HW4 Distance on the Coordinate Plane
Find the perimeter of the trapezoid.
456
P
B
G
10
Units
Answers
The required perimeter of the trapezoid is22 units.
How to find the perimeter of trapezoid?The given vertices of the trapezoid are (1,3), (4,7), (9,7), and (9,3). To find the perimeter of the trapezoid, we need to add up the lengths of all four sides.
We can use the distance formula to find the length of each side of the trapezoid:
\({Side 1: }&(1,3) \text{ to } (4,7) \&d = \sqrt{(4 - 1)^2 + (7 - 3)^2} = \sqrt{9 + 16} = 5 \\\text{Side 2: }&(4,7) \text{ to } (9,7) \&d = \sqrt{(9 - 4)^2 + (7 - 7)^2} = \sqrt{25} = 5 \\\text{Side 3: }&(9,7) \text{ to } (9,3) \&d = \sqrt{(9 - 9)^2 + (3 - 7)^2} = \sqrt{16} = 4 \\\text{Side 4: }&(9,3) \text{ to } (1,3) \&d = \sqrt{(1 - 9)^2 + (3 - 3)^2} = \sqrt{64} = 8\end{align*}\)
Therefore, the perimeter of the trapezoid is:
\($\begin{align*}P &= \text{Side 1} + \text{Side 2} + \text{Side 3} + \text{Side 4} \&= 5 + 5 + 4 + 8 \&= 22\end{align*}\)
Thus, the perimeter of the trapezoid is22 units.
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Related Questions
What would the equation look like if you
completely simplified the RIGHT SIDE ONLY?
5 = 4(x – 2) – 7x
A) 5 = 3x – 2
B) 12 = 4(x - 2)
C) 5 = -6x + 8
D) 5 = -3x – 8
Answers
4x - 8 -7x
-3x - 8
Three negative charges of equal magnitudes are positioned along the x-axis at x = -a, x=0, and x = +a respectively. The charge located at x=0 is moved away along the y-axis to a position (x,y) = (0, +a). How does the potential energy of the system of charges change as a result?Answera) The potential energy may increase or decrease depending on the magnitude of the charges.b) The potential energy decreases.c) The potential energy stays the same.d) The potential energy increases.e) More information is needed to answer the question.
Answers
The potential energy of the system of charges change as a result option (b) the potential energy decreases.
The potential energy of a system of charges depends on their relative positions and magnitudes. In this case, the system consists of three negative charges of equal magnitudes, and we are moving one of them away from the x-axis to a new position (0, +a).
Initially, the potential energy of the system can be calculated using the formula for the potential energy of a system of point charges
U = (1/4πε₀) × q₁q₂/r₁₂ + (1/4πε₀) × q₁q₃/r₁₃ + (1/4πε₀) × q₂q₃/r₂₃
where U is the potential energy of the system, q₁, q₂, and q₃ are the charges, r₁₂, r₁₃, and r₂₃ are the distances between the charges, and ε₀ is the electric constant.
Assuming that the charges are equal and using the distance formula for the distances, we get
U = (1/4πε₀) × q² [(1/|x+a|) + (1/|x|) + (1/|x-a|)]
When x=0, this simplifies to
U = (1/4πε₀) × (3q²/a)
When we move the charge at (0,0) to (0,a), we are effectively increasing the distance between this charge and the other two charges along the x-axis. This means that the distances r₁₃ and r₂₃ increase, while the distance r₁₂ remains the same.
As a result, the potential energy of the system decreases.
Therefore, the correct answer is (b) the potential energy decreases.
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context switching is required by all preemptive algorithms.
true/false
Answers
The given statement "context switching is required by all preemptive algorithms " is False.
Context switching is not required by all preemptive algorithms. Preemptive algorithms allow the operating system to interrupt the currently executing process and switch to another process.
Context switching involves saving the state of the currently running process and restoring the state of the next process to be executed. While context switching is a common mechanism in preemptive scheduling algorithms, there are non-preemptive algorithms that do not require context switching as they allow processes to run until they voluntarily release the CPU.
So, the statement that context switching is required by all preemptive algorithms is false.
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True or false: (log x)2 = 2logx. Explain your thinking.
Answers
Well we can’t put 2 log x it’s opposite it’s 2 x log
a farmer wants to rebuild a section of fencing on her property, which can be described as a portion of the first quadrant of the xy-plane. there is an old fence post at the point (2, 3) that marks the original fencing her grandfather built that she wants to keep as part of the new fence. to connect with the rest of the fencing, the farmer needs the fencing to form a straight line to the x- and y-axes. however, she also wants to keep the fenced area as large as possible and so she wants the fencing positioned in such a way that it cuts off the least area from the first quadrant. help the farmer find the equation of the line that meets all of her requirements
Answers
The equation of the line that meets all the requirements is y = (-3/2)x + 6.
The farmer wants to rebuild the fencing in such a way that it cuts off the least area from the first quadrant. This means that the line should be positioned in such a way that it forms a right triangle with the x- and y-axes and the point (2,3) on the line. The area of the triangle should be as small as possible.
Let the line be represented by the equation y = mx + b, where m is the slope and b is the y-intercept. The point (2,3) is on the line, so we have:
3 = 2m + b
To find the slope that minimizes the area of the triangle, we need to find the x-intercept and y-intercept of the line. The x-intercept is given by:
0 = mx + b
x = -b/m
The y-intercept is given by:
y = 0 + b
y = b
The area of the triangle is given by:
A = (1/2)bh
where b is the base of the triangle (the distance between the x-intercept and the point (2,3)) and h is the height of the triangle (the distance between the y-intercept and the point (2,3)).
b = |(-b/m) - 2| = |2 + (b/m)|
h = |b - 3|
So, the area of the triangle is:
A = (1/2)|2 + (b/m)||b - 3|
To minimize A, we can take the derivative with respect to b and set it equal to zero:
dA/db = (1/2)m(2 + (b/m))(b - 3) - (1/2)(b/m)|2 + (b/m)| = 0
Simplifying, we get:
2b - 3m = 0
Solving for b, we get:
b = (3/2)m
Substituting this value of b into the equation y = mx + b and using the fact that (2,3) is on the line, we get:
3 = 2m + (3/2)m
Solving for m, we get:
m = -4/3
Substituting this value of m into the equation y = mx + b and using the fact that (2,3) is on the line, we get:
3 = (-4/3)(2) + b
b = 6
So, the equation of the line is:
y = (-4/3)x + 6
However, we want the fence to pass through the point (2,3), so we need to adjust the equation. We can use point-slope form to find the equation of the line:
y - 3 = (-4/3)(x - 2)
Simplifying, we get:
y = (-4/3)x + 6
So, the equation of the line that meets all the requirements is y = (-3/2)x + 6.
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Question 11
1 pts
In Rodger's state, unemployment compensation is calculated by finding the total of the
quarterly wages of two consecutive quarters and dividing by 26. The weekly
unemployment is 65% of that amount. In the quarter including January, February, and
March, Rodger made a total of $13,950.80. In the quarter including April, May, and
June, he made a total of $14,250.10. Find Rodger's weekly unemployment amount.
Answers
Rodger's weekly unemployment amount is $697.54
What is the total of the quarterly wages of two consecutive quarters?
The total of the of the quarterly wages of two consecutive quarters is the sum of first quarter and second quarter wages
total of quarterly wages=$13,950.80+$13,950.80
total of quarterly wages=$27,901.60
unemployment compensation=total of quarterly wages/26
unemployment compensation=$27,901.60 /26
unemployment compensation=$1,073.14
The weekly unemployment amount is 65% of Rodger's state, unemployment compensation
weekly unemployment=65%*$1,073.14
weekly unemployment=$697.54
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10 is what percentage of 50 
Answers
Answer:
20%
Step-by-step explanation:
10 of 50 can be written as:1050To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 1001050 × 100100= (10 × 10050) × 1100 = 20100 Therefore, the answer is 20%
Which represents the inverse of the function f(x) = 4x?
•
O h(x) = x + 4
O h(x) = x-4
O h(x) = 3/4x
O h(x) = 1/4x
Answers
Answer:
\( {f}^{ - 1} (x) = \frac{1}{4} x\) (last/fourth option)
Step-by-step explanation:
\(f(x) = 4x\)
\(y = 4x\)
\(x = 4y\)
\(4y = x\)
\( \boxed{\green{{f}^{ - 1} (x) = \frac{1}{4} x}}\)
For the linear regression y = ẞ1 + ẞ2x + e, assuming that the sum of squared errors (SSE) takes the following form:
SSE = 382 +681 +382 + 18ẞ1ẞ2
Derive the partial derivatives of SSE with respect to B1 and B2 and solve the optimal values of these parameters.
a. B₁ = B1
b. B₂ =
Answers
The optimal values of these parameters are:
a. β₁ = 0
b. β₂ = 0
The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:
SSE = 382 + 681 + 382 + 18β1β2
Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.
Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0
Now, we need to find the partial derivative of SSE with respect to β1.
∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0
Therefore, we obtain the optimal value of β2 as 0.
Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0
Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.
Thus, the optimal values of β1 and β2 are 0 and 0, respectively.
Therefore, the answers are: a. β₁ = 0 b. β₂ = 0
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The distance traveled is equal to the rate of speed multiplied by the time traveled. If the distance is measured in feet and the time is measured in minutes, then the rate of speed is expressed in which units?
Answers
ВС
Round your answer to the nearest hundredth.
С
?
B
35
6
A
Answers
Answer:4.91
Step-by-step explanation: it’s cosine
So multiply 6 x cos (35°)= 4.91
What are the two types of microscopic composites?
Show the mechanism for strengthening of each type.
Answers
The required, two types of microscopic composites are particle-reinforced composites and fiber-reinforced composites.
The two types of microscopic composites are particle-reinforced composites and fiber-reinforced composites.
Particle-reinforced composites strengthen through load transfer, barrier effect, and dislocation interaction. The particles distribute stress, impede crack propagation, and hinder dislocation motion.
Fiber-reinforced composites gain strength through load transfer, fiber-matrix bond, fiber orientation, and crack deflection. Fibers carry load, bond with the matrix, align for stress distribution, and deflect cracks.
These mechanisms enhance the overall mechanical properties, including strength, stiffness, and toughness, making microscopic composites suitable for diverse applications.
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A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 25% real fruit juice and Drink B contains 5% real fruit juice. How many liters of real fruit juice would be needed to produce 150 liters of Drink A and 200 liters of Drink B? How many liters of real fruit juice would be needed to produce aa liters of Drink A and bb liters of Drink B?
Answers
Answer:
a). 12.5 liters of real fruit juice would be needed to produce 250 liters of Drink A, and 20 liters of real fruit juice would be needed to produce 250 liters of Drink B
b). 0.05aa liters of real fruit juice would be needed to produce aa liters of Drink A, and 0.1bb liters of real fruit juice would be needed to produce bb liters of Drink B
Step-by-step explanation:
a). Drinks A(250 liters) and Drink B(200 liters)
Total amount of Drink A=250 liters
Real fruit juice=5% of Drink A=(5/100)×250=12.5 liters
12.5 liters of real fruit juice would be needed to produce 250 liters of Drink A
Total amount of Drink B=200 liters
Real fruit juice=10% of Drink B=(10/100)×200=20 liters
20 liters of real fruit juice would be needed to produce 250 liters of Drink B
b). Drinks aa and bb
Total amount of Drink A=aa liters
Real fruit juice=5% of Drink A=(5/100)×aa=0.05aa liters
0.05aa liters of real fruit juice would be needed to produce aa liters of Drink A
Total amount of Drink B =bb liters
Real fruit juice=10% of Drink 10=(10/100)×bb=0.1bb liters
0.1bb liters of real fruit juice would be needed to produce bb liters of Drink B
Given the passage, what determination can you make about the setting? How does the setting affect Jonathan’s behavior?
Answers
Answer: the area is affected by crime. He is protective of his money. Both right on edge
Step-by-step explanation:
Answer: a b
Step-by-step explanation:
Write the positive or negative integer that this situation represents.
Lucy made a $12 profit.
Answers
Answer:
12
Step-by-step explanation:
A profit, or money you have, or money you deposit in a bank account is usually positive.
A debt, or money you withdraw from a bank account, or money you give away is usually negative.
Answer: 12
Solve and SIMPLIFY your answer the questions is, 3 5/8 x 4/7. remember SIMPLIFY
Answers
3 5/8 = 29/8
29 x 4 116
---- ---- = -----
8 x 7 56
116/56 = 29/14 = 2 1/14
---
hope it helps
Answer:
2 1/14
step by step:
3×8+5 x 4/7
24+5/8 x 4/7
29/8 x 4/7
29 x 4 and 8 x 7
116/8 x 7
116/56 divided by 4
29/14 simplifies to =
2 1/14
What is the quotient?
x-3) 4x2+3x+2
+
O 4x2 + 15 +
47
X-3
O 4x + 15 +
43
X - 3
0 4x2 + 15 +
43
X - 3
0 4x + 15 +
47
X-3
What is the answer ??
Answers
The quotient of the division x - 3 | 4x^2 + 3x + 2 is 4x + 15
How to determine the quotientFrom the question, we have the following parameters that can be used in our computation:
x - 3 | 4x^2 + 3x + 2
Using the long division method of quotient, we have
x - 3 | 4x^2 + 3x + 2
The division steps are as follows
4x + 15
x - 3 | 4x^2 + 3x + 2
4x^2 - 12x
------------------------------------------------
15x + 2
15x - 45
------------------------------------------------
47
Hence, the quotient is 4x + 15
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A diver dives from the board at a local swimming pool. Her height, y, in metres, above the water in terms of her horizontal distance, x, in metres, from the end of the board is given by y= -x^2 + 2x + 3. What is the diver's maximum height?
Answers
Answer:
4 meters
Step-by-step explanation:
Given a quadratic equation in which the coefficient of \(x^2\) is negative, the parabola opens up and has a maximum point. This maximum point occurs at the line of symmetry.
Since the divers height, y is modeled by the equation
\(y= -x^2 + 2x + 3\)
Step 1: Determine the equation of symmetry
In the equation above, a=-1, b=2, c=3
Equation of symmetry, \(x=-\dfrac{b}{2a}\)
\(x=-\dfrac{2}{2*-1}\\x=1\)
Step 2: Find the value of y at the point of symmetry
That is, we substitute x obtained above into the y and solve.
\(y(1)= -1^2 + 2(1) + 3=-1+2+3=4m\)
The maximum height of the diver is therefore 4 meters.
5. Can more than one triangle be drawn with side lengths of 5 inches and 7 inches and an included angle with a measure of 50 degrees? Explain.
PLEASE PROVIDE AN EXPLANATION!
I'll give brainliest
Answers
No, it is not possible to draw more than one triangle with side lengths of 5 inches and 7 inches and an included angle with a measure of 50 degrees.
To understand why, let's consider the law of sines, which states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is the same for all three sides. In other words, if we know two sides and the angle opposite one of them, we can use the law of sines to find the measure of the third angle and the lengths of the other two sides.
Using this formula, we can see that for a triangle with sides of 5 inches and 7 inches and an included angle of 50 degrees, there is only one possible triangle that can be drawn. This is because the sine of an angle is always between -1 and 1, so there is only one value for the sine of 50 degrees that can be used to calculate the length of the third side of the triangle.
Therefore, we can conclude that there is only one possible triangle that can be drawn with side lengths of 5 inches and 7 inches and an included angle with a measure of 50 degrees.
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28. Given M₁ = 35, M₂ = 45, and SM1-M2= 6.00, what is the value of t? -2.92 -1.67 O-3.81 2.75
Answers
The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.
M₁ = 35
M₂ = 45
SM1-M2 = 6.00
The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:
t = (M₁ - M₂) / SM1-M2
Substituting the given values into the formula:
t = (35 - 45) / 6.00
t = -10 / 6.00
t = -1.67
Therefore, we can conclude that the value of t is -1.67 for the samples given.
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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.
Given, M₁ = 35
M₂ = 45
SM1-M2 = 6.00
The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.
To calculate the t-value,
the formula we need to use here is:
t = (M₁ - M₂) / SM1-M2
Substituting the given values into the formula:
t = (35 - 45) / 6.00
t = -10 / 6.00
t = -1.67
Therefore, we can conclude that the value of t is -1.67 for the samples given.
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Can someone please help me
Answers
Answer:
3. Add 11, then multiply by 3
4. Subtract 43, then multiply by 9
Step-by-step explanation:
Does that make sense?
Consider the following data drawn independently from normally distributed populations: (You may find it useful to appropriate table: z table or t table)
xˉ1 = −17.1
s1^2 = 8.4
n1=22
xˉ2 = −16.0
s2^2 = 8.7
n2 = 24
a. Construct the 90% confidence interval for the difference between the population means. Assume the population va unknown but equal. (Round final answers to 2 decimal places.)
confidence interval is __ to __
Answers
The 90% confidence interval for the difference in the population means is -2.51 to 0.31
Calculating the 90% confidence interval for the population mean differenceFrom the question, we have the following parameters that can be used in our computation:
xˉ₁ = −17.1
s₁² = 8.4
n₁ = 22
xˉ₂ = −16.0
s₂² = 8.7
n₂ = 24
Calculate the pooled variance using
P = (df₁ * s₁² + df₂ * s₂²)/df
Where
df₁ = 22 - 1 = 21
df₂ = 24 - 1 = 23
df = 22 + 24 - 2 = 44
So, we have
P = (21 * 8.4 + 23 * 8.7)/44
P = 8.56
Also, we have the standard error to be
SE = √(P/n₁ + P/n₂)
So, we have
SE = √(8.56/22 + 8.56/24)
SE = 0.86
The z score at 90% CI is 1.645, and the CI is calculated as
CI = (x₁ - x₂) ± z * SE
So, we have
CI = (-17.1 + 16.0) ± 1.645 * 0.86
This gives
CI = -1.1 ± 1.41
Expand and evaluate
CI = (-2.51, 0.31)
Hence, the confidence interval is -2.51 to 0.31
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Find the measure of the smallest angle
Answers
Answer:
44°
Step-by-step explanation:
We Know
The sum of three angles in a triangle must add up to 180°.
Let's solve
3x + 15 + 4x - 12 + 79 = 180°
7x + 82 = 180°
7x = 98°
x = 14
Now we put 14 in for the x and find the other 2 missing angles.
3x + 15
3(14) + 15
42 + 15
57°
4x - 12
4(14) - 12
56 - 12
44°
So, the measure of the three angles are: 44°, 57°, and 79°. So, the measure of the smallest angle is 44°
4x-5.2y + 6y + 7.9x - 8x
Answers
Answer:
3.9x + 0.8y
Step-by-step explanation:
this is your answer
Show all steps please4. Evaluate the derivative of the given function for the given value of x: √x y = у ,x=4 = 1- x
Answers
To evaluate the derivative of the given function for the given value of x, we will use the power rule of differentiation. The function given is: y = √x(1-x)
Step 1: Rewrite the function using the product rule: y = (√x)(1-x)
Step 2: Apply the power rule of differentiation to the first factor, √x:
y' = [(1/2)x^(-1/2)](1-x) + (√x)(-1)
Step 3: Simplify by combining like terms:
y' = [(1-x)/2√x] - √x
Step 4: Plug in x = 4 to find the derivative at that specific value:
y' = [(1-4)/2√4] - √4
y' = [-3/4] - 2
y' = -2.75
Therefore, the derivative of the given function for the given value of x=4 is -2.75. I believe you meant to ask for the derivative of the function y = √x - x, evaluated at x = 4. Here are the steps to find the derivative and evaluate it:
1. Write down the given function: y = √x - x
2. Rewrite the function using exponents: y = x^(1/2) - x
3. Apply the power rule to find the derivative: dy/dx = (1/2)x^(-1/2) - 1
4. Simplify the derivative: dy/dx = (1/2)(x^(-1/2)) - 1
5. Evaluate the derivative at x = 4: dy/dx = (1/2)(4^(-1/2)) - 1
6. Calculate the values: dy/dx = (1/2)(1/2) - 1
7. Simplify the final answer: dy/dx = 1/4 - 1 = -3/4
So, the derivative of the given function at x = 4 is -3/4.
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savanna is sitting in a bucket of a farris wheen at the 3 oclock position. the ferris wheel has a radius 62 feet long. the ferris wheel begins moving clockwise. what is the measure of savanna's angle of roatation when she is 42 feet above the ferris wheel's horizontal diameter
Answers
Therefore, when Savannah is 42 feet above the ferris wheel's horizontal diameter, her angle of rotation is approximately 68.6 degrees.
Given by the question.
Let's first draw a diagram to visualize the situation.
*
* *
* * <-- Ferris wheel at 3 o'clock position
* *
* * <-- Highest point
*______________*______
62 ft
The Ferris wheel is a circle with radius 62 feet, and Savannah is sitting in a bucket that moves along the circle. When she is at the highest point, she is 62 feet away from the center of the circle, and when she is on the horizontal diameter, she is 62 feet - 42 feet = 20 feet away from the center of the circle.
To find Savannah's angle of rotation, we can use the cosine function.
cos(theta) = adjacent / hypotenuse
In this case, the adjacent side is 20 feet, and the hypotenuse is 62 feet.
cos(theta) = 20/62
To solve for theta, we need to take the inverse cosine of both sides.
theta = cos^-1(20/62)
Using a calculator, we get:
theta = 68.6 degrees
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what’s the answer ? i don’t understand this one. please show me the answer
Answers
Answer:
hello,
Step-by-step explanation:
n+2*(2n-5)=20
5n-10=20
5n=30
n=6
There are 5 pizzas, 3 breads, and 2 cookies in the restaurant . What is the probability of NOT getting bread
ANSWER NEEDED ASAP
Answers
A couple pays £1200 for a holiday in Portugal. Unfortunately, due to the pandemic the holiday
company cancels the holiday and gives the customers this option:
Rebook another holiday and get a 20% incentive*
We have a range of alternative holidays available for you to choose from and would love to take
you are away on holiday. Plus, if the holiday you book is more expensive than your original holiday,
you’ll automatically receive an incentive worth up to 20% of the value of the holiday*.
a. The customers find an alternative holiday in Greece costing £1800, for them both, before discounts. Use a non-calculator method to show what the cost of this holiday will be once the discount mentioned above has been applied.
Answers
The cost of the holiday after the discount has been applied is £1440.
What is discount?Discount is a term used to refer to a reduction in the cost of a product or service. It is typically used by businesses to incentivize customers to purchase their products or services. Discounts can come in many different forms, such as a percentage off the original cost, free shipping, or a dollar amount off the purchase price. Discounts can be offered on individual items, entire orders, or even as a reward for being a loyal customer. Discounts are a great way for businesses to create loyalty among customers, and to increase sales.
The cost of the holiday in Greece is £1800. The incentive offered is 20% of the value of the holiday, which is 20% of £1800, which is £360.
Therefore, the cost of the holiday after the discount has been applied is £1800 - £360 = £1440.
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If the PPF is a downward-sloping straight line, then the law of increasing opportunity cost does not hold. Instead, the opportunity cost of producing an additional unit of good 1 or good 2 remains constant as more of either is produced (i.e., there are constant opportunity costs in production).
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A straight line PPF indicates constant opportunity costs in production is TRUE.
The Production-Possibility Frontier (PPF) is a graphical representation of the maximum amount of two goods that can be produced given a certain number of resources.
If the PPF is a straight line, then the opportunity cost of producing an additional unit of one good is the same regardless of how much of that good is already being produced. This means that the resources used to produce the two goods are perfectly substitutable and there are no increasing opportunity costs.
However, if the PPF is a curved line, then the opportunity cost of producing an additional unit of one good increase as more of that good is produced. This is because the resources used to produce the two goods are not perfectly substitutable and there are increasing opportunity costs.
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