According to the use and the fundamental knowledge behind these formulas, The top 5 formulas in mathematics are quadratic, Pythagorean , slope-intercept , exponential and Euler's Formula.
What is mathematics?Mathematics is the study of numbers, shapes, and patterns. It is the science of studying the properties and relationships of quantities and shapes using logic, symbols and mathematical operations. It is a way of understanding the world and solving problems using quantitative reasoning.
What do you mean by formula?A mathematical formula is a set of symbols, numbers and mathematical operations that express a relationship or equation. These formulas are used to model, describe and explain phenomena in the natural and physical world, as well as in abstract mathematical theories. Formulas can take many forms, including equations, identities, and inequalities. They allow us to make predictions and calculations, and can be used in various fields of science, engineering and other fields to solve problems.
1. root of [tex]ax^2+bx+c[/tex] is [tex]x= \frac {-b+- \sqrt{b^2-4ac}}{2a}[/tex].
2.[tex]h^2 = p^2 +b^2[/tex]
3. [tex]y =mx+c[/tex]
4.[tex]e^x[/tex]
5.[tex]e^{ix} = cosx+isinx[/tex]
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Shelley drew a scale drawing of a neighborhood park. The volleyball court, which is 8 meters wide in real life, is 4 millimeters wide in the drawing. What is the scale factor of the drawing?
Simplify your answer and write it as a fraction.
I need IXL answer's PLEASE
The scale factor of the drawing of the neighborhood park would be = 2000.
What is a scale factor?The scale factor is defined as the ratio between the scale of the original object and the new object, which represents it but in a different size (larger or smaller).
The width of the neighborhood park. in real life = 8 meters
To convert 8 meters to millimetres is to multiply by 1000
= 8 × 1000 = 8000 mm
The scale factor = 4 × X = 8000
make X the subject of formula;
X = 8000/4
X = 2000.
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The piggy bank in the video was filled with pennies and
quarters worth a total of $62. 0.
What are three possible combinations of pennies and
quarters that are worth $62. 00?
Enter your combinations in the table.
Number of Pennies
Number of Quarters
I
The three combinations of pennies and quarters are:
A. 1,560 Pennies and 124 Quarters
B. 2,600 Pennies and 49 Quarters
C. 3,120 Pennies and 24 Quarters
The total value of the pennies and quarters is $62.00. This can be achieved with either 1,560 pennies and 124 quarters (1,560 x 0.01 + 124 x 0.25 = 62.00), 2,600 pennies and 49 quarters (2,600 x 0.01 + 49 x 0.25 = 62.00) or 3,120 pennies and 24 quarters (3,120 x 0.01 + 24 x 0.25 = 62.00).
To find the combinations of pennies and quarters that are worth $62.00, begin by finding the number of pennies that equal $
62.00. 62.00/0.01 = 6,200 pennies.
Next, subtract the value of the pennies from the total to find the value of the quarters.
62.00 - (6,200 x 0.01) = 24.00.
Divide the value of the quarters by 0.25 to find the number of quarters. 24.00/0.25 = 96 quarters.
To arrive at the three combinations
, 1,560 pennies and 124 quarters
(1,560 + 96 = 1,656, 1,656 x 0.01 + 124 x 0.25 = 62.00),
2,600 pennies and 49 quarters
(2,600 + 49 = 2,649, 2,649 x 0.01 + 49 x 0.25 = 62.00)
and
3,120 pennies and 24 quarters
(3,120 + 24 = 3,144, 3,144 x 0.01 + 24 x 0.25 = 62.00).
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The numerator of a fraction is 2 less than its denominator. If 3 is subtracted from the numerator and from the
denominator, the new fraction obtained is. Find the fraction.
A set of multimedia equipment costs $1900, By setting up an inequality, find the maximum number of sets of
The Fraction for the given word problem is x/y = 9/11
What is Fraction?A fraction, which derives from the Latin word fractus, meaning "broken," is a portion of a whole or, more broadly, any number of equal parts. A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of parts of a particular size when it is used in everyday speech.
Let the fraction be x/y
The numerator of a fraction is 2 minus its denomination.
⇒ x = y - 2 .....(i)
When 3 is subtracted from numerator and from denomination the new fraction obtained is 3/4
⇒ x - 3/y - 3 = 3/4
Can also be written as
⇒ 4(x + 3) = 3(y - 3)
⇒ 4x - 12 = 3y - 9
⇒ 4x - 3y = -9 + 12
⇒ 4x - 3y = 3 .....(ii)
Substitute the value of (i) in (ii)
⇒ 4x - 3y = 3
⇒ 4(y - 2) - 3y = 3
⇒ 4y - 8 - 3y = 3
⇒ y - 8 = 3
⇒ y = 3 + 8
⇒ y = 11
Putting the value of y in (i).
⇒ x = y - 2
⇒ x = 11 - 2
⇒ x = 9
Hence, Fraction = x/y = 9/11
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At the end of a snowstorm, Peyton had 8 inches of snow on her lawn. The temperature then increased and the snow began to melt at a constant rate of 1 inch per hour. Assuming no more snow was falling, how much snow would Peyton have on her lawn 2 hours after the snow began to melt? How much snow would Peyton have on her lawn after t hours of snow melting?
The amount of snow on Peyton's lawn after 2 hours is 4 inches
amount of snow after t hours y = 8 - t
How to model the required equationA linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable = amount of snow remaking
m = slope = 1 inch per hour
x = input variable = number of hours
c = y intercept = 8 inches of snow on Peyton's lawn
The equation as described in the problem is represented using linear function as as follows
y = 8 - x
in 2 hours x = 2
y =8 - 2 = 4 inches
The quantity of snow after t hours
x = t
y = 8 - t
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which operation should be completed first to find the value of the expreesion below 12 + 30 / (6 -3) + 1
A developer wants to develop a 18-acre subdivision. He figures that the streets and common area will take up about 20% of this overall area. If the minimum lot size is to be 10,000 SF, how many lots can the developer have on this property
Developer has 627264 square feet land available.
What means lot size?The minimum permissible quantity of an asset that is accepted for purchasing.
How many lots the developer has as per question?
A developer wants to develop 18-acre property = 784080 square feet area
he notices that street and common area will take up about 20% of total area.
hence, the remaining area for developing works = 80%
the amount of land rest for the developer = 784080 ×80 /100
= 627264 square feet.
there is a rule that minimum lot size is to be 10000 square feet for developing works,
the above amount 627264 square feet lot can the developer have on this property that is higher than the minimum lot value.
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What are the 3 algorithms?
Sequencing, selection, and iteration are the three fundamental building blocks that make up an algorithm.
What is algorithm?An algorithm in mathematics is a process, a description of a series of steps that can be used to solve a mathematical computation, but they are now much more prevalent than that. The long division algorithm is perhaps the most well-known application of algorithms in science (and in daily life, for that matter).
Algorithms are all about figuring out the most effective ways to perform the math, despite the fact that the above explanation might sound a little fussy and detailed. Mathematicians are known for being lazy, so they frequently seek out shortcuts, as the anonymous mathematician puts it. For locating these short cuts, algorithms are used.
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PLEASE HELP I WILL GIVE FIVE STARS AND BRAINLIEST Transformation and plot image.
Answer: You need to drew , this arrow , to each point K,L,M,N,
Drawing must be parallel to , this arrow, AND , exactly the same length, as the arrow .
step 2. when you drew it , then at the end are your new points, K",L",M",N".
Ok?
step 3.
Then you just read the coordinates. of new points .
I would gladly drew it , but I do not knew how to put picture in this , jet .
Step-by-step explanation:
Dariu ha a 40-ounce port drink. He drink 18 ounce. Enter the percentage of ounce Dariu ha left of hi port drink
The percentage of ounce Dariu has left of his port drink is 55%.
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.
It is given that Dariu ha a 40-ounce port drink.
He drank 18-ounce port drink.
First calculate what percentage of port drink Dariu drank.
The equation is -
= (18/40) × 100
= 45%
So, Dariu drank 45% of the port Drink.
Now, subtract the percentage Dariu drank from the 100% (40 Ounce) drink Dariu had -
100 - 45 = 55
Therefore, Dariu has 55% drink left.
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PLEASE HELP!!! WILL GIVES BRAINIEST!! PLEASE SHOW YOUR WORK!!
Answer:
0.0558
Step-by-step explanation:
3% is out of hundred so we multiply
3%×1.86=0.0558
Checking:
0.0558÷1.86=0.03
0.03=3%
Suppose you know the answer to 4/5*(20*1 7/8). Explain how the Commutative and Associative Properties of Multiplication can make the computation easier. Then find the answer
You can rearrange terms in an expression using the commutative and associative qualities to arrange compatible numbers next to one another and in groups.
What distinguishes an associative property from a commutative property?According to the associative property, numbers can be added to or multiplied while still maintaining the same result. According to the commutative property, even if the numbers are added or multiplied, the solution will remain the same.
Explain:
[tex]\frac{4}{5}[/tex] ×(20×17/8)
20×17/8
340÷8
[tex]\frac{4}{5}[/tex]×[tex]\frac{340}{8}[/tex]
= [tex]\frac{64}{2}[/tex]
= 32
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Geometry Questions....need help pls
This given figure carries onto themself at 360, 180, and 60 degrees respectively.
What does carrying a figure onto itself mean?If a rotation between 0° and 360° around the center of a figure in the plane may map the figure onto itself, the figure possesses rotational symmetry. From its starting point, the figure can be rotated and mapped onto itself. The symmetry is of order 4. As a result, the figure displays both rotational and line symmetry.
Given three figures those figures have rotational symmetry from their center point. The fixed point that the rotation revolves around in a figure or object with rotational symmetry is referred to as the center of rotation.
for figure 1
figure 1 does not have rotational symmetry on any given angles thus, its rotational symmetry would be 1 since it carries onto itself at 360°.
for figure 2
figure 2 has rotational symmetry at 180°. thus, its rotational symmetry would be 2 since it carries onto itself at 180° and 360°.
for figure 3
figure 3 has rotational symmetry at 60, 120, 180, and 240. thus, its rotational symmetry would be 6 since it carries onto itself at 60, 120, 180, 240, and 360°.
therefore, the given figures have 1, 2, and 6 rotational symmetry.
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Tyler has a baseball bat that weighs 28 ounces. Find the weight in kilograms and in grams. (Note: 1 kilogram=35 ounces)
Answer:
1/ 0.8 kilograms
2/ 800 grams
Step-by-step explanation:
We know
1/
Baseball bat = 28 ounces
1 kilogram = 35 ounces
To find weight in kg we take
28 / 35 = 0.8 kg
2/
We know
1 kg = 1000 g
0.8 kg = 800 grams
So, the baseball bat weights 0.8kg or 800 grams
What are the first 3 triangular numbers?
The depiction of numbers as an equilateral triangle organized in a series is known as a triangular number sequence. These numerals follow a 1, 3, 6 order.
Explain the term triangular numbers?A number that may be expressed as the sum of the initial n positive integers is referred to as a triangular number.
For instance, the fact that 6 may be expressed as 1+2+3, being sum of the initial three positive integers, indicates that it is a triangular number. If one takes the sum of the initial positive integer to be the first element, then sum of the earliest two positive integers to be the second element, then so on, triangular numbers comprise a sequence. In this scenario, n signifies the position of such a triangular number with in sequence if a number equals the sum of the initial n positive integers. Triangles can be formed from triangular numbers.Thus, the first three triangular numbers 1, 3, 6.
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Suppose that a company wishes to predict sales volume based on the amount of advertising expenditures. The sales manager thinks that sales volume and advertising expenditures are modeled according to the following linear equation. Both sales volume and advertising expenditures are in thousands of dollars.
Estimated Sales Volume=46.41+0.45(Advertising Expenditures) If the company has a target sales volume of $200,000 how much should the sales manager allocate for advertising in the budget? Round your answer to the nearest dollar.
The sales manager should allocate approximately 341311.111 for advertising in the budget.
What is advertising expenditure?Generally, Advertising expenditure refers to the amount of money that a company or organization spends on promoting their products or services through various forms of advertising media, such as television, radio, print, and online.
This can include costs for creating and producing advertisements, as well as fees for placing them on different platforms. Advertising expenditure can also be referred to as "advertising budget" or "advertising spend."
To find the advertising expenditure needed to reach a target sales volume of $200,000, we can use the equation provided: Estimated Sales Volume = 46.41 + 0.45(Advertising Expenditures)
We can set the target sales volume as the left-hand side of the equation and solve for the advertising expenditure:
200,000 = 46.41 + 0.45(Advertising Expenditures)
Subtracting 46.41 from both sides:
153,590 = 0.45(Advertising Expenditures)
To find the Advertising Expenditures, divide 153,590 by 0.45:
Advertising Expenditures = 341311.111
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What is the y-intercept of the quadratic function f/x )=( x 6 )( x 2?
The y-intercept of the quadratic function f(x) = (x - 6)(x + 2) is -12.
The y-intercept of a quadratic function is the point at which the graph of the function crosses the y-axis. This means that when x = 0, the value of y is equal to the y-intercept. In the case of the function f(x) = (x - 6)(x + 2), when x = 0, the value of y is equal to -12. This means that the y-intercept of the function is -12. To find the y-intercept, we can also substitute 0 for x in the equation, which would give us 0 = (0 - 6)(0 + 2), which simplifies to 0 = -12, and thus the y-intercept is -12.
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The library has 1,500 fiction books and 8,500 non-fiction books. What percentage of the books at the library are fiction books?
15%
If you take fiction plus non fiction it equals 10k books. 1500/10000 is 15%
Simplify algebraic expression
Answer: 40
Step-by-step explanation:
We will substitute x = 8 and simplify the given expression.
Given:
6x-x
Substitute:
6(8) - 8
Multiply:
48 - 8
Subtract:
40
Graph the following system of equations.
y = 3x + 15
3x + 3y = 9
What is the solution to the system?
There is no solution.
There is one unique solution (-3, 6).
There is one unique solution (0, 15).
There are infinitely many solutions.
Answer:
There is one unique solution (-3, 6)
Step-by-step explanation:
Desmos graphing calculator helps a lot with this stuff
Answer: b) there is only one unique solution (-3, 6)
Step-by-step explanation:
Which is 536,900 in scientific notation
Answer:
5.369 x 105
Step-by-step explanation:
Answer:
5.369 x 105
Cause in scientific notation, the decimal point is always after the first number from the left.
I need help for number 2
The measure of the exterior angle for Object 1 - a decagon is 36°, while th measure of the exterior angle for Object 2 - a dodecagon is 30°.
What is a Decagon and a Dodecagon?n object with 12 sides is called a dodecagon while an object with 10 sides is called a decagon.
Note that the exterior angles of all shapes, regular or irregular is 360°. In this case, the shapes are regular, which means that the sides are equal, hence their angles will be equal.
To derive the exterior angle of a regular geometric shape, the formula is given as:
Exterior angle measure = 360 / number of sides
Hence for A (the decagon), we have:
EAM = 360/10
= 36°
For B (the dodecagon) we have:
EAM = 360/12
= 30°
Thus the exterior angle for both shapes are 36° and 30° respectively.
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RADIO FRIENDS Polly, Autumn, and Terry each have a two-way radio with a two-mile range. Their houses are located as shown, with Autumn and Polly being two miles apart. Which friends can talk with each other on the radio?
Autumn and Terry can talk because the distance between them is 2 miles
Polly and terry can not talk because the distance between them is 2.27 miles.
Polly and Autumn's distance can talk because the distance between them is 1.56 miles.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Autumn and Terry distance = 2 mile
Polly and Autumn's distance = x miles
Polly and terry's distance = y miles
Now,
Applying the Sin rule of a triangle.
2 / sin 59° = x / sin 42° = y / sin 79°
2 / 0.86 = x / 0.67 = y / 0.98
Find x.
2 / 0.86 = x / 0.67
x = 1.56
Find y.
2/0.86 = y / 0.98
y = 2.27
Now,
Polly and Autumn's distance is 1.56 miles.
This means they can talk.
Polly and terry's distance is 2.27 miles.
This means they can not talk.
Thus,
Polly and Autumn can talk.
Polly and terry can not talk.
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25PTS don’t explain
Answer:
y = 2x+ 3
Step-by-step explanation:
How many terms are there in the expression 2p3 3p2 4p 7 *?
Answer: 4
Explanation:
In Algebra a term is either a single number or variable, or numbers and variables multiplied together.
Terms are separated by + or − signs, or sometimes by divide.
What is the solution of 2x 3 7?
Answer: It is a straight line
Step-by-step explanation:
A quadrilateral with vertices at A(4, -4), B(4, -16), C(12, -16), and D(12,-4) has been dilated with a center at the
origin. The image of D, point D', has coordinates (36, -12). What is the scale factor of the dilation? 1/9. 1/3
3
9
Answer:
scale factor = 3
Step-by-step explanation:
since the origin is the centre of dilatation then the scale factor is the ratio of corresponding coordinates, image to original.
given D (12, - 4 ) and D' (36, - 12 ) , then
scale factor = [tex]\frac{36}{12}[/tex] = [tex]\frac{-12}{-4}[/tex] = 3
Jasmine has $26 to spend on binders and one pack of pens. The pack of pens costs $4. 75. Each binder costs $5. Write an inequality to determine the maximum number of binders she can buy, (Define your variable. )
Jasmine can buy a average of 4 binders because the cost of the binders, multiplied by the number of binders she wants to buy, plus the cost of the pens, must not exceed her total budget of $26.
Step 1: Define the variable. Let x represent the number of binders Jasmine can buy.
Step 2: Write the inequality. 5x + 4.75 ≤ 26
Step 3: Solve the inequality. 5x ≤ 21.25
Step 4: Isolate the variable. x ≤ 4.25
Step 5: The maximum number of binders Jasmine can buy is 4.
Let x represent the number of binders Jasmine can buy
5x + 4.75 ≤ 26
5x ≤ 21.25
x ≤ 4.25
Jasmine has a total of $26 to spend on binders and one pack of pens. The cost of the pens is $4.75, and each binder costs $5. To determine the maximum number of binders she can buy. The inequality we need to solve is 5x + 4.75 ≤ 26. We can solve this inequality by first multiplying both sides of the equation by 5, which gives us 5x ≤ 21.25. We can then isolate the variable by dividing both sides of the equation by 5, which gives us x ≤ 4.25. This means that the maximum number of binders Jasmine can buy is 4.
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What is the value of v?
Answer: v = 100
Step-by-step explanation:
v+15 = v-37 + v-48
v + 15 = 2v - 85
85 + 15 = 2v - v
100 = v
Uri buys two burgers and a soda for $\$2.10$, and Gen buys a burger and two sodas for $\$2.40$. How many cents does a soda cost
The cost of soda as calculated from the data given is found to be as 0.9 cents.
the price of 1 burger = x
the price of 1 soda =y
Therefore, the equation for Uri and Gen becomes,
2x + y = $2.10
x+ 2y = $2.40
On solving these two equations we will get the value of x and y which represents their cost.
on multiplying equation 2 with 2 , we will get ,
2x + 4y = 4.80
Therefore , on subtracting equation 1 and 2 ,
2x + y = $2.10
- 2x + 4y = 4.80
=> -3y = - 2.7
=> y = 0.9
Therefore x will be ,
x+ 2y = $2.40
x+ 2(0.9) = $2.40
x + 1.8 = $2.40
x = 2.40 - 1.8
= 0.60
Therefore, cost of soda is 0.9 cents.
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It take Thorton 4 hour to edit a video for hi chool. If he ha already pent 2. 5 hour on thi video, what percent of the video i edited?
Using the concept of fraction, the percentage edited on the video is 62.5 percent.
What is Percentage
Percentage is a standard mathematical concept used to express a portion of a whole number in terms of a hundred. It is denoted by the symbol “%” and is often expressed as a fraction or a decimal. For example, 25% can be expressed as 0.25 or 1/4.
In this problem, Thorton has done a 2.5 hours work. The percentage he has edited can be calculated using fraction or ratio as;
percentage edited = (2.5 / 4) × 100
Percentage = 0.625 × 100
Percentage = 62.5 %
From the above, Thorton has edited 62,5 percent of the video for his school project.
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