Density of wood is a very important trait for furniture making. There are two main important mechanical properties: strength and stiffness. Research has shown that a increase density equals an increase strength, hardness and stiffness of sawn timber.


A carpenter has two pieces of wood. He wants to find the density of each piece.


The first piece came from a birch tree. The piece of birch wood measures 2 meters by 4 meters by 3 meters and weighs (mass) 16 kilograms.


The second piece came from a cypress tree. The piece of cypress wood measures 3 meters by 5 meters by 2 meters and weighs (mass) 15.3 kilograms.


Which piece of wood has a greater density? You must show your work in order to receive credit.

Answer: =20 feet

= 35 feet

Explanation :

let width = a

length = a+15

Now,

2(2w+15)=110

2w=55-15

w=40/2

w=20

Answer: x = 0.79128784 and -3.79128784

Step-by-step explanation: Round them up

Factorizing an expression involves writing the expression in simpler forms

The expression cannot be factorized.

The expression is given as:

[tex]0 = x^2 + 3x - 3[/tex]

Rewrite the expression as:

[tex]x^2 + 3x - 3 = 0[/tex]

The above expression cannot be factorized.

This is so because 3x can not be expressed using terms that have the product of -3 and x^2

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Answer:

the question was not correctly solved

Step-by-step explanation:

A=½bh

23=½*b*h

²/1×23= bh

²/1×23=6h

46=6h

h=7.666666667 / h=23/3

I hope this is helpful

Answer:

lets get started

Step-by-step explanation:

[tex]\left \{ {-3x-2y = -6} \atop {-3x+2y=18} \right. <=>\left \{ {-6x=12} \atop {-3x+2y=18} \right. <=> \left \{ {x=-2} \atop {y=6} \right.[/tex]

The answer: ( x ; y ) = ( -2 ; 6 )

Ok done. Thank to me :>

Answer:

Length of the shadow = 20.5 cm

Step-by-step explanation:

Given the 32-meter height of a tall building, and its casted shadow of 38 meters, we can find the unknown length of the shadow by using the Pythagorean Theorem.

The Pythagorean Theorem states that the squared length of the hypotenuse of a right triangle is equal to the sum of the squared lengths of the legs.

The algebraic representation of the Pythagorean Theorem is:  

                     c² (hypotenuse) = a² (leg₁) + b² (leg₂)

To solve for the given problem:

Let c = 38 m (distance from the top of the building to the tip of the shadow)

a = unknown length of the shadow

b = 32m (height of the building)

Since we have to solve for the value of a (unknown length of the shadow), we must algebraically solve for a:

c² = a² + b²

Subtract b² from both sides:

c² - b² = a²  + b² - b²

a² = c² - b²

Substitute the given values into the formula for solving a :

a² = c² - b²

a² = (38)² - (32)²

a² = 1444 - 1024

a² = 1444 - 1024

Next, take the square root of both sides to solve for a:

[tex]\displaystyle\mathsf{\sqrt{(a)^2}\:=\:\sqrt{420}}[/tex]

a = 20.49 or 20.5 cm

Therefore, the length of the shadow is 20.5 cm.

The equation has one extraneous solution which is n ≈ 2.38450287.

Given that,

The equation;

[tex]\dfrac{9}{n^2+1} =\dfrac{n+3}{4}[/tex]

We have to find,

How many extraneous solutions does the equation?

According to the question,

An extraneous solution is a solution value of the variable in the equations, that is found by solving the given equation algebraically but it is not a solution of the given equation.

To solve the equation cross multiplication process is applied following all the steps given below.

[tex]\rm \dfrac{9}{n^2+1} =\dfrac{n+3}{4}\\\\9 (4) = (n+3) (n^2+1)\\\\36 = n(n^2+1) + 3 (n^2+1)\\\\36 = n^3+ n + 3n^2+3\\\\n^3+ n + 3n^2+3 - 36=0\\\\n^3+ 3n^2+n -33=0\\[/tex]

The roots (zeros) are the  x  values where the graph intersects the x-axis. To find the roots (zeros), replace  y

with  0  and solve for  x. The graph of the equation is attached.

n  ≈  2.38450287

Hence, The equation has one extraneous solution which is n  ≈  2.38450287

For more information refer to the link.

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Answer:

y=5/6x+5

Step-by-step explanation:

Just ask!

Hope this helps.

Sorry if I'm wrong.

~Happy Holidays!!~ o(*￣▽￣*)ブ

Answer:

B(if the option is 10^7 instead of  107

Step-by-step explanation:

no. of people in New York=19000000

no. of people in Vermont =626,000

difference in populations = 19000000-626,000 =18374000

therefore, the difference in populations is 18374000

(which can also be written as 1.8374x10^7)

[tex]\frac{13^5}{13^x} =13^4 =>13^{5-x} =13^4\\ =>5-x=4=> x=5-4=1[/tex]

ANSWER: x = 1

ok done. Thank to me :>

Answer:

Here is a screenshot of my graph.

Step-by-step explanation:

Answer: Tanaka is wrong becausee...

2 x 3 = 6

Since Tanaka said "When you multiply an odd number and an even number together, you will always get an odd number." we do not need to show more examples.

Hope this helps :)

Answer:

Look at photo for answer, I have not done a piecewise function for a long time... so double check my work.

Step-by-step explanation:

Answer:

y+1 = [tex]\frac{3}{11}[/tex](x-5)

Step-by-step explanation:

First, find the slope.

-4--1= -3

-6-5= -11

3/11 is the slope

Plug in the slope and one the the points.

y+1 = [tex]\frac{3}{11}[/tex](x-5)

Follow me on  i n s t a g r a m, send a message, and I'll follow you back : ifaulkner24

Answer:

no

Step-by-step explanation:

no I said no no nono nooooooo

Answer:

-2

Step-by-step explanation:

f(x)≈ -0.86x+13.5

  putting x=18 in f(x), we get

    f(x)≈ -0.86×18+13.5

 ⇒      f(x)≈ -15.48+13.5

 ⇒      f(x)≈ -1.98

 ⇒      f(x)≈ -2

Answer:B

Step-by-step explanation:

The answer is B also known as -2

Answer:

c. is correct answer I think

Answer:

b. [tex]a_{12}=-177147[/tex]

Step-by-step explanation:

This is a geometric sequence:

[tex]a_n=a_1x^{n-1}[/tex]

where n is the index in the sequence and x is the common scale factor.

In the given sequence here, the common factor is 3:

[tex]-3\div-1=3\\-9\div-3=3\\-27\div-9=3[/tex]

That's the factor, and we know the first term is -1, so you can write the equation for this sequence:

[tex]a_n=(-1)(3)^{n-1}[/tex]

Finally, plug in 12 for n and solve:

[tex]a_{12}=(-1)(3)^{12-1}\\a_{12}=(-1)(3)^{11}\\a_{12}=(-1)177147\\a_{12}=-177147[/tex]

Answer:

b=a^2-6

Step-by-step explanation:

Answer:

square both sides, you will get

[tex]a^{2} = b + 6\\b = a^{2} - 6[/tex]

Step-by-step explanation:

square both sides, you will get

[tex]a^{2} = b + 6\\b = a^{2} - 6[/tex]

Answer:

  x = 60 cm

Step-by-step explanation:

If we assume the figures are similar, then corresponding sides are proportional.

  x/36 = 35/21

  x = 36(35/21) = 60 . . . . cm

_____

You can consider the ratios of side lengths. Shortest to longest, they are ...

  7 : 9 : 12 = 21 : 27 : 36 = 35 : 45 : 60

The smaller figure is 3 times the basic ratio; the larger figure is 5 times the basic ratio.

Answer:

[tex]x=-10-8 = -18[/tex]

Step-by-step explanation:

Answer:

x=-10-8=18

Step-by-step explanation:

Answer:19.2

Step-by-step explanation:

Using proportions, it is found that it would take 24 minutes if there were 5 people distributing the pamphlets.

The rule of three is:

3 people - 40 minutes

5 people - x minutes

Applying line multiplication:

[tex]5x = 120[/tex]

[tex]x = \frac{120}{5}[/tex]

[tex]x = 24[/tex]

It would take 24 minutes if there were 5 people distributing the pamphlets.

You can learn more about proportions at https://brainly.com/question/24372153

Answer:

[tex]\frac{11}{10}[/tex]

Step-by-step explanation:

[tex]\frac{8}{10}[/tex] - [tex]\frac{x}{10}[/tex] = [tex]\frac{3}{10}[/tex]

so [tex]\frac{8}{10}[/tex] +[tex]\frac{3}{10}[/tex] =[tex]\frac{x}{10}[/tex]

since all the denominators are the same we simply add the numerators to find x

x would be 8 +3 = 11

so [tex]\frac{11}{10}[/tex] is the answer

Answer:

8 units

Step-by-step explanation:

Area of square = 2x3 = 6 units

Area of triangle = (2x2)/2 = 2 units

Total area = 6 +2 = 8 units

Answer:

As previous answer stated, 8 units

Step-by-step explanation:

You multiply one side of the square by another to get 6 units, then, add the units from the triangle

Answer:

B

Step-by-step explanation:

40/100 is equal to 40% so 24/x =40/100 means 24 is 40% of x

Answer:

11

Step-by-step explanation:

(f/g)(5)=

f(5)=(5)2+1÷g(5)=5-4

10+1/1

11/1

(f/g)=11

The required simplified value of the given function as (f/g)(5)  is 26.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
f(x) = x² +1

f(5) = 5² + 1
f(5) = 26

g(x) = x - 4
g(5) = 5 - 4 = 1

f/g(5) = f(5) / g(5)
       = 26 / 1 = 26

Thus, the required simplified value of the given expression (f/g)(5)  is 26.

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Answer:

C

Step-by-step explanation:

C