The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 72% of the carbon-14 expected in living matter, when did the tree die?

Answer:

[tex] t - 9 [/tex]

Step-by-step explanation:

Given that t represents a number which is unknown to us, the difference of the number and 9 can be expressed algebraically as:

[tex] t - 9 [/tex].

The difference of t and 9 = [tex] t - 9 [/tex].

Answer:

4 x 3 + 6 x 2 has 4 terms so it's an quadrinomial

Step-by-step explanation:

D quadrinomial

Answer: 4th figure , where XY is a line.

Step-by-step explanation:

From up to down, The first figure is representing ray( end point at X ) which is an defined term and it is defined as "A ray is a line with one end point."

The second figure is representing a line segment with 2 end-points at X and Y and it is and defined term and it is defined as "A line segment is a line with 2 end points."

The third figure is a joint of two rays and they are making an angle which is again an defined term.

The last figure is representing a line which has no endpoints and is an undefined term.

Hence, the last figure is representing an undefined term "line".

Answer:

j = 2z + 1

jennifer is one year older or jennifer is plus one.

twice zacks age or two times zacks age.

jennifer's age is two times zacks age plus one or

j = 2z + 1

Answer:

The volume of the rectangular prism is 20.

Answer:

The answer is A, 19/49

Step-by-step explanation:

normally you would do the equation as usual, but if you notice the words (without replacing the first) then that means there will be 24 marbles left.

that means it can't be B C or D because 24 can't be simplified into the denominators 5, 20, or 15

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ \: 14.25 \: \% \: }}}}}[/tex]

Step-by-step explanation:

Given,

Principal ( P ) = $ 6000

Amount ( A ) = $ 14550

Time ( T ) = 10 years

Rate ( R ) = ?

Finding the Interest

The sum of principal and interest is called an amount.

From the definition,

[tex] \boxed{ \sf{Amount = \: Principal + Interest}}[/tex]

plug the values

⇒[tex] \sf{14550 = 6000 + Interest}[/tex]

Swap the sides of the equation

⇒[tex] \sf{6000 + Interest = 14550}[/tex]

Move 6000 to right hand side and change its sign

⇒[tex] \sf{Interest = 14550 - 6000}[/tex]

Subtract 6000 from 14550

⇒[tex] \sf{Interest = \: 8550 \: }[/tex]

Interest = $ 8550

Finding the rate

[tex] { \boxed{ \sf{Rate = \frac{Interest \times 100}{Principal \times Time}}}} [/tex]

plug the values

⇒[tex] \sf{ Rate = \frac{8550 \times 100}{6000 \times 10} }[/tex]

Calculate

⇒[tex] \sf{Rate = \frac{855000}{60000} }[/tex]

⇒[tex] \sf{Rate = 14.25 \: \% \: }[/tex]

Hope I helped!

Best regards!!

Answer:hi

Step-by-step explanation:Let me first warn you that I CANNOT get the denominators of this problem to go underneath the numerators. It looks good on my answer page but when I click "preview your answer" the denominators are ALL over the place. Grrrrr.

I think the weirdly placed denominators make this explanation hard to understand but you give this a go and see if you understand things. If it is too hard to see, maybe this website will let you instant message me or email me. If so, then I will send you the solution via email. I'm very sorry the denominators are SO scattered.

See what you think of the explanations below but it might help if you write down my answer on paper, so that you can move the number to rest more closely under their proper numerators. :-)

Ok then......

Let's start with your first problem. A quick way to do this work is to cross multiply. Here's what I mean:

__3___ = __6___

r - 1 r + 2

Ok, so you can cross multiply:

3(r + 2) = 6(r - 1) (cross multiply)

3r + 6 = 6r - 6 (use the distributive property)

Now you will have to put the "r" variables on the left side of the equal sign and numbers without variables on the right side of the equal sign. To get 6r from the right side to the left, you can subtract 6r from the right side. If you subtract it from the right, you must subtract it from the left.....

To get 6 from the left side to the right, you can subtract it from the left. If you subtract it from the left, you must subtract it on the right.....

So now you have:

3r - 6r = -6 - 6 This becomes.........

- 3r = -12

Now to solve for "r" you will have to divide by -3. Why? Well, -3r is really saying: -3 times r. The -3 and the r are actually being multiplied together so to isolate the "r" you have to sort of "undo" the multiplication. What is the opposite of multiplication? It's DIVISION. Soooo, you must divide by -3 on both sides. SO you have:

- 3r = -12

r = 4 (-12 divided by -3 is a positive 4)

Now you know "r" equals 4. If we "plug" 4 back into the original equation, we can see the answer is correct. Check this out:

__3___ = __6___ (original equation)

r - 1 r + 2

__3___ = __6___ (substitute "4" in for "r"

4 - 1 4 + 2

__3___ = __6___ (do the math in the denominator area)

3 6

1 = 1 (3/3 equals 1 and 6/6 also equals 1, so our

solution that r = 4 is correct!) :-)

Now to your 2nd problem..........

4/2x-5 = 24/2x

___4___ = __24___

2x � 5 2x

Let's cross multiply again:

4(2x) = 24(2x - 5)

8x = 48x - 120

8x - 48x = - 120

-40x = - 120

(divide both sides by -40)

x = 3

Now let's "plug" 3 in where we had the variable "x" in the original equation to see if we are correct.

___4___ = __24___ (original equation)

2x � 5 2x

___4___ = __24___ (substituted 3 for "x")

2(3) � 5 2(3)

___4___ = __24___

6 - 5 6

___4___ = __24___

1 6

4 = 4

SO once again we have found the correct answer. Yay for us! :-)

I hope this helps. :-)

Answer:

[tex]r=9[/tex]

Step-by-step explanation:

So we have the equation:

[tex]-8(6-r)=24[/tex]

Divide both sides by -8:

[tex]6-r=-3[/tex]

Subtract 6 from both sides:

[tex]-r=-9[/tex]

Divide both sides by -1:

[tex]r=9[/tex]

And we're done!

Answer:

2.7 [tex]g/mL[/tex]

Step-by-step explanation:

The density of an object will be its mass over volume.

We know that the mass of this rock is 54 grams because it took 54 grams of gram stackers to balance the scale. If we have a balanced scale, that means the amount of weight on either side is equal. So the mass is 54 grams.

Also, we can tell that the volume of the rock is 20 mL. This is because, according to Archimedes principle, if you put an object in water, the amount of water displacement will be it's volume. So the amount of water displacement is [tex]60-40=20[/tex] mL.

Density is mass over volume, so the density is [tex]54\div20 = 2.7[/tex]. Density is measure in mass over volume, so [tex]g/mL[/tex].

So 2.7  [tex]g/mL[/tex] is the density of the rock.

Hope this helped!

Answer:

D. 424 m³

Step-by-step explanation:

Use the formula for the volume of a cylinder

V = [tex]\pi[/tex]r²h

Plug in the values we know

V = (3.14)(3²)(15)

V = 423.9 m³

This is closest to answer choice D, 424 m³

So, D is correct

50

(-1) + 2 + (-3) + 4 + ... + (-99) + 100 =

= 2 - 1 + 4 - 3 + .. + 100 - 99

= 1 + 1 + .. + 1

= 50×1

= 50

Answer:

50.

Step-by-step explanation:

Each pair of numbers add up to 1:

-1 + 2 =  1,  -3 + 4 = 1   and so on

There are 50 of theses pairs so the value is 50.

Answer:

1. square root 9/4

2. 5/3

3. square root 5

4. 2.5

Step-by-step explanation:

The first one would equal 1.5.

The second is 1.6.

The third is 2.2.

And obviously the last is 2.5.

Answer:

x^2 +6x -15

Step-by-step explanation:

(3x^2 +2x -8) - (2x^2 -4x+7)

Distribute the minus sign

(3x^2 +2x -8) - 2x^2 +4x-7

Combine like terms

x^2 +6x -15

Answer:

x²+6x-15

Step-by-step explanation:

We are given this expression:

[tex](3x^2+2x-8) - ( 2x^2-4x+7)[/tex]

We want to simplify the expression. First, distribute the negative sign in front of the second set of parentheses. Multiply each term inside the parentheses by -1.

[tex](3x^2+2x-8) + (-1*2x^2) + (-1*-4x) + (-1*7)[/tex]

[tex](3x^2+2x-8) -2x^2+ 4x -7[/tex]

Next, combine like terms. The 2 terms with an x² can be combined, just like the two terms with an x, and the two terms without a variable.

[tex](3x^2-2x^2) + (2x+4x) + (-8-7)[/tex]

[tex]x^2+(2x+4x)+(-8-7)[/tex]

[tex]x^2+6x+(-8-7)[/tex]

[tex]x^2+6x-15[/tex]

The expression x²+6x-15 is equivalent to (3x²+2x-8)-(2x²-4x+7)

Answer:

Step-by-step explanation:

A). If a function 'f' is inverse of another function 'g',

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

In this question the given functions are,

f(x) = [tex]\frac{1}{x-3}[/tex] and g(x) = [tex]\frac{3x+1}{x}[/tex]

Then, f[g(x)] = [tex]\frac{1}{\frac{3x+1}{x}-3}[/tex]

                    = [tex]\frac{x}{3x+1-3x}[/tex]

                    = x

Similarly, g[f(x)] = [tex]\frac{(\frac{3}{x-3})+1}{\frac{1}{x-3} }[/tex]

                         = [tex]\frac{3+x-3}{1}[/tex]

                         = x

Therefore, Both the functions are inverse of each other.

B). Domain of the compositions of these functions will be a set of all real numbers, (-∞, ∞)

Answer:

72 words per minute

Step-by-step explanation:

The unit rate in this case is words per minute. Therefore, the answer is 1872 / 26 = 72 words per minute.

Answer:

The answer is 3.

19+17=36.

36/12=3.

Answer:

Step-by-step explanation:

Hello, let's note n this integer.

n+ (n+1) + (n+2) = 168

3n+3=168

3(n+1)=168

n+1=168/3=56

n = 56-1=55

Thanks

Answer:

angle congruent to a given angle.

Step-by-step explanation:

This is the construction of an angle congruent to a given angle.

Answer:

8/15

Step-by-step explanation:

1 hour = 60 minutes

32 minutes / 60 minutes

Divide top and bottom by 4

8/15

Answer:

The answer is:

The Moon, on average, is about 150 million kilometers away from the Sun.

Answer:

it IS b

Step-by-step explanation:

Answer:

[tex]\frac{dy}{dx}=(\frac{(2x-2)(x^3+3)-(x^2-2x)(3x^2)}{(x^3+3)^2})[/tex]

Step-by-step explanation:

So we want to find the derivative of the rational equation:

[tex]y=\frac{x^2-2x}{x^3+3}[/tex]

First, recall the quotient rule:

[tex](\frac{f}{g})'=\frac{f'g-fg'}{g^2}[/tex]

Let f be x^2-2x and let g be x^3+3.

Calculate the derivatives of each:

[tex]f=x^2-2x\\f'=2x-2[/tex]

[tex]g=x^3+3\\g=3x^2[/tex]

So:

[tex]\frac{dy}{dx}=(\frac{x^2-2x}{x^3+3})'[/tex]

Use the above format:

[tex]\frac{dy}{dx}=\frac{f'g-fg'}{g^2}\\\frac{dy}{dx}=(\frac{(2x-2)(x^3+3)-(x^2-2x)(3x^2)}{(x^3+3)^2})[/tex]

And that's our answer :)

(If you want to, you can also expand. However, no terms will be canceled.)

Answer:

A. 2.27 kg

B. 61.23 kg

Step-by-step explanation:

A. 31.75 - 29.48 = 2.27

B. 31.75 + 29.48  = 61.23

The speed of the object in feet per minute to nearest whole number is 164feet/min

Speed is the ratio of the distance to the time of an object. Mathematically;

Speed = Distance/Time

Given the following

Speed = 3km/hr

Using the conversion ratio

1km = 3280.84feet

3km = x

Cross multiply

x = 3 * 3280.84

x = 9,842.52feet

Convert 1 hour to minute

1 hour = 60minutes

Get the speed in feet per minutes

Speed in feet/minutes = [tex]\frac{9,842.52}{60}[/tex]

Speed in feet/minutes = 164.042 feet/minutes

Hence the speed of the object in feet per minute to nearest whole number  is 164feet/min

Learn more here: https://brainly.com/question/1462592

The speed in feet per  minute is 164.

Given the following data:

In this exercise, you're required to convert the value of the speed given in kilometers per hour to feet per minute.

Conversion:

1 kilometer = 3280.84 feet

3 kilometer = X feet

Cross-multiplying, we have;

X [tex]= 3280.84[/tex] × [tex]3[/tex]

X = 9842.50 feet

Since we know that one (1) hour is equal to sixty (60) minutes, we would divide the value of X by 60 in order to convert it to feet per minute.

[tex]X = \frac{9842.50}{60}[/tex]

X = 164.042 feet per minute.

To the nearest whole number;

X = 164 feet per minute

Therefore, the speed in feet per  minute is 164.

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Answer:

[tex]\huge \boxed{h= \displaystyle \frac{SA}{2\pi r} -r}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

[tex]SA=2\pi r^2 +2\pi rh[/tex]

Subtracting [tex]2\pi r^2[/tex] from both sides:

[tex]SA-2\pi r^2 =2\pi rh[/tex]

Dividing both sides by [tex]2\pi r[/tex]:

[tex]\displaystyle \frac{SA-2\pi r^2}{2\pi r} =h[/tex]

Simplifying the equation:

[tex]\displaystyle \frac{SA}{2\pi r} -r=h[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

x = -12

Step-by-step explanation:

Let x be the number.

The product of 5 and x increased by 9 is equal to 15 less than 3 times x.

5x + 9 = 3x - 15.

We can isolate x, getting (5-3)x = -15-9

Then we can solve:

2x = -24

x = -12.

The required number is -12.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, The product of five and a number, increased by 9 is equal to fifteen less than three times then number.

Let x be the number.

Establishing the equation,

5x + 9 = 3x - 15.

(5-3)x = -15-9

Then we can solve:

2x = -24

x = -12.

Hence, the number is -12

For more references on equations, click;

https://brainly.com/question/29657988

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