Astand is a frustum shape, formed by removing a small square based pyramid from the top of
a large square based pyramid,
The wood has a density of 80 g/cm!
Calculate the mass of the stand in g.

11 cm base
5 cm frustum height
9 cm height of pyramid

A perfect square trinomial factors to a binomial squared, option a.

A perfect square trinomial is a trinomial expression that can be factored into the square of a binomial. It has the form:

(ax² + bx + c)²

To factor it, you can take the square root of the first term (ax²) and the square root of the last term (c). The middle term (bx) will be twice the product of these square roots. Therefore, the factored form of the perfect square trinomial is:

(ax² + bx + c)² = (√(ax^2) + √(c))² = (√(ax^2) + √(c))(√(ax^2) + √(c))

This can be simplified to:

(ax² + bx + c)² = (√(ax²) + √(c))² = (√(a)x + √(c))²

So, a perfect square trinomial factors into the square of a binomial, where the first term of the binomial is the square root of the coefficient of the squared term, and the second term is the square root of the constant term.

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Step-by-step explanation:

LCM is lowest common factor and HCF is highest common factor.

Given numbers are 236 and 92.

We can find it using prime factorization method.

Prime factorization of 236 = 2 x 2 x 59

Prime factorization of 92 = 2 x 2 x 23

HCF = 2 x 2 = 4

LCM = 2 x 2 x 59 x 23 = 5428

We know that,

LCM×HCF = product of two numbers

⇒ LCM×HCF = 5428×4 = 21712

⇒ product of two numbers = 236× 92 = 21712

Hence, proved.

The solution to the expression (12-√-8)/2 as a complex number is 6 - i√2.

What is expression?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, division, exponents, and roots.

The expression (12-√-8)/2 involves a square root of a negative number, which cannot be represented by a real number. Therefore, we need to extend the real numbers to the complex numbers to solve this expression.

To evaluate the square root of a negative number, we can use the imaginary unit, denoted by i, which is defined as the square root of -1. Then, we have:

√-8 = √(8) √(-1) = 2i√2

Substituting this value back into the original expression, we get:

(12-√-8)/2 = (12 - 2i√2)/2

Simplifying the expression by dividing both the numerator and denominator by 2, we get:

(12 - 2i√2)/2 = 6 - i√2

Therefore, the solution to the expression (12-√-8)/2 as a complex number is 6 - i√2.

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Answer:

1/6 a cup

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

Step 1:

a² + b² = c²

Step 2:

56² + 42² = 4900

Step 3:

4900 ÷ 70 = 70

Answer:

70

Hope This Helps :)

The maximum area that the 60 m can enclose is 225m², the dimensions of the maximal region are 15m x 15m, and the height as an fcn of the base is 30 - b.

Let the base of the rectangular region be "b",

and the height be "h" and,

it is given that the perimeter of the rectangular region = 60m

(a) write height as an fcn of base

by using the formula of the perimeter of a rectangle,

2(h+b) = 60m

we can write, h = 30 - b

⇒Area of the rectangular region

area(A) = height × base

substituting the value of h.

= (30 - b) × b

thus, A(b)= 30b - b²

to find the maximum area that the 60 m can enclose

\(\frac{dA(b)}{db}\) should be equal to 0.

substituting the value of A(b).

30 - 2b = 0

thus, b = 15

maximum area = 30b - b²

substituting the value of b.

= (30 × 15) - 15²

thus, maximum area = 225m².

dimensions of the maximum region,

for maximum area height = base = 15m

thus, the dimensions of the maximum rectangular region are 15m x 15m.

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oh come on

(read the comments(all of them))

On solving the provided question we cans ay that function  In the auction, 180 carrots cost £18.00.

Mathematicians examine numbers with their modifications, equations and associated structures, forms and their locations, and feasible positions for these things. The term "function" indicates the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs where each supply leads to a specific, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible capabilities are on functions, yet another skills, so multiple capabilities, in capabilities, and on operations.

The initial cost of 20 carrots was £2.80. Thus the cost per carrot is £2.80 20 = £0.14.

If the price is decreased by 30%, the new carrot price is: £0.14 - (30% £0.14) = £0.098 or £0.10 (rounded to the nearest penny)

As a result, 180 carrots at the current sale price will cost: 180 £0.10 = £18.00

In the auction, 180 carrots cost £18.00.

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Answers:

D'' = (1, -3)

E'' = (1, -1)

F'' = (3, -1)

G'' = (3, -4)

A diagram is shown below.

========================================================

Explanation:

The center of dilation is point E, which means this point does not move when the dilation is applied. Every other point will move.

As your diagram indicates, segment DE is 4 units long. If we apply the scale factor 1/2, then D'E' will be half as long meaning D'E' = 2. So point D' is 2 units above point E at (1,3)

Point F is 4 units away from point E. The scale factor 1/2 will bring F closer to E leading to segment F'E' = 2. So we'll start at E and move 2 units to the right to land on F ' (3, 1)

From F to G is 6 units, which cuts in half to 3. So from F' to G' is 3 units telling us we start at F ' (3, 1) and go up three units to get go G ' (3, 4)

So far we have

D ' = (1, 3)

E ' = (1, 1) ... fixed point doesn't move

F ' = (3, 1)

G ' = (3, 4)

-------------

From here we'll apply the reflection over the x axis rule which says

\((x,y) \to (x, -y)\)

the x coordinate stays the same, and the y coordinate flips from positive to negative (or vice versa).

Based on what was mentioned for D', E', F' and G', we get the following

D'' = (1, -3)

E'' = (1, -1) .... this point does move now

F'' = (3, -1)

G'' = (3, -4)

Points E' and E'' are in different locations because all fixed points in this reflection are along the mirror line y = 0 (aka the x axis). In other words, if E was on the x axis, then it would not move if we applied this reflection.

Check out the diagram below see a visual summary of what happened. Note how the red points moved in closer to point E (since the distances from the center E have been cut in half) compared to the blue counterparts.

Jeremy's claim that the number 5.676677666777... is a rational number because it is a decimal that goes on forever with a pattern is false

The number is given as:

Number = 5.676677666777...

The above number is a decimal number.

The dots (...) at the end of 5.676677666777... implies that the number is a repeating number

Repeating numbers are irrational numbers.

This is so because they cannot be expressed as a fraction of two integers

Hence, Jeremy's claim that the number 5.676677666777... is a rational number because it is a decimal that goes on forever with a pattern is false

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Answer:

A,

23/6v+28

Step-by-step explanation:

Answer:

D. 23/6v+28

Step-by-step explanation:

She graphed it correctly.

The inequality \(3y \le 2x\) is the same as \(y \le \frac{2}{3}x\) after dividing both sides by 3 to isolate y.

From here you graph \(y = \frac{2}{3}x\) which is a straight line through (0,0) and (3,2). This line is made solid because of the "or equal to" as part of the inequality sign above.

We shade below the solid boundary due to the "less than" portion of the inequality sign.

Answer:

-1

Step-by-step explanation:

1(+-)2=

step 1: a positive and a negative is a negative

1-2=-1

Answer:

-1

Step-by-step explanation:

negative and positive is negative

1+(-2)

1-2

-1

Answer:

-8,-9,-10,-11,-12,-13

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Two polygons are similar if their corresponding angles are congruent and the corresponding sides have a constant ratio.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

A Polygon is a closed figure made up of line segments (not curves) in a two-dimensional plane. Polygon is the combination of two words, i.e. poly (means many) and gon (means sides). A minimum of three line segments is required to connect end to end, to make a closed figure.

Triangles, hexagons, pentagons, and quadrilaterals are all examples of polygons.

A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°.

Therefore;

Two polygons are similar if their corresponding angles are congruent and the corresponding sides have a constant ratio.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

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Answer:

The formula you are referring to is the quadratic formula, which is used to solve quadratic equations of the form ax^2 + bx + c = 0. The formula is:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are coefficients of the quadratic equation.

The weighted average cost of capital (WACC) for company C is 6.63%.

The weighted average cost of capital (WACC) is a financial metric that represents the average rate of return a company must earn on its investments to satisfy its shareholders and creditors. It takes into account the proportion of debt and equity in a company's capital structure and the respective costs associated with each.

To calculate WACC, we need to consider the cost of debt and the cost of equity. The cost of debt is the interest rate a company pays on its debt, adjusted for taxes. In this case, the pre-tax cost of debt is 2% and the tax rate is 24%. Therefore, the after-tax cost of debt is calculated as (1 - Tax Rate) multiplied by the pre-tax cost of debt, resulting in 1.52%.

The cost of equity represents the return required by equity investors to compensate for the risk associated with owning the company's stock. Here, the cost of equity for company C is 6%.

The debt represents 10% of the total capital, while the equity represents the remaining 90%. To calculate the weighted average cost of capital (WACC), we multiply the cost of debt by the proportion of debt in the capital structure and add it to the cost of equity multiplied by the proportion of equity.

WACC = (Proportion of Debt * Cost of Debt) + (Proportion of Equity * Cost of Equity)

In this case, the calculation is as follows:

WACC = (0.10 * 1.52%) + (0.90 * 6%) = 0.152% + 5.4% = 6.552%

Therefore, the weighted average cost of capital (WACC) for company C is approximately 6.63%.

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6 is the answer. Look below for solution.

We know that:

Nearest square number to 42 is 36.

√36 = 6

Hence, 6 is the smallest square number.

\(BrainiacUser1357\)

Answer:

The volleyball team won 15 games.

Answer:

That would be 15

Step-by-step explanation:

Good Luck!

Answer:

its 10

Step-by-step explanation:

Solution is x≈3.2  & y≈22.8

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

An online furniture store sells chairs for $200 each and tables for $450 each.

Every day, the store can ship a maximum of 26 pieces of furniture and must sell at least $6000 worth of chairs and tables.

Let, x represents the number of tables sold and y represents the number of chairs sold.

Then, the inequalities are,

we get,

$200y + $450x ≥ 6000

and, x+y≤26

Solving we get,

x≈3.2

y≈22.8

Hence, we get, Solution is x≈3.2  & y≈22.8

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The cost of the apples is 2.9 dollars.

The cost of the bananas is 5.7 dollars.

The total cost is 6 dollars, each apple cost $1.50 each banana cost $.30 and there’s two more bananas then apples.

Therefore,

let

x = number of apples

y = 2x

where

Therefore, using equations,

1.5(x) + y(0.30) = 6

Hence,

where

y = 2x

1.5(x) + 2x(0.30) = 6

1.5x + 0.6x = 6

2.1x = 6

divide both sides by 2.1

x = 6 / 2.1

x = 2.9 dollars

y = 2(2.9) = 5.7 dollars

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DNA contains the instructions needed for an organism to develop, survive and reproduce. To carry out these functions, DNA sequences must be converted into messages that can be used to produce proteins, which are the complex molecules that do most of the work in our bodies. Hope this helps!

Answer:

the answer would be(0, -1) happy to help you ahmed

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

hope this helps

Answer:

.20 per mile.

Step-by-step explanation:

300 x .25 is 75. 75/375 is .20

Answer:

32

Step-by-step explanation:

The measure of angle c is 70 degrees.

If angle a and angle b are complementary, it means that the sum of their measures is equal to 90 degrees.

Given:

Measure of angle a = 10x + 10

Measure of angle b = 20

We can set up the equation:

(10x + 10) + 20 = 90

Simplifying the equation:

10x + 30 = 90

Subtracting 30 from both sides:

10x = 60

Dividing both sides by 10:

x = 6

Now, we have found the value of x to be 6.

To find the measure of angle c, we can substitute the value of x into the equation for angle a:

Measure of angle a = 10x + 10

Measure of angle a = 10(6) + 10

Measure of angle a = 60 + 10

Measure of angle a = 70

As a result, angle c has a measure of 70 degrees.

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