A piece of charcoal was unearthed at an archeological site and found to contain 10% of its original carbon-14. The half-life of carbon-14 is 5,730 years. Which equation can be solved to determine the age of the charcoal?

0.10Ao = Aoe0.000121t
Ao = 0.10Aoe0.000121
0.10Ao = Aoe –0.000121t
Ao = 0.10Aoe –0.000121t

Answer:

12m^2(a)

Step-by-step explanation:

Multiply 3m by 4m for a paralolegram.

(l*w)

Answer:

1/4n - 3

Step-by-step explanation:

1/4 of a number means multiplying 1/4 to n. So we can write 1/4n. Now we write the subtract 3 portion. 1/4n - 3.

The expression n = 1/4n - 3 shows that Emily's number can be obtained by adding 3 to one-fourth of her number.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

Emily's number can be represented as:

n

One-fourth of Emily's number can be represented as:

1/4n

Subtracting 3 from one-fourth of Emily's number gives us:

1/4n - 3

Therefore, the expression that represents Emily's number is:

n = 1/4n - 3

This expression shows that Emily's number can be obtained by adding 3 to one-fourth of her number.

Learn more about the algebraic expression here :

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Answer:

2) Exact

3) Exact

4) Exact

5) Approximation

Step-by-step explanation:

Step-by-step explanation:

Hey there!

Here,

The equation is:

[tex]7 \sqrt{3 \: } {x}^{2} + 10x - \sqrt{3 } = 0[/tex]

Comparing the equation with ax^2+bx+c=0. We get;

[tex]a = 7 \sqrt{3} [/tex]

[tex]b = 10[/tex]

[tex]c = \sqrt{3} [/tex]

Now,

Discriminant= ?

We have,

[tex]discriminant = {b}^{2} - 4ac[/tex]

Put all values.

[tex]discriminant = {10}^{2} - 4 \times 7 \sqrt{3} \times \sqrt{3} [/tex]

[tex]discriminant = 100 - 4 \times7 \times 3[/tex]

[tex]discriminant = 100 - 84[/tex]

Therefore the discriminant = 16.

Hope it helps...

Answer:

k=3/12

k=.25

Step-by-step explanation:

we need to get k by itself

because 12 is over k we need to get rid of it by moving it to the other side (multiplying) because it is 12/k we need to multiply it by 1/12

This eliminates 12 and leaves us with k=3/12

Answer:

chips 1.50 cents hot dogs 2 dollars

Step-by-step explanation:

Hot do is 2 dollars because the same chips were put but 1 extra dog is 2 dollard and you divide from there and get 1.50 for chips

Answer:

y = 8x - 26

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, - 2) and (x₂, y₂ ) = (4, 6)

m = [tex]\frac{6+2}{4-3}[/tex] = 8 , thus

y = 8x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (4, 6) , then

6 = 32 + c ⇒ c = 6 - 32 = - 26

y = 8x - 26 ← equation of line

Answer:

5x - y = -20

Hope this helps.

Answer:

Shalini = 12

Poonam = 60

Step-by-step explanation:

Let p = poonams age

Let s = shalini's age

p = 5s

p+s = 72

Substitute the first equation into the second equation

5s+s = 72

Combine like terms

6s= 72

Divide by 6

6s/6 = 72/6

s = 12

p = 5s =5*12 = 60

Shalini = 12

Poonam = 60

Answer:

The pattern is that each time, 8 is added. The next 2 numbers are 47, 55.

Step-by-step explanation:

7+8=15

15+8=23

23+8=31

31+8=39

39+8=47

47+8=55

Answer:

C.) 2x+3 = 12

Step-by-step explanation:

x+x=2x

2x-(-3) is 2x+3

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Answer:

96 and 192 calories

Step-by-step explanation:

Given

Divide both by 3/4 to find the unit rate:

Then multiply both by 2 to get the calories for 2 cups:

Answer:

0

Step-by-step explanation:

4x+ 2( 3 – 3x) = 6

4x+6-6x=6

6-2x=6

6-6=2x

0/2=x

x=0

Answer:

[tex]x=0[/tex]

Step-by-step explanation:

[tex]4x+2\left(3-3x\right)=6[/tex]

Expand:

[tex]4x+2\times3-2\times3x=6[/tex]

[tex]4x+6-6x=6[/tex]

[tex]-2x+6=6[/tex]

Subtract 6 from both sides:

[tex]-2x+6-6=6-6[/tex]

[tex]-2x=0[/tex]

Divide both sides by -2:

[tex]\frac{-2x}{-2}=\frac{0}{-2}[/tex]

[tex]x=0[/tex]

Answer:

4544

Step-by-step explanation:

1136 *4 = 4544

Answer:

- 3, - 11, - 35, - 107

Step-by-step explanation:

Using the recursive formula with f(1) = - 3 , then

f(2) = - 2 + 3f(1) = - 2 + 3(- 3) = - 2 - 9 = - 11

f(3) = - 2 + 3f(2) = - 2 + 3(- 11) = - 2 - 33 = - 35

f(4) = - 2 + 3f(3) = - 2 + 3(- 35) = - 2 - 105 = - 107

Thus the first four terms are

- 3, - 11, - 35, - 107

Answer:

There are no x-intercepts

Step-by-step explanation: This is because the parabola does not pass through the x-axis at all.

Answer:

no x intercept

Step-by-step explanation:

The x intercept is the value where it crosses the x axis.

This functions does not cross the x axis

There is no x intercept

Answer:

1/2 probably

Step-by-step explanation:

[tex]\text{Hello!}[/tex]

=+=+=+=+=+=+=+=+=+=+=

[tex]\text{Formula: } \boxed{5/4n - 7 = m}[/tex]

[tex]\text{ When n = 40, } \boxed{m = 43}[/tex]

[tex]\text{ Isolate for m:}[/tex]

[tex]\text{Begin by dividing both sides by 4/5 (multiply by reciprocal):}[/tex]

[tex]n = 4/5(m + 7 ) \text{ becomes } 5/4n = m + 7[/tex]

[tex]\text{Subtract 7 from both sides to isolate "m"}[/tex]

[tex]5/4n - 7 = m[/tex]

[tex]\text{Substitute n = 40 into the equation to solve for "m":}[/tex]

[tex]5/4(40) - 7 = m\\\\50 - 7 = m\\\\m = 43[/tex]

Answer:

a = - 2, b = - 6

Step-by-step explanation:

Substitute the values of the zeros into the polynomial and equate to zero.

x² +(a + 1)x + b

x = - 2 → (- 2)² - 2(a + 1) + b = 0 , that is

4 - 2a - 2 + b = 0

2 - 2a + b = 0 ( subtract 2 from both sides )

- 2a + b = - 2 → (1)

x = 3 → 3² + 3(a + 1) + b = 0, that is

9 + 3a + 3 + b = 0

12 + 3a + b = 0 ( subtract 12 from both sides )

3a + b = - 12 → (2)

Subtract (1) from (2) term by term to eliminate b

5a = - 10 ( divide both sides by 5 )

a = - 2

Substitute a = - 2 into either of the 2 equations and evaluate for b

Substituting into (2)

3(- 2) + b = - 12

- 6 + b = - 12 ( add 6 to both sides )

b = - 6

Thus a = - 2 and b = - 6

Answer:

200 cc

Step-by-step explanation:

Volume of the prism = Area of base * height

= 40*5

= 200 cubic cm

Answer:

1/8^5 is the simplified answer  

Step-by-step explanation:

Answer:

2.80×50

Step-by-step explanation:

2.80×50 step by step

Answer: 2.83

Step-by-step explanation:

Use the distance formula

Answer:

Step-by-step explanation:

Put (-6,0) and (0,3) into a table of values

form of the equation: mx+b

x -6 0

y 0 3

3/-6=-0.5 (m)

3=b (the value of y when x=0)

equation: y=0.5x+3

Answer:

-2.5 is correct answer

How much does it cost to buy 10 computer mice (not the living thing :) ) that are $24.75 each.

10(24.75)=247.5

It will cost $247.5

It would be $247.50

Step-by-step explanation:

24.75 x 10

Answer:576cm

Step-by-step explanation:

Multiply length width

And height

Answer:

[tex] \boxed{ \bold{ { \boxed{ \sf{576 \: cubic \: centimeters}}}}}[/tex]

Step-by-step explanation:

Given,

Length of the rectangular prism ( l ) = 16 cm

Height of the rectangular prism ( h ) = 4 cm

Width of a rectangular prism ( w ) = 9 cm

Finding the volume of the rectangular prism. having length of 16 cm , width of 9 cm and height of 4 cm

[tex] \boxed{ \sf{volume \: of \: a \: rectangular \: prism = lwh}}[/tex]

[tex] \longrightarrow{ \sf{volume \: = 16 \times 9 \times 4}}[/tex]

[tex] \dashrightarrow{ \sf{576 \: {cm}^{3} }}[/tex]

Hope I helped!

Best regards! :D

Answer:

SU= 14

Step-by-step explanation:

if QU= 24 and RU= 19 then you can subtract 24-19=5. and if QR=RS=ST then you subtract 19-5=14