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Algebra has many rules, but one of the most fundamental rules is the distributive property. The distributive property states that for any real numbers a, b, and c, the following equation holds true:

a(b + c) = ab + ac

This property allows us to "distribute" a common factor across the sum of two or more terms. For example, using the distributive property, we can simplify the expression 2(x + 3) to 2x + 6.

Another important rule in algebra is the order of operations, also known as PEMDAS ( Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This rule tells us the order in which we should perform mathematical operations to get the correct answer.

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The number of students in Erwin Middle School is 1195.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Erwin Middle School has 478 boys.

If 60% of the students are girls, then 40% of the students are boys 40%.

Let the number of students be x.

Now, 40% of x=478

40/100 ×x=478

0.4x=478

x=478/0.4

x=1195

Therefore, the number of students in Erwin Middle School is 1195.

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Therefore , the solution to the given problem of function comes out to be the drone and toy rocket are at the same 20-foot height there.

Variables and their variations, formulas and related structures, locations of forms and forms themselves are all included in the field of mathematics. The term "function" describes the connection between a group of inputs, of which each has a corresponding output. A function is an association between outputs and inputs where equation results in a single, unique output. A realm and a made the request, or scope, are assigned to each function. Functions are typically denoted by the letter f. (x). The entry is an x. On activities, one-to-one functions, many-to-one features, within features, and on functions are the four basic categories of functions that are available.

Here,

R(2)>D(2) is true because, on the graph, R = 45 and D = 20 when time is 2 seconds.

The drone has a 20-foot height.

R=0 at 5 seconds is where that is. D=20 at 5 seconds,

t=4.25 at R(t)=D (t).

The drone and toy rocket are at the same 20-foot height there.

Therefore , the solution to the given problem of function comes out to be the drone and toy rocket are at the same 20-foot height there.

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Answer:

6/98

Step-by-step explanation:

The four primary methods of factoring of polynomial are the Grouping method, the Difference in Two Squares, the Sum or Difference in Cubes, and the Greatest Common Factor (GCF).

A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.

The four primary methods of factoring are the Grouping method, the Difference in Two Squares, the Sum or Difference in Cubes, and the Greatest Common Factor (GCF).

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The formula for a lens is the lens maker's equation, which states that the focal length of a lens is equal to the inverse of the sum of the inverse of the object distance and the inverse of the image distance.

The formula is an equation or expression that describes the relationship between different variables. It is typically represented by an algebraic expression with symbols representing different constants, variables, and operations. It is used to calculate the unknown values of the variables from the known values of other variables.

This equation can be written as 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. This equation shows that the focal length of a lens is directly proportional to the sum of the inverse of object and image distances.

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Therefore, the volume of the cone to the nearest whole number is 94 m^3.

The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

The units that may be produced in terms of basic units to measure quantities other than those measured in those units are known as derived units. Examples of derived units are the meter per second (distance), mole per cubic meter (material concentration), and specific volume (cubic meter per kilogram).

We are given, the radius of the cone as 3m and a height is 10m

Using formula,

V = (1/3) * pi * r^2 * h

V = (1/3) * 3.14 * 9 * 10

V = 94 m^3

So, The correct answer is B. 94 m^3

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If in 1990 the cost of tuition at a state university was 4300 during the next eight years that tuition rose 4% each year.  the equation is A = $4300 (1+0.04)^t and the tuition is $5,231.61.

Using this formula to find the tuition

A = P (1+ r)^t

The equation is:

A = $4300 (1+0.04)^t

Where:

A =Amount = ?

P = Principal = $4300

r = rate = 4%

t = time =?

Now let find the tuition in 1995

A = P (1+ r)^t

A =Amount = ?

P = Principal = $4300

r = rate = 4%

t = time =  (1995 - 1990) = 5 years

Let plug in the formula

A = $4300 (1+0.04)^5

A = $4300 (1.04)^5

A = $5,231.61

Therefore the equation is A = $4300 (1+0.04)^t and the tuition is $5,231.61.

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The complete question is:

In 1990 the cost of tuition at a state university was 4300 during the next eight years that tuition rose 4% each year.  Write an equation to model the amount of  tuition  (in dollars) for t years after 1990. Then find the tuition in 1995

The coordinates of  the intersection of the diagonals of STUV with vertices S(-2, 3), T(1, 5), U(6, 3), and V(3, 1) is solved to be (2, 3)

In a coordinate graph, the position of a point is represented by an ordered pair (x, y), where x is the number on the x-axis and y is the number on the y-axis.

Coordinates refer to the two numbers in the ordered pair (x, y) of x and y.

The quadrialteral was plotted on a graph and the point o fht intersection was read from the coordinate graph. The value of the point of the intersection from the graph is (2, 3)

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The formula for the midpoint Riemann sum is: (b-a)/(2n) × [f(x1)+f(x2)+f(x3)+...+f(xn)] where xi = a+i(b-a)/n ( i = 1 to n)

The midpoint Riemann sum formula is a method of approximating the definite integral of a function over a given interval [a,b].

It involves dividing the interval into n subintervals of equal width, and for each subinterval, taking the midpoint of the subinterval as the x-coordinate and the function value at that point as the y-coordinate.

The sum of the areas of rectangles formed by these coordinates and the subinterval widths is then used as an approximation for the definite integral.

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Answer:

19.5 miles

Step-by-step explanation:

6.5 x 3 = 19.5

A real image is an image that is formed by the actual convergence of light rays, it can be projected onto a surface, located in the front or behind the lens, and can be inverted or upright depending on the properties of the lens or mirror used to form the image.

A real image is an image that is formed by the actual convergence of light rays. Real images can be projected onto a surface, such as a screen or a wall, and can be captured by a camera or viewed directly by an observer.

Real images can be produced by both converging and diverging lenses and can be located either in front of or behind the lens or mirror that forms them.

In the case of a converging lens, real images are located on the same side of the lens as the object, whereas in the case of a diverging lens, real images are located on the opposite side of the lens as the object.

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Answer: Marsha earned $375 in interest. ✅

Step-by-step explanation:

Multiply the amount Marsha deposited, which was $7,500, by the interest rate, which was 5%. 5% of $7,500 is $375, so that's the amount of interest Marsha earned.

The distance between the two points rounding to the nearest tenth is 6.7 units.

In the field of mathematics known as graph theory, the number of edges in the shortest path (also known as a graph geodesic) connecting two vertices in a graph is the distance between them. This distance is also referred to as the geodesic or shortest-path distance.

It should be noted that there may be more than one shortest path between any two vertices. Traditionally, the distance is thought of as infinite if there is no path connecting the two vertices, or if they are a part of different connected components.

If at least one such arc-based directed path exists, the distance d(u,v) between two vertices u and v in a directed graph is defined as the length of that path.

The distance between two point's formula is

[tex]$ \sqrt{(\text x_2 - \text x_1)+(\text y_2 -\text y_1)}[/tex]

Putting the values in formula we get

= [tex]\sqrt{( -3 - (-9))^2+(4 -1)^2}[/tex]

= [tex]3\sqrt{5}[/tex]

= 6.7

Thus, the distance between the two points rounding to the nearest tenth is 6.7 units.

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To find out how much money you would save on car 1, you would multiply the sticker price by the discount percentage (expressed as a decimal). In this case, that would be $20,000.00 x 0.23 = $4,600.00. So you would save $4,600.00 on car 1.

To find out how much money you would save on car 2, you would multiply the sticker price by the discount percentage (expressed as a decimal). In this case, that would be $17,000.00 x 0.10 = $1,700.00. So you would save $1,700.00 on car 2.

Based on the calculations, Car 1 would be a better deal. Even though Car 2 is cheaper by $3,000.00 before discount, Car 1 saves more on discount of $4,600.00 compared to Car 2's $1,700.00. So Car 1 would be more affordable overall.

On solving the provided question, we can say that in right angled triangle the value of x = 5√3 and value of y = 10.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

Using the table of trig values, we find that

sin30°=1/2

So, this gives us:

1/2 = sin 30° = 5/y

1/2 = 5/y

(1xy)/2 = 5

y= 2×5 =10

Next, using the Pythagorean Theorem, we find that

5²+x²=10²

x²=100−25=75

Solve for x:

x=√75=√3×25=5√3

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Step-by-step explanation:

-4x+2=-14

-2 -2

-4x=-16

÷-4 ÷-4

X=4

-4(4)+2=-14

-16+2=14

-14=-14

Answer:

Step-by-step explanation: -4x + 2 = -14                                                                        

Answer:

Step-by-step explanation:

All except "E", "C", and "B".

A and D are true.

The line is negative and the slope is -5, not 5.

Answer: The formula for the future value of an account earning interest compounded continuously is given by:

FV = P * e^(rt)

Where:

FV = future value of the account

P = principal or initial deposit

r = annual interest rate as a decimal

t = number of years the account earns interest

In this case:

FV = $550 * e^(0.066*10)

FV = $550 * e^0.66

The future value of the account is $984.96

So, the answer is $984.96

It's worth noting that the result is the future value of the investment, it doesn't take into account any withdrawal or addition of funds. If any of these occurs the final value will be different.

Step-by-step explanation:

Answer:

$984.96

You can use the formula for continuously compounded interest: A = P * e^(rt) where A is the final balance, P is the principal, r is the interest rate (as a decimal), and t is the time in years.

Plugging in the given values:

A = 550 * e^(0.066 * 10)

A = 550 * e^(0.66)

A = 550 * 2.92469798

A = $984.96

Answer:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope (rate of change) and b is the y-intercept (where the line crosses the y-axis).

In this case, the number of times the insect beats its wings is the dependent variable (y) and the flying time in seconds is the independent variable (x). We know that the insect beats its wings 240 times per second, so the slope of the equation is 240.

To find the y-intercept, we need to know the number of times the insect beats its wings when it has flown for 0 seconds. Since the insect starts beating its wings immediately, the y-intercept is 0.

So the equation in slope-intercept form is:

y = 240x + 0

This equation represents the relationship between flying time in seconds (x) and the number of times the insect beats its wings (y).

Also, it is important to note that, the slope (240) is the rate of change of the number of times the insect beats its wings per second.

Step-by-step explanation:

To change the weight of kilograms into pounds, multiply the weight in kilograms by 2.2

According to the conversion systems, 1 kg = 2.2046 lbs

To facilitate conversion on a pen-paper basis we cannot use 2.2046 whole.

Hence we generally consider 1 k = 2.2 pounds.

The symbol for pounds is lbs and for kilograms is kg.

Now, 1 kg is 2.2 lbs

2 kg = 1 kg + 1 kg

= 2.2 lbs + 2.2 lbs

= 4.4lbs = 2 X 2.2

3 kg = 1 kg + 2 kg

= 2.2 lbs + 4.4 lbs

= 6.6 lbs. = 3 X 2.2

Hence we can see that for all these numbers we can multiply 2.2 to the given weight in kg to get the pounds form.

Hence we need to multiply 2.2

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If a function yields the result y, then its inverse function, denoted by the symbol , will return the value x.

A function's output is returned when its inverse function does the same action variable. The inverse function of a function, or f-1(y), will return the value x if the function f(x) produces the output y.A function that reverses the action of a function, or f, is known as its inverse in mathematics.

Here,

A function that reverses the effects of another function is said to have an inverse. If y = f(x), then x must always equal g, then a function g is the inverse of a function f. (y). Application of f followed by application of g is equivalent to doing nothing, in other words. As g(f(x)) = x, this can be expressed in terms of the relationship between f and g.

Because they allow for the reversal of mathematical operations, inverse procedures are crucial for solving equations (e.g. logarithms, the inverses of exponential functions, are used to solve exponential equations). How to invert a mathematical technique is one of the most crucial questions whenever one is introduced.

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The complete question : " In Exercises 15-18, match the graph of the function with the graph of its inverse function. [The graphs of the inverse functions are labeled (a), (b), (c), and (d).]"

In particular, you can do this and it is beneficial to do so, a table within a form, or vice versa.

The length of the sequence is the number of ordered elements (potentially infinite). You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences. A set of numbers connected by a rule is referred to as a number sequence. You can determine the following numbers in the sequence if you figure out the rule. In this instance, there is a difference of 6 between each number.

given

In particular, you can do this and it is frequently beneficial to do so, a table within a form, or vice versa.

Nevertheless, you must be aware of your actions. Any way allows for nesting of tables and forms.

However, if you insert forms into tables, you must fully include each form in a single table cell (one TD element in practice).

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Answer:

C=2πr

Step-by-step explanation:

C=2[tex]\pi r[/tex]

(this might be a little hard to read so I’m gonna explain by saying c = 2 pi r)

Answer:

Step-by-step explanation:

I would help you but i can't read it.

Answer:

any number raised by power 0 is always one

ie 10000000000^0 = 1

99999999^0 =1

23^0 = 1

Answer:

Yes. If x=0, then 2ˣ = 0

Step-by-step explanation:

I presume you mean 2ˣ

Any number raised to the power zero is 1 so if x = 0, 2⁰ = 1. There are debates about what 0⁰ evaluates to but I don' think you need to worry about that for this question

I hope I interpreted your question correctly.

The correct option is C. 2n which is the expression for the number of strawberries, if bananas and strawberries are bought in the ratio of 1 : 2.

A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. It can be used to express one quantity as a fraction of the other ones.

The ratio 1 : 2 expressed as fraction is 1/2

when n bananas is bought, then we derive the expression for the number of strawberries as follows:

1/2 = n/number of strawberries

number of strawberries = (2×n)/1 (cross multiplication)

number of strawberries = 2n

In conclusion, with the ratio of 1 : 2 , the number of strawberries bought when n bananas is bought is equal to the expression 2n.

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Answer: 5.

Step-by-step explanation: The .57 doesn't matter so we can remove that.

Multiply 32 by 0.15

32 x 0.15 = 4.8

After you get your result, round it to the nearest tenths.

4.8 = 5

hope this helps