What is the equation of the line shown in the graph?

By using the the application of ASA we can determine the two angles are congruent by AAS.

AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

AAS congruence can be proved in easy steps.

Suppose we have two triangles ABC and DEF, where,

Diagram attaches at the end of the solution.

∠B = ∠E [Corresponding angles]

∠C = ∠F [Corresponding angles]

AC = DF [Adjacent sides]

By angle sum property of triangle, we know that;

∠A + ∠B + ∠C = 180 ………(1)

∠D + ∠E + ∠F = 180 ……….(2)

From equation 1 and 2 we can say;

∠A + ∠B + ∠C = ∠D + ∠E + ∠F

∠A + ∠E + ∠F = ∠D + ∠E + ∠F [Since, ∠B = ∠E and ∠C = ∠F] ∠A = ∠D

Hence, in triangle ABC and DEF,

∠A = ∠D

AC = DF

∠C = ∠F

Hence, by ASA congruency, (AAS: the application of ASA)

Δ ABC ≅ Δ DEF

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The function's standard form equation is equivalent to [tex]\frac{-x^2}{4}+1=0[/tex].

A mathematical expression (equation) that can be used to define and represent the relationship between two or more variables on a graph is known as a quadratic function.

The standard form of a quadratic equation in mathematics is given by;

[tex]ax^2+bx+c=0\\y=f(x)=ax^2+bx+c[/tex]

Next, using the information in the previous table, we would create the following system of equations:

[tex]-3=a(-4)^2+b(-4)+c\\-3=16a-4b+c[/tex].......equation (i)

[tex]0=a(-2)^2+b(-2)+c\\0= 4a-2b+c[/tex]........equation(ii)

[tex]1=a(0)^2+b(0)+c\\1=c[/tex].........equation (iii)

Inputting the value of c into equations 1 and 2 results in:

[tex]-4=16a-4b[/tex]......ewuation(iv)

[tex]-1=4a-2b[/tex]......equation(v)

Equation 5 is multiplied by two and solved concurrently to yield:

[tex]-2=8a\\a=\frac{-2}{8} \\a=\frac{-1}{4}[/tex]

What we have for b's value is:

[tex]-1=4a-2b\\-1=4(\frac{-1}{4})-2b\\ -1=-1-2b\\2b=0\\b=0[/tex]

Inputting the values of a, b, and c into a quadratic equation in standard form:

[tex]ax^2+bx+c=0\\\frac{-1}{4}x^2+(0)x+1=0\\ \frac{-x^2}{4} +1=0[/tex]

When x equals 2, we get:

[tex]\frac{-x^2}{4} +1=0\\\frac{-2^2}{4}+1=0\\ \frac{-4}{4}+1=0\\ -1+1=0[/tex]

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If a₁ = 4 and an = -4an-1 +5 then the value of a5 is 72, in the given sequence.

A group of enumerated objects where repetitions are allowed and order is crucial is referred to as a sequence in mathematics. Similar to a set, it has members. The sequence's length is expressed in terms of its number of elements.

Given that, sequence  

[tex]a_1=4, a_n=4 a_{n-1}+5[/tex]

Now

[tex]a_2=4 a_1+5[/tex]

[tex]a_2=4 \times 4+5[/tex]

[tex]a_2=21[/tex]

[tex]a_2=4 \times 4+5[/tex]

[tex]a_2=21[/tex]

And the common difference d = 21 - 4 = 17

Therefore [tex]a_5=a_1+4 d[/tex]

[tex]a_5=4+4 \times 17[/tex]

[tex]a_5=4+68[/tex]

[tex]a_5=72[/tex]

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Therefore , the solution to this problem is yes 8 has multiple which are 16,24,32 etc.

A multiple in mathematics refers to the product produced by multiplying two numbers or variable. In this instance, the number 7 is multiple by 56.

The expression is termed as multiple .Fun Facts is an additional example of multiples. 0 is a multiple of all numbers since it produces zero when multiplied by any other number.

Here,

There are eight multiples: 8, 16, 24, 32, 40, 48, 56, 64, 72, and so on.

There are two consecutive results in this sequence, and there is an 8-digit gap between each subsequent number and the one before it.

The results of multiplying any integer by other natural numbers are known as multiples.

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Yes, a 4 year old can typically count to 100.

Counting is the process of determining the number of elements in a given set or group of objects. Counting is a basic numerical skill that is used in mathematics and other fields. It involves recognizing patterns and comparing numbers to identify how many items are in a given set. Counting is an important part of early childhood education, as it introduces children to the concepts of number and quantity.

Depending on the child's exposure to numbers, they may be able to count even higher. Counting to 100 is a fundamental skill that can be developed through practice and repetition. Teaching a 5 year old to count to 100 can be done through activities such as counting objects, counting steps, and playing counting games.
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we will find the length of rectangle when area is divided by the breadth of rectangle.

Some properties are rectangle are stated below:

1. rectangle has four right angles

2. rectangles has four sides and equal opposite sides which are parallel to each other.

3.rectangle has two diagonals which are similar in length.

The bigger side lengths are called length and the smaller sides are called breadth of rectangle.

if area of rectangle is given, we can find length when area is divided by its breadth.

 length = area/breadth

hence, length of rectangle is determined from the value of area and breadth.

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The total cost for Bob's ride is C = x + m and no. of minutes of the ride is

m = C - x.

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

Given,  A ride on a rental scooter, bob paid a fee to start the scooter plus cents per minute of the ride.

Let, 'x' be the fee in cents to start the scooter and 'm' be the no. of minutes of riding.

Therefore, The total bill(C) for Bob's ride is,

C = x + m.

The no. of minutes Bob ride the scooter is simply,

m = C - x.

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Using the linear function y = -5/3x + 3000, the boulder will touch the ground at 1800m

A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

A model of a linear function is given as y = mx + c

where m is the slope or rate of change of the function and c is the constant value or y - intercept

In this function;

The slope is - 5/3 and the constant is 3000

The linear function can be written as

y = -5/3x + 3000

The height at which the boulder will strike the ground, the value of y = 0

0 = -5/3x + 3000

5/3x = 3000

x = 1800

The point is at 1800m

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The equation that defines the fines with respect to the number of days overdue is written as: y = 0.1x + 1.

The equation that defines the fines with respect to the number of days overdue can be written as a linear equation that is expressed in slope-intercept form as y = mx + b, where the slope or unit rate is m, while the y-intercept or initial value is b.

Using two points from the chart, (2, 1.20) and (5, 1.50), find the slope or unit rate:

Slope / unit rate (m) = change in y / change in x = (1.50 - 1.20) / (5 - 2)

m = 0.3 / 3

m = 0.1

Find the y-intercept by substituting m = 0.1 and (x, y) = (2, 1.20) into y = mx + b:

1.20 = 0.1(2) + b

1.20 = 0.2 + b

1.20 - 0.2 = b

1 = b

To write the equation, substitute m = 0.1 and b = 1 into y = mx + b:

y = 0.1x + 1

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The total free throws Amadou attempts, if Amadou misses 2% of the free throws he attempts in a season, he missed 32, is 1600.

As it is clear from the term, percent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.

Given:

Amadou misses 2% of the free throws he attempts in a season, he missed 32,

Calculate the total number of throws as shown below,

2% of x = 32

Here, x is the total number of throws,

0.02 × x = 32

x = 32 / 0.02

x = 1600

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Y- intercept for the line y = 5x is 0. This can be get from the standard equation for a line.

For the The standard equation for a line is,

     y = ax + b

y is called the dependent variable because its value depends on the value of x

a is the slope of the line

x is called the independent variable because it can be any value

b is the y-intercept

Here y is a function of x. You could simply write it as y = 5x.  Thus if we compare to the standard form equation y = ax + b, a=5 and b=0.  Thus the y-intercept is zero.  The reason that this is the case is that when you set x=0 the value is plotted on the y axis because the equation for the y axis is the line defined by x=0.  Any value in the x, y plane where x is equal to zero plots on the vertical line going through (0,0) or in other words the y axis.

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Take the function y = f(x), with the independent variable x as well as the dependent variable y, to determine the domain of a. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.

The collection of all potential inputs for a function is its domain.

For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

The set of numbers x for which a function is defined in a valid manner is known as the domain of the function.

A function's domain is referred to as a closed interval if it is specified across the interval a ≤ x ≤ b.

So, to find the domain of a, consider the function y = f(x), which has the independent variable x and the dependent variable y.

A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

Therefore, take the function y = f(x), with the independent variable x as well as the dependent variable y, to determine the domain of a. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.

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Answer:

googolplex

Step-by-step explanation:

it just is

Answer:

A Googolplex

Step-by-step explanation:

It is written as 10^googol and 10^10^100

The value of A + B + C based on the information is A. 5.

From the information, we have digit number 4,ABC,239,040 A B and C are digits. if the number is the product of 6 consecutive positive multiples of 3.

It should be noted that all multiple of 8 have it's digits add up to a multiple of 9. This can be illustrated as:

4 + A + B + C + 2 + 3 + 9 + 0 + 4 + 0

= 22 + A + B + C

This will be equated to 27 which is the nearest multiple of 9

22 + A + B + C = 27

A + B + C = 27 - 22

A + B + C = 5

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Complete question

In this 10 digit number 4,ABC,239,040 A B and C are digits. if the number is the product of 6 consecutive positive multiples of 3 what is the value of A + B + C?

A 5

B 6

C 7

D 8

The estimated population in 2025 is 356.9

What is estimation ?

In math, estimating can be used to roughly calculate an answer (getting a "rough response") or to verify its accuracy (getting the "proper answer"). Even when estimating large numbers or decimal numbers, you shouldn't need to utilize a calculator or other documented techniques.

Estimation is frequently performed by sampling, which involves counting a small sample of a given thing and extrapolating that number to a wider population. Calculating the number of sweets of a particular size that are contained in a glass jar serves as an illustration of estimation.

There are 125 years from after 1900 to 2025

P = 0.00892t^2 + 1.1149t + 78.4491

P= (0.0089x125x125)+(1.1149x125)+78.4491

 =139.0625+139.3625+78.4491

 =356.87

 =356.9

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Answer:

2 feet

Step-by-step explanation:

(60 / 157.5) * 63 inches = 24 inches = 2 feet

Now, when a system has at least one solution, it's called consistent. When it has only one solution, it's called independent. otherwise inconsistent

The classification which best describes the system of equations is; Consistent and dependent

A linear or nonlinear system of equations as the case may be is termed consistent if there is at least one set of values for the unknowns that satisfies each equation in the system. In essence, when substituted into each of the equations, they make each equation hold true.

Additionally, the system of equations is dependent because the value of each variable is dependent on the others.

Now, when a system has at least one solution, it's called consistent. When it has only one solution, it's called independent.

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An inverse relationship in math is a relationship between two quantities where one quantity increases as the other decreases and vice versa.

An example of an inverse relationship is the relationship between the temperature in degrees Celsius and the temperature in degrees Fahrenheit.

The relationship between temperature in degrees Celsius (C) and temperature in degrees Fahrenheit (F) is defined by the following equation:

F = (9/5)C + 32

This equation shows that as the temperature in degrees Celsius increases, the temperature in degrees Fahrenheit decreases. For example, if the temperature in degrees Celsius is 20, the temperature in degrees Fahrenheit is 68. If the temperature in degrees Celsius is 40, the temperature in degrees Fahrenheit is 104.

Therefore, the relationship between temperature in degrees Celsius and temperature in degrees Fahrenheit is an inverse relationship.

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The formula that can be used to calculate the half-life is: [tex]N(t)=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1 / 2}}}[/tex]

The half-life is the amount of time required for a quantity (of substance) to reduce to half of its initial value.

The expression is commonly used in nuclear physics to describe how quickly unstable atoms decay radioactively or how long stable atoms remain.

Additionally, a broader definition of the term is used to characterize any exponential decay (or, very infrequently, nonexponential decay).

For instance, the medical sciences may refer to the biological half-life of drugs and other substances in the human body.

Time doubles in proportion to life's exponential expansion.

The formula to calculate half-life: [tex]N(t)=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1 / 2}}}[/tex]

Where N(t) is the quantity of the substance remaining, N₀ is the initial quantity of the substance, t is the time elapsed and t₁₎₂ is the half-life of the substance.

Therefore, the formula that can be used to calculate the half-life is: [tex]N(t)=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1 / 2}}}[/tex]

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The table showing trading account is given below

he trading account gives details of total sales, total purchases and direct expenses relating to purchase and sales. Trading account format for the year contains Particulars, Amount, Dr., Cr., Purchases, Sales, etc.

Given here,

Particulars                         Amount

Cash purchases               Rs.4,50,000

Credit purchases              Rs.27,00,000

Returns inwards                Rs.60,000

Cash sales                         Rs.4,80,000

credit sales                        Rs.33,00,000

Returns outward               Rs.30,000

freight inwards                 Rs.9000

carriage inwards              Rs.9000

Wages and salaries         Rs.12000

Opening stock                Rs. 4,50,000

closing stock                  Rs. 2,64,000

Market value                     Rs.2,52,000​

Hence the trading account for the year ended 31st March, 2013 is given above

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y = 3/x equation is an example of inverse variation between the variables x and y .

Now, According to the question:

The equation with the inverse variation between the variables 'x' and 'y' .

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.

y = 3/x is an example of inverse variation.

Hence, y = 3/x equation is an example of inverse variation between the variables x and y .

Let's know:

What is an Inverse variation equation?

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases.

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The average change in the volume of water per day is obtained as 0.625  litres.

The rate change of volume is the change of volume with respect to time.

For instantaneous change the derivative of the expression of volume can be taken.

The average change in the volume of water can be obtained as follows,

Average change = Volume of water ÷ Number of days

                            = 2.5 ÷ 4 = 0.625

Hence, the average change in water volume is given as  0.625 liters per day.

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Answer:

x =  - 28/101

Step-by-step explanation:

Answer:

x=-42

Step-by-step explanation:

[tex]-3x-28=98\\(-3x-28)+28=(98)+28\\-3x=126\\\frac{-3x}{-3}=\frac{126}{-3}\\x=-42[/tex]

A prime number is a positive integer greater than one that has no positive integer divisors other than one and itself. To find if a number is prime or not, if a number is divide by any other positive number other than 1 and itself it is not a prime number.

A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.

Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.

8 is not a prime number because 8 is divided by 2 and 4 other than 1 and itself.

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The simulation to estimate the standard deviation of the sampling distribution of the sample median for random samples of size 50 is given as follows:

Sampling is a technique for when a group of elements from a population is taken to represent the entire population.

Hence, for this problem, multiple samples of 50 students are taken, and for each sample, the median is computed and then stored in a list, according to the procedure described at the beginning of the answer.

Then, after the entire procedure runs, we will have a sample of 50 values, which represent the median for each sample. Then the standard deviation is calculated as the square root of the sum of the difference squared between each of these observations and the mean of all these observations, divided by 50, which is the cardinality of the data-set.

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The formula or equation used to determine the slope of a straight line is as follows:

m = (Y₂-Y₁)/(X₂-X₁)

An equation is about two expressions, either arithmetic or algebraic, that are related with a "=" sign that indicates equality of expressions.

Equations can be graphed, they are used to model many problems and theories.

The straight lines are characterized by a finite succession of points, when they have an inclination they adopt a slope value different from 0, and to determine that slope it is necessary to know two points of the line and use the following equation:

m = (Y₂-Y₁)/(X₂-X₁)

Where the points are:

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The equation that represents a proportional relationship is y/X = 2.5. That is option D.

A proportional relationship is the type of relationship that exist when between two variables which can be represented as y and x where a constant of proportionality exists between the two variables as k.

The relationship between these two variables can either be directly proportional or indirectly proportional.

The relationship that exists between X and y is a direct proportional relationship with a constant of proportionality of 2.5.

y = 2.5 X

= y/X = 2.5. Where 2.5 is the constant.

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Answer:?=93/14

Step-by-step explanation:

the ? is the variable in this equation so we have to solve for it

1. distributive property ->

5(?+3) = 5?+15

?(6+3) = 9?

so 5?+15+9?=108 -> 14?+15=108

2. then solve,

14? -15 = 108 -15

14?=93

?=93/14

Answer:

801.66

Step-by-step explanation:

calculator

Answer:

801.6632653061

Step-by-step explanation:

.......

Answer:

Calculate: 48.78/0.9 = 54.2

Write a situation: Richard has 48.78 ounces of grape juice that he wants to ration out for his friends at his birthday party. Each cup the friends get can hold 0.9 ounces of grape juice.

What does the quotient mean: The quotient, 54.2, means that Richard had given 54.2 ounces of grape juice to all of his friends combined.