Complete these sentences by selecting the correct answers from the drop-down menus.

After one half-life,
% of the atoms will change to a stable isotope and
% will remain radioactive.

After three half-lives,
% of the atoms will change to a stable isotope and
% will remain radioactive.

The equations a + 4 = 14 and a = 6 - 4 are not equivalent.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

From the information, a - 4 = 14

Therefore a = 14 + 4

a = 18.

a + 4 = 6

a = 6 - 4.

a = 2

They are not equivalent.

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a - 4 = 14

a + 4 = 6

Are these 2 equivalent.

AB is congruent to CD.AB = CD =[tex]\sqrt{14} units[/tex] (proved)

In coordinate geometry, we use the distance formula to find the distance between two coordinates in a straight line. It represented D.

Let's consider two points on a coordinate plane given as A and B (x₂, y₂).

D = [tex]\sqrt{(x2 -x 1)^2 + (y2 - y1)^2}[/tex]

Given:

The coordinates of the given quadrilateral are,

A(1, 5), B(6, 1), C(−2, 8), D(−6, 3).

According to the question we need to determine AB = CD.

By using the distance formula of coordinate geometry.

[tex]\sqrt{(x2 -x 1)^2 + (y2 - y1)^2}[/tex]

Distance between A and B,

[tex]AB =\sqrt{(6 - 1)^2 + (5-1)^2 } \\AB = \sqrt{5^2 + 4^2} \\AB = \sqrt{25 + 16} \\AB = \sqrt{41} units[/tex]        .......(1)

Distance between C and D,

[tex]CD =\sqrt{(-6 -(-2))^2 + (3-8)^2 } \\CD = \sqrt{(-4)^2 + (-5)^2} \\CD = \sqrt{16 + 25} \\CD = \sqrt{41} units[/tex].......(2)

From equation (1) and (2) we find that

AB = CD =[tex]\sqrt{14} units[/tex]

Hence, AB is congruent to CD.AB = CD =[tex]\sqrt{14} units[/tex] (proved).

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Points of inflection does this curve have is:

Concave Up: [tex]$\left(-\infty,-\sqrt{\frac{5}{3}}\right),\left(\sqrt{\frac{5}{3}}, \infty\right)$[/tex]

Concave Down: [tex]$\left(-\sqrt{\frac{5}{3}}, \sqrt{\frac{5}{3}}\right)$[/tex]

Points of Inflection: [tex]$(-1.2910,2.1111),(1.2910,2.1111)$[/tex]

To find the concavity of a function?

We need to take the second derivative.

y' = 4x^3 - 20x

y'' = 12x^2 - 20

Finding the points of inflection involves setting the second derivative equal to 0. Add 20 over, divide by 12, and take the square root. The positive and negative square roots of 5/3 are the potential points of inflection.

Setting up a number line can help to determine concavity. Let's plug in -2 into the second derivative. From this, we have found that from negative infinity to the negative square root of 5/3, the graph is concave up, as f''(-2) > 0. f''(0) < 0, so from the negative square root of 5/3 to the positive square root of 5/3, the graph is concave down. f''(2) is also > 0, and therefore from the positive square root of 5/3 to infinity, the graph is concave up.

Since the graph shifted direction at both potential points of inflection, they are both actually points of inflection. To find the y-values for each point of inflection, plug the x-value back into the original polynomial equation.

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Matching the formulas and their respective definitions are;

W/t = Power

F/d = Work

(v₂-V₁)/t = Acceleration

m/v = Density

d/t = Speed

ma = Force

A) W/t

This means work done divided by the time taken. This results in an expression called Power.

B) F/d

This means force divided by the distance. This results in an expression called Work.

C)  (v₂-V₁)/t

This means change in velocity divided by time. This results in an expression known as acceleration.

D) m/v

This means mass divided by volume. This results in an expression known as density.

E) d/t

This means distance divided by time and this results in an expression called "speed"

F) ma

This means mass multiplied by the acceleration and this results in an expression called Force.

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Answer:

Breadth = 10 ft

Step-by-step explanation:

Given information,

→ Perimeter (P) = 50 ft

→ Length (L) = 15 ft

→ Breadth (B) = ??

Now we have to,

→ find the required value of Breadth.

Formula we use,

→ P = 2(L + B)

Then the required Breadth will be,

→ P = 2(L + B)

→ 50 = 2(15 + B)

→ 30 + 2B = 50

→ 2B = 50 - 30

→ B = 20/2

→ [ B = 10 ft ]

Hence, required Breadth is 10 ft.

There is 20% decrease in the number of people who went to the pool over these four weeks.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we mean that it is 50% of everything.

Attendance of pool in first week of July = 1120

In second week, 125 fewer people joined.

Thus, attendance in second week is = 1120-125 = 995

In third week, 130 more people joined.

Thus, attendance in third week is = 995+130 = 1125

In fourth week, 229 fewer people joined.

Thus, attendance in fourth week is = 1125-229 = 896

Difference of attendance in first and fourth week = 1120-896 = 224

Percentage decrease = (Decrease number/Initial number)×100%

= (224/1120)×100%

= 0.20×100%

= 20%

Thus, there has been a 20% decrease over the four weeks.

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distributive property

Answer:

a) 125

Step-by-step explanation:

[tex]\frac{8}{50}[/tex] = [tex]\frac{20}{x}[/tex]  Cross multiply and solve for x

8x = 1000  Divide both sides by 8

[tex]\frac{8x}{8}[/tex] = [tex]\frac{1000}{8}[/tex]

x = 125

Answer:

What is the slope of 0,70 and 20,80

Step-by-step explanation:

What is the slope of 0,70 and 20,80

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Answer:

Yes, the company will break even at some point in time

Step-by-step explanation:

I am not sure what methodology your teacher has been using. I am going to provide a simple methodology

Therefore the company will break-even at some point

Other Notes

I hope that helps you

Answer:

I think she is forming a letter but not so sure. I don't understand your question. Sorry

The only true given statement about debtors and creditors is; C. Debtors receive loans as capital from creditors.

Debtors are defined as the party from whom we have to receive the payment in the form of cash or any negotiable instrument.This means an asset for the firm.

Meanwhile, the creditors are defined as the party to which we will pay in the future agreed date in the form of cash or any negotiable instrument. This means liability for a firm.

A) This is not true because creditors don't receive  loans from consumers as capital. This is the role of debtors.

B) This is not correct because it is not true that every debtor is guaranteed a loan.

C) This is true as defined earlier on the role of debtors and creditors.

D) This is not true because different creditors have different lending rates as the case may be.

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Answer: 15/16 hour

Step-by-step explanation:

Answer:

Step-by-step explanation:

d

The required life is any living thing that has the property to be born, grow and end of the life cycle is life.

Any object that has characteristics of life is called living a being.

Here,

Life can be defined as the ability for growth, response to encouragements, metabolism, energy vitality and reproduction are characteristics that set life apart from matter that lacks biological activities, such as signaling and self-sustaining processes.

Thus, the required life is any living thing that has the property to be born, grow and end the life cycle is life.

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Either the slope intercept form or the point-slope form can be used to express the equation of a line-, the line's equation is - 3x - 5.

A line's steepness and direction are measured by the line's slope.

Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two distinct points on a line can be used to calculate the slope of any line.

The ratio of "vertical change" to "horizontal change" between two different points on a line is calculated using the slope of a line formula.

According to our question-

the points are given as

(x1,y1)=0,-5

(x2,y2)=-3,4

m = y2-y2/x2-x2

Hence, the line's equation is - 3x - 5.

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"NOT EVERYONE who attended ratio the fundraiser owned a home in the Hamptons or Palm Beach."

What is statement type questions?

In research, a statement of the problem is used as a claim that outlines the problem addressed by a study. The problem statement answers the question briefly: What is the problem that the research will address? What are the objectives of a problem statement?

Consider the following diagram in the attachment (12) for both statement

H = the number of people who owned a home in the Hamptons but did not own a home in Palm Beach.

P = the number of people who owned a home in Palm Beach but did not own a home in the Hamptons.

N = the number of people who did not own a home in Palm Beach or the Hamptons.

Union = H+P+180 Universal = H+P+180 + N P/H =??

Statement 1: (P+180) / (H + P + 180 + N) = 1/2 Inadequate

Statement 2: (H+180) / (H + P + 180 + N) = 2/3 Inadequate

1 and 2 statements

Solve for H and P to find P/H; however, N cannot be eliminated.

This is insufficient.

We should find the ratio of red boxes, however with the information provided, this is impossible.

"NOT EVERYONE who attended the fundraiser owned a house in the Hamptons or Palm Beach.".

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If you think about this, we can figure out that 66 is 2/3 of 99. To find out what 2/3 of 125 is, we can divide 125 by 3.

So, no. This is not proportional.

If one amount is proportional to another, the two amounts increase and decrease at the same rate so there is always the same relationship between them.

The formula for a proportional equation is y = kx. The letters y and x are the variables in the equation. The letter k represents the constant of proportionality, which remains the same.

What is a proportional relationship example?

Now, we're going to consider an example of proportional relationship in our everyday life: When we put gas in our car, there is a relationship between the number of gallons of fuel that we put in the tank and the amount of money we will have to pay. In other words, the more gas we put in, the more money we'll pay.

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It is true that very small and very large and small numbers can be expressed in terms of scientific notation.

Scientific notation is a method of expressing numbers in terms of a decimal number between 1 and 10, but not 10 itself multiplied by a power of 10.

The general for of scientific notation is

In scientific notation, all numbers are written in the general form as

N × [tex]10^{m}[/tex]

N times ten raised to the power of m, where the exponent m is an integer, and the coefficient N is any real number. The integer m is called the order of magnitude and the real number N is called the significand.

The digit term in the scientific notation indicates the number of significant figures in the number. The exponential term only places the decimal point. As an example,

4660000 = 4.66 x 106

This number only has 3 significant figures. The zeros are not important, they are just placeholders. As another example,

0.00053 = 5.3 x 10-4

This number has 2 significant figures. The zeros are only placeholders.

Scientific Notation Rules:

While writing the numbers in the scientific notation we have to follow certain rules they are as follows:

The scientific notations are written in two parts one is the just the digits, with the decimal point placed after the first digit, followed by multiplication with 10 to a power number of decimal point that puts the decimal point where it should be.

If the given number is greater than 1 and multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive

Example: Scientific notation for 8000 will be 8 × 103.

If the given number is smaller than 1 means in the form of decimal numbers, then the decimal point has to move to the right, and the power of 10 will be negative.

Example: Scientific notation for 0.008 will be 8 × 0.001 or 8 × 10-3.

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The value of n when is divided by 6 and it gives 42 is 252

Division is the opposite of multiplication. If 3 groups of 4 make 12 in multiplication, 12 divided into 3 equal groups give 4 in each group in division and 12 divided by 4 gives 3 in each group. This means that 3 and 4 are factors of 12

When dividing a number by another number that is not it's factor, there will be remainder for example 12 divided by 5 . It will give 2 remainder 2. This is because 5 is not a factor of 12.

Similarly, n divided by 6 to give 42. This means that 42 and 6 are factors of n

Therefore to find n we multiply 42 and 6.

n = 42×6

n = 252

therefore the value of n is 252

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In kite wxyz where  m∠zwy=43° and m∠xyw=12°, m∠wxy = 125°

Therefore the answer is 125.

A kite is a quadrilateral with pair of two adjacent equal sides. In the given kite wxyz, adjacent sides wx = wz and zy = xy

Here, from the figure it is evident that Δwyz is congruent to Δwyx as wx = wz, xy = zy and wy as common side by SSS congruent criteria. Thus

m∠xwy = m∠zwy = 43°

Now considering Δxwy, m∠xwy + m∠xyw + m∠wxy = 180° by angle sum property of triangle. Angle sum property of triangle states that the sum of interior angles of a triangle is 180°. Therefore,

m∠wxy = 180° -  m∠xwy - m∠xyw

= 180° - 43° - 12°

= 125°

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Answer:

24/1

Step-by-step explanation:

[tex] \frac{2400}{ \\ 100} [/tex]

and u get 24/1

Given graph is satisfied by System A.

Inequality refers to formulas or equations that define relationships (such as less than, larger than, etc.).

As for Type 1:

Consider the location (3,1) for y>2x.

1 > 6, which is false Hence Since the area opposite point (3,1) will satisfy the equation and since y > 2x and not y 2x, a dotted line will be drawn on the graph.

Consider (-3, -4) for x + 2y -8.

⇒ -3 + 2(-4) ≤ -8

Since x + 2y -8 and not x + 2y -8 is the correct equation, the area containing the points (-3, -4) will be included, and the line of the graph will be solid.

The presented figure is formed by these two equations.

Therefore, System A is accurate.

The Complete Question is inequality.

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Answer:

5x + 16

Step-by-step explanation:

First you have to distribute the 2 into the parentheses

2 times x is 2x

2 times 6 is 12

so now the equation is

2x + 12 + 3x + 4

add the 2x and 3x and that is 5

so now the equation is...

5x + 12 + 4

add 12 + 4 and that is 16

so now the answer is

5x + 16

4 inches is the rim's radius

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The area of sector FIJ is 233.4cm².

What is the area of the sector?

The quantity of space included within the sector's perimeter is referred to as the sector's area in a circle. A sector always starts at the circle's center. The area of a circle encompassed between its two radii and the arc next to them is known as the sector of a circle.

Here, we have

Given: FI = 13cm and angle = 160°

The area of a sector is given as

= (θ/360)×π×r²

= (160/360)×π×13²

= 0.44×3.14×13²

= 233.4cm²

Hence, the area of sector FIJ is 233.4cm².

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The perimeter of the right triangle shown is given by the following option:

39 units.

The perimeter of a figure is composed by the sum of the lengths of the outer edges of the figure.

The sides of the right triangle in this problem are given as follows:

Then, applying the Pythagorean Theorem, the hypotenuse of the triangle is given as follows:

h² = 5² + 17²

h = square root(5² + 17²)

h = 17.7.

The hypotenuse is the third side length of the triangle, hence it's perimeter is calculated as follows:

5 + 17 + 17 = 39 units.

(I suppose there was a typing mistake on the options).

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Answer:

its D

Step-by-step explanation:

30

The solution of the set of equation 2x-3y=-6 and x+3y+-12 is (-6,-2).

By Substitution Method:

1. Resolve ONE of the x or y equations. If one of the equations has previously been solved for x or y, this step can be avoided.

2. Substitute the outcome for that variable in the other equation.

3. Either all x terms or all y terms will now make up the new equation. Fix the variable's place in the equation.

4. To obtain the alternative answer, plug the solution back into the beginning equation (the one you used to solve for x or y).

When using the Elimination method,

start by aligning the x- and y-coordinates on the same side of the equation.

2. Whichever you decide to remove, find a common multiple for the Xs OR the Ys.

3. To enable the addition of the equations, make one of those multiples negative.

4. One of the variables will be removed when the equations are combined. Give the variable that is still present its final solution.

5. To determine the other number, enter your response from step four into either of the equations.

Graphing a solution:

1. Rewrite the initial y equation in the form y = mx + b a. Step 2 can be immediately followed if the line has previously been solved for y.

2. Draw a line to represent the first equation.

3. Apply the second equation to steps 1 and 2 as before.

4. The intersection of the two lines represents the system's solution. There are infinitely many solutions if the lines match. There are no solutions if the lines are parallel and do not intersect.

Substitution methord,

The equations are

2x -3y = -6

⇒ x  = 3/2y - 3.

Putting this value in the second equation we get,

(3/2)y - 3 + 3y = -12

⇒(9/2)y = -9

⇒y = -2.

Therefore,

x = (3/2)y - 3 = (3/2)(-2) - 3 = -6

x = -6, y = -2.

By Elimination Methord ,

2x- 3y = -6

x + 3y =-12

simply adding both equation we get,

3x = -18

x = -6.

and y = -2

For graphical methord plot both lines in the graph then find the point where they intersect it will be (-6,-2).

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