If the decay of 742 mg of an isotope is described by the function A(t)= 742e-0.03t, where t is time in years. Find the amount left after 84 years. Round your answer to the nearest mg. 

Answer:

Step-by-step explanation:

Given triangle ABC and a translated triangle A'B'C'.

Coordinates of triangle ABC are

A(-1,-1)

B(-3,-3) and

C(2,-2).

Coordinates of triangle A'B'C' are

A'(3,3)

B'(1,1)

C'(6,2).

Let us check the translation is being applied there.

A(-1,-1)  ---> A'(3,3)

We can see that A(-1,-1)  ----> A'(-1+4, -1+4) to get (3,3).

Therefore, (x,y) ---> (x+4,y+4) rule is being applied there to get the translated triangle A'B'C'.

So, the correct option is first option:

The change in internal energy (δe) of the system, calculated using the first law of thermodynamics, and considering that the heat and work quantities are converted to the same unit, is 1629 J.

The query you've presented seems to be about the first law of thermodynamics, which states that the change in internal energy (ΔE or in your notation, δe) of a system is equal to the heat (q) added to the system minus the work (w) done by the system. Both heat and work quantities need to be in the same units for this calculation, whereas your values are given in different units: kJ for heat and J for work. To facilitate this calculation, let's first convert the heat quantity from kJ to J (1 kJ equals 1000 J).

So, q = 0.769 kJ = 0.769 * 1000 J = 769 J.

Given, w = -860 J.

Now, according to the first law of thermodynamics, δe = q - w.

Substituting the given values, we get δe = 769 J - (-860 J) = 769 J + 860 J = 1629 J.

Therefore, the change in internal energy, δe, is 1629 J.

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The distance walked together, is the sum of their distances.

Molly walked 1.37 miles farther  than her brother and sister

The given parameters are:

[tex]\mathbf{Molly = 3.45\ miles}[/tex]

[tex]\mathbf{Sister = 1.23\ miles}[/tex]

[tex]\mathbf{Brother = 0.85\ miles}[/tex]

The combined distance walked by her brother and her sister is:

[tex]\mathbf{Both = Sister + Brother}[/tex]

Substitute known values

[tex]\mathbf{Both =1.23\ miles + 0.85\ miles}[/tex]

Evaluate like terms

[tex]\mathbf{Both =2.08\ miles}[/tex]

The distance Molly walked farther is calculated as follows:

[tex]\mathbf{Farther = Molly - Both}[/tex]

Substitute known values

[tex]\mathbf{Farther = 3.45\ miles - 2.08\ miles}[/tex]

Evaluate like terms

[tex]\mathbf{Farther = 1.37\ miles}[/tex]

Hence, Molly walked 1.37 miles farther  than her brother and sister combined

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The correct scientific notation for the number 0.00050210 is 5.0210 x 10^(-4).

The correct scientific notation for the number 0.00050210 is 5.0210 x 10-4. In scientific notation, the decimal point is moved to the right, and the number is multiplied by a power of 10. The exponent indicates how many places the decimal point was moved.

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Answer:

3x+3+2x+4>0

5x>-7

x>-7/5

B

Step-by-step explanation:

Answer:

12.08 units.    

Step-by-step explanation:

We have been given that line segments JK and JL in the xy-coordinate plane both have a common endpoint J (-4,11) and midpoints at [tex]M_1 (2,16)[/tex] and [tex]M_2 (-3,5)[/tex].

To find the distance between [tex]M_1[/tex] and [tex]M_2[/tex] we will use distance formula.

[tex]\text{Distance}=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]

[tex]x_2[/tex] and [tex]x_1[/tex] are x-coordinates of two points.

[tex]y_2[/tex] and [tex]y_1[/tex] are corresponding y-coordinates of two points.    

Let [tex]M_2[/tex] our first point, then  [tex]x_1=-3[/tex] and  [tex]y_1=5[/tex].

Let [tex]M_1[/tex] will be our second point, then [tex]x_2=2[/tex] and [tex]y_2=16[/tex]  

Upon substituting coordinates of point [tex]M_1[/tex] and [tex]M_2[/tex] in distance formula we will get,    

[tex]\text{Distance}=\sqrt{(2--3)^{2}+(16-5)^{2}}[/tex]

[tex]\text{Distance}=\sqrt{(2+3)^{2}+(11)^{2}}[/tex]

[tex]\text{Distance}=\sqrt{(5)^{2}+(11)^{2}}[/tex]  

[tex]\text{Distance}=\sqrt{25+121}[/tex]

[tex]\text{Distance}=\sqrt{146}[/tex]

[tex]\text{Distance}=12.0830459735945721\approx 12.08[/tex]  

Therefore, distance between [tex]M_1[/tex] and [tex]M_2[/tex] is 12.08 units.

Answer:

l = (S - πr²) / π

Step-by-step explanation:

The problem gives us the formula for the surface area of a cone S, we will solve the formula for l.

The formula is

S = πl + πr²

If we take the πr² to the other side, we get:

S - πr² = πl

Now we divide by π, and we get:

(S - πr²) / π = l

Therefore solving for l, we get that

l = (S - πr²) / π.

Answer:  [tex]10\ m^2\ n^7[/tex]

Step-by-step explanation:

The given monomials : [tex]-50m^4n^7\text{ and }40 m^2 n^{10}[/tex]

The prime factorization of coefficients :-

[tex]50=5\times5\times2\\\\40=5\times2\times2[/tex]

GCF(50, 40)=[tex]2\times5=10[/tex]

The greatest common degree of m is 2

The greatest common degree of n is 7

So , the GCF of the given monomilas will be :-

[tex]10\ m^2\ n^7[/tex]

Answer:

y = 3+6x

Step-by-step explanation:

Let us substitute x = 0, then we get

y = 3

This is not the case as the graph clearly shows that when x = 3, then y = 2

y = 2+6x

when x = 0 then y = 2 which valid from the graph

Now put x values from the table into the equation

y = 2+6×-1

⇒y = -4

x = 0 already solved

x = 2

y = 2+6×2

⇒y = 14

All the values fit in the equation. So, the bottom two options are valid.

Hence, the first equation is not valid.

No, it does not.

x and x + 6 are both prime and cannot be factored.

There are no common factors to divide out.

x over x + 6 is already simplified.

If you substitute in a value for x, the fraction will not be equal to 1/6.

The expression x/(x+6) does not simplify to 1/6 because there are no common factors in the numerator and denominator that can be canceled out.

The expression x/(x+6) does not simplify to 1/6. To understand this, we need to recognize that simplification involves reducing a fraction to its simplest form by factoring or canceling common factors in the numerator and the denominator.

If x were a factor in both the numerator and the denominator, then we could simplify by canceling out the x's.

However, in the expression x/(x+6), the term x+6 in the denominator cannot be simplified with x in the numerator because they are not factors of each other. They are connected by the addition of 6, which means that there are no common factors to cancel out.

The only way x/(x+6) would simplify to 1/6 is if 'x' were to be somehow removed from the denominator, leaving only the constant 6. But since this is not the case, the fraction cannot be simplified to 1/6. Therefore, the original expression is already at its simplest form unless a specific value is given for x, which may then allow further simplification.

The linear system is 6s+10a = 2380.

s represents student tickets and a represents adult tickets, and the total amount collected from the tickets is $2380.

Linear means something associated with a line. All the linear equations are used to construct a line. A non-linear equation is such that does no longer form a direct line. It looks as if a curve in a graph and has a variable slope price.

If the connection between y and x is linear (instantly line) and crossing through starting place then the system is linear. If you locate any time t at which the system is not linear then the system is non-linear.

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Final answer:

To represent the ticket sales information as a linear system, we use two equations: a + s = 330 for the total number of tickets, and 10a + 6s = 2380 for the total revenue from ticket sales.

Explanation:

The question involves writing a linear system of equations based on the information provided about ticket sales for a school event. Given that 330 tickets were sold in total, comprising adult tickets (a) and student tickets (s), and that the total revenue from these tickets was $2380, with student tickets priced at $6 each and adult tickets at $10 each, we can represent this scenario with two equations.

The first equation represents the total number of tickets: a + s = 330.

The second equation represents the total revenue: 10a + 6s = 2380.

This linear system can be solved to find the values of a and s, which would give us the number of adult and student tickets sold, respectively.

The value of b is 0.5 m if your aim is to have a rectangle with the maximum area.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.

It is given that:

A long piece of wood of length 2.0 m is broken into 4 pieces with two pieces of length a and the other two pieces of length b.

Total wooden length:

2a + 2b = 2

a + b = 1

Area = ab  

A = a(1 - a)

dA/da = 0

1 - 2a = 0

a = 0.5 m

b = 0.5 m

Thus, the value of b is 0.5 m if your aim is to have a rectangle with the maximum area.

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Darryl had $43 at the beginning of the day.

Let's denote the initial amount of money Darryl had as [tex]\( M \)[/tex].

He spent $16 on a book, which we can denote as [tex]\( S_{book} = \$16 \)[/tex].

He spent $20 on a compact disc, which we can denote as [tex]\( S_{CD} = \$20 \)[/tex].

He spent $2 on a magazine, which we can denote as [tex]\( S_{magazine} = \$2 \)[/tex].

He has $5 left at the end of the day, which we can denote as [tex]\( L = \$5 \)[/tex].

The total amount spent, [tex]\( S_{total} \)[/tex], is the sum of the amounts spent on the book, the compact disc, and the magazine:

[tex]\[ S_{total} = S_{book} + S_{CD} + S_{magazine} \][/tex]

[tex]\[ S_{total} = \$16 + \$20 + \$2 \][/tex]

[tex]\[ S_{total} = \$38 \][/tex]

The initial amount of money Darryl had, [tex]\( M \)[/tex], is the sum of the total amount spent and the amount left:

[tex]\[ M = S_{total} + L \][/tex]

[tex]\[ M = \$38 + \$5 \][/tex]

[tex]\[ M = \$43 \][/tex]