Put the following equation of a line into slope-intercept form, simplifying all fractions. 4x−3y= −21

The rational function is of the form
f ( x ) = 50 ( x + 1 ) ( x - 2 ) / ( x - 5 ) ( x + 5 )

What is rational function equation?

A rational equation can be defined as an equation that involves at least one rational expression

A rational function is a function of the form f( x )=P( x ) / Q( x ) ,

f( x ) = P( x ) / Q( x ) , where P( x ) and Q( x ) are both polynomials.

A rational function f ( x )=P( x ) / Q( x )

f( x ) = P( x ) / Q( x ) may have a vertical asymptote

The domain is the set of all real numbers for which Q( x ) ≠ 0

Given data ,

The function has vertical asymptote at x = 5 and x = -5

So , the denominator of the fraction of rational function contains the terms (x - 5) and (x + 5)

The x intercept is at ( 2 , 0 ) and ( -1 , 0 )

The y intercept is at ( 0 , 4 )

So , the numerator of the fraction of the rational function contains the terms

( x- 2 ) and ( x + 1 )

So , the rational function is of the form

f ( x )=P( x ) / Q( x )

f ( x ) = A ( x + 1 ) ( x - 2 ) / ( x - 5 ) ( x + 5 )

Now , we have the y intercept at ( 0 , 4 )

So , f ( 0 ) = 4

Substituting the value of f ( 0 ) in the above equation , we have

4 = A ( 0 + 1 ) ( 0 - 2 ) / ( 0 - 5 ) ( 0 + 5 )

4 = A ( -2 ) / ( -25 )

4 = 2A / 25

Multiply 25 on both sides , we get

2A = 100

Divide by 2 on both sides , we get

A = 50

Therefore , the rational function becomes

f ( x ) = 50 ( x + 1 ) ( x - 2 ) / ( x - 5 ) ( x + 5 )

Hence , the rational function is of the form
f ( x ) = 50 ( x + 1 ) ( x - 2 ) / ( x - 5 ) ( x + 5 )

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Using scientific notation, the number can be expressed as 1.73 * 10⁻²

Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form. As we know, the whole numbers can be extended till infinity, but we cannot write such huge numbers on a piece of paper. Also, the numbers which are present at the millions place after the decimal needed to be represented in a simpler form. Thus, it is difficult to represent a few numbers in their expanded form. Hence, we use scientific notations.

Scientific notation helps us to represent the numbers which are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent. The exponent is positive if the number is very large and it is negative if the number is very small.

When the scientific notation of any large numbers is expressed, then we use positive exponents for base 10. For example:

20000 = 2 x 10⁴, where 4 is the positive exponent.

When the scientific notation of any small numbers is expressed, then we use negative exponents for base 10. For example:

0.0002 = 2 x 10⁻⁴, where -4 is the negative exponent.

From the above, we can now approach the problem and convert 0.0173 into scientific notation.

This will result into a negative exponent and can be expressed as

0.0173 = 1.73 * 10⁻²

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Answer:

[tex]5x-4y=-3[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

The equation of the circle C is x² + y² = 80 when it passes through the tangent points (-20, 0) and (0, 10).

Equation of circle:

Equation of the circle refer the position of a circle on a cartesian plane.

Given,

C is a circle with center the origin.

A tangent to C passes through the points (-20, 0) and (0, 10)

Here we need to find the equation of the circle C.

In order to find the equation of our line:

We have to identify the y-intercept which is (0,10).

Now, we need to find the gradient of our line which is:

Than can be calculated by,

=> (10 - 0) / (0- (-20))

=>  10/20 = 0.5

Now, the equation of our line is written as,

y = 0.5x + 10

But, here we know the center of our circle is the origin:

Which is in the following form:

=> x² + y² = r²

where r refers the radius

So, here we need the line to meet our circle at one point, we can substitute the equation for our straight line in for y.

Then the equation of the circle is written as,

=> x² + (0.5x + 10)² = r²

When we simplify it, then we get,

=> x² + (0.5x + 10)(0.5x + 10) = r²

Now, we can expand and simplify the brackets to leave us with:

=> 1.25x² + 10x + 100 = r²

=> 1.25x² + 10x + 100 - r² = 0

Here we know that this is a tangent and so it only meets the circle at one point.

So, this equation should only have one solution.

Then it can be written as,

=> b² - 4ac = 0

=> 10² - 4(1.25)(100 - r²) = 0

When we simplify this one then we get the value of

=> r² = 90

Therefore the equation of the circle is x^2 + y^2 = 80.

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Answer:

5m-19

Step-by-step explanation:

distribute

4(2m-1)-3(m+5)

8m-4-3m-15

Combine like terms

8m-3m-4-15

5m-19

Hopes this helps please mark brainliest

Answer:

5m-19

Step-by-step explanation:

thank me later :)

Steps to Solving:

1) Distribute

2) Distribute the products again

3) Subtract the numbers

4) Combine like terms

Wyatt has to drive more than 50 miles to save his earnings after spending it.

Given,

The cost for training and license = $500

The cost for gas and insurance = $4 per mile

The amount paid for the first delivery = $400 + $6 per miles

We have to find the total cost he spends and earns;

Here,

x be the distance he drives in mile

Then,

The amount he spends = $500 + $4x

The earnings of him = $400 + $6

Then,

Equate this;

500 + 4x ≥ 400 + 6x

500 - 400 ≥ 6x - 4x

100 ≥ 2x

x ≥ 100/2

x ≥ 50

That is,

Wyatt has to drive more than 50 miles to save his earnings after spending it.

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Answer:

63.75 litres

Step-by-step explanation:

the original amount of water is 100%

then a reduction of 15% = 100% - 15% = 85% of original

multiply 75 litres by 85% to obtain reduction

75 × 85%

= 75 × [tex]\frac{85}{100}[/tex] = 75 × 0.85 = 63.75

75 litres reduced by 15% = 63.75 litres

Answer:

Step-by-step explanation:

Let the number of weeks be x after which both boys have same weight.

Mike's weight after x weeks:

Tom's weight after x weeks:

Equate both expressions and solve for x:

Answer:

After 8 weeks, both boys weigh same.

Step-by-step explanation:

Forming the equation,

→ 200 - 2x = 160 + 3x

Now the value of x will be,

→ 200 - 2x = 160 + 3x

→ -2x - 3x = 160 - 200

→ -5x = -40

→ x = -40/-5

→ x = 40/5

→ [ x = 8 weeks ]

Hence, the value of x is 8.

The piecewise-defined function that gives the cost C(n) for a museum visitor who is n years old is C(n) = 0 for  0≤ n ≤ 12

Cn) = 3 for 12 ≤ n ≤ 17

C(n) = 8 for 18 ≤ n ≤ 64

C(n) = 4 for 65 ≤ n

The range of the function is {0, 3, 4, 8}.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Children under 12: free

Kids aged 12-17: $3

Adults aged 18-64: $8

Senior citizens 65 and over: $4

The function for the above can be written as,

C(n) = 0 for 0≤ n ≤ 12

Cn) = 3 for 12 ≤ n ≤ 17

C(n) = 8 for 18 ≤ n ≤ 64

C(n) = 4 for 65 ≤ n

The range of the function  C(x) is {0, 3, 4, 8}

Thus,

The piecewise-defined function that gives the cost C(n) for a museum visitor who is n years old is C(n) = 0 for  0≤ n ≤ 12

Cn) = 3 for 12 ≤ n ≤ 17

C(n) = 8 for 18 ≤ n ≤ 64

C(n) = 4 for 65 ≤ n

The range of the function is {0, 3, 4, 8}.

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Answer:

The rate of change, or slope, is 1/2.

To find the slope of a line, first, pick two points on the line and determine their coordinates. Then, determine the difference in y-coordinates of these two points (rise). After that, determine the difference in x-coordinates for these two points (run). Then you have your slope!

The set of scores has a mean of 5 and a standard deviation of 2. The score which corresponds to a z score of -2.0 is 1.

Given in the question,

Mean (m) = 5

Standard deviation σ =2

Z-score = -2

The score x,

= Z = x - m / σ

= -2 = x - 5 / 2

= -4 = x - 5

= x = 1

Standard deviation in statistics means the amount of dispersion or variations in the set of values. A lower standard deviation means the value is closer to the mean while a higher standard deviation means the value is farther away from the mean.

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The approximate difference between the maximum and minimum distances of the Earth from the Sun in thousands of kilometers, considering the graph, in thousands of kilometers, is of:

50.

The approximate difference between the maximum and minimum distances of the Earth from the Sun in thousands of kilometers, is obtained by the subtraction of the maximum value and the minimum value of the graph.

From the graph shown at the end of the answer, these parameters are presented as follows:

Hence the difference between these two values is obtained as follows:

25,000 - (-25,000) = 25,000 + 25,000 = 2 x 25,000 = 50,000 km.

In thousands of km, the difference is:

50000/1000 = 50.

The graph is given by the image shown at the end of the answer.

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Answer: X = 1.12

Y = 1.75

Step-by-step explanation:

8/10 = 5/X +5

5(10) = 8(X + 5)

CROSS MULTIPLY AND DIVIDE

50 - 40 = 8X + 40 -40

10 = 8X

10/8 = 8X/8

1.25 = X

8/10 = 7/7 +Y

CRPSS MULTIPLY AND DIVIDE

7(10) = 8(7 +Y)

70 = 56 + 8Y

70 -56 = 56 -56 + 8Y

14 = 8Y

14/8 = 8Y/8

1,75 = Y

We can write z = x + y using thee Exterior Angle Property of a Triangle

What is Exterior Angle Property of a triangle?

If a triangle side is constructed, the outside angle formed is equal to the sum of the two inside opposing angles.

Solution:

Using the Exterior Angle Property of a Triangle it can be observed that z = x + y

Sum of angles in a triangle is 180 degrees

w + x + y = 180 degree -----(1)

Also, using linear angle sum property

w + z = 180 degree -----(2)

From equation 1 and 2

w + x + y = w + z

Therefore, x + y = z

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The height is 31.51 inches.

From the question, we have

Let height= h

width = h+6

diagonal = 49 inches

Using Pythagoras Theorem

49²  = h²  + (h+6)²

2401 = h² +h² +36+12h

2401 = 2h² +36+12h

2h²+12h-2365 = 0

Solving this, we get

h=−3+1/2√4766

h=31.51 inches

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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The numerical expression to model the situation when Kristen read her book is 2 + 1.

A numerical expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, Kristen read her book for 2 hours after school, then she read for another hour before she went to sleep. The expression will be:

= 2 + 1

= 3

She read for 3 hours.

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The angles x of the right angle triangle is 36.87 degrees.

A right angle triangle is a triangle that has one angle as 90 degrees. The angles of a right angle triangle can be found using trigonometric ratios.

Therefore, let's find the angle M(x)

sin x = opposite / hypotenuse

where

Therefore,

sin x = 6 / 10

sin x = 0.6

x = sin⁻¹ 0.6

x = 36.8698976458

x = 36.87 degrees.

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The rule that describes the function is (c) Output = (0.5)(Input) + 1.5

The points on the coordinate plane are given as

(negative 1, 1), (1, 2), (3, 3), (5, 4)

Express as numbers

So, we have

(-1, 1), (1, 2), (3, 3), (5, 4)

Divide the input values by 2

So, we have

0.5(Input) => (-1/2, 1), (1/2, 2), (3/2, 3), (5/2, 4)

Add 1.5 to the input values

So, we have

0.5(Input) + 1.5 => (1, 1), (2, 2), (3, 3), (4, 4)

So, we have

Output = 0.5(Input) + 1.5

Hence, the equation is (c)Output = 0.5(Input) + 1.5

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Answer:

12

Step-by-step explanation:

(5+7)/7=12/7.

Green box = 12.

The market price of the watch after a discount of 10% is  $3500   .

In the question ,

it is given that

the price at which the trader sold the wrist watch = $3150

the amount of discount given by trader = 10% ,

we need to find the market price of the watch ,

let the market price of the watch be "x" .

so , the formula that can be used to calculate the market price is

selling price = market price - (discount percent)×(market price)

Substituting the values , we get

3150 = x - 10% of x

3150 = x - 0.10x          ....because 10% = 0.10

(1 - 0.10)x = 3150

0.90x = 3150

Dividing both sides by 0.90 , we get

x = 3150/0.90

x = 3500

market price is $3500  .

Therefore , The market price of the watch after a discount of 10% is  $3500   .

The given question is incomplete , the complete question is

A trader sold a wrist watch for $3150 after giving a 10% discount. Find the marked price of the watch ?

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Answer:

Although square roots are generally taken to be positive, a square root can be negative as a negative number multiplied by a negative number is always positive.

Step-by-step explanation:

In general, when someone is asking for a square root, they are seeking the positive value. This is called the principal square root. However, square roots can also be negative. Thus, the number -6 can be a square root of the number 36, just not a principal square root. So the negative square root is the same number as the principal square root, but the negative version. The negative square "squared" will give the same positive result as the principal square root, for instance,

3⋅3=9 and −3⋅−3=9.

Answer: The correct answer is 0. Negative numbers don't really have any square roots since a square cannot be negative it can only be positive or a 0.

Step-by-step explanation: I hope this helps!

Sides XY and YZ are both equal to √45 units, therefore, triangle XYZ is an isosceles triangle.

If a triangle has two side lengths that are equal to each other, the triangle is called an isosceles triangle. Therefore, two of the sides of an isosceles triangle must be equal.

Given the vertices of triangle XYZ as:

X(0, 2)

Y(3, 8)

Z(6, 2).

Find the length of each side using the distance formula, [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].

XY = √[(3−0)² + (8−2)²]

XY = √45

XZ = √[(6−0)² + (2−2)²]

XZ = √36

XZ = 6

YZ = √[(6−3)² + (2−8)²]

YZ = √45

The triangle has two equal sides YZ and XY, therefore it is an isosceles triangle.

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Answer:

r=-40

Step-by-step explanation:

[tex]\frac{-0.4r}{-0.4} = \frac{16}{-0.4}[/tex]

r=-40

The inequality using variables x and y which satisfy the points are; y>-3x+3.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

Given that the points (2,5) and (-3,-5) lie on the boundary line.

The system of inequality is given by:

y>-3x+3-

Now, the point that will lie in the solution set to the following system of inequality are the point that satisfies the inequality.

a)  (6, 5)

when x=6 and y= 5

then we have:

y>-3x+3

6 > -3×5 + 3

6>- 15+3

5 > -12

This means that the point will lie in the solution set.

Also, (-2, -3) when x= -2 and y= -3

then we have:

5 > -3×(-2) + 3

5> 6 + 3

5> 9

Hence, the inequality using variables x and y which satisfy the points are; y>-3x+3.

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Answer:

Step-by-step explanation:

Ok: It me again!

1. Since Greg earned 53$ for washing cars, he said he earned twice as much than mowing as a equation that would be:

2*m=53$ he made in total

So:

2. Answer: 2m=53$

The measure of angle (12x + 18)° is 102 degrees and the measure of angle (8x +10) ° is 66 degrees.

An equation is an expression that shows the relationship between two or more numbers and variables.

We have been given the angles as;

(12x + 18)° and (8x +10)

We need to solve the value of x by an alternate interior angle;

(12x + 18)° = (8x +10)

Solving;

(12x - 18)° = (8x +10)

(12x - 8x)° = (18 +10)

4x = 28

x = 7

The value of x is 7.

Thus, (12x + 18)° = 102 degree

(8x +10) = 66 degree

Hence, the measure of angle (12x + 18)° is 102 degrees and the measure of angle (8x +10) ° is 66 degrees.

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The measure of angles are

The length of the hypotenuse of the right triangle = 11 inches

The length of the one leg = 10 inches

Then the length of the other leg is the square root of the sum of the hypotenuse square and one leg square

Then the equation will be

The length of the other leg = [tex]\sqrt{11^2-10^2}[/tex]

= [tex]\sqrt{121-100}[/tex]

= 4.58 inches

Therefore AC = 11 inches

AB = 10 inches

BC = 4.58 inches

The angle B = 90 degrees

Consider the angle A

cos θ = Adjacent side / hypotenuse

cos θ = 10 /11

θ = 24.61 degrees

Consider the angle C

cos θ = Adjacent side / Hypotenuse

cos θ = 4.58 / 11

θ = 65.39 degrees

Hence, the measure of angles are

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The length of the third side is 9

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle) in familiar algebraic notation, a2 + b2 = c2

Given that

By using Pythagoras' theorem.

A^2+B^2=C^2

13 is c because it is the hypotenuse and across from the right angle

a is unknown and b is 15

A^2+12^2=15^2

A^2 +144 = 225

A^2 = 225- 144

A^2= 81

A = 9

Therefore the length of the third side is 9

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