Adalyn is stocking up on cans of soup for the winter. They are on sale for $2.25 each and she has a $3 coupon. If she can spend no more than $30 on soup, how many cans can she buy?

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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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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On solving the question of the polynomial The quotient = 3x+8 and remainder are  and 2 respectively.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.

Polynomial long division is an extended variant of the well-known mathematical operation known as long division. It is an algorithm for dividing a polynomial by another polynomial of the same or lower degree. Due to the fact that it breaks down a more difficult division issue into simpler ones, it may be completed quickly by hand.

Dividing 3x^3 - 2X^2 + 2x - 1 by x-1

= 3x+8

The quotient = 3x+8 and remainder are  and 2 respectively.

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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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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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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:

1 cap costs 17 dollars

1 wallet is 11

Step-by-step explanation:

45 - 28 = 17

The difference between one wallet and a cap and two caps and a wallet is 17, therefore each cap is 17 dollars

28 - 17 = 11

I hope this helps have a good day (:

So, here on solving the provided question, we can say that the New balance is as [tex]397.51[/tex]

A balance is the sum owing to an account in banking and accounting. The difference between the total debits and total credits posted to an account during an accounting period is referred to as a "balance" in accounting. The account will display a debit balance if the total of all debits exceeds the total of all credits.

Using the above data, first calculate the outstanding balance by using the formula below:

Previous balance-payments  is as  Unpaid balance

Unpaid balance is as [tex]95.85-45[/tex]

Unpaid balance is as [tex]50.85[/tex]

Finance charge is as [tex]50.85*1.5%[/tex]

Finance charge is as [tex]0.76[/tex]

New balance is as [tex]50.85+0.76+345.90[/tex]

New balance is as [tex]397.51[/tex]

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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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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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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

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( )) /

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:

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 time she has left to match the record is 16.11 seconds. The correct answer would be an option (B).

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

To match Lisa's obstacle course record of 68.2 seconds, Julie needs to complete the course in 68.2 seconds.

We know that she has already spent 39.25 seconds on wall climbing and 12.84 seconds on the ropes.

So, the time she has left to match the record is:

68.2 - (39.25 + 12.84) = 68.2 - 52.09 = 16.11 seconds

In the above step, use the arithmetic operations to solve.

Hence, the answer is 16.11 seconds.

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The unit rate of the diamond block is 9

The equivalent ratio of the unit rate of the diamond block is 9/1

A unit rate is the cost for only one of anything.

This is expressed as a ratio with a denominator of 1.

For instance, if you covered 60 meters in 10 seconds, you did so at an average speed of 6 meters per second.

Although both of the ratios 60 meters in 10 seconds and 6 meters in one second are rates, only the latter is a unit rate.

For the problem, 9 gems will craft a diamond block this means that

9 gems = 1 diamond block, hence for every diamond block 9 gems will be used

The unit rate is 9/1

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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

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:

independent

Step-by-step explanation:

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

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 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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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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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

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:

Answer: 3k^2

Step-by-step explanation:

The perpendicular bisector can be found by solving for the equation of the line and substituting the two points.

The perpendicular bisector of a line segment can be found by using the midpoint formula. The midpoint formula is used to find the midpoint of two points (x1,y1) and (x2,y2). The formula is:

Midpoint = (x1 + x2)/2, (y1 + y2)/2

Once the midpoint is found, the slope of the perpendicular line is found by using the negative reciprocal of the original line. The formula for the slope of the perpendicular line is y = -1/m * x + b, where m is the slope of the original line.

The equation of the perpendicular bisector is then found by substituting the slope and the midpoint into the equation of a line, y - y1 = m(x - x1).

Finally, the perpendicular bisector can be found by solving for the equation of the line and substituting the two points. The resulting equation is the equation of the perpendicular bisector.

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