HELP NOW PLZ 20-30 POINTS FOR BRAINLIEST LOOK AT MY PROFILE FOR THE SAME QUESTION WITH MORE POINTS Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant! (Recall: Standard Form of a quadratic equation is Ax^2 + Bx + C ). You need to choose a value for A, B, and C that satisfies each of the following conditions. You can use a value of 0 for B for no more than 1 of the 5 questions! Step 2: Solve each of the equations you create. YOU MUST SHOW YOUR WORK TO RECEIVE CREDIT FOR THIS STEP! Write your Exact answer in simplest form AND if necessary, round your estimate to the nearest tenth. 1) Equation 1 should represent a parabola that opens up and has a negative y-intercept. Equation 1: ____________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 2) Equation 2 should represent a parabola that opens down and has a negative y- intercept. Equation 2:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 3) Equation 3 should represent a parabola that is a vertical stretch of the parent function and has a y-intercept greater than 3 and opens down. Equation 3:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 4) Equation 4: You decide what type of parabola you would like to create by answer the following questions: Does your parabola open up or down? _______________ Is there a vertical stretch or vertical compression? _______ What is the y-intercept? __________ Equation 4: ____________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 5) Write a quadratic equation that can only be solved using the quadratic formula. Equation 4: _________________________________________________________________ Show your work for how you use the quadratic formula to solve this equation:

Answers

Answer 1

Step-by-step explanation:

Equation 2: -\(x^{2}\) + 3x - 6

Equation 2 should represent a parabola that opens down and has a negative y-intercept.

Parabola that opens down = a<0

Ax^2 + Bx + C

-\(x^{2}\) + 3x - 6

Negative y-intercept: -(0)^2 +3(0) -6 = y= -6

Strategy to solve: Quadratic formula

Why? - This equation doesn't factor cleanly.

Show your work:

a= -1 b= 3 c= -6

Write the quadratic formula down (\(x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}\)) ± not just +

Show step, solve.

x​= 1.5 + 1.9365i

Equation 3:

Sorry, I can't do this.

Equation 4 :\(x^{2} -1\)

You decide.

Alright, easy parabola.

1. Does parabola open up or down. UP

2. Is there a vertical stretch or compression? NO

3. What is the y-intercept- (0,-1)

\(x^{2} -1\)

Strategy: Simple factoring patterns (Difference of squares) -

(x+1)(x-1)

x = + 1

Show work: x^2 is square of x,

Equation 5: \(x^{2} -3x+15\)

x^2−3x+15

a=1 b= -3 c=15

(\(x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}\)) ± not just +

Good luck! Sorry that I couldn't do equation 3, vertical stretches are not my thing.


Related Questions

When coding the phrase "supravesical fissure of urinary bladder," the main term to reference in the index is ________ .a. urinaryb. bladderc. fissured. supravesical

Answers

The correct option of the given question is option (c)  fissure.

When coding the phrase "supravesical fissure of urinary bladder," the main term to reference in the index is c. fissure.

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The main term to reference in the index when coding the phrase "supravesical fissure of urinary bladder" is c. fissure.

In medical coding, the index is typically organized alphabetically based on the main terms or significant words within medical terminology. In this case, "fissure" is the main term that represents the specific condition or anatomical feature being coded.

The other terms, such as "urinary," "bladder," and "supravesical," provide additional context but are not the primary focus when searching for the appropriate code in the index.

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help i need a good grade

help i need a good grade

Answers

Answer:

7.141

.133

9.902

Step-by-step explanation:

give me brainliest please! :) also, hope it helps have a great day

A company orders 27 boxed lunches from a deli for $245.70. if each boxed lunch costs the same amount, what is the unit cost of each boxed lunch?
pls help

Answers

If the company orders 27 boxed lunches from a deli for $245.70 and each boxed lunch costs the same amount then the unit cost of each boxed lunched is $9.1.

What is the unit cost of each boxed lunch?

Given that;

27 boxed lunches from a deli cost $245.70Cost of 1 box = ?

To determine the unit cost of each boxed lunch, we say;

Cost of each box = $245.70 ÷ 27

Cost of each box = $9.1

Hence, if the company orders 27 boxed lunches from a deli for $245.70 and each boxed lunch costs the same amount then the unit cost of each boxed lunched is $9.1

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Determino la altura de la torre de refrigeración de una central nuclear si se sabe que su sombra mide 271 m cuando los rayos solares forman un ángulo de 30°

Answers

Respuesta:

156,46 m

Explicación paso a paso:

Podemos obtener la altura de la torre de enfriamiento usando trigonometría;

Tan θ = opuesto / adyacente

Altura de la torre de enfriamiento = opuesto

Altura de la sombra = 271 m = adyacente

Tan 30 = opuesto / 271

Opuesto = 271 tan30

Altura de la torre de enfriamiento = 0.5773502 * 271

Altura de la torre de enfriamiento = 156,46 m

Use the relationship between quantities to calculate the
missing values in the table
A =
B =
HELP ME PLEASE ILL DO ANYTHING

Answers

Answer:

Step-by-step explanation:

Photo Proof

Use the relationship between quantities to calculate themissing values in the tableA =B =HELP ME PLEASE

The missing value should be in the table is 750 and 1250.

Calculation of the missing value:Minutes       Words

1                     250

2                    500

3                     750

4                    1000

5                    1250

Since we can see that there is the gap of 250 in each words

like

= 250 + 250

= 500

So

= 500 + 250

= 750

And, so on

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3. Assume that a small open economy can be described as follows: Y=C+I+G + NX Y = F(L,K) = Y = 5000 C = 1000+ 0.5(Y - T) I = 2000 20r G = G = 1600 T = T = 1000 r = r* = 6% Please note that economists are treating interest rates as whole numbers, not decimals, e.g., if the interest rate is 3%, then r = 3. a. What is the trade balance? Is the country experiencing a trade surplus, a trade deficit, or balanced trade? Explain. b. Is the country borrowing or lending money on the world financial markets? If so, how much? Explain.

Answers

The country is borrowing 1600 units of money on the world financial markets.

a. To determine the trade balance, we need to calculate the net exports (NX) using the given information. The formula for net exports is:

NX = Y - (C + I + G)

Given:

Y = 5000

C = 1000 + 0.5(Y - T) = 1000 + 0.5(5000 - 1000) = 1000 + 0.5(4000) = 1000 + 2000 = 3000

I = 2000

G = 1600

T = 1000

Plugging these values into the net exports equation:

NX = 5000 - (3000 + 2000 + 1600) = 5000 - 6600 = -1600

The trade balance is -1600. A negative trade balance indicates a trade deficit, which means that the country is importing more goods and services than it is exporting. In this case, the country is experiencing a trade deficit.

b. To determine whether the country is borrowing or lending money on the world financial markets, we need to examine the relationship between domestic investment (I) and national saving (S). If domestic investment exceeds national saving, the country is borrowing money. If national saving exceeds domestic investment, the country is lending money.

The formula for national saving (S) is:

S = Y - C - G

Plugging in the given values:

S = 5000 - 3000 - 1600 = 400

The national saving is 400.

Since investment (I) is 2000, which is greater than national saving (400), the country is borrowing money on the world financial markets. The amount being borrowed is the difference between investment and national saving:

Borrowing = I - S = 2000 - 400 = 1600

Therefore, the country is borrowing 1600 units of money on the world financial markets.

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Finnish Furniture manufactures tables in facilities located in three cities--Reno, Denver, and Pittsburgh. The tables are then shipped to three retail stores located in Phoenix, Cleveland, and Chicago. Management wishes to develop a distribution schedule that will meet the demands at the lowest possible cost. The shipping cost per unit from each of the sources to each of the destinations is shown in the following table:
To
From Phoenix Cleveland Chicago
Reno 10 16 19
Denver 12 14 13
Pittsburgh 18 8 12
The available supplies are 130 units from Reno, 200 from Denver, and 160 from Pittsburgh. Phoenix has a demand of 140 units, Cleveland has a demand of 160 units, and Chicago has a demand of 200 units.
1. How many units should be shipped from each manufacturing facility to each of the retail stores if cost is to be minimized?
2. What is the total cost?

Answers

To minimize costs, the optimal distribution schedule for Finnish Furniture would involve shipping 130 units from Reno to Phoenix, 20 units from Denver to Cleveland, and 160 units from Pittsburgh to Chicago. This allocation is determined by using the transportation algorithm, specifically the Vogel's Approximation Method (VAM), which considers the lowest shipping costs per unit for each source-destination combination. By following this approach, the total cost for the distribution is calculated to be $4,360.

To determine the optimal distribution schedule that minimizes costs, we need to allocate the available supplies from the manufacturing facilities to the retail stores based on the shipping costs per unit. We can achieve this by employing the transportation algorithm, such as the North-West Corner Rule or the Vogel's Approximation Method (VAM).

Using VAM, we begin by identifying the lowest shipping cost per unit for each row and column in the given table. We then select the highest difference between the two lowest costs, considering both rows and columns. This difference indicates the most cost-effective allocation.

In this case, the VAM suggests shipping 130 units from Reno to Phoenix since the shipping cost per unit is 10, which is the lowest for the Reno row. For Cleveland, Denver has the lowest cost at 14, so we allocate 20 units from Denver to Cleveland. Lastly, we allocate 160 units from Pittsburgh to Chicago, as the cost per unit is the lowest at 12 for the Pittsburgh column.

Now, let's calculate the total cost. The cost of shipping 130 units from Reno to Phoenix is 130 x 10 = $1,300. Shipping 20 units from Denver to Cleveland costs 20 x 14 = $280. Lastly, shipping 160 units from Pittsburgh to Chicago costs 160 x 12 = $1,920. Adding these costs together gives us a total cost of $1,300 + $280 + $1,920 = $4,360.

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nolan is taking a multiple choice test his grade is given by the equation y=70-2x where y represents his final score and x represents the number of questions he got wrong . waht could the number 70 represents in the equation? ​

Answers

Answer:

70 could represent the total number of points nolan can earn on the test

Step-by-step explanation:

Michael opened a savings account at an annual interest rate of 5%. At the end of 3 years, the account balance is $4630.50. If Michael did not add any other amounts to this account, how much was his initial deposit?

Answers

Answer:

$4026.52

Step-by-step explanation:

Given data

rate= 5%

time= 3years

A=$4630.50

P=?

we know that

A=P(1+rt)

$4630.50=P(1+0.05*3)

$4630.50=P(1+0.15)

$4630.50=P(1.15)

P=4630.50/1.15

P=$4026.52

The intitial amount is $4026.52

Point M is on line segment
L
N

LN
. Given
L
N
=
9
,
LN=9,
M
N
=
4
x
,
MN=4x, and
L
M
=
5
x
,
LM=5x, determine the numerical length of
M
N

.
MN

Answers

The value of x from the given expression is 1

Addition postulate

If the point M is on the line LN, then the equivalent addition postulate is expressed as;

LM+MN = LN

Given the following

LN=9,

MN =4x

LM=5x

Substitute

5x + 4x = 9

9x = 9

x =9/9

x = 1

Hence the value of x from the given expression is 1

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The roots of 7x^2 + x - 5 = 0 are a and b. Compute (a - 4)(b - 4).

Answers

Answer:

just divide

Step-by-step explanation:

and just use the formula


Use FOIL (First, Outer, Inner, Last) to compute (a-4)(b-4)

(a-4)(b-4) =
ab - 4a - 4b + 16

complete the explanation of how a model can help you solve surface area and volume provlems. A (graph drawing or net) shows faces and helps you find ( surface area or volume problems). A (graph net or drawing) helps you choose a base. and height when finding (surface area volume or area)


pls i need it done in 20 mins ​

Answers

A model can help you solve surface area and volume problems because shows faces and helps you find the volume or area.

Why are surface area and volume problems challenging?

These problems can be challenging for some students because it implies imaging or visualizing 3-d objects to understand the dimensions of the figure, the number of faces, and then to calculate the volume or surface area.

This can be solved by using a model such as a graph or drawing that will help you to get a better idea of the object that is being analyzed.

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PLEASE HELP FAST!!!!!
Let f(x)=8^x and g(x)=8^x+5 +1. Which transformations are needed to transform the graph of f(x) to the graph of g(x)? Select each correct answer.
horizontal translation 5 units right
vertical translation 5 units up
horizontal translation 1 unit left
vertical translation 1 unit down

Answers

Answer:

See below

Step-by-step explanation:

Given functions

f(x)=8^xg(x)=8^(x+5) + 1

As we see g(x) = f(x + 5) + 1, which means horizontal translation 5 units left and vertical translation 1 unit up.

Answer options are all incorrect

PLEASE HELP FAST!!!!!Let f(x)=8^x and g(x)=8^x+5 +1. Which transformations are needed to transform the

use green's theorem to find the counterclockwise circulation and outward flux for the field f=(7x−4y)i (9y−4x)j and curve c: the square bounded by x=0, x=4, y=0, y=4.

Answers

The counterclockwise circulation around c is 12 and the outward flux through c is zero.

Green's theorem is a useful tool for calculating the circulation and flux of a vector field around a closed curve in two-dimensional space.

In this case,

we have a field f=(7x−4y)i+(9y−4x)j and

a square curve c bounded by x=0, x=4, y=0, y=4.

To find the counterclockwise circulation, we can use the line integral of f along c, which is equal to the double integral of the curl of f over the region enclosed by c.

The curl of f is given by (0,0,3), so the line integral evaluates to 12.

To find the outward flux, we can use the double integral of the divergence of f over the same region, which is equal to zero since the divergence of f is also zero.

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during the winter, the ice festival committee measures the depth of the ice during the month of february. what is the type of measurement scale? multiple choice ratio interval nominal numerical

Answers

The type of measurement scale used by the ice festival committee to measure the depth of the ice during the month of February is the ratio scale. Here option A is the correct answer.

A ratio scale is a type of measurement scale that possesses all the properties of an interval scale with an additional feature of a true zero point. This means that the measurements on a ratio scale have a meaningful zero point, indicating the complete absence of the measured quantity. For example, in the case of measuring the depth of the ice, a ratio scale would allow us to say that the depth of the ice is zero when there is no ice present.

In contrast, interval scales, which are commonly used in temperature measurements, do not have a true zero point. While zero on an interval scale represents the absence of a particular value, it does not imply that the quantity being measured is absent altogether.

Nominal scales, on the other hand, are used to categorize data into distinct and separate groups without any inherent order or numerical value. These scales are used to measure qualitative variables, such as gender or race.

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Complete question:

During the winter, the ice festival committee measures the depth of the ice during the month of February. what is the type of measurement scale? multiple choice

A - ratio

B - interval

C - nominal

D - numerical

Order the measurements from greatest to least. 45 inches, 6 yards, and
2 1/2 feet

Answers

Answer: 6 yards then 2 1/2 feet and then 45 inches

Step-by-step explanation: It is what it is.

While using bisection method to find the solution of the equation f(x)=x⁴ +3x-2=0 on interval [0, 1], after the first step the interval becomes ___

Answers

While using bisection method to find the solution of the equation f(x)=x⁴ +3x-2=0 on interval [0, 1], after the first step of the bisection method, the interval becomes [0.5, 1].

To use the bisection method to find the solution of the equation f(x) = x⁴ + 3x - 2 = 0 on the interval [0, 1], we start by evaluating the function at the endpoints of the interval.

f(0) = 0⁴ + 3(0) - 2 = -2

f(1) = 1⁴ + 3(1) - 2 = 2

Since the function changes sign on the interval [0, 1] (f(0) < 0 and f(1) > 0), we can conclude that there is at least one root within this interval.

The bisection method involves iteratively dividing the interval in half and selecting the subinterval where the function changes sign. In each iteration, we calculate the midpoint of the interval and evaluate the function at that point.

After the first step, we find the midpoint of the interval [0, 1]:

midpoint = (0 + 1) / 2 = 0.5

We then evaluate the function at the midpoint:

f(0.5) = (0.5)⁴ + 3(0.5) - 2 = -0.375

Since f(0.5) is negative, we can update our interval to [0.5, 1]. The new interval now contains the root of the equation.

This updated interval allows us to continue the bisection method and refine our approximation of the root of the equation f(x) = x⁴ + 3x - 2 = 0 within the specified interval.

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An account with an initial balance of $5000 earns 5% interest for 3.5 years.

Answers

Answer:

The investor will earn $875 over the course of 3.5 years.

Step-by-step explanation:

Sounds like simple interest (not compound interest).

The appropriate formula is i = prt, which here is

i = $5000(0.05)(3.5) = $875

The investor will earn $875 over the course of 3.5 years.

Consider the following linear transformation of a random variable y = x - mu x/sigma x where mu_x is the mean of x and sigma x is the standard deviation. Then the expected value and the standard deviation of Y are given as: 1 and 1. cannot be computed because Y is not a linear function of X. 0 and 1. mu_x/sigma_x and sigma_x.

Answers

The expected value of Y is mu x  (mu x²/ sigma x) and the standard deviation of Y is 1  (mu x / sigma x)| × sigma x.

The expected value and the standard deviation of Y computed using the given linear transformation.

The linear transformation is defined as y = x  (mu x / sigma x) × x

To find the expected value of Y (E[Y]) substitute the transformation into the formula for expected value

E[Y] = E[x  (mu x / sigma x) × x]

Since the expected value is a linear operator split it into two parts

E[Y] = E[x]  (mu x / sigma-x) × E[x]

The first part E[x]  is simply the mean of the random variable x which is mu-x.

E[Y] = mu x - (mu x / sigma x) × mu-x

Simplifying further

E[Y] = mu x  (mu x² / sigma x)

The standard deviation of Y (sigma Y), the formula for the standard deviation of a linear transformation

sigma Y = |1  (mu x / sigma x)| × sigma x

Substituting the given transformation

sigma Y = |1  (mu x / sigma x)| × sigma x

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What’s the answer ?

Whats the answer ?

Answers

Answer:

24

Step-by-step explanation:

Use implicit differentiation to find dx
dy

. x 5
+siny=x 3
y 4
dx
dy

=

Answers

The value of dx/dy is cos(y) - 90000000y³ / (33750000y⁴ - 18750000000).

The given equation is x⁵ + sin(y) = x³y⁴.We need to use implicit differentiation to find dx/dy.

The implicit differentiation formula is given by

df/dx = (df/dy) / (dx/dy)

Differentiating the given equation with respect to x, we get

5x⁴ + cos(y) dy/dx = 3x²y⁴ + 4x³y³ dy/dx

Taking the terms involving dy/dx on one side, we get

cos(y) dy/dx - 4x³y³ dy/dx = 3x²y⁴ - 5x⁴

Dividing both sides by (cos(y) - 4x³y³), we get

dy/dx = (3x²y⁴ - 5x⁴) / (cos(y) - 4x³y³)

Therefore, dx/dy = (cos(y) - 4x³y³) / (3x²y⁴ - 5x⁴)

Substituting x = 150, we get

dx/dy = cos(y) - 90000000y³ / (33750000y⁴ - 18750000000)

Hence, the value of dx/dy is cos(y) - 90000000y³ / (33750000y⁴ - 18750000000).

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complete the problems using synthetic division

complete the problems using synthetic division

Answers

Answer:

Step-by-step explanation:

Write k for the divisor.

Write the coefficients of the dividend.

Bring the leading coefficient down.

Multiply the leading coefficient by k.

Add the terms of the second column.

Multiply the result by k.

Repeat steps 5 and 6 for the remaining columns.

Hello guys ^-^
I have a bad news I taking a break from Brainly from today till October 16 or less

Sorry guys I can’t answer the questions but I request you all to give me brainiest for the questions I answered please mark me brainlist please please

Ok guys enjoy with given points

By€​

Answers

Answer:

Thanks for points though.

Step-by-step explanation:

Hope this helps

Have a great day ahead

The area of a regular octagon is 45 ft2. What is the area of a regular octagon with sides 1/3 the length of sides of the larger octagon

Answers

The area of a regular octagon with sides 1/3 the length of sides of the larger octagon is 173.82 ft sq.

The area of a polygon = n side^2 / (4 tan(180/n))

where "n" is the number of sides

To calculate area for side = 2

area = 8 x 2^2 / (4  tan(180/8))

area = 32 / (4  tan(22.5))

area = 32 / 4 x 0.41421

area = 19.3138746047

To calculate area for side = 6

area = 8*6^2 / (4 * tan(180/8))

area = 288 / 1.65684

area = 173.824871442

173.824871442 / 19.3138746047 =  9

So, the area would be 9 times larger.

Therefore, if we increase the side length is increased by 1/3, then the area increases by 1/9.

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What is the true solution to the equation below? ln e^lnx + on e ^lnx2 = 2 on 8

Answers

After solving the given equation In \(e^{lnx} +\) in \(e ^{lnx2}\) = 2 in 8, we know that the value of x is (B) 4.

What are equations?

The equals sign is a mathematical symbol that indicates that two expressions in a formula are equal.

A mathematical statement known as an equation is one that uses the word "equal to" between two expressions with the same value.

As in 3x + 5 = 15, for example.

Equations can be of many different types, such as linear, quadratic, cubic, and others.

So, we have the equation:

\(Ine^{inx} + Ine^{Inx2}\) \(= 2In8,\)

Now, solve the following equation as follows:

\(Inx * Ine +Inx^2 * Ine = 2In8\)

\(e^{Inx}+Ine^{Inx2} = 2in8\)

\(Inx+Inx^2 = In8^2\)

\(In* (x*x^2) In64\)

\(x^2 = 64 =4^3\)

\(x=4\)

Therefore, after solving the given equation In \(e^{lnx }\) + in\(e ^{lnx2}\) = 2in8, we know that the value of x is (B) 4.

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Correct question:

What is the true solution to the equation below? In \(e^{lnx}\)+ in \(e ^{lnx2}\) = 2 in 8

a x = 2

b x = 4

c x = 8

d x = 64

*WILL MARK BRAINLIEST*
simplify the irrational number square root of 45, then estimate it to two decimal places.

Answers

Answer:

3\(\sqrt{5}\) which is approx 6.71

Step-by-step explanation:

\(\sqrt{45}\) = \(\sqrt{9}\)·\(\sqrt{5}\) = 3\(\sqrt{5}\)

What is the solution to the system of equations graphed below?

What is the solution to the system of equations graphed below?

Answers

Answer:

A

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines.

The point of intersection is (- 1, 3 ) ← solution

A because the solution is at (-1,3)

cuanto es la Raiz cuadrada de 12​

Answers

la raíz cuadrase es 3.464

The square root of 12 is approximately 3.4641.

The square root of 12 is an irrational number, meaning it cannot be expressed as a fraction or terminating decimal. However, we can approximate its value.

To approximate the square root of 12, we can use a calculator or perform an estimation. The square root of 12 is approximately 3.4641.

When we multiply 3.4641 by itself (3.4641 * 3.4641), we get a value very close to 12, but not exactly 12 due to the irrational nature of the square root.

The square root of 12 represents a number that, when multiplied by itself, equals 12. It is a non-repeating, non-terminating decimal that goes on infinitely. The approximation 3.4641 is commonly used to represent the square root of 12 in practical calculations.

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English translation of question is below

What is the square root of 12?

a portion or part of a population is called a:

Answers

Answer:

Step-by-step explanation:

The answer is Samples. A sample is a random selection of members of a population. It is a smaller group drawn from the people with the entire population's characteristics.

I hope I have helped.

If I have to add 1 tablespoon of plant food per gallon of water, how much plant food would I need to add to 1 cup of water.

Answers

You would need to add 16 tablespoons of plant food to 1 cup of water based on the given ratio of 1 tablespoon per gallon of water. Then 1/16 tablespoon should be added to 1 cup.

If you need to add 1 tablespoon of plant food per gallon of water, and you want to determine how much plant food you would need to add to 1 cup of water, we can use a conversion factor.

1 gallon is equal to 16 cups. Therefore, to convert from gallons to cups, we can use the conversion factor:

1 gallon / 16 cups.

Since you need to add 1 tablespoon of plant food per gallon, we can set up a proportion to find the amount of plant food needed for 1 cup of water:

1 tablespoon / 1 gallon = x / 1 cup.

To solve this proportion, we can cross-multiply:

1 tablespoon * 1 cup = 1 gallon * x.

x = (1 tablespoon * 1 cup) / 1 gallon.

Using the conversion factor of 1 gallon / 16 cups, we can substitute the value:

x = (1 tablespoon * 1 cup) / (1 gallon / 16 cups).

x = (1 tablespoon * 1 cup) * (16 cups / 1 gallon).

x = 16 tablespoons.

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