Write the equation in standard form given the following information (with solutions please)

1. The roots are 1/2 and -1/2

Answers

Answer 1

The Quadratic equation in standard form given the following roots are

f(x) = 2x^2 - 3x + 1

The root 1 is associated with the factor (x - 1).

The root 1/2 is associated with the factor (x - 1/2), which in turn is equivalent to (2x -1)

The quadratic in question is f(x) = (x - 1)(2x - 1).  To write this in standard form, perform the indicated multiplication:

f(x) = 2x^2 - 2x - x + 1, or f(x) = 2x^2 - 3x + 1

What is Quadratic equation?

Any equation in algebra that can be written in standard form as where x is an unknown and a, b, and c denote known numbers, where a 0 is a quadratic equation.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as a[tex]x^{2}[/tex] + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

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Related Questions

a racetrack charges $80 each seat in the lower section, $65 for each seat in the upper sections, and $30 for field tickets. there are three times the number of seats in the upper section as compare to the lower section. the revenue from selling all 21,200 seats is $915,000. how many of each ticket were sold at the racetrack?​

Answers

The number of each ticket sold was:

The upper section contains 5160 seats, the lower section contains 1720 seats, and the field contains 17320 seats.

Given Information:

Each seat in the lower section costs $80, each seat in the upper section costs $60, and field tickets cost $40.The upper section has three times the number of seats as the lower section.The total revenue from the sale of all 24,200 tickets is $1,140,000.

The steps below can be used to calculate the total number of seats in each section:

Step 1 - In the lower section, enter 'x' as the total number of seats.

So, based on the data provided, the total number of seats in the upper field is '3x'. Let y be the total number of seats in the field.

Step 2 - The linear equation that represents total ticket revenue.

80x + 60(3x) + 40y = 1140000260x + 40y = 1140000 ...(1)

Step 3 - The linear equation representing the total number of tickets is as follows:

x + 3x + y = 24200y = 24200 - 4x ...(2)

Step 4: Change the value of y in the equation (1).

260x + 40(24200 - 4x) = 1140000x = 1720 tickets

Step 5: Change the value of 'x' in equation (2).

y = 24200 - 4(1720)y = 17320 tickets

Therefore, the number of each ticket sold was:

The upper section contains 5160 seats, the lower section contains 1720 seats, and the field contains 17320 seats.

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The correct question is given below:
A racetrack charges $80 for each seat in the lower section, $60 for each seat in the upper section, and $40 for field tickets. There are three times the amount of seats in the upper section as the lower section. The revenue from selling all 24,200 tickets is $1,140,000. write a system to represent the situation. How many seats are in each section

show working out I’ll give u brainless if u help mehhhh

Answers

10% out of $2.50 you saved about 6€ cent’s

Speed and travel time are inversely related, the faster you go, the less time it takes
to get to your destination. If it takes 20 minutes to get to school when you go 30 mph,
how long will it take to get to school if you travel 45 mph? (hint: speed=k/time)

Answers

Answer:

Step-by-step explanation:

speed = distance/time

however speed is a compound measure

distance to school = speed x time

                               = 30mph x 1/3hr

                               = 10m

time =  10m / 45mph

       = 13.3 (recurring)

       = 13 mins

Please help with explanation

Answers

The perimeter of the sandbox is 2x+2y.

Therefore, the inequality is

[tex]\boxed{2x+2y \leq 20}[/tex]

jillian is trying to save water, so she reduces the size of her square grass lawn by 8 feet on each side. the area of the smaller lawn is 144 square feet. in the equation (x – 8)2

Answers

The dimensions of original lawn are a. 4 feet by 4 feet.

As per the equation and information mentioned in question, x represents the dimension of original lawn. The equation in question represents the relation between area of lawn at side of reduced lawn and it's area. We will solve this equation to find the value of x.

[tex](x - 8)^{2} = 144[/tex]

The expression on Left Hand Side is same as [tex](a - b)^{2}[/tex]. We know, on expansion, we write it as [tex]a^{2} + b^{2} - 2ab[/tex]. Thus, new equation will be -

[tex]x^{2} + 8^{2} - 2*x*8 = 144[/tex]

[tex]x^{2} + 64 + 16x = 144[/tex]

[tex]x^{2} + 16x + 64 - 144 = 0[/tex]

[tex]x^{2} + 16x - 80 = 0[/tex]

[tex]x^{2} + 20x - 4x - 80 = 0[/tex]

x (x + 20) -4 (x + 20) = 0

(x + 20) (x - 4) = 0

So, the two values of x that we get are:

x = 4 and -20.

The dimensions of lawn can not be negative. Hence, the value of x will be x.

Therefore, the dimensions of original lawn are a. 4 feet by 4 feet.

The complete question is -

Jillian is trying to save water, so she reduces the size  of her square grass lawn by 8 feet on each side. The area of the smaller lawn is 144 square feet. In the equation [tex](x - 8)^{2} = 144[/tex], x represents the side measure of the original lawn. What were the dimensions of the original lawn?

a. 4 feet by 4 feet

b. 8 + [tex]6\sqrt{2}[/tex] feet by 8 + [tex]6\sqrt{2}[/tex] feet

c. 8 - [tex]6\sqrt{2}[/tex] feet by 8 + [tex]6\sqrt{2}[/tex] feet

d. 20 feet by 20 feet

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Insert <,>,or = to make the following sentence true. square root of 17 and 4

Answers

we can insert > to make the following sentence true that is [tex]\sqrt{17}[/tex] > 4

we have to solve the following sentence

[tex]\sqrt{17}[/tex] --- 4     ( insert <,>, = to make the following sentence true)

what is square root ?

The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is  [tex]\sqrt{}[/tex] .

we know that

square root of 17 is 4.12310563

which is 4+ 0.12310563

that is if we add 4+0.12310563 we get 4.12310563

therefore square root of 17 is greater than 4

that is [tex]\sqrt{17}[/tex] > 4  

since 4.12310563 > 4

hence,   we can insert > to make the following sentence true that is [tex]\sqrt{17}[/tex] > 4

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write the algebraic expression for two less than for times a number
PLEASE SHOW WORK

Answers

two less=-2
four times a number(x)=4x
Combine it
4x-2 is the right answer

What is the distance from the origin to point P graphed on the complex plane below?
4
3
2
4
-5-4-3-2-₁
√√7
√29
7
20
-2-
34 32 4
Mark this and return
2 3 45 x
Save and Exit
Next
Submi

Answers

Step-by-step explanation:

the point is (2, -5).

the origin is (0, 0).

the distance between 2 points is calculated via Pythagoras due right-angled triangles :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle). a and b are the legs.

the direct distance is the Hypotenuse, and the x coordinate and y coordinate differences are the legs.

so,

distance² = (2 - 0)² + (-5 - 0)² = 2² + (-5)² = 4 + 25 = 29

distance = sqrt(29) = 5.385164807...

so, the second answer option is correct.

donald is studying the buying habits of all women attending his store. he samples the population by dividing the women into groups by age and randomly selecting a proportionate number of women from each group. he then collects data from the sample. which type of sampling is used?

Answers

According to the statement Donald is using Stratified sampling to collects data from the sample.

The correct option is A.

Briefing:

A simple random sample is then taken from each separate or subgroup using the stratified sampling survey method, which first divides the population being studied into distinct subgroups or groups known as strata.

The ability to reduce the sample size needed to obtain reliable results is one of the main benefits of stratified sampling.

What accomplishes stratified sampling?

When attempting to evaluate data from various subgroups or strata, researchers frequently use stratified random sampling. They can quickly find a population sample that most accurately reflects the entire population they are studying.

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I understand that the question you are looking for is:

Donald is studying the eating habits of all students attending his school. He samples the population by dividing the students into groups by grade level and randomly selecting a proportionate number of students from each group. He then collects data from the sample. Which type of sampling is used?

a. Systematic sampling

b. Convenience sampling

c. Stratified sampling

d. Cluster sampling

25 POINTS PLEASE HELP

Answers

Answer:

Step-by-step explanation:

This is the answer………………………..

A scientist created a scatter plot to represent the heights of four plants over time. Then, she found a line of best-fit to model the height in centimeters of each plant after x days. The equations of each trend line are given in the table.


Trend Line Equations
Plant
Equation of trend line
1
y = three-halves x + three-halves
2
y = 2 x + 1
3
y = one-half x + 3
4
y = three-halves x + 1

According to the trend line equations, which plants are growing at the same rate per day?

Answers

The plants which are growing at the same rate are Plant 1 and Plant 4.

Both the plants are growing at the same rate because they have same slope when their growth rate is expressed in the form of equation. Slope may be defined as the amount of steepness of the graph when plotted on graph paper. The slope-intercept form of equation of line is given by y = mx + c where m is the slope of the line and c is the intercept formed by the line. The slope-intercept form of the growth rate equation of Plant 1 is given by y = 3/2x + 3/2 and the slope-intercept form of the growth rate equation of Plant 4 is given by y = 3/2x + 1.

If we compare them from the slope-intercept form of line, then both the Plants have same slope and thus their growth rate is same.

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Answer:

B. 1 and 4

Step-by-step explanation:

Edge 2023

Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form..

Answers

Answer:

y = 4/5x + 27/5

or 5y = 4x + 27

or 5y - 4x = 27

Step-by-step explanation:

Look at (-3,3) and (2,7)

So the line rises 4 units and runs 5 units, then slope is 4/5

using m = 4/5, y = 3, x = -3

y = mx + b

3 = 4/5(-3) + b

3 = -12/5 + b

b = 15/5 + 12/5 = 27/5

so y = 4/5x + 27/5

or 5y = 4x + 27

or 5y - 4x = 27

A number d is decreased by 5 and then doubled

Answers

Let us assume the given number is x.

If it is decreased by 5 and then doubled, then we can represent that event with an algebraic expression as:

= (x-5) × 2

Formation of equation:

The number decreased by 5 can be written as: x - 5

Now, to double it, we will multiply it by 2 = (x-5) × 2

Therefore, we have the algebraic form of the given condition as :

= (x-5) × 2

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A triangle has height of 15 in. And area 120^2 . What is the length of its base

Answers

Answer:

16 inches

Step-by-step explanation:

Multiply 120 by 2 to start reversing the triangle area equation.

120*2 = 240.

Now divide by 15

240/15=

16

The length is 16 inches

Subtract using a number line.
-3.3-(-0.6)
Plot the minuend and, the difference on the number line.

Answers

Answer:

2.7

Step-by-step explanation:

When you subtract a negative number, you are actually adding because the negatives cancel out. So, it will be -3.3+0.6, which is -2.7

hope this helps! ibrahim

Hi there! Your answer is 2.7

Step-by-step explanation:

Add: -3.3+-0.6 = 2.7

When subtracting two negative numbers, this will result in a positive number since the negatives cancel each other out.

Hope this helps! :)

in a random sample of 77 residents of the state of texas, the mean waste recycled per person per day was 1.01.0 pounds with a standard deviation of 0.290.29 pounds. determine the 98�% confidence interval for the mean waste recycled per person per day for the population of texas. assume the population is approximately normal. step 1 of 2 : find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.

Answers

Answer:

(0.63789 ; 1.38211 ) is the 98% confidence interval for the mean waste recycled per person per day for the population of texas and  Tcritical = 3.143

In a random sample of 7 residents of the state of texas ,the mean waste recycled per person per day was 1.01 pounds and standard deviation 0.29 pounds

we have to find the 98% confidence interval for the mean waste recycled per person per day for the population of texas

Mean, xbar = 1.01

Standard deviation, s = 0.29

Sample size, n = 7

Confidence interval  : xbar ± margin of error

Margin of Error = Tcritical * s/sqrt(n)

Degree of freedom (df) = n - 1 = 7 - 1 = 6

Hence Tcritical = 3.143

Margin of Error = 3.143 * 0.29/sqrt(6)

Margin of error = 0.37211

Lower boundary = (1.01 - 0.37211) = 0.63789

Upper boundary = (1.01 + 0.37211) = 1.38211

(0.63789 ; 1.38211 )

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How to find the greatest number of identical arrangements that can be made what is 54 roses and 42 tulips or no flowers left over.

Answers

The greatest number of identical arrangements that can be made is 6 arrangements of 7 tulips and 9 roses.

The above problem we can use the greatest common factor, we are provided with the information that there are a total of 42 tulips and 54 roses. Now, we will find the greatest common factor of 54 and 42.

42- 54|2

21- 27 | 3

7 - 9

So the greatest common factor of 54 and 42 is 6, here we are left with 7 and 9 which indicates the number of tulips and roses

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The expression for the nth term of a sequence is 5n^2

work out the third term in this sequence

Answers

Answer:45

Step-by-step explanation:

5n²

5(3)²

5(9)

∴ The third term in the sequence 5n² is 45

please help!! (answer is NOT undefined)

Answers

[tex]-8\sqrt{-165} \\ \\ =-8\sqrt{-1}\sqrt{165} \\ \\ =\boxed{-8i\sqrt{165}}[/tex]

bro's please help like fr I don't know WHAT IS 4 1/4 TIMES 6 AND PLAESE GIVE ME BOTH SIMP AND NOT THANK YOU <33

Answers

Answer:

Exact Form:

51/2

Decimal Form:

25.5

Mixed Number Form:

25 1/2

Step-by-step explanation:

The answer the answer would be 25.5

A forest covers 61,000 acres. A survey finds that 0.4​% of the forest is​ old-growth trees. How many acres of​ old-growth trees are​ there?

Answers

Answer:

2,440 acres of old-growth trees.

Step-by-step explanation:

61,000*0.04=2,440

There are 2,440 acres of old-growth trees.

Hope this helps!

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Prove that cos 4θ = 8 cos⁴ θ - 8 cos² θ + 1

Answers

Answer:

Step-by-step explanation:

Answer is in the pic.

Answer:

See below for proof.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Trigonometric Identities}\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\ \\$\sin^2 \theta + \cos^2 \theta=1$\\\end{minipage}}[/tex]

Use the trigonometric identities to prove the given equation:

[tex]\begin{aligned} \implies \cos 4 \theta & = \cos (2 \theta +2 \theta)\\& = \cos 2 \theta \cos 2 \theta - \sin 2 \theta \sin 2 \theta\\& = \cos^2 2 \theta - \sin^2 2 \theta\\& = \cos^2 2 \theta - (1-\cos^2 2 \theta)\\& = 2\cos^2 2 \theta - 1\\ & = 2\left(\cos 2 \theta \right)^2-1\\& = 2\left(\cos\theta \cos\theta-\sin \theta\sin \theta\right)^2-1\\& = 2\left(\cos^2\theta-\sin ^2\theta\right)^2-1\\& = 2\left(\cos^2\theta-(1-\cos^2\theta)\right)^2-1\\& = 2\left(2\cos^2\theta-1\right)^2-1\\\end{aligned}[/tex]

                 [tex]\begin{aligned}& = 2\left(4\cos^4\theta-4\cos^2\theta+1\right)-1\\& =8\cos^4\theta-8\cos^2\theta+2-1\\ & =8\cos^4\theta-8\cos^2\theta+1 \end{aligned}[/tex]

Mrs. Genebe worked all year and earned $23,400. How much did she earn per week?

Answers

Answer:

$448.766754 per week or $448

Step-by-step explanation:

i gotchu

theres 52.1429 weeks

divide 23,400 by 52.1429

u get $448.766754 per week

Miguel saves 1/6 of his wage. He spends one third of his wage on his mortgage. How much does he have left ?

Answers

hi

1/3 =2 /6

so 1/6 +2/6 = 3/6

as 3/6 is half if his income, then he remains the other half

Deanna and Raquel ride a merry-go-round together. Deanna sits on a horse on the outer edge of the merry-go-round, 10 feet from the center of the ride. Raquel sits on a horse that is 2 feet closer to the center than Deanna. This ride makes one full rotation every 15 seconds. When the ride starts spinning, which girl is traveling faster? Explain how you know.

Answers

As Deanna is sitting farther from the center she is travelling at a faster rate.

What is circumference of a  circle ?

Circumference of a circle is the distance around the circle.

We know that merry-go-round covers distance in form of circles and we also know that circumference of a circle is 2πr.

As Deanna sits on a horse on the outer edge of the merry-go-round, 10 feet from the center of the ride it can thought of as the radius.

∴ In one rotation Denna will cover (2πr) feet which is

= (2π×10 feet.

= 62.8 feet in 15 seconds.

Now if we do the previous calculation for Raquel with r taken as 8 she will cover:

= 50.24 feet in 15 seconds.

Therefore Deanna is spinning at a faster speed.

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Simplify:
4(10+2³-5)
O a. 52
O b. 44
O c. 6892
O d. 17

Answers

Answer:

A. 52 is your answer

Step-by-step explanation:

Explained below

Answer:

Ans is a

First you solve the inside of the bracket u will get 4(13)

which will give u 52

a professor wants to randomly select 4 students to go to the board. she decides to randomly select the third student who enters the classroom and every seventh student after that. determine the students who will be going to the board. write down the student numbers.

Answers

The total number of students chosen is 4, 13, 22, and 31.

What is random selection?Random selection, also known as random sampling, is a method of selecting members of a population to be included in your study's sample. Random assignment, on the other hand, is a method of dividing the sample into control and experimental groups. The goal is to make the results more generalizable. The goal of selecting a random sample from a larger population is to ensure that the sample is representative of the larger group and less likely to be biased.

To determine the students who will be going to the board:

The professor wishes to choose four students at random.She then chose the fourth and ninth students at random.The fourth student is chosen first.

Now, using the following term formula, a + d (n - 1).

The second student is up next.

= 4 + 9(2-1) = 4 + 9(1)= 4 + 9= 13

The third student will:

= 4 + 9(3-1)= 4 + 9(2)= 4 + 18= 22

The fourth student will:

= 4 + 9(4-1)= 4 + 9(3)= 4+ 27= 31

Therefore, the total number of students chosen is 4, 13, 22, and 31.

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How would I solve these problems

Answers

Answer:

1a. -( x + 1)² + 4

1b. y-intercept at y = 3

1c. x-intercepts at x = -3 and x = 1

Derivation of 1b and 1c below

Step-by-step explanation:

Question 1a

The vertex equation form of a parabola is given by

y = a(x-h)²  + k where (h, k) are the coordinates of the vertex

If a > 0 then the parabola is facing up(vertex is at a minimum)  and if a < 0 then parabola is facing down (vertex at a maximum)

From the graph we see that the parabola is facing down so a = -1

The vertex is at (-1, 4) so h = -1 and k = 4

Therefore the equation of the parabola is

y = -1(x - h)² + k = -1(x- (-1))² + 4 = -1(x + 1)² + 4

y = -( x + 1)² + 4   (Answer 1a)

Question 1b

The y-intercept is the y-value where the parabola crosses the y-axis. From the graph we see that the parabola crosses the y-axis at y = 3 and x = 0

So y-intercept from the graph is 3

To solve algebraically, set x = 0 in the parabola equation and solve for y

We get, for x = 0,

y = - (0 + 1)² + 4

y = -(1²) + 4 = -1 + 4 = 3

Hence verified

Question 1c

There will be two x-intercepts for a parabola. Looking at the graph we see that the parabola intersects the x-axis at two points (-3, 0) and (1, 0). So the two x-intercepts are -3 and 1

Algebraically we can determine the x-intercepts by setting y = 0 and solving for the two values of x

Setting y = 0 in the parabolic equation, we get
y = 0 = -(x + 1)² + 4

Switch sides
-(x + 1)² + 4 = 0

-(x + 1)² = -(x² + 2x + 1) = -x² -2x - 1

-(x + 1)² + 4 = 0
==> -x² -2x - 1 + 4 = 0

==> -x² - 2x +3 = 0

Multiply by -1 both sides
==> x² + 2x - 3 = 0

Solve this quadratic equation by factoring

x² + 2x - 3 = (x - 1)(x + 3) = 0

The solutions are
x - 1 = 0   ==> x = 1

x + 3 = 0 ==> x = -3

Hence verified

what is the value of 32 ⅗ ?​

Answers

Answer:

8

Step-by-step explanation:

I attached my answer........

25 points plus brainliest

Answers

Answer:

The first answer is correct

Step-by-step explanation:

y = mx + b is the slope intercept form of a line

15x - 5y = 30  Subtract 15x from both sides

-5y = -15x + 60  Divide both sides by -5

y = 3x -6  The -6 is your y-intercept.  It is the point (0.-6)  We could stop here because that is the only choice that shows (0,-6), but let's find the x intercept.

The x-intercept is when y = 0

y = 3x -6

0 = 3x - 6 Add 6 to both sides

6 = 3x  Divide both side by 3

2 = x This is the point (2,0)

We could have taken the original equation and set x=0 and y=0

15x - 5y = 30

15(0) - 5y = 30

-5y = 30  Divide both sides by -5

y = -6

15x -5y = 30

15x - 5(0) = 30

15x = 30  Divide both sides by 15

x = 2

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Which number sentence is not true? A.|-20||9|D.|9| What general information about the serengeti do we need to research to further investigate the causes for the changes in the african buffalo population? Shazad and her twin brother, Amir, have recently turned 13 years old. Over the past year, family and friends recognize that Shazad has become more impulsive and easily loses her temper; Amir, on the other hand, loses his temper less frequently but has become more aggressive overall. What are some physical changes that males and females experience during puberty that may account for their behavior? What are some emotional and hormonal changes that males and females experience during puberty that may account for their behavior? PLEASE HELP!!!!!! If an index fossil is never found below a key bed what can you infer from this information? QUESTION 4On the playground, Jake stole the (girls/girl's/girls') jump rope. (meaning one girl)girlsgirl'sOgirls' Write and solve an equation to answer the question.How many people must attend the third show so that the average attendance per show is 3000?Write an equation. Write an equation write one Equation:_ =3000 Check all the formulas below that represent binary compounds.NH4CLCaSP05CaSO4NOCl Name:9. A ball is thrown vertically in the air from rest and soars for 4.2 seconds.If the acceleration due to gravity is 9.8 m/s, what is the final velocityof the ball when it is caught? which is the best translation of the dialect in the excerpt? "ah, i hear you crying again. you shouldnt do that. we will make the thieves go away." "ah, your wife is crying again. there is no need for that. we said we were good thieves." "ah, your kids are crying again. there is no need for that. we will make the thieves go away." "ah, your wife is crying again. we will call the other thieves over here if she doesnt stop." conifer leaves are generally thin and needle-like, while seeds are contained in cones. conifers include blank and blank jan smith, the marketing manager of big wheel autos, has noticed that in many european countries more of the population is moving into urban centers. this has resulted in an increased demand for subcompact cars that can maneuver through these congested streets rather than full-size automobiles. in the context of external information sources, this is an example of how can influence marketing management decisions. the objective of financial reporting as outlined in the conceptual framework guides the financial reporting process. identify whether each of the following phrases aligns with the objective of financial reporting or not. What is the quotient of 204 decided by 34 Sarah has a class assignment to debate how globalization has impacted business organizations. She will need to research both positive and negative effects of having a global economy. What are four arguments she can make about how the global economy impacts business organizations? Point T is on line segment \overline{SU} SU Given SU=19SU=19 and ST=15,ST=15, determine the length \overline{TU}. TU What are the limitations of your model in explaining fusion? Jerry and ralph are consumers of hockey tickets. For this exercise, suppose that all seats in the arena are of the same quality and have the same price. When tickets cost $160, neither will buy a ticket. If tickets cost $140, jerry is willing to buy one, but ralph will still not buy any. When each ticket costs $120, jerry will buy two tickets during the course of the hockey season and ralph will still buy no tickets. At a price of $100 per ticket, jerry is willing to buy three and ralph is willing to buy two tickets in a season. At a price of $60, jerry will buy five tickets and ralph will buy six tickets a season. At $40 a ticket, jerry will buy six and ralph will buy eight tickets during the season. Describe jerrys demand curve and ralphs demand curve. Then, suppose that jerry and ralph are the only individuals in the market and describe the market demand curve that shows the total number of tickets the market will buy at each price. Explain how you derive the market demand curve. What is the difference between a shift along a demand curve and a shift of a demand curve. the stamp act crisis was not the only example of social turmoil during the 1760s. identify the statements that describe the regulator movement. What type of price elasticity of demand results from a relatively small percentage change in quantity demanded divided by a relatively larger percentage change in price?.