What is the pattern?

Answer:

The ratio of the new area to the old area will be 16:1

Step-by-step explanation:

I remember learning this in class. The radius is quadrupled, which means the radius is 4 times bigger. This will make the new area 16 times bigger than the old area.

Let's check

Area of circle: 3.14 x r^2

Area of the circle when radius 6:

3.14 (6)^2 = 113.04 ft^2

Area of the new circle when the radius is quadrupled:

3.14 (24)^2 = 1808.64 ft^2

1808.64 divided by 113.04 = 16

So, the ratio of the new area to the old area will be 16:1

Answer:

x ≈ 70.6°

Step-by-step explanation:

using the tangent ratio in the right triangle

tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{17}{6}[/tex] , then

x = [tex]tan^{-1}[/tex] ( [tex]\frac{17}{6}[/tex] ) ≈ 70.6° ( to the nearest tenth )

Distributive Property

Factoring

Functions

Let's organize what is given to us in the problem.

We are given a function f, defined as f(x) = x² + 3x - 10.

We are asked to find the values of b and c in f(x - 2) = x² + bx + c.

In order to solve the question, we first must find the full function of f(x - 2):

[tex]\displaystyle\begin{aligned}f(x - 2) & = (x - 2)^2 + 3(x - 2) - 10 \\& = \underbrace{x^2 - 4x + 4}_{\text{FOIL}} + \underbrace{3x - 6}_{\text{Distribute}} - 10 \\& = \boxed{ x^2 - x - 12 } \\\end{aligned}[/tex]

∴  [tex]\displaystyle \boxed{ f(x - 2) = x^2 - x - 12 }[/tex]

Now, we can correlate our variables to the f(x - 2) function by comparing them side-by-side:

[tex]\displaystyle\begin{aligned}f(x - 2) & = x^2 - x - 12 \\& = x^2 + bx + c \\& \Rightarrow \boxed{ b = -1 ,\ c = -12 }\end{aligned}[/tex]

∴ we have found the values of b and c.

∴ the value of b is equal to -1 and the value of c is equal to -12.

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Topic: Algebra I

Unit: Factoring

Each friend of Arya will receive 0.625 cupcakes.

To divide 5 cupcakes equally among 8 friends, we can use simple division. We would divide the total number of cupcakes (5) by the total number of friends (8) to find the number of cupcakes each friend would receive. In this case, 5 divided by 8 is equal to 0.625. This means that each friend will receive 0.625 cupcakes. However, since cupcakes are not divisible it is not possible to divide 5 cupcakes equally among 8 friends. In this case, either Arya will have to make more cupcakes or they will have to decide on a different way to divide the cupcakes.

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Over the course of the three hours, 41.25 gallons of water passed through the pipe in total.

We know that the rate of flow for the first hour was 50% slower than the rate of flow for the second hour. So, if the rate of flow in the second hour was 15 gallons per hour, the rate of flow in the first hour would be:

15 gallons/hour * (100% - 50%) = 15 gallons/hour * 50% = 7.5 gallons/hour

We also know that 25% more water flowed through the pipe in the third hour than in the second. So the rate of flow in the third hour would be:

15 gallons/hour * (1 + 25%) = 15 gallons/hour * 1.25 = 18.75 gallons/hour

To find the total number of gallons of water that flowed through the pipe during the entire three hours, we can multiply the rate of flow for each hour by the number of hours:

First hour: 7.5 gallons/hour * 1 hour = 7.5 gallons

Second hour: 15 gallons/hour * 1 hour = 15 gallons

Third hour: 18.75 gallons/hour * 1 hour = 18.75 gallons

Adding these values we can find the total amount of water that flowed through the pipe during the entire three hours

7.5 gallons + 15 gallons + 18.75 gallons = 41.25 gallons

So, in total 41.25 gallons of water flowed through the pipe during the entire three hours.

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Table A is a function.

Table B is not a function.

Table C is a function.

Table D is not a function.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

We know a relation is a function if it is one-to-one or many-to-one.

But a relation is not a function if it is one to many.

Table A is a function and it is a many-to-one function.

Table B is not a function as input 1 leads to two different outputs 1, - 1.

Table C is a function and it is a one-to-many function.

Table D is not a function as one input leads to 3 different outputs.

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The movie need to earn $ 1,512,500 in the next 7 weeks.

The unitary technique involves first determining the value of a single unit,

followed by the value of the necessary number of units.

For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A company spent 762500 to make a movie.

The total movie will be earned

= 762500 + 2000000

= 2,762,500

First week the movie earned 1, 250,000.

So, in 7 weeks the movie needs to earned

= 2,762,500 - 1, 250,000

= 1,512,500

Hence, the movie earn 1,512,500 more.

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Based on the information provided, the best description of the relationship between the variables in the scatterplot is: option D, "Those with higher 200-meter times tend to have longer javelin distances. The relationship is moderate."

The scatterplot shows a positive relationship between the two variables, as indicated by the points being grouped loosely together in a line with a positive slope.

This means that as the 200-meter dash time increases, the javelin throw distance also tends to increase. The coefficient of correlation, r, also supports this relationship, as a value of 0.369 indicates a moderate positive correlation between the two variables. Though the correlation is moderate, it's important to note that this does not imply causality.

Therefore, note that, based on the description in the question, the relationship is moderate, not strong. The statement is accurate only when the correlation coefficient is between 0.3-0.7 which is considered as moderate correlation.

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Answer:

d

Step-by-step explanation:

The factorization of the polynomial x² + 3x + 2 gives (x + 1)(x + 2)

An equation is an expression that shows how numbers and variables relate with each other.

A polynomial is an expression consisting of variables and their exponents with operations of addition and subtraction. Polynomials are classified based on degree as linear, quadratic and cubic.

The standard form of a quadratic equation is:

y = ax² + bx + c

where a, b and c are constants.

Given the polynomial:

x² + 3x + 2

Factorizing the polynomial:

x² + 2x + x + 2

= x(x + 2) + 1(x + 2)

= (x + 1)(x + 2)

The factorization gives (x + 1)(x + 2)

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A function whose equation is of the form y = ax + b, where a and b are constants, a does not equal zero, and x is any real number, and whose graph is a straight line.

Given an equation y = 14x -4 there is an equation that is perpendicular to this given equation.

from the slope-intercept of a linear equation:

The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.

thus the slope of the given equation is 14

The slope of the required equation = 1/14

Since both equations are perpendicular

From the slope intercept of the required line equation of a line:

y = 1/14x + c...(2)

Since, it passes through the point (28, 16)

Thus, 16 = 1/14 *28 + c

c = 16

from equation 2

y = 1/14 x + 14

from the table, two given coordinates of a linear function are (4, 36) and (6, 56)

thus slope of the line = (y₂ - y₁) / (x₂ - x₁)

Slope of the line = 20/2 = 10

Equation of a line:

y = 10x +c

Since, it passes through the point  (4, 36)

Thus, 36 = 40 + c

c = -4

Therefore, the required equation from the table is y = 10x - 4

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In the case of Typical behavior of the sales prices of houses median is the best term. In the case of Ages of 1st graders mean is the best way of central tendency and for Heights of women mode is the best measure.

First of all we have to know the Mean, median and mode. The mean of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

In the case of typical behavior of the variable sales price of houses, the Median will be the best measure of central tendency because the median will not get affected by the higher/lower prices of houses.

The age of each kid will be almost the same.  In order to represent the typical behavior of the variable Age of 1st graders, the mean will be the best measure of central tendency.

Incase of Heights of women, the mode will be the best measure of central tendency as it will describe the height that most of the females have. 

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An example of when renting from parabolas would be a better deal than renting from Arc of Hawk's is when the rental period is 8 hours.

A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.

The total cost of renting parabolas would be 8 × $4.50 + $35 = $43.

The total cost of renting from Arc Hawk's would be 8 × $5.25 + $25 = $45.75

So Parabola is cheaper by $2.75

In general, any rental period of 8 hours or less would be a better deal with Parabola's, as per hourly rate is cheaper and the rental fee is higher than Arc Hawk but still, the total cost is lesser.

As the rental period increases beyond 8 hours, the per-hour rate difference becomes negligible and Arc Hawk becomes cheaper.

It is important to compare the cost for the same rental period, to accurately determine which rental company offers a better deal.

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Answer: Okay this is the formula for slope: y=mx+b 2 would be the slope and -1 would be the y intercept so select b.

Step-by-step explanation:

There were 8 bhajis in the second bag if he have 2 bags of onion bhajis, one of which holds 42 bhajis.

What is an equation ?

In mathematics, an equation is a statement that asserts the equality of two expressions, typically containing one or more variables. Equations are often written in the form of "expression = expression" or "expression - expression = 0"

Let's call the number of bhajis in the second bag "x".

We know that he total number of bhajis after emptying both bags onto the plate is 50.

So we can write an equation:

42 + x = 50

To solve for x, we can subtract 42 from both sides:

x = 50 - 42

x = 8

Therefore, there were 8 bhajis in the second bag.

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The measure of the angle ∠6 = 112°

What are parallel lines?

Parallel lines are two or more lines that are always the same distance apart and never meet, no matter how far they are extended. They are coplanar lines that do not intersect or cross each other, and they have the same direction.

As given

a∥e, m∥n, and m∠2 = 112°.

As  m∥n

a is the transversal (A line that cuts across two or more (usually parallel) lines is called transverasl.)

Thus

∠ 2 = ∠3 ( Corresponding angle property )

∠3 = 112°

Also

a∥e and m are transversal.

∠ 3 = ∠6 = 112 ° ( Corresponding angle property )

Hence, the measure of the angle ∠6 = 112°

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The measure of the angle ∠6 = 112°

What are parallel lines?

Parallel lines are two or more lines that are always the same distance apart and never meet, no matter how far they are extended. They are coplanar lines that do not intersect or cross each other, and they have the same direction.

As given

a∥e, m∥n, and m∠2 = 112°.

As  m∥n

a is the transversal (A line that cuts across two or more (usually parallel) lines is called a transversal.)

Thus

∠ 2 = ∠3 ( Corresponding angle property )

∠3 = 112°

Also

a∥e and m are transversal.

∠ 3 = ∠6 = 112 ° ( Corresponding angle property )

Hence, the measure of the angle ∠6 = 112°

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On solving the provided, we can say that - here in graphs by solving the equation - [tex]x^2 + y^2 = > 2^2 = > 4[/tex]

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

here from graph,

x= 0

and y = 2

so, in equation

[tex]x^2 + y^2 \\2^2\\4\\[/tex]

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quadrilateral with both pairs of opposite sides congruent

What is a parallelogram?

A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.

Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.

If both pairs of opposite sides of a quadrilateral are congruent , then the quadrilateral is a parallelogram.

So, the option  I only is correct

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A power of 3 equation is called as cubic equation.

The term equation in math is known as a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Here we need to find the term that has been used for power of 3 equation.

Here we have to know that the power of 3 equation is known as cubic equation.

in other terms the polynomial equation which has a degree of three is called a cubic polynomial equation or trinomial polynomial equation.

As we all know that the power of the variable is the maximum up to 3, therefore, we get three values for a variable, say x.

The general form of the power of 3 equation is written as

=> ax³ + bx² + cx + d = 0

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A triangle is a polygon with 3 sides, and the sum of its interior angles is 180 degrees.

The properties of a triangle are:

There are several types of triangles, including:

Equilateral triangle: This is a triangle with three sides of equal length and three angles of 60 degrees.

Isosceles triangle: This is a triangle with two sides of equal length and two angles of equal measure.

Scalene triangle: This is a triangle with three sides of different lengths and three angles of different measure.

Right triangle: This is a triangle with one 90-degree angle.

Acute triangle: This is a triangle with three angles that are all less than 90 degrees.

Obtuse triangle: This is a triangle with one angle that is greater than 90 degrees.

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To prove a number is irrational we divide the integer by another integer is the decimal is non terminating and non repeating then it will be a irrational number .

What are Irrational Numbers ?

The Irrational numbers can be defined  a number that cannot be expressed as a fraction [tex]\frac{p}{q}[/tex] for any integers p and q.

The Irrational numbers have decimal expansions that do not terminate nor repeat (periodic) . Every transcendental number is an irrational number .

(i) To prove a number irrational  when we divide an integer by another integer, and  if decimal expansion does not terminate and do not  repeat then it is an irrational .

(ii) if the number cannot be expressed in the form of [tex]\frac{p}{q}[/tex] , then also the number will be called as irrational numbers .

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The perimeter of ΔABE is 70 units.

The  perimeter of ΔCDF​ is 35 units.

A triangle is a polygon with threes sides. The sum of angles in a triangle is 180 degrees.

Therefore, the perimeter of a triangle is the sum of the whole sides.

Triangle mid point theorem is used to find the perimeter of the triangles.

It states that the line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

Let's find the perimeter of triangle ABE.

Hence,

perimeter of triangle ABE = AB + BE + AE

BE = 24

AE = 13 + 13 = 26

AB = 10 + 10 = 20

perimeter of triangle ABE = 24 + 26 + 20 = 70 units

perimeter of triangle CDF = DF + CD + CF

perimeter of triangle CDF = 10 + 13 + 12

perimeter of triangle CDF = 35 units

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To find the terminal point of a line segment, identify the starting point, measure the length and direction, and use these parameters to calculate the coordinates of the terminal point.

To find the terminal point of a line segment, first identify the starting point of the line. Then, measure the length of the line segment and the direction in which it is going. Finally, use a combination of the starting point coordinates, the length, and the direction to calculate the coordinates for the terminal point of the line.

1. Identify the starting point of the line.

2. Measure the length of the line segment and the direction in which it is going.

3. Use the starting point coordinates, the length, and the direction to calculate the coordinates of the terminal point.

4. The coordinates of the terminal point are the location of the line segment’s endpoint.

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Answer: Shift right 20 units

When Donovan flips a coin a total of 96 times, the number of times he should expect the coin to land on heads will be 48 times.

The times he should expect the coin to land on tail based on the table will be 27 times.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

When Donovan flips a coin a total of 96 times, the number of times he should expect the coin to land on heads will be:

= 1/2 × 96

= 48

The number of times he should expect the coin to land on tail based on the table will be:

= 18/50 × 75

= 27 times

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The percent error in the amount of water Rich added is 15.93%.

When compared to the actual value, the percent error is the difference between the estimated and actual values.

The difference between the estimated value and the actual value in relation to the actual value is given as a percentage and is known as the percent error. In other words, the relative error times 100 equals the percent error.

Given that Rich added water to a solution in science class is 26.2 milliliters

Whereas the directions said to add water is 22.6 milliliters

The amount of water that is added more is 26.2 -22.6 = 3.6 milliliters

The percent error is = (3.6/22.6)*100%

The percent error is = 15.9292*100%

Therefore, the correct answer is option b) 15.93%.

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Answer:

The cost for 1 pizza is $8.99

Step-by-step explanation:

We know

Natalia paid a total of 38.95 for 3 pizzas and a salad

A salad = $11.98

We first find the total cost of 3 pizzas by

38.95 - 11.98 = $26.97

$26.97 is the cost for 3 pizzas; to find the cost of 1 pizza, we take

26.97 divided by 3 = $8.99

So, the cost for 1 pizza is $8.99

Answer:

The cost of 1 pizza is $8.99.

Step-by-step explanation:

Let

[tex]t[/tex] = total price

[tex]p[/tex] = pizzas

[tex]s[/tex] = salads

Natalia bought 3 pizzas and 1 salad

[tex]38.95=3p+1s[/tex]

We are given the price of the salad.

[tex]38.95=3p+11.98[/tex]

Now we can find the cost of 1 pizza.

Lets solve for [tex]p[/tex].

Subtract 11.98 from both sides of the equation.

[tex]26.97=3p[/tex]

Divide both sides of the equation by 3.

[tex]p=\frac{26.97}{3}\\p=8.99[/tex]

Answer:

36 sq ft

Step-by-step explanation:

The area of a square is equal to the length of one side squared. Therefore, if all sides of a square are 6 feet long, the area of the square is 6 feet * 6 feet = 36 square feet.

Answer:

36

Step-by-step explanation:

you multiply just two of the sides hxw and you get your answer

The number 1.2 × 10⁶ is 11.5 times smaller in comparison to the number 1.38 × 10⁷.

The two given numbers here have been written using the method of powers of 10. In this method, very large or very small numbers are easily simplified and written by denoting the powers of 10. These power are integral in nature. Very large numbers are of the form y × 10ⁿ and very small numbers can be expressed in the form z × 10⁻ⁿ.

In the given problem, we have the numbers 1.2 × 10⁶ and 1.38 × 10⁷ and we have to tell how much the former number is from the latter. For this, we divide the two and easily find our solution. Before this, we have to make the powers of 10 in both numbers the same. We can rewrite the  1.38 × 10⁷ as 13.8 × 10⁶. Now, we divide the two and get-

⇒ 11.5

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Answer: B. 11.5

Step-by-step explanation: I took the test