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The division property of equality informs us quite simply that if we divide both sides of an equation by the same number, then the resulting equation is unaltered. This is known as the distributive property of equality.

It is important to keep in mind that the value of a fraction is always equivalent to the numerator of the fraction if the denominator of the fraction is 1 and the numerator of the fraction is anything other than zero.

To speak in terms of fractions is to refer to numbers that are not whole.

The value of the numerator in a fraction is determined by whether or not the numerator is nonzero and whether or not the denominator is 1.

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rise over run to find the slope

y = mx+b

we rose 1 and went over by 2

which means the equation is 1/2 x or 0.5x

The tape diagram to represent the context regarding the number of gigabytes of data Julian can use while staying within his budget is Tape D.

A tape diagram simply has to do with a diagram that's used to illustrate the relationship between the numbers that are given.

In this case, Julian pays a flat cost of $52 per month and $3 per gigabyte and she wants to keep his bill at $58 per month.

This will be illustrated as:

let g = the number of gigabytes of data.

The expression will be:

52 + 3g = 58

The appropriate tape diagram is D.

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In linear equation, He 3 boxes of pencils and 8 boxes of pens.

What are instances of linear equations?

He bought 3 boxes of pencils and 8 boxes of pens.

Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120

Mulitples of 40: 40, 80, 120

This means that there are 120 people at the conference, and that he bought 3 boxes of pencils (40x3=120) and 8 boxes of pens (15x8=120)

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The amount of water that Lucy should drink more is 750 ml.

From the information, Lucy between breakfast and lunch she pours 2 glasses of water each measuring 250ml. This will be:

= 250ml × 2

= 500ml

Between lunch and her dinner she pours 3 glasses also measuring 250 ml. This will be:

= 3 × 250ml

= 750 ml

Since Lucy wants to drink 2L of water, the amount needed to drink more will be:

= 2L - (750 + 500)

= 2000ml - 1250ml

= 750ml

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The total time for the boxing match will be 9 minutes.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a woman's boxing match consists of four 2-minute rounds, there is a 1-minute rest interval between each round.

The time of the match will be calculated as:-

Time = 2 x Total rounds + 1

Time = ( 2 x 4 ) + 1

Time = 8 + 1 = 9 minutes

Therefore, the total time for the boxing match will be 9 minutes.

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Answer:

Slope = 0

Step-by-step explanation:

[tex]\text{Slope} = m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}[/tex]

where (x1, y1) and (x2, y2) are any two points on the line

Given he two points (4, 9) and (-6, 9)

m = (9 - 9)/(-6 - 4) = 0/-10 = 0

Answer:

length of I'J'= 4 units

length of IJ= 16 units

scale factor = 16/4 = 4

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None of the given expressions are equivalent to 25.

What is an expression?

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (operands), variable, operations, units, brackets, punctuation, and groups can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's sequence of operations and other features.

Many writers make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects. However, in contemporary mathematics, and particularly in computer algebra, formulae are seen as expressions that, depending on the values supplied to the variables present in the expressions, can be evaluated to true or false.

The expressions are solved as follows

6-6-6-6-6-6 = -24

2-6 = -4

12-12 = 0

2-2-2-2-2-2 = -8

4-16 = -12

8-8 = 0

Hence, none of the expressions are equivalent to 25.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:f{}^{-1}(x) = x +5 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

We need to find the inverse of given function; f(x) = x - 5

[tex]\qquad \tt \rightarrow \: y = x - 5[/tex]

here, write x in terms of y.

[tex]\qquad \tt \rightarrow \: x = y + 5[/tex]

replace x with [tex]{\tt{{f}^{-1} (x)} } [/tex] and y with x, you will get your required inverse function.

[tex]\qquad \tt \rightarrow \: f {}^{ - 1} (x) = x + 5[/tex]

And it's already in slope intercept form

[tex]\qquad \tt \rightarrow \: y = mx + c[/tex]

where, slope (m) = 1 and y intercept (c) = 5

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

In distance, the penguin speed in mi/hr is 1.67mi/hr.

What is distance in math?

Distance = 1/3 mile

Time = 1/5 hour

Speed of the penguin = Distance/Time taken

Substitute the given data into the speed formula;

Speed = (1/3)/(1/5)

Speed = 1/3 * 5/1

Speed = 5/3

Speed = 1.67miles/hour

Hence the penguin speed in mi/hr is 1.67mi/hr

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Answer:

The distance between the two cities is 360 miles.

Step-by-step explanation:

Let value "a" equal the airspeed of the plane in still air, and let value "d" be the distance between the two cities. Then:

d/a+30=1.5

d=1.5a+45

and

d/a-30=2

d=2a-60

So

2a-60=1.5a+45

.5a=105

a=210

d/210-30=2

d=360

The distance between the two cities is 360 miles.

The percent of the people he paid claimed to be his friends is 67.5%

Given,

Mr. McCullough paid 80 people to say they were his friends.

and, After he paid them, 26 of them still did not claim to be his friend.

To find the percent of the people he paid claimed to be his friends

Now, According to the question:

Based on the given condition,

Formulate :

(80- 26) ÷ 80

Calculate:

(80- 26) / 80

= 54/80

Simplify

= 27/40

=0.675

Convert to percentage;

Multiply a number to both the numerator and the denominator

0.675 × 100/100

Calculate

67.5 / 100

= 67.5%

Hence, The percent of the people he paid claimed to be his friends is 67.5%.

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The 32° measure of A and the length of side a which is 17, and side B with length 11, using the law of sines, gives;

The law of sines can be stated as follows;

The ratio of the sine of an interior angle in an oblique triangle to the length of the side opposite the given angle, is a constant for the angles and their opposite sides of the triangle.

Mathematically, we have;

[tex] \frac{sin( A) }{a} = \frac{sin( B )}{b} =\frac{sin( C )}{c} [/tex]

Where;

Angle A is the angle opposite to side a

Angle B is the angle opposite to side b

Angle C is the angle opposite to side c

The given measure of angle A = 32°

The length of segment, a = 17

The length of segment, b = 11

Taking the given dimensions as the measurements of parts of a triangle, using sine rule, we have;

From the question, we have;

A = 32°

a = 17

b = 11

Which gives;

[tex] \frac{17}{sin( 32^{ \circ} ) } = \frac{11}{sin( B )} [/tex]

Therefore;

[tex] sin( B ) = \frac{11 \times sin( 32^{ \circ} ) }{17} [/tex]

Which gives;

[tex] \displaystyle{ B = arcsin \left( \frac{11 \times sin( 32^{ \circ} ) }{17} \right) \approx 20.1 ^{ \circ} }[/tex]

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After thoroughly calculating we have come to find that, a number twice the sum of -17 and -14 is −62

To sum and complete mathematical operations, numerical values are needed. Numbers are used to represent numerical values, and they can also be used to represent them alphabetically. For instance, the number 22 can be expressed in writing or by using the alphabet 22. One more example is the number 3, which can be written as 3.

Numbers can take many different forms. Examples of opposites include odd and even, fraction and integer, rational and irrational, natural and whole, and many more. A few of the operations include arithmetic, algebra, and trigonometry.

Twice the sum of -17 and -14 is

2((-17) + (-14))

⇒ 2(-17 -14)

⇒ 2 × (-31)

⇒ −62

So, a number twice the sum of -17 and -14 is −62.

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Based on the calculations, the age of this person is equal to 25 years.

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In order to solve this word problem, we would assign a variable to the age of this person and then translate the word problem into algebraic equation as follows:

Let x represent the age.

Translating the word problem into an algebraic equation, we have;

x + 65 = 6(x - 10)

Opening the bracket, we have:

x + 65 = 6x - 60

Re-arranging the equation, we have:

6x - x = 60 + 65

5x = 125

Dividing both sides by 5, we have:

x = 125/5

x = 25 years.

In conclusion, we can reasonably infer and logically state that this person's age was 25 years ten (10) years ago.

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Complete Question:

In 65 years I will be 6 times as old as I was 10 years ago. How old am I?

[tex]5 {x}^{2} - 28x + 23 = 0 \\ \\ 5 {x}^{2} - 23x - 5x + 23 = 0 \\ (5 {x}^{2} - 23x) - (5x - 23) = 0 \\ x(5x - 23) - (5x - 23) = 0 \\ (x - 1)(5x - 23) = 0 \\ \\ x - 1 = 0 \\ \\ or \\ \\ 5x - 23 = 0 \\ \\ \\ x = 1 \\ \\ or \\ \\ x = \frac{23}{5} [/tex]

ATTACHED IS THE SOLUTION

Answer:

y = -2x + 11

Step-by-step explanation:

When two lines are parallel, their gradients are the same. So the gradient of the line parallel to this equation will be -2 as well.

Now we substitute values from this point to find the rest of the equation :

y = -2x + c

3 = -2(4) + c

3 = -8 + c  

c = 11

So the equation of the line parallel will be y = -2x + 11

Hope this helped and have a good day

The solution of the inequality will be;

⇒ x > 4 or x < -10/3

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is;

|3x - 1| > 11

Now, The inequality is solved as;

|3x - 1| > 11

⇒ 3x - 1 > 11 or 3x - 1 < -11

Solve the inequality as;

⇒ 3x - 1 > 11

Add 1 we get;

⇒ 3x - 1 + 1 > 11 + 1

⇒ 3x > 12

Divide by 3;

⇒ x > 4

And, Solve the inequality as;

⇒ 3x - 1 < - 11

Add 1 we get;

⇒ 3x - 1 + 1 < - 11 + 1

⇒ 3x < -10

Divide by 3;

⇒ x < -10/3

Thus, Solution of the inequality will be;

⇒ x > 4 or x < -10/3

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Answer:

56.6 estimated= 56

7.21 estimated=7

56/7= 8

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Answer:

56.6 estimated= 56

7.21 estimated=7

56/7= 8

Step-by-step explanation:

With 19.5% annual interest on a daily basis, the finance charge due on October 14 will be $623.

So, the finance charge due:

Therefore, with 19.5% annual interest on a daily basis, the finance charge due on October 14 will be $623.

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The expression 63a–35 factored as a product with a whole number greater than 1 is 7(9a - 5)

Algebraic expressions are defined as expressions made up of variables, terms, coefficient, constants, and factors.

The are also made up of arithmetic or mathematical operations which includes;

Factorization can be defined as the mathematical method of breaking a number down into similar and smaller numbers which are the products of the original number.

Given the expression;

63a–35

To factor expression, we need to find a common product of the values

We have;

7(9a - 5)

This cannot be further factorized

Hence, the factored form is 7(9a - 5)

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Answer:

16.25 pascal

Step-by-step explanation:

pressure=force/area

pressure=650/40

pressure=16.25 pascal

Considering the definition of parallel line, the equation y= 1/3x - 2 is parallel to y=1/3x and it goes through (6,0).

A linear equation o line can be expressed in the form y = mx + b

where

Parallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope and different y-intercepts.

In this case, the line is y=1/3x

where:

If two lines are parallel if they have the same slope, the parallel line has a slope of 1/3 and has a form of: y= 1/3x + b

The line passes through the point (6, 0). Replacing in the expression for parallel line:

0= 1/3× 6 + b

0= 2 + b

0 -2 = b

-2= b

Finally, the equation of parallel line is y= 1/3x - 2.

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The population of the country in 1990 will be 274.7 million.

From the information given, the population of a country in 2015 was estimated to be 321.4 million people and this was an increase of 17% from the population in 1990.

Therefore,since let the population on 1990 be x. Therefore, this will be illustrated as:

x + (17% × x) = 321.4

x + 0.17x = 321.4

1.17x = 321.4

Divide

x = 321.4 / 1.17

x = 274.7

The population is 274.7 million.

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If you have a right triangle, then you have 2 legs and 1 hypotenuse. The hypotenuse is the longest side across from the 90 degree angle. Pythagoras came up with the theorem for right triangles that states that the sum of the squares of the 2 legs is equal to the hypotenuse squared.

By using matrix operations, the resulting matrix is [tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex] is  [tex]\left[\begin{array}{cc}3&6\\12&15\end{array}\right][/tex].

In this problem we must simplify a combination of two matrices, this can be done by using properly the fundamental operations for matrices. Matrices are algebraic constructions characterized by a number of row and a number of columns. For instance, there is a matrix with two rows and three columns:

[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\end{array}\right][/tex]

There are two fundamental operations for matrices:

Sum - The respective elements of the same row and the same column of the matrix are summed:

[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] + \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] = \left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right][/tex]

Where C(i, j) = A(i, j) + B(i, j), i is the row index and j is the column index.

Scalar mutiplication - Every element of the matrix is multiplied by a scalar:

[tex]2 \cdot \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] = \left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right][/tex]

Where B(i, j) = k · A(i, j), k is the scalar.

Now we show the complete procedure to find the simplified expression:

[tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex]                         Given

[tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] + (- 1) \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex]               Definition of subtraction

[tex]\left[\begin{array}{cc}4&8\\16&20\end{array}\right] + \left[\begin{array}{cc}- 1&- 2\\- 4&- 5\end{array}\right][/tex]                     Scalar multiplication

[tex]\left[\begin{array}{cc}3&6\\12&15\end{array}\right][/tex]                                             Sum of matrices / Result

The simplifed form of the matrix is [tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex] is  [tex]\left[\begin{array}{cc}3&6\\12&15\end{array}\right][/tex].

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we have the equation

Find out the first derivative

equate to zero the derivative, to find out the critical points

The value of cosine is zero when the angle is 90, 270 degrees (pi/2 and 3pi/2)

so

For x=pi/10

Find out the y-coordinate

Verify for x=3pi/10

Answer:

L'(0,-2)

K' (3, -2)

J' (0,3)

Step-by-step explanation: