Harry Potter has a potion that can change voracious vampires into harmless hobbits. But the chemical evaporates over time and when the concentration in the potion is too weak, it turns the vampires into destructive Demogorgons. Oh no! The half-life of the potion means the amount of time it takes for the potion to lose half of its existing power, measured in magical units. This potion has a half-life of 2 months. Which statement about the potion's strength is correct? * a. Of the original 160 magical units, 5 magical units are left after 10 months of mixing the potion. b. Of the original 160 magical units, 16 magical units are left after 10 months of mixing the potion. c. Of the original 160 magical units, less than 1 magical unit is left after 10 months of mixing the potion. d. Of the original 160 magical units, 20 magical units are left after 10 months of mixing the potion e. Of the original 160 magical units, 80 magical units are left after 10 months of mixing the potion.

Since 0 = 0 for any value of x, the system of equations has infinite solutions.

What is  infinite solution?

Both sides of an infinite solution are equal. As an illustration, 6x + 2y - 8 = 12x + 4y - 16 Using a formula or method for infinite solutions, you can simplify the equation and make both sides to equal one another, making it an infinite solution. The concept of infinite connotes boundlessness or infinity. Typically, it is denoted by the symbol "".

What is an infinite number?

There are an unlimited number of numbers in a series. a collection of infinitely many natural integers, as an illustration. The initial value 0, and the initial value infinite, are represented by the logarithms and +, respectively.

                     The original values 0 and infinity are similarly treated when we consider both of the conceivable values and + as a single infinity.

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Answer: 3k^2

Step-by-step explanation:

The 3 different types of solutions a 2 variable system can have are a unique solution, no solution and many solutions.

There are 3 types of systems of linear equations which are as follows:

Dependent: The system has infinitely many solutions. The graphs of these equations represent the same lines.

Example: [tex]\left \{ {{2x + 2y = 4} \atop {4x + 4y = 8}} \right.[/tex]

The system has infinitely many solutions.

Independent: The system has exactly one solution. The graphs of these equations intersect at a single point.

Example: [tex]\left \{ {{x + y = 5} \atop {x - y = -1}} \right.[/tex]

The only solution to the system is (2, 3)

Inconsistent: The system has no solution. The graphs of these equations are parallel lines.

Example: [tex]\left \{ {{x + 2y = 9} \atop {2x + 4y = 7}} \right.[/tex]

The system has no solution.

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To find the center of enlargement, draw line segments between corresponding vertices of pre-image and image triangles, the point where they intersect is the center of enlargement, check that all the line segments intersect at the same point, or use the coordinates of the triangle and the scale factor.

You can follow these steps:

Another way to find the center of enlargement is to use the coordinates of the triangle and the scale factor. The center of enlargement is the point that remains the same distance from all points on the image and the pre-image. The center of enlargement is the point that the coordinates of the image triangle obtained from the coordinates of the pre-image triangle by multiplying each coordinate by the same scale factor greater than 1.

It's important to note that, the center of enlargement is the same as the center of dilation.

In both ways, it's important to have the pre-image triangle and the image triangle to find the center of enlargement.

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Answer:

5x + y = 34

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 )

given

x - 5y = 8 ( subtract x from both sides )

- 5y = - x + 8 ( divide through by - 5 )

y = [tex]\frac{1}{5}[/tex] x - [tex]\frac{8}{5}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{1}{5}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{5} }[/tex] = - 5 , then

y = - 5x + c ← is the partial equation

to find c substitute (5, 9 ) into the partial equation

9 = - 25 + c ⇒ c = 9 + 25 = 34

y = - 5x + 34 ← equation of perpendicular line in slope- intercept form

add 5x to both sides

5x + y = 34 ← equation in standard form

The expression's coefficients have values of 3 and -5, and the constant term has a value of 2.

The formula is 0 = 2 + 3x² - 5x.

We obtain = 3x² - 5x + 2 = 0 by arranging the equation in the form of the general equation ax2 + bx + c = 0.

The leading coefficient is a, the intermediate term's coefficient is b, and the constant term is c.

We may locate the equation's roots or the parabola's vertex by knowing the values of a, b, and c.

After comparing the equation to the general equation, the coefficient and constant term values are as follows.

A = 3

B = -5

C = 2

So, now both the polynomial and the coefficients are available.

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The equivalent expression to 3/4 of 2 1/5 is 3/4 × 11/5

Caleb:

Length of rope = 2 1/5 yards

Length used for dog leash = 3/4 of 2 1/5

= 3/4 × 11/5

Manny:

Distance hiked = 6 2/5 miles

Distance he stopped to climb a lookout tower = 1/4 of 6 2/5 miles

Number of miles Manny hiked before he stopped to climb a lookout tower = 1/4 of 6 2/5 miles

= 1/4 × 6 2/5

= 1/4 × 32/5

= 32/20

= 1 12/20

= 1 3/5 miles

Dante and friends:

Length of the poster = 1 1/2 yards

Width of the poster = 3/4 yard

Area of the poster = Length × width

= 1 1/2 yards × 3/4 yard

= 3/2 × 3/4

= 9/8

= 1 1/8 square yards

Therefore, the area of the poster can be calculated by multiplying length by width and written in square units.

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1. The expression to illustrate the fact that Caleb has 2 1/5 yards and then used 3/4 of the rope is B. 3/4 × 11/5.

2. The number of miles that Manny hiked before he stopped is D. 1 3/5 miles.

3. The fraction of the writing area is D. 1 1/8 square yards.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Caleb has 2 1/5 yards and then used 3/4 of the rope. The expression to illustrate this will be:

= 3/4 × 2 1/5

= 3/4 × 11 / 5

The number of miles that Manny hiked before he stopped is;

= 1 /4 × 6 2/5

= 1/4 × 32/5

= 32 / 20

= 8 / 5

= 1 3/5 miles.

The fraction of the writing area is:

= 1 1/2 × 3/4

= 3/2 × 3/4

= 9/8

= 1 1/8 square yards.

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The Factor Theorem states that if a polynomial P(x) has a factor (x-a), then P(a) = 0. In other words, if x-a is a factor of the polynomial, then the value of the polynomial when x=a is equal to zero.

The factor theorem is a fundamental concept in algebra and polynomial functions. This can be useful for determining the roots of a polynomial equation.

Key points:

In summary, The Factor Theorem is a fundamental concept in Algebra and Polynomials, it helps us understand the relationship between the roots and the factors of a polynomial equation and how a root of a polynomial is related to the value of the polynomial evaluated at that point.

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Answer: 5 1/3 - 3 2/3 = 1 2/3. 8 4/7 - 7 5/7 = 6/7. Yes its simplified and 100% correct.

Step-by-step explanation:

When a number has an exponent of 0, it means that the number is being multiplied by itself 0 times. In other words, it is multiplied by 1.

To determine this:

In the case of 3 with an exponent of 0, it would be represented as 3^0. To calculate the value, we would take 3 and multiply it by 0 times.

3 x 1 = 3

So, 3 with an exponent of 0 is equal to 3.

It is important to note that any number with an exponent of 0 will always equal 1, except for 0 which will always be 0. This is because any number multiplied by 1 is itself, and 0 multiplied by any number is always 0.

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A relation could be a function or it could not. Since b. (6, 8) and d. (4, 3), the connection would no longer be a function.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

You can choose the components of combos in any order.

Permutations and combinations can be mixed up.

So, given is the ordered pair:

(x, y) = (1, 2); (2, 3); (4, 5); (6, 7); (12, 13)

All of the x-values in a relation must be distinct for it to be a function (i.e. no repetition)

The x values of choices (b) and (d) already exist in the ordered pair, namely (6,7) and (d), from the list of alternatives given (4,5)

Accordingly, (b) and (d) would prevent the relation from being a function.

Therefore, a relation could be a function or it could not. Since b. (6, 8) and d. (4, 3), the connection would no longer be a function.

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Correct question:

A bakery sells different packages of muffins. The number of muffins, x, and the price in dollars, y, of their packages of muffins are given in the ordered pairs below. The set of ordered pairs is a relation that is also a function.

{(1,2),(2,3),(4,5),(6,7),(12,13)}

The bakery is considering adding a new package of muffins. which ordered pairs would make the relation NOT a function? Choose all that are correct.

a. (10,13)

b. (6,8)

c. (8,12)

d. (4,3)

e. (24,18)

The area of a circle with a diameter of 5 m is 19.63 m², rounded to the nearest tenth, it would be 19.6 m². So the answer is c. 19.6 m².

What is circle ?

A circle is a two-dimensional geometric shape defined as the set of all points that are a fixed distance, called the radius, from a central point, called the center. A circle is the set of all points in a plane that are at a given distance from a given point, the center.

The area of a circle is given by the formula A = [tex]\pi r^{2}[/tex], where r is the radius of the circle. To find the area of a circle with a diameter of 5 m, we first need to find the radius. We can do this by dividing the diameter by 2:

r = 5 m / 2 = 2.5 m

Then we can substitute this value of r into the formula for the area of a circle:

A = [tex]\pi r^{2}[/tex] = π(2.5 m)^2 = 3.14 * 6.25 m^2 = 19.63 m²

So the area of a circle with a diameter of 5 m is 19.63 m², rounded to the nearest tenth, it would be 19.6 m². So the answer is c. 19.6 m².

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Answer:

The Area of a circle with a diameter of 5 m is 19.63 m² rounded to the Nearest tenth, it would be 19.6 m².  the answer is c. 19.6 m².

Step-by-step explanation:

good luck to you

Using simultaneous equations, the cost of each pecan cheesecake and chocolate marble cheesecake is as follows:

Simultaneous equations are a system of equations (two or more equations) solved concurrently or simultaneously.

                                  Pecan    Chocolate   Total Revenue

Adam's sales                8                6                   $182

Daniel's sales               7               12                  $274

Let sales units of Pecan = p and sales units of chocolate = c

Equation 1: 8p + 6c = 182

Equation 2: 7P + 12C = 274

Multiply Equation 1 by 2:

Equation 3: 16p + 12c = 364

Subtract Equation 2 from Equation 3:

16p + 12c = 364

-

7P + 12C = 274

9p = 90

p = 10

= $10

Substitute, p = 10, in Equation 1:

8p + 6c = 182

8(10) + 6c = 182

80 + 6c = 182

6c = 102

c = 17

= $17

Check:

8p + 6c = 182

8(10) + 6(17) = 182

80 + 102 = 182

Thus, based on a system of equations, the pecan cheesecake costs $10 per unit while the chocolate marble cheesecake costs $17 per unit.

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The standard form of the given equation is expressed as; 3x + y = -1

The standard form for linear equations in two variables is expressed as; Ax + By = C

We are given the equation as;

y - 5 = -3(x + 2)

Expanding the bracket gives us;

y - 5 = -3x - 6

Add 3x to both sides to get;

y - 5 + 3x = -6

Add 5 to both sides to get;

3x + y = -1

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On solving the provided question we can say that the value of multiplication is x^34.

A math problem is a problem or question that requires the application of mathematical concepts and skills to solve.It is an extension of repeated addition. The operation is symbolized by the multiplication sign "x" or an asterisk (*), a dot (•) or the letter "m" . .

For example, if we multiply 4 and 5, the product will be 20 (4x5 = 20).

In addition, multiplication can also be represented using the distributive property, which states that for any three numbers a, b and c, a(b+c) = ab + ac.

In Multiplication, order of numbers doesn't matter, meaning a x b = b x a.

It's also commutative, meaning the order of numbers doesn't change the result.

Multiplication is the foundation for many other mathematical concepts, including algebra and geometry. It's an essential operation in many fields such as science, engineering, and finance.

And answer for above question is given by,

If each of the 5 students in a class has 3 apples, the total number of apples among the students is 3 apples/student * 5 students = 15 apples.

To find the product of the number of apples and the number of students, we multiply the number of apples (15) by the number of students (5) which is 15*5 = 75

So the product of the number of apples and the number of students is 75.

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Answer:

independent

Step-by-step explanation:

A system of linear equations with exactly one solution is a _independent   system.

Answer:

6cm*4.5cm = 27cm²

5cm*5cm = 25cm²

The first has a greater area - by 2 square centimeters.

Step-by-step explanation:

Answer:5 1/2

Step-by-step explanation:

4 1/2+4 1/2=9

14 1/2 -9=5 1/2

There is no numbers provided, but this is how you solve it.

We can use the tangent function to solve for the height of the lighthouse.

Let h be the height of the lighthouse from the top of the cliff.

tan(angle of elevation from sea level to the top of the lighthouse) = (h+ height of lighthouse from sea level ) / distance from the base of the cliff

tan( angle of elevation from sea level to the top of the lighthouse) = (h+x) / distance from the base of the cliff

tan(angle of elevation from sea level to the base of the lighthouse) = (h) / distance from the base of the cliff

By dividing the first equation by the second equation

(h+x) / distance from the base of the cliff = tan( angle of elevation from sea level to the top of the lighthouse) / tan( angle of elevation from sea level to the base of the lighthouse)

(h+x) = (h) * (tan( angle of elevation from sea level to the top of the lighthouse) / tan( angle of elevation from sea level to the base of the lighthouse))

h = (x * tan( angle of elevation from sea level to the base of the lighthouse)) / ( tan( angle of elevation from sea level to the top of the lighthouse) - tan( angle of elevation from sea level to the base of the lighthouse))

After plugging in the values into the equation, we get:

h = (x * tan( )) / ( tan( ) - tan( ))

Round to the nearest tenth

h = (x * tan( )) /

Based on the information, we can conclude that we have a 5% chance (probability) of getting 1 in this test of throwing the dice 50 times.

Taking into account the results of the graph, we can establish the probability of getting the number 1 in the 50 throws made. To do this, we must perform the following procedure:

In accordance with the above and based on the results of the test we can establish that we have a 5% probability of getting 1. This could be expressed as a 0.05 probability, in which 0 is not at all likely and 1 is very likely.

Note: This question is incomplete because there is some information missing. Here is the complete information:

Image attached

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Therefore , the solution to the given problem of expression comes out to be 5 is the exponent of the variable z.

Math allows for the conceivable operations of multiplication, division, addition, and subtraction. The structure of the expression is as follows: Calculator, expression, and a number or variable A mathematical expression is made up of variables, numbers, and operations (such as addition, subtraction, multiplication, or division, etc.). You can contrast two statements or expressions.

Here,

The following expression (27x2)z/3x2)(z6) can be simplified as follows:

If your base is the same, you can subtract the exponents using the properties of powers.

Then:

=(27x^2)z/(-3x^2)(z^6)

=-9z/z^6 You can see that x2-2=x0=1

=-9/z^5 (Thereafter, z6-1=z5)

Consequently, the response is: 5 is the exponent of the variable z.

Therefore , the solution to the given problem of expression comes out to be 5 is the exponent of the variable z.

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The area of a rectangle is found by multiplying the length and width.The area of a triangle is found by taking half the base multiplied by the height.  

The formula for this is A = lw, where A is the area, l is the length, and w is the width. For example, if the length of the rectangle is 10 cm and the width is 5 cm, then the area of the rectangle is A = 10 * 5 = 50 cm2.

The area of a triangle is found by taking half the base multiplied by the height. The formula for this is A = 1/2bh, where A is the area, b is the base, and h is the height. For example, if the base of the triangle is 10 cm and the height is 5 cm, then the area of the triangle is A = 1/2 * 10 * 5 = 25 cm2.

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The 4:5 ratio in terms of pixels is nothing but the measure of 1080×1350 pixels in an image of the video.

A colon separates two numbers that represent the width-to-height proportion of an image or video. This proportion or ratio is referred to as the aspect ratio. In terms of height and width, it shows how wide the size is. It makes sure the videos or images are presented without stretching or resolution loss.

The resolution in pixels for the aspect ratio 4x5 or 4:5 is 864 x 1080 or 1080 x 1350 pixels. This establishes how many pixels are present in an image's or video's width and height. The most popular pixel ratio is this one.

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In triangle ABC and triangle PQR , DC IS PROPORTION TO SR.

A triangle in geometry is a three-sided polygon with three edges and three vertices.

The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.

This characteristic is known as the triangle's angle sum property.

If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.

In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.

A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.

The vertex is the intersection of two straight lines. The triangle therefore has three vertices.

Hence, In triangle ABC and triangle PQR , DC IS PROPORTION TO SR.

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Answer: If the ratio of soccer balls to basketballs is 3:2, that means for every 3 soccer balls, there are 2 basketballs.

Let's say there are x soccer balls at the gym.

The ratio can be represented as 3x:2x

So the number of basketballs at the gym would be 2x.

So if you know the number of soccer balls at the gym, you can find the number of basketballs by multiplying the number of soccer balls by 2/3.

For example, if the gym has 18 soccer balls, the number of basketballs would be 2/3 * 18 = 12 basketballs

Step-by-step explanation:

There are three vectors in three-dimensional space, namely the X-axis, the Y-axis, and the Z-axis.

Vector is a term used to describe a mathematical quantity that has both magnitude and direction, such as velocity, force, and acceleration. A vector can be represented by an arrow, with its length representing the magnitude and its direction indicating the direction. Vectors can be added together or scaled to create new vectors. Vector operations are essential in physics, engineering, and other fields of mathematics.

Each of these vectors has a magnitude and direction and can be used to represent any point in 3D space. All three axes intersect at the origin, which is the point (0,0,0). Vector algebra can be used to describe and calculate the relationships between these vectors in 3D space.

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The set B represent the side length in inches of a right triangle.

Now, According to the question:

Let's know:

What is Pythagoras Theorem?

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, [tex]a^2 + b^2 = c^2.[/tex]

Where  a and  b are the two legs of the triangle and c is the length of the hypotenuse [THE LONGEST SIDE].

We can square each leg on the triangle and take the sum, if that is equal to the square of the longest side, we have a right triangle. Let's check for all of these.

A) [tex]8^2+12^2=15^2[/tex]

64 + 144 = 225

208 ≠ 225

This is not a right triangle.

B) [tex]10^2+24^2=26^2[/tex]

100 + 576 = 676

676 = 676

This is a right triangle.

C) [tex]12^2 + 20^2=25^2[/tex]

144 + 400 = 625

544 ≠ 625

This is not a right triangle.

D) [tex]15^2+18^2=20^2[/tex]

225 + 324 = 400

549 ≠400

This is not a right triangle.

Hence, The set B represent the side length in inches of a right triangle.

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The ordered pair that is a solution to the inequality:

y > (1/4)*x + 5

is (4, 7)

Here we have the inequality:

y > (1/4)*x + 5

To check if an ordered pair is a solution, we just need to replace the values of the ordered pair on the inequality and see if it is true.

For example, for (12, 8)

We will get:

8 > (1/4)*12 + 5

8 > 3 + 5

8 > 8

This is false, so (12, 8) is not a solution.

The pair that is a solution is:

(4, 7)

7 > (1/4)*4 + 5

7 > 1  + 5

7 > 6

This is true.

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