What is the slope of a line that is perpendicular to a line represented by the equation 6y=−7x+4?

Enter your answer, as a fraction in simplest form, in the box.

The following cases are described:

Algebraically speaking, rational functions are expressions of the form f(x) = p(x) / q(x), such that q(x) ≠ 0, where p(x) is the numerator and q(x) is the denominator. Rational functions can be found by using the defintion of division between two functions:

(f / g) (x) = f(x) / g(x)

And the domain of (f / g) (x) is every value of x such that g(x) ≠ 0. Now we proceed to find all the required information for each case:

Case 1 - f(x) = x² - 3 · x - 18, g(x) = x + 3

Rule: (f / g) (x) = (x² - 3 · x - 18) / (x + 3)

         (f / g) (x) = [(x - 6) · (x + 3)] / (x + 3)

         (f / g) (x) = x - 6

Domain: Since the resulting expression is a linear function, then the domain of (f / g) (x) is all the real numbers.

Case 2 - f(x) = x - 3, g(x) = x² - x - 6

Rule: (f / g) (x) = (x - 3) / (x² - x - 6)

         (f / g) (x) = (x - 3) / [(x - 3) · (x + 2)]

         (f / g) (x) = 1 / (x + 2)

Domain: The domain of the rational function is any real number except x = - 2.

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Answer:

The area of the given triangle is 10 sq meters

Explanation:

The area of a triangle is given by the formula:

Area = 1/2 base . height

Given that the triangle has base = 10m, and height = 2m

Area = 1/2 * 10 * 2

= 10 square meters

The mean and standard deviation of the vehicle speed are 58.33 and 11.64 respectively.

The vehicle speed on a particular bridge in china has normal distribution.

5% represents the 5th percentile which is here, 39.18 m/h.

Since 10% travels more than 73.27 m/h, 90% travels less than 73.27 m/h.

So here the 90th percentile is 73.27 m/h.

Also the z-score, z = (x-μ)/σ, where μ is the mean of normal distribution and σ, the standard deviation.

So 39.18 corresponds to the z with p-value 0.05, i.e., z = -1.645 [from the normal tables]

Hence, z = (x-μ)/σ

⇒ -1.645 = (39.18 - μ)/σ

⇒ -1.645σ = 39.18 - μ

⇒ μ = 39.18 + 1.645σ  ----------(1)

Also 73.27 corresponds  to the z with p-value 0.9,i.e., z = 1.28.

Hence , z = (x-μ)/σ

⇒ 1.28 = (73.27 - μ)/σ

⇒ 1.28σ = 73.27 - μ

⇒ μ = 73.27 - 1.28σ  ----------(2)

Equating (1) and (2), we get,

39.18 + 1.645σ  =  73.27 - 1.28σ

2.925σ = 34.05

σ = 11.64

hence μ = 39.18 +1.645 x 11.64

⇒ μ = 58.33

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Answer:

2k + 5

Step-by-step explanation:

Since this is a subtraction problem, you need to change it to an addition problem. When you do this, you also need to change the sign of each term in the second set of parentheses.

(-4k - 1) - (-6k - 6)

(-4k - 1) + (6k + 6)

Remove the parentheses and add like terms.

-4k - 1 + 6k + 6

2k +5

We need to know simple division to solve the problem. The maximum number of men in the lift is 8 and the maximum number of women in the lift is 10.

We will be using the simple concept of division to find the number of people that the lift can carry. The average weight of a man is given to be 84 kg and the average weight of  a woman is given to be 70kg. The lift can carry 720 kg, we will find separately the number of men and women that can be carried in the lift. Inorder to find the maximum number of men we divide the total weight the lift can carry by the average weight of a man, we will similarly calculate the maximum number of women.

number of men= 720/84=8.57 which means that the number of men is 8

number of women =720/70=10.28 which means that number of women is 10.

Therefore the lift can carry at most 8 men and at most 10 women.

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Answer:

pretty sure its WZX

Step-by-step explanation:

Answer: If you want the result as a fraction it should be 3.7/5. but if you want a whole number it's 4.2. if you want a mixed number its 4 1/5

Step-by-step explanation:

Distances Sandra recorded in order from least to greatest is 1/9, 5/18, 11/36, 7/18, 17/36, 2/3.

Given that, the fractions represent the distances that Sandra recorded is 7/18, 2/3, 1/9, 11/36, 5/18, 17/36.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Here, distance is 10/36

So, the equivalent fractions for the given fractions are

7/18 = 14/36

2/3 = 24/36

1/9 = 4/36

11/36

5/18 = 10/36

17/36

So, least to greatest is

4/36 < 10/36 < 11/36 < 14/36 < 17/36 < 24/36

1/9 < 5/18 <11/36 <7/18 <17/36 <2/3

Therefore, distances Sandra recorded in order from least to greatest is 1/9, 5/18, 11/36, 7/18, 17/36, 2/3.

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Answer: 9. 189 divided by 21 is 9.

Step-by-step explanation:

The kilometres that she has cycled in total by the end of the 18th week is 105.

Based on the information, this is an arithmetic sequence and the formula is illustrated as

= a + (n - 1)d

where a = first term = 20

d = common difference = 5

n = numbers = 18

Therefore, the 18th term will be:

= a + (n - 1)d

= 20 + (18 - 1)5

= 20 + (17 × 5)

= 20 + 85

= 105

The number of kilometers is 105 kilometers.

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The equation in slope intercept form is C(h) = 50h+25  ,the total cost for 8 hours of work is $425 , and for 10 hours of work  is  $525.

In the question;

it is given that

the fixed charge of plumber = $25

charge for per hour of service = $50

the hours of service be "h"

and the total cost be "C"

according to the question

C(h) = 50h+25

the equation in the slope intercept form is C(h) = 50h+25

to find the total cost for 8 hours of work , put h=8

C(8) = 50(8) + 25

= 400+25

= 425

to find the total cost for 10 hours of work , put h=10

C(10) = 50(10) + 25

= 500+25

= 525

Therefore , total cost for 8 hours of work is $425 , and for 10 hours of work  is $525 .

The given question is incomplete , the complete question is

A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service. What will be the total cost for 8 hours of work? 10 hours of work?

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The value of a³b for the value of a=3 and b=-5-2i is -135-54i for the given complex number that defines "Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number called “iota”."

Complex numbers are those that are expressed as a+ib, where a and b are real numbers and I is a fictitious number called a "iota." I has the value (√-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im). In the 19th century, the term "complex numbers"—which denotes that they have both real and imaginary components—became widely used. Occasionally, the term "imaginary number" is used to describe a complex number that is not real or, more commonly, a number whose real part is zero (a.k.a "pure imaginary").

Here,

The value of a³b

=3³(-5-2i)

=27(-5-2i)

=-135-54i

For the given complex number that defines "Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and I is an imaginary number called "iota," the value of a³b is -135-54i.

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The table represent a direct proportional relation.

In this question we find a table with four pairs of elements that have to be tested with respect to the direct proportional formula, which is defined below:

y = k · x

Where:

The table represents a direct proportional relation if and only if there is only one constant of proportionality:

k₁ = 12 / 3

k₁ = 4

k₂ = 20 / 5

k₂ = 4

k₃ = 8 / 2

k₃ = 4

k₄ = 32 / 8

k₄ = 4

As k₁ = k₂ = k₃ = k₄, the table represent a proportional relationship.

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The number 2n and 2n + 2 will always are 2 consecutive even numbers.

From the given option in the question;

2n and 2n + 2 will always be two consecutive even number.

For, n = 1, the numbers be 2 and 4.

For, n = 2, the numbers be 4 and 6.

For n = 3, the numbers be 6 and 8....and so on.

Thus, the number 2n and 2n + 2 will always are 2 consecutive even numbers.

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Answer:

1. 12

2. 4:5

3. 5

4. 30

5. 42

6. 15

7. 36

8. 1120

9. 10 2/3

Step-by-step explanation:

Answer:

In photo

Step-by-step explanation:

Answer: -2 and -3

Step-by-step explanation:

Answer: No.

Step-by-step explanation:

    To test this ordered pair, we plug it back into the equation given as (x, y), and then simplify to solve. If we end up with an equal equation, the answer is yes. If not, the answer is no.

y = 1/2x - 3

(1) = 1/2(-8) - 3

1 = -4 - 3

1 ≠ -7

           This ordered pair is not a solution.

Answer:

1:1 or one red circle to one blue circle

There is one red and one blue circle

Step-by-step explanation:

Answer:

if you meant %, the answer is 2016

Step-by-step explanation:

1120 + 80% is 2016

20 shares purchased at $30, means that the initial inversion is 20 times 30 = $600

they are sold for $710, so the difference is 710 - 600 = 110

the commision is 6, so the final gain is 110 -6 =104

profit divided by the inversion:

104/600 = 0.1733

the answer is 17.33 %

2(x -2) = 50 is also true for the same value of x.

Given,

Part 1:

When a cardboard box is empty, its weight is 0.6 pounds.

It is filled with 15 bags of beans and a 4-pound bag of rice.

The total weight of the box and the contents inside it is 25.6 pounds.

Let the weight of 15 bean bags is 15b. The given scenario can be represented by the equation as follows :

0.6+15b+4=25.6 ....(A)

Taking like terms together,

15b=25.6-0.6-4 ...(1)

15b = 21  ....(2)

Equation (1) or (2) can be the equivalent equation for the equation (A).

Part 2:

Solve the equation:

7.5d = 2.5d, Lin divides each side by 2.5d,

and Elena subtracts 2.5d from each side.

Now, 7.5d/2.5d = 2.5d/2.5d

3 = 1

It is not equal, There is no solution.

a. 7.5d - 2.5d = 2.5d - 2.5d

5d/5 = 0/5

b. What is the solution ?

Solution is d = 0

Part 3:

Given,
The equation 4(x - 2) = 100  is a true equation for a particular value of x.

Explanation: The basic property of the equation is that if you multiply or divide both sides of the equation by the non-zero whole , the equation still holds.

In the Equation : 4 (x - 2) =100 divide by 2 on both sides because 2 is common factor of (4,10)

So, 4(x - 2) =100

1/2 x 4(x-2) = 1/2 x 100

= 2(x-2) = 50

Above all, 2(x -2) = 50 is also true for the same value of x.

Hence, 2(x -2) = 50 is also true for the same value of x.

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The people of the Plymouth Colony fail to achieve the ideals of the Mayflower Compact as A. They did not come together to create a government.

The Mayflower Compact was the Plymouth colony's first government instrument. The Pilgrim Fathers, the emigrants who crossed the Atlantic on the Mayflower in search of religious freedom, wrote the manifesto. On November 11, 1620, it was signed on the sands of what is now Provincetown, near Cape Cod. The pilgrims knew they were in a land unfamiliar to the London Company when the Mayflower docked in Plymouth.

The strangers claimed that the Virginia Company contract was null and void. They believed that because the Mayflower landed outside of Virginia Company territory, they were no longer bound by the charter of the company. Because there was no official government over them, the stubborn strangers refused to acknowledge any regulations.

Many of the pilgrims were already weak from disease and a lack of food when they arrived in Plymouth. The journey had been lengthy, and they were running low on supplies. During the winter, the colony lost about half of its population owing to disease and famine.

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Answer:its A i did it on edge

Step-by-step explanation:

Answer:

y=4/3x+2

Step-by-step explanation:

In linear equation, The price at which the quantity demanded equals the quantity supplied is $ 260."  option (b) is answer.

What in mathematics is a linear equation?

a.  The demand for a product is given by p+3q= 315 or, q = (315 - p)/3 and the supply for this product is given by  p-7q = 65 or, q = (p- 65)/7

The price at which the quantity demanded equals the quantity supplied is given by

              315 - p/3 = p - 65/7

         7( 315 - p ) = 3( p - 65 )

        2405 - 7p = 3p - 195

        2405 + 195 = 3p + 7p

           2600 =  10p

            p = 2600/10 = 260

Thus, the required price is $ 260.

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An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

 ((((x4)+(5•(x3)))-(2•5x2))-20x)+24

((((x4) +  5x3) -  (2•5x2)) -  20x) +  24

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Answer:

-60x + 32 = -60x - 32

Step-by-step explanation:

The first step to solve this question is combining the like terms in each option.

In those that we end up with:

0x = c

In which c != 0, we have no solution. So

-60x + 32 = 32x + 60

-60x - 32x = 60 - 32

-92x = 28

No 0x, so it has solution

-60x + 32 = 32x - 60

-60x - 32x = -60 - 32

-92x = -92

No 0x, so it has solution

-60x + 32 = -60x - 32

-60x + 60x = -32 - 32

0x = -64

0x equaling a value different of 0, so no solution.

-60x + 32 = -60x + 60

Step-by-step explanation:

y varies INVERSELY as x.

that means

y = k/x

therefore,

22 = k/6

k = 22×6 = 132

and then, when y = 15

15 = 132/x

15x = 132

x = 132/15 = 8.8