a straight line through points p and q is drawn perpendicular to a line through points p(x,y) and r(x,(y+10)) . the possible coordinates of the point q are_?

Answers

Answer 1

On the X-Y plane, the points p and r are on the vertical line X=x. Then the perpendicular (horizontal) line through p will have the equation Y=y. Points q on that line will have coordinates

... q(<anything>, y)

Related Questions

Fill in the table and guess the value of the limit: \lim\limits_{x \to 3} f(x), where f(x)= \frac {x^3 - 27} {x^2 - 9}

Answers

Try this option:
[tex] \lim_{x \to 3} \frac{x^3-27}{x^2-9} = \lim_{x \to 3} \frac{x^2+3x+9}{x+3}= \frac{27}{6}= \frac{9}{2} [/tex]

Final answer:

To find the limit of f(x) as x approaches 3, factor the numerator and denominator as differences of squares, cancel common terms, and substitute x = 3 into the simplified fraction to get the limit, which is 4.5.

Explanation:

The student's schoolwork question involves calculating the limit of a function as x approaches a certain value. Specifically, the function in question is f(x) = (x^3 - 27) / (x^2 - 9) and the limit to be computed is limx → 3 f(x). To solve this, first recognize that directly substituting x = 3 would result in a 0/0 indeterminate form. To find the limit, we'll use algebraic manipulation.

Since both the numerator and the denominator are differences of squares, factoring them would give (x-3)(x^2+3x+9) for the numerator and (x-3)(x+3) for the denominator. The x-3 terms cancel out, leaving us with x^2+3x+9 over x+3. Now, substituting x = 3 into the simplified fraction will provide the value of the limit.

Calculating the limit step by step:

Original function: f(x) = (x^3 - 27) / (x^2 - 9)

Factor both numerator and denominator: f(x) = [(x-3)(x^2+3x+9)] / [(x-3)(x+3)]

Cancel out (x-3) terms: f(x) = (x^2+3x+9) / (x+3)

Substitute x = 3: f(3) = (3^2+3*3+9) / (3+3) = (9+9+9) / 6 = 27 / 6 = 4.5

Find two different sets of parametric equations for the given rectangular equation (there are many correct solutions)

x^2+4y^2 - 16=0

Answers

Wait, i need to know what ^ is

Wastewater is filling barrels at the rate of 11 quarts per hour. The recycling facility picks up 120 full barrels on each trip, and each barrel holds 12 quarts of wastewater. How many days are between each pickup? Show your work to receive full credit. (10 points)

Answers

(1 h)/(11 qt) * (12 qt)/(1 barrel) * (120 barrels/pickup) * (1 day)/(24 h)
.. = 12*120/(11*24) day/pickup
.. = 5 5/11 days/pickup

120 barrels will be filled every 5 5/11 days. Some trips will be 5 days apart, some trips will be 6 days apart.

A baseball team has three different pitchers. Randy pitched 333 innings and allowed 222 runs, Felix pitched 555 innings and allowed 444 runs, and Johan pitched 777 innings and allowed 555 runs.
Which pitcher has the lowest number of runs allowed per inning?

Answers

the correct question is
A baseball team has three different pitchers. Randy pitched 3 innings and allowed 2 runs, Felix pitched 5 innings and allowed 4 runs, and Johan pitched 7 innings and allowed 5 runs.
Which pitcher has the lowest number of runs allowed per inning?

we have that
we calculate the number of runs allowed in 1 inning

if Randy pitched 3 innings and allowed ------------2 runs
in 1 inning-----------------------------------> X
X=2/3----------> 0.67 runs

if Felix pitched 5 innings and allowed-------------> 4 runs
in 1 inning-----------------------------------> X
X=4/5----------> 0.80 runs

if Johan pitched 7 innings and allowed-------------> 5 runs
in 1 inning-----------------------------------> X
X=5/7----------> 0.71 runs

the answer is
Randy has the lowest number of runs allowed per inning with 0.67

Answer: the andswer is randy

Step-by-step explanation:

andy earned $38 on monday and $34 on tuesday.how many lucky bamboo plants can he buy with the total money he earned?

Answers

How much does each bamboo plant cost. This is impossible to solve without knowing the cost. I you have the cost i would be happy to help.

Thirty runners compete in a cross country race. your school has five runners in the race. what is the probability that three runners from your school place first, second, and third.

Answers

Final answer:

The probability that three runners from the same school finishing first, second, and third can be calculated as the product (5/30) * (4/29) * (3/28). This uses the principles of probability in mathematics.

Explanation:

The problem involves the concept of probability in Mathematics. Let's break this question down using the principles of probability.

For the first runner to be from your school, the probability would be 5/30 as there are 5 runners from your school out of 30 total runners. After one runner from your school has won, there are now 4 runners left from your school and 29 total runners left. So, the probability of the second runner being from your school is 4/29. Similarly, the probability that the third runner is also from your school is 3/28 since there are now three left from your school and 28 in total.

The final probability is the product of all three of these probabilities, so:

P(all three top spots are from your school) = (5/30) * (4/29) * (3/28), which needs to be calculated to get the final result.

Learn more about Probability here:

https://brainly.com/question/32117953

#SPJ11

The result is 0.00246, or about 0.25% chance.

To find the probability that three runners from your school place first, second, and third in a race with 30 runners, we need to consider the number of ways to select these three positions from your school's five runners and divide it by the total number of ways to select any three runners from all 30 participants.

Calculate the number of ways to choose 3 runners out of the 5 from your school:

[tex]C(5, 3) = $ \frac{5!}{3!(5-3)!} $ = 10[/tex]

Calculate the number of ways to arrange these 3 runners in the first, second, and third positions. This is equal to the number of permutations of 3 elements:

P(3) = 3! = 6

Calculate the total number of ways to choose 3 runners out of the 30 participants:

[tex]C(30, 3) = $ \frac{30!}{3!(30-3)!} $ = 4060[/tex]

Calculate the number of ways to arrange these 3 runners in the first, second, and third positions:

P(3) = 3! = 6

Finally, calculate the probability that 3 runners from your school place first, second, and third:

[tex]Probability = $ \frac{C(5, 3) \times P(3)}{C(30, 3) \times P(3)} $ = $ \frac{10 \times 6}{4060 \times 6} $ = $ \frac{10}{4060} $ = $ \frac{1}{406} $[/tex]

Thus, the probability is approximately 0.00246 (or 1/406).

A pitcher of fruit punch holes 2 gallons of nine people share the entire pitcher equally how much punch does each person get?

Answers

Well, first you must divide the amount of gallons by the amount of people.
2/9 = 2/9 gallons which would be about 3.5 cups.

(Personally I would do 2/9 cups)

bank discount look at the file please to answer questions

Answers

Given:
Bank discount formula:
Interest/Discount = Face Value/Principal * Rate * term

Maturity Value = Face Value/Principal

Proceeds = Maturity Value - Bank Discount

2) Face Value = 9,700 ; Discount Rate = 9.5% ; Term = 135 days
Discount = 9,700 * 0.095 * 135/360
Discount = 345.56
Proceeds = 9,700 - 345.56 = 9,354.44

3) Face Value = 15,600 ; Discount rate = 7.25% ; Term = 270 days
Discount = 15,600 * 0.0725 * 270/360
Discount = 848.25

4) Proceeds = 15,600 - 848.25 = 14,751.75

A survey found that 25% of pet owners had their pets bathed proffesionally rather than doing it themselves. If 18 pet owners are randomly selected, the probability that exactly 5 people have their pets bathed proffesionally is

A. 19.99%
B. 19.88%
C. 18.99%
D. 18.88%

Answers

The probability is 19.88%.

This is a binomial distribution, because there are two outcomes, the events are independent of each other, and there is a fixed number of trials. The binomial distribution is given by:

[tex](_k^n)p^k(1-p)^{n-k}[/tex]

For this, n is 18; k is 5; p is 0.25:
[tex](_5^{18})(0.25)^5(1-0.25)^{18-5} \\ \\=\frac{18!}{5!13!}(0.25)^5(0.75)^{13} \\ \\=8568(0.25)^5(0.75)^{13} \\=0.1988=19.88%[/tex]

What is the value of a, if a2 – 64 = 0 and a > 0?

Answers

a^2 -64 = 0

isolate the a

a² - 64 (+64) = 0 (+64)

a² = 64

√a² = √64

a = √64

a = 8

hope this helps

the sales of lawn mowers t years after a particular model is introduced is given by the function y= 5500 in (9t+4) where y is the number of mowers sold how many mowers will be sold 3 years after a model is introduced

Answers

Given the sales of the mowers is modeled by y=5500ln(9t+4)
where t is the number in year, then the sales after t=3 will be:
f(3)=5500ln(9*3+4)
f(3)=5500 ln(31)
f(3)=$18,886.93

If $8,500 is deposited in a compound interest account paying 3.9% interest annually, how much will be in the account after 12 years? Round your answer to the nearest cent.

Answers

$8,500/12 yr = $13,452.58

The formula for amount is given by:

[tex] A=P(1+\frac{r}{n})^{nt} [/tex]

Now we are given ,

Principal (P) =$8500

rate (r) =3.9% = 0.039

period of interest (n) =1 for compounded annually

time (t) = 12 years

Plugging these values in the formula,

[tex] A=8500(1+\frac{0.039}{1})^{1*12} [/tex]

Amount =$13452.5773053

Answer : There will be $13452.5773053 in the account after 12 years.

Cedric has $0.45 in his pocket which fraction of a dollar does Cedric have

Answers

Final answer:

Cedric has 9/20 of a dollar.

Explanation:

To find the fraction of a dollar that Cedric has, we need to convert $0.45 into a fraction with a denominator of 100, which represents cents. Since 1 dollar is equal to 100 cents, we can write $0.45 as 45 cents. So, Cedric has 45/100 of a dollar, which can be simplified to 9/20.

Determine whether the variable is qualitative or quantitative. number of flights

Answers

quantitative

Because you can count the number of flights, it is quantitative.

Find the absolute maximum and minimum of values of the set
d. f(x,y)= 2x^2+y^2-4x-2y+1 d={(x,y) | 0 <= 3, 0 <= y <= 2}

Answers

Find the critical points within the region:

[tex]f(x,y)=2x^2+y^2-4x-2y+1[/tex]
[tex]\implies\begin{cases}f_x=4x-4=0\implies x=1\\f_y=2y-2=0\implies y=1\end{cases}[/tex]

So (1, 1) is the only critical point of the function and it happens to fall within the rectangle [tex]D[/tex]. At this point, we get a value of [tex]f(1,1)=-2[/tex].

Now check along the boundaries for potential extreme values.

If [tex]x=0[/tex], then [tex]f(0,y)=y^2-2y+1=(y-1)^2[/tex], which has a maximum when [tex]y=2[/tex] and has a minimum when [tex]y=1[/tex]. So we have a potential extrema at [tex]f(0,2)=1[/tex] and [tex]f(0,1)=0[/tex].

If [tex]x=3[/tex], then [tex]f(3,y)=y^2-2y+7=(y-1)^2+6[/tex], with a max when [tex]y=2[/tex] and min when [tex]y=1[/tex]. So we have [tex]f(3,2)=7[/tex] and [tex]f(3,1)=6[/tex].

If [tex]y=0[/tex], then [tex]f(x,0)=2x^2-4x+1=2(x-1)^2-1[/tex], with a max when [tex]x=3[/tex] and a min when [tex]x=1[/tex]. So we have [tex]f(3,0)=7[/tex] and [tex]f(1,0)=-1[/tex].

If [tex]y=2[/tex], then [tex]f(x,2)=2x^2-4x+1=2(x-1)^2-1[/tex] again, with a max when [tex]x=3[/tex] and a min when [tex]x=1[/tex]. So we have, again, [tex]f(3,2)=7[/tex] and [tex]f(1,2)=-1[/tex].

So there are absolute maxima of 7 at (3, 0) and (3,2), and an absolute minimum of -2 at (1, 1).

What ratio can be used to covert meters to kilometers A.100km/1m B.1000km/1m C. 1km/1000m D. 1km/10m

Answers

1 km = 1000m

Answer C

At the Golden Gopher Mall , 1,300 People Took the Coke/Pepsi Challenge, 55% Of those challenged preferred Coke. how many people selected coke?

Answers

whatever% of anything is just (whatever/100) * anything.

therefore, 55% of 1300 is just, (55/100) * 1300, that many.

The three-dimensional figure shown consists of a cylinder and a right circular cone. The radius of the base is 10 centimeters. The height of the cylinder is 16 centimeters, and the total height of the figure is 28 centimeters. The slant height of the cone is 13 centimeters. Which choice is the best approximation of the surface area of the figure? Use 3.14 to approximate pi.

Answers

This is an incomplete question, here is the complete question.

(1) 1727 cm²

(2) 2355 cm²

(3) 2041 cm²

(4) 6699 cm²

Answer : The surface area of the figure is, 1727 cm²

Step-by-step explanation :

The formula for curved surface area of triangle is:

[tex]A=\pi \times r\times l[/tex]

where,

r and l are radius and slant height of triangle.

The formula for curved surface area of cylinder is:

[tex]A=2\pi \times r\times h[/tex]

where,

r and h are radius and height of cylinder.

The formula for area of circle is:

[tex]A=\pi r^2[/tex]

where,

r is radius circle.

Now we have to calculate the surface area of total figure.

Surface area of total figure = Surface area of triangle + Surface area of cylinder + Area of circle

Surface area of total figure = [tex]\pi \times r\times l+2\pi \times r\times h+\pi r^2[/tex]

Surface area of total figure = [tex]\pi \times r(l+2h+r)[/tex]

Given:

r = 10 cm

h = 16 cm

l = 13 cm

Now put all the given values in this formula, we get:

Surface area of total figure = [tex]3.14\times 10\times (13+2\times 16+10)[/tex]

Surface area of total figure = 1727 cm²

Thus, the surface area of the figure is, 1727 cm²

a motorboat travels 432 kilometers on 6 hours going upstream and 384 km in 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current.
please help slove and steps

Answers

Going upstream: 432 km / 6 hours = 72 km/h
Going downstream: 384 km / 4 hours = 96 km/h
Going upstream against the current means that the effective speed is:
r_boat - r_current = 72
Meanwhile, going downstream with the current means;
r_boat + r_current = 96
Adding both equations (to cancel out r_current) gives:
2r_boat = 72 + 96
r_boat = 84 km/h
Substituting back into one of the original equations: r_current = 12 km/h.

Answer:

the answer is 12

hope i helped

Step-by-step explanation:

Balancing chemical equations lab answers is the number of total molecules on the left side of a balanced equation always equal to the number of total molecules on the right side of the equation?

Answers

Since no reaction creates or destroys atoms, every balanced chemical equation must have equal numbers of atoms of each element on each side of the equation. However, the number of molecules does not necessarily have to be the same.

The answer is
No, the total number of molecules can be equal or not

Yes, in a balanced chemical equation, the number of total molecules (or atoms) on the left side of the equation is always equal to the number of total molecules (or atoms) on the right side of the equation. This principle is known as the Law of Conservation of Mass.

The Law of Conservation of Mass states that in a chemical reaction, matter is neither created nor destroyed. This means that the total mass of the reactants must be equal to the total mass of the products. Since molecules are composed of atoms, the number of atoms of each element on the left side of the equation must equal the number of atoms of the same element on the right side of the equation.

To balance a chemical equation, coefficients are placed in front of the chemical formulas to ensure that the number of atoms of each element is the same on both sides of the equation. Balancing the equation ensures that the total number of molecules (or atoms) is conserved, maintaining the principle of the Law of Conservation of Mass. Therefore, in a balanced chemical equation, the number of total molecules on the left side is always equal to the number of total molecules on the right side.

COMPLETE QUESTION:

Balancing chemical equations lab answers is the number of total molecules on the left side of a balanced equation always equal to the number of total molecules on the right side of the equation?

What is the volume of the coffee in a can if the can has a radius of 4 inches and a height of 9 inches? (Use 3.14 for π.)

Answers

use the formula of v = pi.(r^2).h that gives approximately v = 3.14x16x9 that gives approximately 452.16

Answer:

452.16 is the answer

Step-by-step explanation:

What are the solutions of the equation x4 + 95x2 – 500 = 0?

Answers

x4+(95x2)-500=0
x4+(190)-500=0
x4-310=0
x4=310
x=4√(310)
x=4.196

Answer:

Step-by-step explanation:

x = plus-or-minus StartRoot 5 EndRoot and x = ±10i

ED 2021

The Chang's neighbor owns a ready-mix company. The company receives an order for 12.5 cubic yards of concrete. This mixture of concrete contains sand, cement, gravel, and water. For each pound of water, there are 5.5 pounds of sand, 2 pounds of cement, and 7.5 pounds of gravel. Determine how many pounds of cement must be used. Assume a cubic yard of concrete weighs 4,000 pounds.

Answers

The quantities in the proportion you give add to 16 pounds, of which 2 pounds are cement. That is, cement constitutes 1/8 of the total weight.

For each yard of concrete, 4000 lb/8 = 500 lb of cement are used.

For 12.5 yards of concrete, 12.5 * 500 = 6,250 pounds of cement will be used.

_____
"yard" in this case is shorthand for "cubic yard".

(A) A bag of trail mix weighs 2 lb. By weight, 20% of the bag is oats. How many pounds is the oats portion of the trail mix? Write an equation for the situation and label the “part,” “whole,” and “percent.”
(B) What is the weight of the oats in the trail mix? Show your work!
20 POINTS !!!
YOU CAN GET BRAINLIEST !!!!!!
THIS IS MY SECOND FREAKIN TIME POSTING THIS IM WASTING POINTS

Answers

PART A
First we define the variables:
x: number of pounds in the bag
y: number of pounds of oats
The equation to find the number of pounds of oats in the bag is:
y = (20/100) x
Simplifying:
y = (1/5) x
(1/5): Represents that 20% of the weight of the bag is oatmeal.
Answer:
y = (1/5) x

PART B
Using the equation of part A, we have:
y = (1/5) (2)
y = 0.4 lb
Answer:
0.4 lb corresponds to the oat weight of the 2 lb that the bag weighs

The trapezoid below has an area of 1575 cm. What equation could you solve to find the height of the trapezoid

Answers

Answer:

Step-by-step explanation:

Whats the sum 3/x + 4/x^2

Answers

the sum is 3x+4/x^2

But that is if the x in the second part is supposed to be squared

Answer:

[tex]\frac{3x+4}{x^2} [/tex]

Step-by-step explanation:

sum of [tex]\frac{3}{x} + \frac{4}{x^2}[/tex]

To find the sum of two fractions we need to make the denominator same

LCD is x^2. we need to get x^2 in the denominator of both fractions

Multiply the first fraction with x

[tex]\frac{3 \cdot x}{ \cdot x} + \frac{4}{x^2}[/tex]

[tex]\frac{3x}{x^2} + \frac{4}{x^2}[/tex]

Denominators are same , now we add the numerators

[tex]\frac{3x+4}{x^2} [/tex]

Find two numbers, if their sum is (−1/3) and their difference is 18

Answers

x + y = - 0.3333333 That's the decimal equivalent of - 1/3
x - y = 18 Add these two together.
2x = 17.66666 Divide by 2
x = 8.833333

8.83333 + y = - 0.333333
y = - 0.333333 - 8.83333
y = - 9.16666

You should check this using the difference.
It will not come out exactly, but you do get a bunch of nines.

An airline sells all tickets for a certain route at the same price. if it charges 250 dollars per ticket it sells 5000 tickets. for every 5 dollars the ticket price is reduced, an extra 500 tickets are sold. it costs the airline a hundred dollars to fly a person. what price will generate the greatest profit for the airline?

Answers

let's look at the demand quantity as a function of price. Th problem tells us that q(250)= 500
the rate of change of q is a constant, thus, q is a line whose slope is -500/5=-100 tickets/ dollar.
therefore we shall have:
q(p)=5000-100(p-250)=3000-100p

the revenue for each price will be:
r(p)=p×q(p)=p(30000-100p)

next we get the total cost which is:
100×q, where q is the number of people who will fly.
but q=30000-100p
hence
c(p)=100(30000-100p)

the profit will be:
Profit=revenue-cost
=r(p)-c(p)=p(30000-100p)-100(30000-100p)
this will be written in quadratic form as:
(p-100)(30000-p)
next we find p that maximizes the profit function
(p-100)(30000-p)=-p²+30100p-3000000
when you take the derivative of the above, the maximum point will be at p=200, this will give us the profit of:
p(200)=-200²+30100(200)-3000000=1000000

Answer:

Scenario II i.e. when the price of ticket is $[tex]$245[/tex] will generate the greatest profit for the airline

Step-by-step explanation:

Scenario I

[tex]5000[/tex] tickets are sold at $ [tex]250[/tex] per ticket

The total money earned by the flight agency is

Number of tickets x price of each tickets

[tex]= 5000 * 250\\[/tex]

[tex]= 1250000[/tex] dollars

Scenario II

The price of each ticket is reduced by $[tex]5[/tex]

The price of new ticket is

[tex]250 -5[/tex]

[tex]= 245[/tex] dollars

The new number of tickets sold after reducing the price is

[tex]5000+ 500\\[/tex]

[tex]5500[/tex]

The total money earned by the flight agency is

Number of tickets x price of each tickets

[tex]5500 * 245\\[/tex]

[tex]1347500[/tex] dollars

Scenario II i.e. when the price of ticket is $[tex]$245[/tex] will generate the greatest profit for the airline

The sum of a number (n) and 20 is 55. Which equation shows this relationship?

Answers

sum is an addition
n + 20 = 55

A shipment of 20tvs contains 5 that are defective. if 10 of them are randomly chosen for inspection, what is the probability that 2 out of 10 will be defective?

Answers

1/4 of the shipment is defective so if half is randomly chosen to test the answer would be 5/20 or 2/10 so 1/4 or 1/5

Final answer:

Using the hypergeometric distribution, the probability that exactly 2 out of 10 TVs randomly chosen from a shipment of 20 are defective is approximately 34.81%.

Explanation:

To find the probability that exactly 2 out of 10 randomly chosen TVs are defective, we can use the hypergeometric distribution. This distribution applies because we are dealing with a scenario where we have a finite population (20 TVs) and a non-replacement condition (once a TV is chosen for inspection, it is not put back).

The probability formula for the hypergeometric distribution is:

P(X = k) = [(C(g, k) * C(N-g, n-k)) / C(N, n)]

Where:

C(a, b) is the combination of a items taken b at a time.N is the total number of items in the population (20 TVs).g is the number of defective items in the population (5 defective TVs).n is the number of items chosen (10 TVs inspected).k is the number of defective items we're interested in finding within the chosen items (2 defective TVs).

Plugging the numbers into the formula, we have:

P(X = 2) = [(C(5, 2) * C(15, 8)) / C(20, 10)]

P(X = 2) = [(10 * 6435) / 184756]

P(X = 2) = [64350 / 184756] ≈ 0.3481

So, the probability that exactly 2 out of 10 TVs inspected will be defective is approximately 0.3481 or 34.81%.

Other Questions

20 Points! Please Help!The point (3, 1) is on the terminal side of angle , in standard position. What are the values of sine, cosine, and tangent of ? Make sure to show all work.Please explain everything! Robert plans to make a box-and-whisker plot of the following set of data. 27, 14, 46, 38, 32, 18, 21 Which of the following should Robert's box-and-whisker plot look like? If the oxidation number of nitrogen in a certain molecule changes from +3 to -2 during a reaction, is the nitrogen oxidized or reduced? how many electrons are gained or lost by the nitrogen atom? If f(x) = x2 + 1 and g(x) =x-4, which value is equivalent to (fg)(10) In at least 100 words, describe the interactions between Rowlandson and the Native Americans she lived with. if you know that 7 + 2i is a root of a polynomial function ,what is another root of that same function? A family's vacation destination is 850 miles from their home. They travel by car 6 hours on the first day of their trip. Their average speed is 45 mph. The next day they travel 7 hours, averaging the same speed. How many miles are left for the family to travel? In a diagram of a landscape plan, the scale is 1 cm = 10 ft. in the diagram, the trees are 4.3 cm apart. How far apart should the actual trees be planted?43 ft 430 ft1.3 ft0.43 ft Would someone please help me with my French? Thank you!! A computer company uses the linear model y = -21x + 13,082 to predict the decline in sales of a computer after it has been on the market more than one year. If x is the number of months after the first year and y is the number of computers sold during that month, how many computers will be sold 11 months after the first year? k=1; f(x)=4x^3-2x^2+2x+4; Lower bound? in the story subha What does the husband do before he marries again? What is 0.125 Point rounded to the nearest hundredth The second leading aide of death among people aged 15-24 is What is the equation of a line with a slope of 7 and a point (1, 8) on the line?A) y = 7x + 1B) y = 7xC) y = 7x + 8D) y = 7x 56 How many times larger is the value 0.75 than the value 0.0075? Please show how to solve the problem. Which was an argument in favor of U.S. imperialism?(Points : 1) Imperialism promoted the Monroe Doctrine. Imperialism would establish Manifest Destiny. Imperialism would make the United States economically competitive with other nations. Imperialism would assist former allies in securing new markets in Africa. PLEASE HELP WILL GIVE BRAINLIEST!!!!!!! This is the graph of f(x). What is the value of f(2)? Write three to five sentences explaining which levels of production provide Alonzos Cycling with the maximum profit. Shakespeare writes in A Midsummer Night's Dream:"Ay me! for aught that I could ever read,Could ever hear by tale or history,The course of true love never did run smooth"-- Act 1, Scene 1PROMPT:K12 PLEASE HELP 30 POINTS-What is Shakespeare saying about love in these lines?-If you had to choose a theme related to love what would it be for this play?-Focus on at least 2 characters in the play to provide support for your theme.Use the RACES method to construct your answer (which includes citing lines/pulling details from the text) and following proper grammar and capitalization rules.