 17 · cos 315°

a = 17√2 / 2

b = 17 · sin 315°

b = - 17√2 / 2

The rectangular form of the complex number is 17√2 / 2 - i 17√2 / 2.

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Answer:

27

Step-by-step explanation:

45/5=9

9*3=27

Answer: 27

Step-by-step explanation:

45/5=9

9x3=27

Options B and C are the following conclusions that are true about the transformation of quadrilateral BLUE.

A four-sided polygon having four edges and four corners is referred to as a quadrilateral in geometry. The name is a combination of the Latin words quadri, which is a variation of four, and latus, which means "side." It is sometimes referred to as a tetragon, which is derived from the Greek words "tetra" for "four" and "gon" for "corner" or "angle," in comparison to other polygons (e.g. pentagon). Because "gon" means "angle," it is sometimes referred to as a quadrangle or 4-angle.

Either simple (not self-intersecting) or complicated quadrilaterals exist (self-intersecting, or crossed). Convex or concave surfaces characterize simple quadrilaterals.

From the given figure,

The points in the quadrilateral BLUE are

B(-8,5), L(-5,5), U(-3,4), E(-6,1)

If the quadrilateral BLUE is rotated 270° then,

B(-8,-5), L(-5,-5), U(-3,-4), E(-6,-1)

Now, the image is reflected

So, the points are switched as,

B'(-5,-8), L'(-5,-5), U'(-4,-3), E'(-1,-6)

Distance of BE is,

√(x₂-x₁)²+(y₂-y₁)²

√(-1+5)²+(-6+8)²

=√16+4

=√20

Distance of B'E' is,

√(-6+8)²+(1-5)²

=√4+16

=√20

∴BE=B'E'

And the quadrilateral B'L'U'E' will be located entirely on third quadrant.

Therefore, B and C are the appropriate choices.

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The GCF: x

answer: x(x+2)

If the function f (x) = 3 logx and g(x) [tex]=[/tex] x² + 1 , then the value of composite function g[f(x)] is (3logx)² + 1 , the correct option is (a) .

In the question ,

it is given that ,

the function f(x) is

f(x) [tex]=[/tex] 3logx

and the function g(x) is

g(x) [tex]=[/tex] x² + 1 ,

the value of the composite function g[f(x)] will be

g[f(x)] = g(f(x))

Substituting the value of f(x) = 3logx , we get

g(f(x)) = g(3logx)

Substituting the value of 3logx in the place of x in the function  g(x) = x² + 1 ,

we get ,

= (3logx)² [tex]+[/tex] 1

Therefore , If the function f (x) = 3 logx and g(x) = x² + 1 , then the value of composite function g[f(x)] is (3logx)² + 1 , the correct option is (a) .

The given question is incomplete , the complete question is

If f ( x ) = 3 log x and g( x ) = x² + 1 , find the value of composite function g[ f ( x )] .

(a) (3logx)² + 1

(b) 3log(x² + 1)

(c) 3(x² + 1)logx

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The amount of paint needed to paint the front of the building knowing that 0.5 kg of paint is needed per m^2 is 20 kg.

We know that,

Area of rectangle = L * W

where L = Length of the rectangle

and W  = Width of the rectangle.

Area of triangle = 1/2 * B * H

where B = Base of the triangle

and H  = Height of the triangle.

From the figure, we are given;

The front of the building has two rectangles that represent the floor and one triangle.

The rectangles are of the same size and it's given;

L = 8 m

W = 4 m

Area of rectangle = L * W = 8 * 4 = 32 m^2

The dimension of the triangle is:

B = 8 m

H = 2 m

Area of triangle = 1/2 * B * H = 1/2 * 8 * 2 = 8 m^2

The total area of the front of the building = 32 + 8 = 40 m^2

Amount of paint required

= total area of the front of the building * paint is needed per m^2

= 40 * 0.5 = 20 kg

So, 20 kg of paint is needed.

Thus, the amount of paint needed to paint the front of the building knowing that 0.5 kg of paint is needed per m^2 is 20 kg.

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Answer:

1) 1 = 120 degrees and 2 = 60 degrees

2) x = 25

3) p = 32

Step-by-step explanation:

1) Angle 1 is 120 degrees, since it is congruent to the corresponding angle below it (because lines a and b are parallel) Angles 1 and 2 are supplementary, meaning they add up to 180, so to find angle 2 we do 180 - 120 to get 60. Angle 1 = 120 degrees and angle 2 = 60 degrees.

I did 2 and 3 on paper, let me know if anything is confusing :))

2) the two lines are parallel, so we know those two angles are congruent since they're corresponding. If they're congruent we can just set them equal to each other to find x. x = 25.

3) the little square mark means a right angle, which is 90 degrees. The two lines are parallel, so we know that the angle below is corresponding and congruent to 90 degrees. So to find p, set 3p - 6 equal to 90. p = 32.

if anythings confusing let me know :-)

Answer:

Step-by-step explanation:

Comment

How many 3 digit numbers are divisible by 4, but do not contain the digit nine?

If you know a computer language, then the main line would be

for x = 100 to 999 do

The dimension of the wood block in centimeter is  40cm by 20cm by 70cm , the volume is  56000 cubic centimeters .

In the question ,

it is given that ,

the dimension of the block of wood is 0.4m by 0.2m by 0.7m ,

that means

the length of the wood block = 0.4 m

we know that 1 m = 100 cm , So 0.4 m = 40 cm

0.2 m = 20 cm

and

0.7 m = 70 cm

So , the length of the wood block = 40 cm

the width of the wood block = 20 cm

the height of the wood block = 70 cm

The Volume of the wooden block = length × width × height

Substituting the values , we get

Volume = 40 × 20 × 70

= 56000 cm³

Therefore , The dimension of the wood block in centimeter is  40cm by 20cm by 70cm , the volume is  56000 cubic centimeters .

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The function for the arithmetic sequence (fn) = 8n

The domain is {1,2,3,…10}

An arithmetic sequence is a series of numbers in which each term (save the first) is obtained by adding a constant number to the preceding term. For example, 2, 4, 6, 8,... is an arithmetic sequence because each term is created by adding 2 (a constant integer) to the previous term.

Given that

The arithmetic sequence is 8, 16, 24, 32, 40, 48, 56

Common difference = 16-8 = 8

The sequence is increasing so the common difference is positive 8

fn = 8 + (n-1)d

fn = 8 + (n-1)8

fn = 8 + 8n – 8

fn = 8n

So the function for the arithmetic sequence (fn) = 8n

b. The points to the graph are represented by (nfn). So the points are (1,8);(2,16);(3,24);(4,32);(5,40);(6,48);(7,56)

The domain of the function is the number 10

So, the domain is {1,2,3,…10}

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Using equivalent equations to equate both caterer A and B need to serve 10 guests to have equal pay

Equivalent equations are systems of equations that have the same solutions. Equations are said to be equivalent when they have the same solution set. For example, x + 2 = 6 and 2x = 8 are equivalent equations, because when we solve each of them as follows, they have the same solution set: x + 2 = 6. Subtract 2 from both sides. x = 4.

In this case, we can set up two equations and equate them to know how many people they need to serve in order to earn equally.

For caterer A;

y = 15x + 100 ...eq(i)

y = 20x + 50 ...eq(ii)

For the equation to be equivalent, equation(i) and (ii) must be equal

15x + 100 = 20x + 50

x = 10

They both need to serve 10 guests to earn equally.

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Answer:

$250

Step-by-step explanation:

He expected to collect 37.5% less than $400.

First, we find 37.5% of $400.

Then we subtract that amount from $400.

37.5% of $400 is:

37.5% of $400 = 0.375 × $400 = $150

Now, subtract $150 from $400:

$400 - $150 = $250

Answer: $250

Answer:

m1 = 33 degrees ; m3 = 33 degrees

Step-by-step explanation:

m8 = m4 = 147 degrees

m4 + m1 = 180

147 + m1 = 180

m1 = 180 - 147

m1 = 33 degrees

m1 = m3 (vertical angles)

The system of inequalities that models this situation is given as follows:

The variables of the system of inequalities are presented as follows:

Gwen charges $3.50 each time she walks a dog. Julia charges $1.25 each time she waters the flowers, and they need to raise at least $250, hence the first constraint is of:

3.5x + 1.25y ≥ 250.

The number of times Julia plans to water the flowers is no more than six times the number of dogs Gwen plans to walk, hence:

y ≤ 6x.

Gwen plans to walk no less than 12 dogs, hence:

x ≥ 12.

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Answer:

Yes, it is a direct variation.  The constant of variation is 4

Step-by-step explanation:

As y changes by 20, x changes by 5

[tex]\frac{20}{5}[/tex] = 4

Answer:  y=2x-6

Step-by-step explanation:

y=2x-6 is the equation of the linear relationship in slope-intercept form

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Let us take any two points from the given table

(1, -4) and (0, -6)

The slope is m=-6+4/-1

=-2/-1

m=2

Now let us find the y intercept

-4=2(1)+b

-4=2+b

-6=b

So the slope intercept form is y=2x-6

Hence,  y=2x-6 is the equation of the linear relationship in slope-intercept form

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The 45° and 55° base angles of the triangle that share a vertex with the inverted triangle that have the vertex angle (at the shared vertex) marked x, indicates that x is 80°

A shared vertex is a common point to two or more figures that is also a vertex to the figures that share the point.

The measure of the vertex angle of the triangle at the top which is inverted = x

The measure of the base angles of the triangle at the bottom are;

45° and 55°

The measure of the vertex angle of the triangle at the base = y

From the diagram of a similar question, angle x and angle y are vertical angles (angle x and angle y are formed by the intersection of two lines)

45° + 55° + y = 180° (angle sum property of a triangle)

y = 180° - (45° + 55°) = 80° (subtraction property of equality)

y = 80°

x ≅ y (vertical angles theorem)

x = y (definition of congruent angles)

x = 80° (substitution property of equality)

The measure of angle x is 80°

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The area of the base and curved surface area is 15400mm²  and 22000 mm² respectively, of the cylindrical surface.

What is the cylindrical surface?

The amount of space that is covered by the curved surface and flat surface of a cylinder's bases is known as the cylinder's surface area. In addition to the area of the curved surface, the cylinder's total surface area also comprises the areas of its two circular bases. Units of surface area are stated as squares, such as square millimeters, square inches, square feet, and so on. Two circular bases joined by a curving face form a 3-D solid object known as a cylinder.

The curved surface area of a cylinder is 2πrh

A = 2 * 22/7*140/2*50

A = 22000 mm²

The base are will be π r²

B= 22/7 * 140/2*140/2

B= 15400mm²

Hence the area of the base and curved surface area is 15400mm²  and 22000 mm² respectively.

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Using the given inequality we can calculate that this is equivalent to

(B) x ≤-1 or x ≥1

The given inequality is |8x| ≥ 2 .

Now we have to solve this inequality to find the range of the value of x.

|8x| ≥ 2

now we will try to remove the modulus function.

either 8x ≥ 2 ⇒ x ≥ 1/4

or, -8x ≥ 2 ⇒ x ≤ -1/4

Therefore the solution of the inequality is x ≤ -1/4 or x ≥ 1/4

Now of the given options the most plausible option or inequality that also satisfies this inequality is given by B)  x ≤-1 or x ≥1

In mathematics, an inequality is a connection that makes an unequal comparison between two numbers and maybe other mathematical expressions. On the number line, size comparisons between two numbers are typically conducted.

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Answer:

4 or -8

Step-by-step explanation:

180-148=x(x+4)

32=x^2 + 4x

x^2 +4x - 32

x = 4 or -8

Answer:Yes, the obtuse angles for both triangles are equailateral

Step-by-step explanation:

Step-by-step explanation:

1+2+3+4+5=15

180÷15=12

12x1=12

12x2=24

12x3=36

12x4=48

12x5=60

Answer: Her mistake is that she would have to make each piece 167.2 inches long to have 5 equal pieces.

Step-by-step explanation:

7 * 5 ≠ 836

836/5 = 167.2