how to solve simplify rational expressions

An unfair comparison between two numbers or other mathematical expressions is referred to as an inequality. It is most frequently used when comparing the sizes of two numbers on a number line. The attachment contains the graph for each inequality or equation.

A graph is a graphical representation of statistical data or the functional relationship of variables. Graphs can highlight broad trends in the quantitative behaviour of data, which is useful for forecasting. They can, however, be inaccurate and occasionally deceptive as mere approximations.

Most graphs have two axes: one for independent variables and one for dependent variables. A broken-line graph is the most common type of graph, with time serving as the independent variable.

16. 2y – 4x < 8

=  2y < 4x + 8

= y < 2x + 4

17. -4y > -x + 12

= y > x/4 + -3

18. | x + 3 |= y

y = | x + 3 |

19.  |2x – 6| + 2 = y

y = |2x – 6| + 2

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Answer: y = 6x + 20, or E = 6t + 20

Step-by-step explanation:

Taking two points on the graph, (10, 80) and (30, 200), you can find the slope ("E") with the equation (y2-y1)/(x2-x1), which when plugged into the formula would be (200-80)/(30-10) = 120/20 = 6. To get your "t", you would plug this back into the formula y=mx+b along with any point on the graph, which would be:

80 = 6(10) + b

80 = 60 + b

b = 20

So the final equation should be y = 6x + 20

Katherine need to invest $432.4 for the value of the account to reach $960 in 16 years.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Katherine is going to invest in an account paying an interest rate of 5.8% compounded monthly.

We know that;

⇒ [tex]A = P e^r^t\\[/tex]

Let the invest amount = x

Here, The amount = $960

And, The time = 16 years

And, Rate = 5.8% = 0.058

So, We can formulate;

⇒ [tex]A = P e^r^t\\[/tex]

⇒ [tex]960 = P * e^{0.058 * 16} \\[/tex]

⇒ 960 = P × 2.22

⇒ P = 960 / 2.22

⇒ P = $432.43

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The sides 7 cm, 24 cm and 25 cm can form a right-angled triangle. The Pythagorean theorem can be used to verify this.

From Pythagorean theorem, it can be said that, the square of hypotenuse side is equal to the sum of other two sides of a right angles triangle.

Let AB, CA and BC be the sides of a right triangle. CA is the hypotenuse side, AB and BC are the base and height sides of the right triangle. Then the equation, can be written as,

CA² = AB² + BC²

Now, let us check this rule for the above given sides of the triangle.

Longest side² = Sum of squares of other two sides

25² = 24² + 7²

625 = 625

Thus, the sides 7 cm, 24 cm and 25 cm can form a right-angled triangle.

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Answer:

-1/3

Slope is a measure of steepness of a line. In Algebra 1, It is how much the y-value changes when the x-value increases by 1.

Slope Formula:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Plug in your points accordingly to find the slope.

What is the slope of a line that goes through the points (-5,4) and (-2-5)

1) To solve, first find your y-values and x-values. y-values are the second value in the coordinate form and a measure of height on a 2D coordinate plane. x-values are the first value in coordinate form and a measure of horizontal distance on a 2D coordinate plane.

(x,y)

y-values: -4, -5
x-values: -5, -2

2) Plug into the formula listed above.

[tex]\frac{-5-(-4)}{-2-(-5)}[/tex]

Simplify.

[tex]-\frac{1}3}[/tex]

Your slope is -1/3.

Answer:

-1/3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-5-(-4))/(-2-(-5))

m=(-5+4)/(-2+5)

m=-1/3

Take the reciprocal of the second fraction, and Multiply it by the first fraction. later reduce the resultant fraction to its lowest terms.

The quotient of a fraction is the whole number that is obtained when we simplify the fraction. If the simplification of a fraction is not a whole number, the quotient is the decimal form of the fraction.

The quotient can also be the solution to a division problem involving two fractions. That division is a method of sharing equally and putting into equal groups. We divide a whole number by the divisor to get the quotient.

The reciprocal of a fraction is a simple way of interchanging the fraction's numerator and denominator.

Consider an example:

2 3/7=3 *2/7 =3 + 2/7

3 is the quotient

2 is the remainder

7 is the divisor

23 is the dividend

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A mirror equation is an equation relating object distance and image distance with focal length. It is also known as the mirror formula.

1/f= 1/u + 1/v.

u is the Object distance

v is the Image distance

f is the Focal Length given by f=R/2.

R is the radius of curvature of the spherical mirror

The above formula is valid under all situations for all types of concave and convex and for all object positions.

Linear magnification is defined as the ratio of the image size to the object size;

Magnification= Image size/ Object size.

it can be expressed as the ratio of the distance of the image to the distance v of object u from the mirror. Magnification has no unit.

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Answer:

y-intercept: -2

Step-by-step explanation:

The Y-intercept is when x = 0. So, to find the y-intercept we just need to put in 0 for x and get the answer of -2. So, the y-intercept is located at (0, -2)

Answer:

Colin's reasoning makes sense. If Marge subtracted 20 from both sides of an equation, the equation she was solving could have been 6 + t = 20. On the left side of the equation, 6 + t would be simplified to t. On the right side of the equation, 20 would be subtracted from 20, resulting in a value of 0. So, the equation t = 0 would be the result of Marge's actions.

Answer: Colin's reasoning makes sense. If Marge subtracted 20 from both sides of an equation, the equation she was solving could have been 6 + t = 20. On the left side of the equation, 6 + t would be simplified to t. On the right side of the equation, 20 would be subtracted from 20, resulting in a value of 0. So, the equation t = 0 would be the result of Marge's actions.

Step-by-step explanation:

As an example, consider 3x + 5 = 3x - 5. This equation has no solution. There is no value that will ever satisfy this type of equation.

What is  infinite solution?

Both sides of an infinite solution are equal. As an illustration, 6x + 2y - 8 = 12x + 4y - 16 Using a formula or method for infinite solutions, you can simplify the equation and make both sides to equal one another, making it an infinite solution. The concept of infinite connotes boundlessness or infinity. Typically, it is denoted by the symbol "".

What is an infinite number?

There are an unlimited number of numbers in a series. a collection of infinitely many natural integers, as an illustration. The initial value 0, and the initial value infinite, are represented by the logarithms and +, respectively.

                   The original values 0 and infinity are similarly treated when we consider both of the conceivable values and + as a single infinity.

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The cost of tip will he leave for the valet person is, $5.25.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Your dad decides to leave a tip of 15% to the valet person.

And, The cost of parking is $35.

Here, The cost of parking is $35.

Hence, The cost of tip for the valet person = 15% of $35

                                                                  = 15/100 × $35

                                                                  = $5.25

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Answer:

27

Step-by-step explanation:

If 9 kilometers is 1/3, the total length of her drive would be 9: 1/3=9•3/1=27

Answer:

27

Step-by-step explanation:

if 9 kilometers is 1/3 of her journey then you should take 9 times 3 to find the total distance she needs to travel which is 27 kilometers

The sum of the polynomials (4x^2+3x-1) + (x^2-5x-6) is 5x^2-2x-7

we will add the coefficients of the same degree terms.

(4x^2+3x-1) + (x^2-5x-6) = (4x^2+x^2) + (3x-5x) + (-1-6) = 5x^2-2x-7

Therefore, the sum of the polynomials (4x^2+3x-1) + (x^2-5x-6)  is 5x^2-2x-7

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Answer:

Step-by-step explanation:

A - Since there are parenthesis on 30 and 10, you would want to find the difference between 30 and 10 first, and then multiply it by 5, hence getting you 5 times the difference of 30 and 10.

The distance from the base of the ladder to the bottom of the house is 6 feet and the distance between the top of the ladder and the ground is 8 feet.

Length of the ladder = 10 ft

Let the distance between the base of the ladder and the bottom of the house = x

Then the distance between the top of the ladder and the ground = (x+2)

x and x+2 distance are perpendicular to each other and making a right-angle triangle with the ladder of length 10-ft.

By applying pythagoras theorem,

(10)² = (x)² + (x+2)²

100 = x²+x²+4+4x

2x² + 4x - 96=0

x² + 2x - 48 = 0

x² + (8x-6x) - 48=0

x(x+8) - 6(x+8)

(x-6)(x+8) = 0

x = 6, x = -8

Taking the positive value

x= 6 feet, and (x+2) = 8 feet

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Answer: -1/4

Step-by-step explanation:

Answer: the answer to your question I believe is d= -1/4 = -0.25

Answer:

A, B, and D

Step-by-step explanation:

Substitute all the coordinates into the equation. (x, y)

3(-2) - (-7) = 1

-6 - (-7) = 1

1 = 1

3(-1) - (-4) =1

-3 - (-4) = 1

1 = 1

3(0) - (1) = 1

0 - (1) = 1

-1 does not equal 1

3(3) - (8) = 1

9 - (8) = 1

1 = 1

Answer:

19

Step-by-step explanation:

if x=5

y=x^2 - 6

y= 5^2 - 6

y= 25- 6

y=19

Since , solution of percentage problem is Kayden has a collection of 120 coins, the number of coins that represent the 5% of his collection is 6.

A percentage is a way to express a number as a fraction of 100.To calculate percentage increase, subtract the original value from the new value and divide by the original value. To calculate percentage decrease, subtract the new value from the original value and divide by the original value.

Here,

As given by the question , the total number ko coins Kayden has in his collection is , 120 coins.

To know how many of his coins represent 5%, we can calculate ,

5% of 120 coins

=  5/100 * 12

= 6 coins

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Using Trigonometric Identities, The value of y equals 20.36.

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence. These are identities that, geometrically speaking, involve certain functions of one or more angles. They are not to be confused with triangle identities, which are identities that may involve angles but may also involve side lengths or other lengths of a triangle.

These identities are in use when trigonometric function-based expressions need to be made simpler. The integration of non-trigonometric functions is a crucial application; a typical method is employing the substitution rule with a trigonometric function first, and then simplifying the resulting integral with a trigonometric identity.

Using Trigonometric ratios,

Sin θ = perpendicular / hypotenuse

Sin 69 = 19 / y

0.933 = 19 / y

y = 19 / 0.933

y = 20.36

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If the last three digits of a number are divisible by 8, then the number is completely divisible by 8. So we can check the last three digits of a number to know whether they are a multiple of 8.

A multiple of 8 is a number that can be evenly divided by 8 without a remainder. To determine if a number is a multiple of 8, you can divide it by 8 and check if the quotient is an integer (a whole number with no remainder).

For example, to check if the number 96 is a multiple of 8, you can divide 96 by 8 and the quotient is 12, which is an integer, so 96 is a multiple of 8.

Another way to check if a number is a multiple of 8 is to check if the last three digits of the number are 000 or divisible by 8. This is because 8 is a power of 2 (2^3=8), and any number that is a multiple of 8 will be divisible by 2^3, which means it must have 3 trailing zeroes.

A more general method to check if a number is a multiple of any number is by using the modulo operator, which returns the remainder of a division. If x is a multiple of y, then x mod y = 0. Therefore, you can use x % 8 == 0 to check if x is a multiple of 8.

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21 days it will take before both bloggers have the same number of followers

Two or more expressions with an Equal sign is called as Equation.

Given a blogger has 460 followers on his social media accounts, but is losing followers at a rate of 6 people per day based on his comments.

y=460-6d

Where d represents the number of days

Another blogger has 128 followers on her social media accounts and gains an average of 10 new followers per day.

y=128+10d

We need to find equation to find the number of days it will take before both bloggers have the same number of followers

460-6d=128+10d

Add 6d on both sides

460=128+16d

Subtract 128 on both sides

460-128=16d

332=16d

d=20.75=21

Hence, 21 days  it will take before both bloggers have the same number of followers

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EZ Fitness shows a monthly cost of $20 dollars per month. Buff Up Gym membership shows a monthly membership cost of $25 dollars per month.

The slope between 2 coordinates can be found using the formula;

Slope = (y₂ - y₁)/(x₂ - x₁)

For the Buff Up Gym, we will pick the coordinates;

(2, 50) and (4, 100)

Thus;

Slope = (100 - 50)/(4 - 2)

Slope = $25 per month

For the function table for  EZ Fitness, we pick two coordinates; (1, 20) and (2, 40). The slope is;

Slope = (40 - 20)/(2 - 1)

Slope = $20 per month

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The (g·g)(t) of the function is (g·g)(t) = 16t - 15

A function is an expression, rule, or law that defines a relationship between an independent variable and a dependent variable

Since g(t) = -4t + 5

What (g·g)(t) means is that you should replace t with the value of g(t)  (i.e. -4t + 5) in the same equation. That is:

(g·g)(t) = g(g(t))

(g·g)(t) = -4(-4t + 5) + 5

(g·g)(t) = 16t - 20 + 5

(g·g)(t) = 16t - 15

Thus, the value of g·g)(t) is 16t - 15

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Answer:

12 inches

Step-by-step explanation:

1 foot = 12 inches

(12 inches)/(1 foot) = 1

1 foot × (12 inches)/(1 foot) = 12 inches

Gill walks for a minute away from home for several minutes, and then turns toward home and walks for a few minutes. He stops when he knows and they talk for a few minutes. Then he starts walking away from home.

Hence option C is correct.

What is a graph?

In discrete mathematics, and more specifically in graph theory, a graph is a structure consisting of a set of objects, some of which are "related" in some way. The items correspond to mathematical abstractions known as vertices, and each pair of connected vertices is known as an edge.

Given graph represents the y-axis is the distance from home and the x-axis is the number of minutes.

There are 4 straight lines in the graph

The first line is increasingly and represents Gill walking away from home.

The second line is decreasing and represents Gill walking toward home.

The third line is parallel to x-axis. It means he stands a point for a few minutes.

The fourth line is increasingly and represents Gill walking away from home.

Hence option C is the correct option.

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The mistake that Yuri has made is that : he divided the equation by n instaed of dividing the equation by n-1

While finding the standard deviation of a group of scores, the formula has the denominator as n - 1

where n is the total number of values in the data set.

the data set is 12, 14, 9 and 21. Hence n = 4

N - 1 = 3

Going ahead to work with n = 4 would give a wrong result.

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the correct question is

Yuri computes the mean and standard deviation for the sample data set 12, 14, 9, and 21. he finds the mean is 14. his steps for finding the standard deviation are below. what is the first error he made in computing the standard deviation

The image is attached as well to the question

The signs of the first and second coordinates of a point in quadrant II are negative.

To determine the signs of the coordinates of a point in quadrant II, we can use the following formula:

Sign of coordinate 1: (-1) * (x-axis)

Sign of coordinate 2: (-1) * (y-axis)

For example, if we need to determine the signs of the coordinates of the point (4, -5) in quadrant II, we can use the formula above. The sign of the first coordinate is (-1) * (+4), which is -4. The sign of the second coordinate is (-1) * (-5), which is +5. Therefore, the signs of both coordinates of the point (4, -5) in quadrant II are negative.

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The equation in y = 2x + 8 for the given coordinates.

Finding the equation of a straight line in the coordinate plane is done using the slope-intercept form. A straight-line's equation will be that relationship that:

any place on the line's coordinates must meet.

Any point that is not on the line will not have coordinates that satisfy.

Given coordinates

x   -2      -1         0        1

y    4        6         8       10

equation is given by y = mx + c

m is the slope and c is y-intercept

let x₁ = -2, x₂ = -1

y₁ = 4, y₂  = 6

m = (y₂ - y₁)/(x₂ - x₁)

m = (6 - 4)/(-1 - (-2))

m = 2

so y = mx + c

substitute value of m

y = 2x + c

at x = 0 and y = 8

8 = 2(0) + c

c = 8

equation of line y = mx + c

y = 2x + 8

Hence the equation is y = 2x + 8.

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the complete question is in image.