(x^2+12x-28) / (6x^2 ) ÷ (x-2) / x^2
Show all steps
/ <-- means divided by

Answers

Answer 1

Factorization is the reverse process of expansion of mathematical expression to simple terms. The factorized term is: [tex]\frac{x + 14}{6}[/tex]

Factorization is a procedure in which a given number of terms of a mathematical expression is reduced by collecting common terms. It involves reducing a given mathematical expression to a simple form of terms.

Given that:

[tex]\frac{x^{2}+ 12x - 28}{6x^{2} }[/tex] ÷ [tex]\frac{x - 2 }{x^{2} }[/tex]

[tex]\frac{x^{2}+ 12x - 28}{6x^{2} }[/tex] x [tex]\frac{x^{2} }{x -2}[/tex]

[tex]\frac{x^{2} + 12x - 28}{6(x - 2)}[/tex]

Factorizing the numerator, we have;

[tex]x^{2} + 12x - 28[/tex] = (x - 2) (x + 14)

So that,

[tex]\frac{(x- 2) (x + 14)}{6(x - 2)}[/tex]

[tex]\frac{(x + 14)}{6}[/tex]

Thus the factorized form of the given question is [tex]\frac{1}{6}[/tex](x - 14).  

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Related Questions

gg is considering two websites for downloading music. the costs are detailed here. website 1: a yearly fee of $15 and $5 for each download website 2: $7 for each download select the equation for website 1.
a. y=-7x
b. y=7x
c. y=5x+15
d. y=15x+5

Answers

The equation for the first website is y = 5x + 15.

What is an equation?

Two or more expressions with an equal sign are defined as an equation.

Given that, the website (1) charges a yearly fee of $15 and $5 for each download.

Therefore, the total cost, y, for x downloads is given by:
y = 15 + 5x

Or, y = 5x + 15

Hence, the equation for the first website is y = 5x + 15.

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Marc mows lawns for $25 each lawn, plus $5 for every hour he spends mowing. The equation for his total earnings per lawn is y = 25 + 5h, where y represents his total earnings and h represents the number of hours he works. What does the flat pay of $25 represent in this situation?.

Answers

The $25 represent the constant for the equation y=25+5h where she lawns for $25 each lawn, plus $5 for every hour she spends mowing.

What is constant?

A constant is a value or number that is consistently the same regardless of how it is expressed. For instance, in the a forementioned figure, when its face value is 36 and 82 respectively, 36 and 82 remain constant. Its worth remains constant. A constant in mathematics is a particular number or symbol that has been given a stable value. In other words, a constant is an expression-unchanging value or integer. It always has the same value.

Here,

The $25 serves as the constant in the equation y=25+5h, where she charges $25 for each lawn she mows and an additional $5 per hour.

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Simplify: 5m + 3b - 9m - 4w Responses 14m + 7b 14m + 7b 14m + 3b - 4w 14m + 3b - 4w -4m + 3b - 4w -4m + 3b - 4w 21

Answers

Answer:

3b-4w-4m

Step-by-step explanation:

3b-4w+5m-9m

3b-4w-4m

Answer:

-4m+3b-4w

Step-by-step explanation:

5m+3b-9m-4w

we combine like terms but in this case only the m are like terms

5m-9m+3b-4w

-4m+3b-4w

i cant really see the options but it looks like it is the second to last or c option

hopes this helps please mark brainliest

14) -3x+3y=3
-5x + y = 13

Answers

Answer:

x = -3, y = 28

Step-by-step explanation:

-5x + y = 13

y = 13+5x

-3x+3(13+5x)=3 substitute

-3x + 39 + 15x = 3

12x + 39 = 3

12x = -36

x = -3

-5(-3) + y = 13 substitute into -5x+y=13

15 + y = 13

y = 28

let x and y be independent gaussian distributed random variables each with zero mean and unity variance. define the gaussian process:

Answers

As per the gaussian distributed random variables , the joint probability density function of the given variable is E [Z(t1)] = cos(2πt1)E [X] + sin(2πt1)E [Y]

Gaussian distribution:

In statistics, the Gaussian distribution refers the normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.

Given,

Here we need to find the the joint probability density function of the variables x and y be independent gaussian distributed random variables each with zero mean and unity variance.

Here we know that every weighted sum of the samples of the Gaussian process Z(t) is Gaussian, Z(t1), Z(t2) are jointly Gaussian random variables. Hence we need to find mean, variance and correlation co-efficient to evaluate the joint Gaussian PDF.

Then the equation is written as,

=> E [Z(t1)] = cos(2πt1)E [X] + sin(2πt1)E [Y]

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These are the times for 200 people to get to work

time people

0
10
30
40
50


A 10% sample, stratified by time, is taken.

complete the table


time people

0
10
30
40
50

got to work out the number of people using the same time

please help


Answers

The entries that complete the table are 1, 2, 8, 6 and 3.

Given:

These are the times for 200 people to get to work time people. A 10% sample, stratified by time, is taken.

Complete the table :

To do this, we multiply the number of people by the proportion of sample i.e. 10%.

The product is then approximated to the nearest unit

So, we have:

7 => 7 * 10 % ≈ 1

22 => 22 * 10 % ≈ 2

77 => 77 * 10 % ≈ 8

63 => 63 * 10 % ≈ 6

31 => 31 * 10 % ≈ 3

Hence, the entries that complete the table are 1, 2, 8, 6 and 3.

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MATH HELP PLEASE ---->

#13 - 16 Solve for x
16.) -31 < 3x – 7 < 14
17.) xy – ab = cd ; solve for b
18.) 3(a – b) = 9mn ; solve for a

#19 – 28 Factor Each Expression (If possible)
19.) 3x2 (y – 2) – 5(y – 2)
20.) kmfd – 3jkm
21.) 49x2– 9
22.) 64x2+ y2
23.) x2+ 7x – 35
24.) 2x2+ 11x + 14
25.) x2- 2x – 63
26.) 3x2– 2x + 7

Answers

Answer:

16.) The solution to this inequality is x < -4 or x > -3.

17.) To solve for b, we need to isolate b on one side of the equation. To do this, we can subtract ab from both sides of the equation, which gives us xy = cd - ab. Then, we can divide both sides of the equation by xy, which gives us b = (cd - ab)/xy.

18.) To solve for a, we need to isolate a on one side of the equation. To do this, we can divide both sides of the equation by 3, which gives us a - b = 3mn. Then, we can add b to both sides of the equation, which gives us a = b + 3mn.

19.) To factor this expression, we first distribute the 3x2 to get 3x2y - 6x2. Then, we notice that the 3x2 and the -6x2 have a common factor of -3x2, so we can factor them out to get -3x2(y - 2) - 5(y - 2). Finally, we notice that the -3x2(y - 2) and the -5(y - 2) have a common factor of -(y - 2), so we can factor them out to get -(y - 2)(3x2 - 5).

20.) To factor this expression, we notice that the kmfd and the -3jkm have a common factor of -jkm, so we can factor them out to get -jkm(f - 3).

21.) To factor this expression, we notice that 49 is a perfect square, so we can write 49 as 72. Then, we can factor out the x from the x2 to get 7x(x - 9).

22.) To factor this expression, we notice that 64 is a perfect square, so we can write 64 as 82. Then, we can factor out the x from the x2 to get 8x(x + y).

23.) To factor this expression, we notice that the x2 and the -35 have a common factor of x - 5, so we can factor them out to get (x - 5)(x + 7).

24.) To factor this expression, we notice that the 2x2 and the 14 have a common factor of 2, so we can factor them out to get 2(x2 + 11x + 7). Then, we notice that the x2 and the 7 have a common factor of x + 1, so we can factor them out to get 2(x + 1)(x + 7).

25.) To factor this expression, we notice that the x2 and the -63 have a common factor of x + 9, so we can factor them out to get (x + 9)(x - 7).

26.) To factor this expression, we notice that the 3x2 and the 7 have a common factor of 3x + 7, so we can factor them out to get 3(x + 1)(x - 2).

when adding √9 and -7 which time of number is the sum'

Answers

I’m going to assume you meant “what type of number”. If so we’ll see that the square root of 9 equals 3. So now we have 3+(-7)= -4 so we are left with a Negative Number as our answer.

Point K i on line egment \overline{JL}
JL. Given JL=x10,JL=x10, KL=4x,KL=4x, and JK=2x,JK=2x, determine the numerical length of \overline{KL}. KL

Answers

If the value of x will be 2. Then the length of KL will be 8 units.

What does cooperation with an example mean?

Being ability to use your body properly while moving around and cooperating with other people or things is the concept of coordination.

                                A gymnast walking on a tightrope without falling is an illustration of coordination. Working together to arrange or coordinate a party is an example of coordination.

Point K is on line segment JL. Given JL = x + 10, KL = 4x, and JK = 2x.

Then the value of x will be

    JL = JK + KL

x + 10 = 2x + 4x

   5x = 10

     x = 2

Then the length of KL will be

KL = 4x

KL = 4 (2)

KL = 8 units

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The complete question is-

Point K is on line segment JL. Given JL = x + 10, KL = 4x, and JK = 2x,

determine the numerical length of KL.

A multiple-choice quiz has 5 questions. Each question has 3 possible answers. A student guesses the answer to each question. Find the probability that the student answers all 5 questions incorrectly.

Answers

Answer: 3^5=243. 1/243

Step-by-step explanation:

We calculate the amount of ways he can answer 5 questions. It's 3x3x3x3x3 because he has 3 questions at the start with each of the 3 having another 3 questions to choose from and so on.

-7x+y=-19,-2x+3y=-19 by elimination

Answers

Answer:

x=2,y=−5

Step-by-step explanation:

pls help due now!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

A. 9x = 18

Step-by-step explanation:

4x - y + 5x + y = - 3 + 21

9x = 18

x = 2

Gavin observed 22 flowers on each block of his neighborhood. Each block has an equal number of flowers. Is this sample of the flowers in the neighborhood likely to be biased?

Answers

Yes, this sample of the flowers in the neighborhood is likely to be biased. This is because the number of flowers observed on each block is relatively small and may not be representative of the entire neighborhood.

What is neighborhood?

A neighborhood is a local geographic area typically containing a cluster of families and individuals who live nearby and interact with each other. It is usually a residential area, although some neighborhoods may be mixed-use, containing both residential and commercial buildings. Neighborhoods are typically identified by geographical boundaries such as a street, a park, or a body of water. People living in a given neighborhood often share certain characteristics including socio-economic status, culture, ethnicity, and even language. Neighborhoods play an important role in the lives of individuals and families, providing a sense of belonging, safety, and identity.

Additionally, if there is any external factor that influences the number of flowers on certain blocks (such as the amount of sunlight or water) then the sample may be skewed.

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Fill in the blank



The _________of a number is the distance between the number and zero on a number line

Answers

The distance on the number line between a number and 0 is its absolute value.

What is number line?

The visual representation of numbers on a straight line, either horizontally or vertically, is known as a number line.

When numbers are written down on a number line, it is straightforward for humans to compare them and perform basic arithmetic operations on them.

One might assume that a number line starts at zero (0). There are only negative numbers to the left of zero and only positive numbers to the right of zero.

In other words, as we move to the right on a number line, the value of the numbers increases.

The part of the number line to the left of zero is called the negative number line. But all is in the region to the right of zero.

Hence, The distance on the number line between a number and 0 is its absolute value.

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HELP pls question in picture 20 points

Answers

Answer:

Step-by-step explanation: why do I have a code to go for a walk in a few weeks to see what you are looking at and see what we can see when we can see how much we will be in our room for a few weeks to get the rest of the stuff done and we can make a new change of the time for you guys and we will miss it it is a great time for us and I will keep you posted if I need your assistance and help with the help for me am 11 sorry

Mommy mommy daddy mommy bye bye daddy daddy mommy daddy daddy bye daddy mommy daddy daddy love mommy mommy daddy mommy bye bye daddy daddy mommy daddy daddy bye daddy mommy daddy daddy love mommy mommy daddy mommy bye bye daddy daddy mommy daddy daddy bye daddy mommy

The sum of two numbers is 45
and their difference is 5.
What are the two numbers?
Larger number
1
Smaller number

Answers

Answer: 20 and 25

Step-by-step explanation: we know that there are 2 numbers and the sum is 45. Let's put one number as x. The other number is x+5 because the difference is 5. So our equation is- x+x+5=45. After we solve the equation by subtracting 5 from each side and simplifying x, we get x=20. The other number should be 5 more so the second number is 25. The numbers are 20 and 25. Please rate this answer!

Answer this question pls

Answers

The answer to this Question based on angles is described below

What is Angle?

It is a measure of how much an ray has turned clockwise or anticlockwise.

wrt to a stationary fixed arc

Solution:

First we need to find A4

A2 is given as 131 hence G is also 131 by Vertically Opposite angles

And A and G are equal as Corresponding angles

Now we need A13 it will be same as A7 which is 74 by Alternate Angles

Now we need A9

we can see A9 + A13 = A7 + A6

A9 + 74 = A4

A9 + 74 = 131

A9 = 57

For A17

A17 + A9 + A13 = 180

A17 + 131 = 180

A17 = 49

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The radius of circle S is half the radius of circle L. The radius of circle L is 8 millimeters.



Which measurement is closest to the area of circle S in square millimeters?

Answers

Area of the circle S be 16π square. millimeter

What is an area of circle ?

The area of ​​a circle is the space the circle occupies in the two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of ​​the circle. The formula for the area of ​​a circle is A = πr2, where r is the radius of the circle. A unit area is a unit square. Examples: m2, cm2, in2, etc. Circle area = π[tex]r^{2}[/tex]in square units (Pi)π = 22/7 or 3.14. Pi (π) is the ratio of the circumference to the diameter of any circle. This is a special mathematical constant.

It is given that the radius of circle S is half the radius of circle L and the radius of circle L is 8 millimeters.

Radius of the circle S = 8/2 = 4 millimeters

Area of the circle S = π[tex]r^{2}[/tex] = π[tex](4)^{2}[/tex] = 16π square. millimeter

Therefore, area of the circle S be 16π square. millimeter

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PLEASE HELP! THANK YOU

Answers

Answer:

1. A repeating decimal is a fraction [tex]\frac{a}{b}[/tex] where a and/or b are fractions and b is not equal to 0.

2. A decimal that ends is a ( n ) terminating decimal

3. Two numbers that have a sum of 0 are additive inverses

Can i please have help?

Answers

Analyzing the graph of the linear equation, we can see that for 1.4 grams of chemical A you will need 1.2 grams of chemical B.

How much of chemical B is needed?

The amounts of chemicals A and B needed are modeled by the linear equation on the graph.

Here we want to see how much of chemical B is needed if we decide to use 1.4g of chemical A.

Chemical A is on the horizontal axis, so we need to find 1.4 on the horizontal axis, and then move upwards until we reach the linear equation, and then move to the left until we reach the vertical axis.

Doing that we can see that we will need 1.2 grams (3 little squares in the vertical axis) of chemical B.

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Which of the following constructions must you know how to do in order to construct an inscribed circle for a given triangle?
angle bisector
perpendicular bisector
duplicating a line segment
bisecting a segment

Answers

For the construction of an inscribed circle the required construction that must be known is the angle bisector. The correct option is (A).

What is an angle bisector?

The angle bisector is a line that divides an angle into two equal parts. For a circle inscribed in a triangle the line joining the center to the vertex is the angular bisector of the interior angle.

The diagram for the given case can be drawn as follows,

For the circle inscribed in the circle, all the sides are tangents.

By the property of tangents to a circle ∠ODB and ∠OFB are right angles.

Now, in ΔODB and ΔOFB the relation is obtained as,

∠ODB = ∠OFB  (right angles)

OB = OB           (Common sides)

And, OD = OF  (radius of the circle)

⇒ ΔODB ≅ ΔOFB (by RHS criteria)

This implies that ∠ODB ≅ ∠OFB.

Thus, the line joining the centre and the vertex of triangle bisects its angles.

Hence, for the given case the required construction to be known is the angle bisector of triangle.

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What i the meaure of an arc correponding to the ector with an area of 24π ft² if the circle ha a 12 ft. Radiu?

Answers

When the arc's area is 24 square feet and its radius is 12 feet, the arc's length is 36.56 feet.

What is arc?

An arc is a section of a circle's or curve's border in mathematics. It is additionally known as an open curve. The circumference, commonly referred to as the perimeter, is the measurement around a circle that defines its edge. A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends. A slice of pizza or a pie can be used as an analogy for the form of a circle's sector.

Here,

area of sector=24π ft²

radius of sector=12 ft

area=θ/360*Π*12²

24π=θ/360*Π*12²

2=θ/360*12

2*360/12=θ

θ=60°

length of arc=2r+θ/360*(2Πr)

=2*12+60/360(2*3.14*12)

=24+2*2*3.14

length of arc=36.56 ft

The measure of arc is 36.56 feet when the area of arc is 24π feet² and it has the radius of 12 feet.

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If the breadth of a rectangle is one-third of its length and perimeter is 32 ft, find the length and breadth of the rectangle. square​

Answers

Answer:

breadth = 4 ft ; length = 12 ft

Step-by-step explanation:

p/2 = 32/2 = 16ft

l + b = 16

b = 1/3 l


l + 1/3 l = 16

(3 + 1)/3 l = 16

4/3 l = 16

l = 16 · 3/4

l = 4 · 3

l = 12 ft


b = 12  · 1/3

b = 4 ft

Angie is working on solving the exponential equation 23x = 6; however, she is not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation.

Hint: Use the change of base formula: log base b of y equals log y over log b.

Answers

The value of x from given exponential equation is 6 / 23. An equation with exponents is called an exponential equation if one of the exponents is a variable.

What is exponential equation ?

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.

Exponential growth and decay are the two different kinds of exponential functions.

23x = 6

Divide both sides by the same factor

23x /23 =6 /23

Simplify

x = 6/ 23

The value of x = 6 /23

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1. predict whether you think this a fair game or not. explain your response. a. play the game 5 times. b. now do you think the game if fair or not? ju

Answers

A game that has an equal probability of winning or losing is said to be fair.

What is probability ?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The foundational elements of fair play can be observed and learned both on and off the field, and include honesty, solidarity, tolerance, care, excellence, and joy. Fair competition, respect, camaraderie, team spirit, equality, and sport without doping are also examples.

A simple game of chance is deemed fair if there is an equal chance of winning for each player. If there is an equal chance of selecting each alternative, the decision is fair. Your understanding of probability can help you evaluate the fairness of games and make just decisions.

Children love playing together more when everyone is being fair. Additionally, it plays a significant role in getting along with people.

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You have 10lbs of bananas after peeling the bananas you 3lbs. 6oz. Of banana peels. What is the yield percent

Answers

To find the yield percentage, you can divide the weight of the peeled bananas by the weight of the unpeeled bananas and multiply by 100%.

The weight of the peeled bananas is 3lbs 6oz = 3 * 16 + 6 = 54 ounces.

The yield percentage is (54 / (10 * 16)) * 100% = 83.3%.

So, the yield percentage is 83.3%. This means that after peeling the bananas, you were left with 83.3% of the original weight of the unpeeled bananas.

Please help me solve!

Answers

Answer:

13.5%

Step-by-step explanation:

Given that μ = 144, σ = 27:

For x = 90: z= 90-144/27=-2

For x = 117: = 117-144/27 = -1

Therefore, From the normal distribution table: -2 gives .02275 and -1 gives .15866

So the required percentage = .02275 - .15866 = -0.13591= 13.5%

Hence, 13.5% of the population would be between 144 and 198

there are 6 people in line to board a plane with 6 seats. the first person has lost his boarding pass, so he takes a random seat. everyone that follows takes their assigned seat if it's available, but otherwise takes a random unoccupied seat. what is the probability the last passenger ends up in his/her assigned seat, as a decimal?

Answers

The probability that the last passenger end up in his/her assigned seats is 0.20.

In the given question, there are 6 people in line to board a plane with 6 seats.

The first person has lost his boarding pass, so he takes a random seat.

Everyone that follows takes their assigned seat if it's available, but otherwise takes a random unoccupied seat.

We have to find the probability the last passenger ends up in his/her assigned seat.

Given 6 people with 6 Seats.

The probability that the last passenger end up in his/her assigned seats = 1/5

The probability that the last passenger end up in his/her assigned seats = 0.20.

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A student raises her grade average from a 75 to a 90. What was the percent of increase in the
student's grade average? Round your answer to the nearest tenth of a percent, if necessary,
20%
016.7%
08.3%
015%

Answers

Answer:

Step-by-step explanation:

D: 15%

CC wants to buy online tickets for a concert. Two options are given here.

Option 1: $85 for each ticket plus a shipping fee of $15

Option 2: $95 for each ticket and free shipping

Select the equation for Option 2.

Responses

y=15x+85y is equal to 15 x plus 85

y=85x+15y is equal to 85 x plus 15

y=95xy is equal to 95 x

y=−95xy is equal to negative 95 x

Answers

The equation for $95 for each ticket and free shipping y = 15 + 95x

How to illustrate the equation?

In this situation, an equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions.

Let the number of tickets be x.

Let the total amount is y.

The equation for $95 for each ticket and free shipping will be:

y = 15 + (95 × x)

y = 15 + 95x

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can cause managers to make mistakes and errors that harm the organization cMultiple ChoiceOExternal locus of controlCognitive dissonanceAffective attitudesDistortions in perception A scientist finds what she thinks is a new species of rodent on a small pacific island. However, some similar-looking rodents inhabit some nearby islands. She mates the new rodent with the nearby rodents and gets viable but infertile offspring. Why?. Chapman, the Monroe County District Attorney, and Bryan don't see eye to eye on his purpose for arriving in Alabama. A) What does Chapman think Bryan is trying to do? How does he feel about Bryan? B) What does Bryan say is his purpose for being there? What happened to some of the commission's prior toAdams leaving office? Why was this important? According to a research study described in your textbook, in which of the following categories did men recall more events than women?A. Personal experiences from the past three yearsB. Personal experiences from the past yearC. Personal experiences from the past weekD. Historical events A line has a slope of 14/19 and passes through the point 0,15 what is its equation in slope intercept form the deadweight loss is smallest when a tax is levied on a good where the elasticity of demand is what is one abiotic-abiotic interaction affected by the wildfires in California? Who is next in line for the presidency both the president and the vice president are able to fulfill the duties of the office? NEED HELP AS SOON AS POSSIBLE please this homework was due he 15th Naturally occurring unsaturated fatty acid chains are ___ and the melting point will ___ as the number of pi-bonds in the fatty acid chain increase.a) conjugated; increaseb) conjugated; decreasec) isolated; increased) isolated; decrease Solve for x ---> -2x - 48 10x 24 an effective delivery requires that a donor retain control and dominion over the subject matter of a gift. true false Window Rock Recruitment Agency just placed Alejandro Rivera in a job as an assistantpharmacist. The job pays $71,500 annually. The agency fee is equal to 40% of the first5 weeks' pay. Demonstrate and explain how you would be able to determine what he willearn during the first 4 weeks if he pays the agency fee weekly? Which point shows the approximate location of [tex]\sqrt{7}[/tex] plotted on the number line 5) The average speed of a sailing ship in the 1700's was about 15m/s. It would take a letterabout 3 months to travel from England to the American colonies. Based on this information,what distance would the letter have traveled to reach America from England? Probability and Statistics Question Many nutrient cycles are coupled and changes in one cycle will affect another. This means that a change in the amount of carbon dioxide fixed is intimately affected by the amount of __________. How much heat is required to change 48. 5 liquid mercury (Hg) at 400 K to vapor at a 700 K? The boiling point of mercury is 629. 88 K-88 kj-204 kj 16. 2 kj 30 kj 29 kj