What characteristics of parallel lines and perpendicular lines create different requirements?.

An equation with infinite solutions has both sides equal.

We know that a solution of an equation is a value that satisfies given equation.

As we know the system of equations has infinitely many solutions if the system of lines are coincident, and if they have the same y-intercept.

In some equations, any value for the variable makes the equation true. This means, an equation has infinitely many solutions.

Consider the equation 5x + 13 = 3x + 13 + 2x

5x + 12 = 5x + 12             .....(combine like terms)

13 = 13                           ........(subtrsct 5x from each side)

As we know 13 = 13 is always true.

To check that above equation has an infinite number of solutions, we try substituting some different values for x

For x = 3

5(3) + 13 = 3(3) + 13 + 2(3)

15 + 13 = 9 + 13 + 6

28 = 28

The statement 28 = 28 is always true. So, x = 3 is a solution.

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Answer:

$182.90

Step-by-step explanation:

Find the cost per kg. To do so, divide the total cost, with the amount of kg that is bought:

(Total Cost/Total weight) = (cost/unit):

[tex]\frac{106.20}{18} = 5.9\\\\[/tex]

$5.9 per kg of apple.

~

Next, solve for the amount that 31 kg of apples would cost. Multiply the unit cost with the amount of kg of apples purchased:

(Total weight of apples x Cost per kg for apples) = Total cost:

[tex]31 * $5.9 = Total Cost\\Total Cost = 182.9[/tex]

$182.90 is your answer.

~

The algebraic expression for the a number that has been multiplied by three is: x + 3*x. In this statement, x stands for the number, while 3*x, or 3x, stands for the number times three.

An algebraic expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division. Algebraic expressions can be evaluated for specific values of the variables in order to find a numerical result.

A mathematical statement with variables, constants, coefficients, or algebraic operations is known as an algebraic expression. A good example of an algebraic expression is 5x2+6xyc. Algebraic expression do not utilize equal signs, in contrast to algebraic equations.

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Longitude and latitude are geographic coordinates that indicate a location on the Earth's surface. They are used to locate a specific point on a map or globe.

Longitude is the measure of a location's east-west position on the Earth's surface. It is measured in degrees east or west of the Prime Meridian, which is an imaginary line that runs from the North Pole to the South Pole through the Royal Observatory in Greenwich, England. Longitude values range from -180 degrees (West) to 180 degrees (East).

Latitude, on the other hand, is the measure of a location's north-south position on the Earth's surface. It is measured in degrees north or south of the Equator, which is an imaginary line that runs around the Earth's middle, dividing it into the Northern and Southern Hemispheres. Latitude values range from -90 degrees (South) to 90 degrees (North).

The diagram below illustrates how longitude and latitude work together to pinpoint a location on the Earth's surface. The intersection of the red line (longitude) and the blue line (latitude) represents the specific location.

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According to the solving  the average of this new list of numbers is 60.

The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

The sum of the original list's four numbers, whose average is 90, is as follows:

4 × 85 = 232

Since 80 is the fourth number inside the original list, the first three numbers in the original list add up to:

232 − 105 = 127

The total of these updated first 3 numbers is also: if the first 3 numbers inside the new list are the same as those in the old list:

127

The total of the first four numbers with in new list, if the fourth number is 96, is:

127 + 115 = 242

As a result, the new list of four numbers' average is:

242 ÷ 4 = 60

According to the solving  the average of this new list of numbers is 60.

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Two numbers are: - 36.65 and 0.655. This can be solved by using the concept of equation.

An equation is an algebraic expression that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. For instance, the equation 7x + 14 = 35 consists of the two equations 7x + 14 and 35, which are separated by the 'equal' sign. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

By deleting parenthesis and grouping like words, each side of the equation may be made simpler. The changeable item on one side of the equation can be separated using addition or subtraction. To determine the variables, apply divisions or multiplication.

Given that,

two numbers multiply to -24 and add 36.

Let, two numbers are: x and y

Now, xy = -24 ............. (1)

or, y = - 24/x

x + y = 36 .............. (2)

Next, put y = - 24/x in equation no. (2) we get -

x + (-24/x) = 36

or, x² - 24 = 36x

or, x² - 36x - 24 = 0

or, x = -36.65

so, y = (-24/x) = (-24/ - 36.65)

y = 0.655

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Answer:

[tex] \sf \: 34 \: isosceles \: triangle \: - - - - - - - - - - - - - - - - - - - - - - - - [/tex]

Step-by-step explanation:

[tex]b = 144 - 2a < 2a [/tex]

So, that

[tex]a > 36[/tex]

and 2a < 144 so that

[tex]a < 72[/tex]

since a = b implies a = 48

{37,38,39.......71}/{48}

There are 71-37 = 34 isosceles triangle

The range of

The logarithmic function f(x) = log_b x is a decreasing function if and only if b > 1.

To see why, consider that for any positive real number x, log_b x increases as x increases. This can be seen by using the definition of logarithms: log_b x is the power to which b must be raised to produce x. As x increases, the power to which b must be raised to produce x must also increase, so log_b x must increase as well.

Therefore, if b > 1, then log_b x is a strictly decreasing function, because as x increases, the power to which b must be raised to produce x increases at an increasing rate, so log_b x decreases at an increasing rate. On the other hand, if 0 < b < 1, then log_b x is a strictly increasing function, because as x increases, the power to which b must be raised to produce x increases at a decreasing rate, so log_b x increases at a decreasing rate.

It is important to note that for b = 1, the logarithmic function is undefined, as log_1 x is not defined for any positive real number x.

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Answer:

The closest estimate to the total cost of Mr. Johnson's turkey (before taxes) is $54.67.

Step-by-step explanation:

You can calculate this by multiplying the weight of the turkey (18 3/4 pounds) by the price per pound ($2.95).

(18 3/4) * ($2.95) = 54.67

Limits are the rate of change of a function and also used in many other concepts such as continuity, differentiability and many other concepts in calculus.

In calculus, limits are used to study the behavior of a function as the input, or independent variable, approaches a specific value. The limit of a function at a particular point, say x = a, is defined as the value that the function approaches as the independent variable x gets arbitrarily close to a, but not necessarily equal to it.

The notation for a limit is usually represented as:

lim x->a f(x) = L

Which means as x approaches a, f(x) approaches L.

Properties of limits include:

1) The limit of a constant is equal to the constant.

2) The limit of a sum, difference, or product of functions is equal to the sum, difference, or product of their limits, respectively.

3) The limit of a function at a point is unique, if it exists.

Limits are an essential concept in calculus as they are used to define the derivative, which is the rate of change of a function and also used in many other concepts such as continuity, differentiability and many other concepts in calculus.

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Answer:

Step-by-step explanation:

The car is moving at 1.36 miles per hour. It will travel 4.09 miles in 3 hours. If you drive like this, I would suggest speeding up.

The percentage of the people that surveyed shop at a local grocery store is 57%.

        The number of people who buy at the local grocery store = 43

        The percentage  [tex]=\frac{43}{76} \\\\[/tex]

                                     = 0.5657 * 100%

                                     = 57 %

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Step-by-step explanation:

the absolute value always generates the positive value of the argument, no matter what the sign of the argument is.

+ stays +

- turns to +

so, we actually have

-3×2 + 4×5 = -6 + 20 = 14

The equation of the line in slope intercept form is  y = 4x + 5.

The equation of line can be represented in slope intercept form as follows:

y = mx + b

where

A line passes through the points (0, 5) and (1,9).  The slope of the line can be found as follows;

m = slope = 9 - 5 / 1 - 0

m = 4 / 1

m = 4

Hence, let' find the y-intercept of the equation using (0, 5).

y = 4x + b

5 = 4(0) + b

b = 5

Therefore, the equation of the line is y = 4x + 5.

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Answer:

Domain: x ≥ 4

Range: y ≥ 6

Step-by-step explanation:

The percent error is a measure of how accurate a measurement is. It is calculated by taking the difference between the measured value and the true value, dividing that difference by the true value, and then multiplying by 100 to get a percentage.

In this case, the true value of the baseball's speed is 4.2 miles per hour and the measured value is 5 miles per hour. To find the percent error:

(5 - 4.2) / 4.2 * 100 = 0.190476 * 100 = 19.0476%

So the percent error in this measurement is 19.0476%. This means that the measurement was off by 19.0476% from the true value.

Alternatively, we can round it to 19% for ease of interpretation

Therefore, the percent error in this measurement is 19%.

If one is the sole factor that connects a fraction's numerator and denominator, then that fraction is said to be in its simplest form.The mixed fraction is 33*3/4

As an illustration, the fraction 89 has only one common component between the digits 8 and 9, which is 1.Since fractions always work or can be calculated when they are in their simplest form, we simplify them.When two numbers are represented together, they are called mixed numbers.

Based on the given conditions, formulate:45 / 1/1/3

Convert the expression into a fraction: 45/1/1+1/1

Expand the fraction to get the least common demominator: 45/ 3/1*3+1/3

Calculate the product or quotient:45/3/3 +1/3

Write the numerators over common denominator:45/3+1/3

Calculate the sum or difference:45/4/3

Divide a fraction by multiplying its reciprocal:45* 3/4

Write as a single fraction:45* 3/4

Calculate the product or quotient:135/4

Convert to mixed fraction: 33*3/4

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The value of S, i.e., prependicular length in right angled triangle is twelve units.

We have, a right angled triangle ABC as see in above figure. From the above figure, we get the following information,

The base length of right angled ∆ ABC, BC = 9 units

The perpendicular length/height of

∆ ABC , AC = S units

The hypotenuse length of ∆ ABC, AB

= 25 units

We have to calculate the value of S i.e., the prependicular length. Using the Pythagoras threoem to solve the value of S,

(hypotenuse)²= (base)² + (prependicular)²

=> AB² = BC² + AC²

=> 15² = 9² + S²

=> 225 = 81 + S²

=> 225 - 81 = S²

=> S² = 144

=> S = ±√144

=> S = ± 12

but S, is represent the length and it's value is always positive. Therefore, the required value of S is 12 units.

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Complete question:

For the above figure, What is the value of S units?.

Using properties of Similar triangles, The measure of QP is 14.49.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

Similar triangles differ in size but have the same shape. Corresponding angles are identical in similar triangles. Similar triangles have corresponding sides that have the same ratio. The ratio of the square of any two of their corresponding sides to any identical triangle's area is the same.

Given two triangles,

ΔPQR and ΔPNO are Similar,

So, their sides are present in the ratio -

NO / QR = NP / PQ

We are given, QR = 10

NP = 21

On putting the values in the NO / QR = NP / PQ equation,

⇒ NO / 10 = 21 / QP

As NO = QP (given)

We can write as -

QP / 10 = 21 / QP

⇒ QP²  =  10 × 21

⇒ QP²  = 210

⇒ QP = 14.49

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Answer:

  2x -1

Step-by-step explanation:

You want to show that (3x+4) is a factor of f(x) = 6x^2+5x-4, and you want the other factor.

When the product, f(x), is divided by one of its factors, the remainder will be zero and the quotient will be the other factor.

The attached long division shows the remainder (bottom line) is zero, and the quotient (top line) is (2x -1), the other factor.

The other factor is (2x -1).

Total thirty-nine months will be take by Johnson family to pay off the balance, $10,000.00.

The monthly payment is the amount paid per month to pay off the principle in the time period of the loan. If your rate is r%, divide r/100 by 12 to calculate your monthly interest rate. Formula for monthly payment is, M = Pr(1+r)ⁿ/{(1+r)ⁿ - 1 }

where, P --> principle

r--> rate of interest in months

n --> number of periods (in months )

In this problem, Johnson family bought the furniture and appliances for a new house that is principle, P = $10,000

Rate of interest, R = 15%

In terms of months, R = 0.15/12

= 0.0125 per month

Monthly payment, M = $325.00

Plugging all known values in above formula we get, $325.00 = {$10,000 × 0.0125(1 + 0.0125)ⁿ}/{(1+ 0.0124)ⁿ - 1 }

=> 325 = 125(1.0125)ⁿ/{(1.0125)ⁿ - 1}

=> 325 {(1.0125)ⁿ - 1} = 125(1.0125)ⁿ

=> 325(1.0125)ⁿ - 325 = 125(1.0125)ⁿ

=> 325(1.0125)ⁿ - 125(1.0125)ⁿ = 325

=> 200 (1.0125)ⁿ = 325

=> (1.0125)ⁿ = 325/200 = 13/8 = 1.6250

Taking natural logarithm both sides

=> ln(1.0125)ⁿ = ln (1.6250)

=> n ln(1.0125) = ln (1.6250) = 0.4855

=> n×0.0124 = 0.4855

=> n = 0.4855/0.0124 = 39.153 ~ 39

Hence, required months are 39.

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The gradient is −3 and the y-intercept is 6.

The gradient of a function is defined to be a vector field. Generally, the gradient of a function can be found by applying the vector operator to the scalar function. (∇f (x, y)).

This kind of vector field is known as the gradient vector field. Now, let us learn the gradient of a function in the two dimensions and three dimensions.

The gradient should take a scalar function (i.e., f(x, y) and produces the vector function (∇ f).

The vector ∇f(x, y) should lie in the plane.

The gradient of a function can be found by applying the vector operator to the scalar function. I.e., ∇f (x, y).

y+3x=6

Rearrange the equation to the slope-intercept form,

y=mx +b,

where ,

m is the slope and b is the y-intercept.

Subtract 3x from both sides.

y=−3x+6

The gradient is −3 and the y-intercept is 6.

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The area on the map in square centimetres is 64 cm².

The scale of the plan is 1:20, meaning that for every 1 unit of measurement on the plan, the corresponding measurement on the actual boat is 20 units.

If the actual area of the base of the boat is 0.64 m², then the area on the map will be:

(0.64 m²) * (1/20)² = 0.0064 m²

To convert this to square centimetres, we multiply by 10,000 (since 1 m² = 10,000 cm²):

0.0064 m² * 10,000 = 64 cm²

Therefore, the area on the map in square centimetres is 64 cm².

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Answer:

16 cm²

Step-by-step explanation:

The scale of the map indicates the ratio of the linear dimensions of the map to the actual ones. Then the area of the map will correlate with the actual one, as with a scale square:

S map = S actual * (1:20)²

S map = 0.64 m² * 1/400

S map = 0.0016 m²

But we know that 1 meter contains 100 cm, so 1 m² = 10,000 cm². Then:

0.0016 m² * 10000 = 16 cm²

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The number of people in the waiting room is 102.

A fraction is a quantity that is a non-integer. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below. An example of a fraction is 2/3.  

The first step is to determine the total number of people in the waiting room. To do this, divide 136 by 2/3.

Number of people in the waiting room = 136 ÷ 2/3

= 136 x 3/2 = 204

Number of people in the waiting room if it is half full = total number of people in the waiting room x 1/2

204 x 1/2 = 102

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A. The answer for part A is $460.

B. The answer for part B is 11,166.67 dollars

What are the Profit and Loss?

A. To find the commission earned on the first $4,000 in sales, we can multiply $4,000 by 4% which is (4,000 * 0.04) = 160 dollars

To find the commission earned on the remaining amount of sales above $4,000, we can subtract $4,000 from $9,000 to find the amount of sales above $4,000 which is (9,000 - 4,000) = 5,000

then we can multiply $5,000 by 6% which is (5,000 * 0.06) = 300 dollars

So the total commission earned is 160 + 300 = 460 dollars.

So the answer for part A is $460.

B. To find the amount of money in sales, we can use the commission formula: commission = (sales * rate)

The commission rate for sales above $4,000 is 6% and the commission earned is $670.

So, we can set up the equation as : 670 = (sales * 0.06)

We can solve this equation to find the value of sales by dividing both sides of the equation by 0.06

sales = 670 / 0.06

sales = 11,166.67

So the answer for part B is 11,166.67 dollars.

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A polynomial of degree 2 is called a quadratic equation. It is a type of equation that can be solved by using the quadratic formula, which looks like this:

where x is the unknown variable and y is the solution to the equation. The quadratic equation can be written in several different ways, but all of them involve solving for y using equations similar to the one above.

Polynomials of degree 2 are common in everyday life, and are used to solve problems such as solving for the slope or height of a line, determining the points at which two lines intersect, or finding the distance between two points.

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