Which shortcut could be used to prove the two triangles are congruent?

Write the algebraic expression for the difference between the squares of two numbers.

V125BC [204]

The algebraic expression for the difference between the squares of the two numbers, supposing the two numbers to be a and b, is

a² - b² = (a + b)(a - b).

An algebraic expression is a combination of terms, where the terms are separated using mathematical operators like plus (+), minus (-), multiply (*), and divide (/).

The terms are combinations of numerals and variables.

Variables are represented alphanumerically, which can hold any value as per the expression they are used in.

In the question, we are asked to write the algebraic expression for the difference between the squares of two numbers.

We assume the two numbers to be a and b respectively.

Thus, we are asked to write an expression for the difference between the square of a and square of b, that is, we are asked to write an expression for a² - b².

We know that a² - b² is an identity, which can be shown as (a + b)(a - b).

Thus, the algebraic expression for the difference between the squares of the two numbers, supposing the two numbers to be a and b, is a² - b² = (a + b)(a - b).

Learn more about algebraic expressions at

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6 0

1 year ago

Any help is appreciated:)<br><br>God blast it the photo didn’t load

mart [117]

... what is the question lol

6 0

3 years ago

A man earned x pesos in 10 days and spent y pesos during each of those days. Write an expression to determine how many pesos he

Vsevolod [243]

Answer: $\dfrac{x}{10}-y$

Step-by-step explanation:

Given : A man earned x pesos in 10 days and spent y pesos during each of those days.

i.e. Total earning in 10 days = x

Earning per day = $\dfrac{x}{10}$ [By unitary method] (1)

Money spent per day =y (2)

We know that

$\text{Savings = Money earned - Money spent}$

i.e. Subtract (2) from (1), we get

$\text{Savings = }\dfrac{x}{10}-y$

Hence, the expression to determine how many pesos he saved per day will be:-

$\dfrac{x}{10}-y$

3 0

3 years ago

A data mining routine has been applied to a transaction dataset and has classified 88 records as fraudulent (30 correctly so) an

Firlakuza [10]

Answer:

The classification matrix is attached below

Part a

The classification error rate for the records those are truly fraudulent is 65.91%.

Part b

The classification error rate for records that are truly non-fraudulent is 96.64%

Step-by-step explanation:

The classification matrix is obtained as shown below:

The transaction dataset has 30 fraudulent correctly classified records out of 88 records, that is, 30 records are correctly predicted given that an instance is negative.

Also, there would be 88 - 30 = 58 non-fraudulent incorrectly classified records, that is, 58 records are incorrectly predicted given that an instance is positive.

The transaction dataset has 920 non-fraudulent correctly classified records out of 952 records, that is, 920 records are correctly predicted given that an instance is positive.

Also, there would be 952 - 920 = 32 fraudulent incorrectly classified records, that is, 32 records incorrectly predicted given that an instance is negative.

That is,

Predicted value

Active value Fraudulent Non-fraudulent

Fraudlent 30 58

non-fraudulent 32 920

The classification matrix is obtained by using the information related to the transaction data, which is classified into fraudulent records and non-fraudulent records.

The error rate is obtained as shown below:

The error rate is obtained by taking the ratio of $\left( {b + c} \right)(b+c)$ and the total number of records.

The classification matrix is, shown above

The total number of records is, $30 + 58 + 32 + 920 = 1,040$

The error rate is,

$\begin{array}{c}\\{\rm{Error}}\,{\rm{rate}} = \frac{{b + c}}{{{\rm{Total}}}}\\\\ = \frac{{58 + 32}}{{1,040}}\\\\ = \frac{{90}}{{1,040}}\\\\ = 0.0865\\\end{array}$

The percentage is $0.0865 \times 100 = 8.65$

(a)

The classification error rate for the records those are truly fraudulent is obtained by taking the rate ratio of b and $\left( {a + b} \right)(a+b)$ .

The classification error rate for the records those are truly fraudulent is obtained as shown below:

The classification matrix is, shown above and in the attachment

The error rate for truly fraudulent is,

$\begin{array}{c}\\FP = \frac{b}{{a + b}}\\\\ = \frac{{58}}{{30 + 58}}\\\\ = \frac{{58}}{{88}}\\\\ = 0.6591\\\end{array}$

The percentage is, $0.6591 \times 100 = 65.91$

(b)

The classification error rate for records that are truly non-fraudulent is obtained by taking the ratio of d and $\left( {c + d} \right)(c+d)$ .

The classification error rate for records that are truly non-fraudulent is obtained as shown below:

The classification matrix is, shown in the attachment

The error rate for truly non-fraudulent is,

$\begin{array}{c}\\TP = \frac{d}{{c + d}}\\\\ = \frac{{920}}{{32 + 920}}\\\\ = \frac{{920}}{{952}}\\\\ = 0.9664\\\end{array}$

The percentage is, $0.9664 \times 100 = 96.64$

6 0

2 years ago

What is the equation for the line?

masha68 [24]

Answer:

The equation of a line is typically written as y=mx+c where m is the slope and c is the y-intercept.

7 0

3 years ago