1-Is the sum of two prime numbers always a prime number?
Solution:
No. Here is an example.
3 + 7 = 10 , 3 and 7 are prime numbers but not their sum 10.
2-Is the product of two prime numbers also a prime number?
Solution:
Never because it will have 1 and itself as factors and also the two numbers involved in the product.
Example: 7 × 11 = 77 ,77 has 1, itself, 7 and 11 as factors.
3-Which is the largest 3 digit prime number?
Solution:
Start with the largest three digit number 999.
4- Which is the smallest 2 digit prime number?
Solution
Start with the smallest 2 digit number 10.
10 is not a prime number
Answer: 11 is a prime number
How long would it take for a ball dropped from the top of a 81ft building to hit the ground round your answer to two decimal places
Answer:
Set the height equal to (1/2)gt^2 and solve for t.
h = (1/2)gt^2
t = (2h/g)^1/2
Plug in the numbers and get your answer in seconds:
h = 81 ft
g = 32 ft/s^2
Step-by-step explanation:
Indicate whether the two functions are equal. If the two functions are not equal, then give an element of the domain on which the two functions have different values.
(a). f: Z → Z, where f(x) = x^2.
g: Z → Z, where g(x) = |x|^2.
(b). f: Z × Z → Z, where f(x,y) = |x + y|.
g: Z × Z → Z, where g(x,y) = |x| +| y|.
(c). B = {0, 1}
f: B × B → B × B, where f(x,y) = (1-y, 1-x)
g: B × B → B × B, where g(x,y) = (x,y)
The functions are equal in option A, and aren't equal in B (try input x =1 and y = -1) and in C (try input x = 0 and y = 0).
Are the functions equal in the domains?The first one is:
(a). f: Z → Z, where f(x) = x^2.
g: Z → Z, where g(x) = |x|^2.
Yes, these functions are equal, this happens because both outcomes will always be positive, indifeterent of the absolute value part.
b) f: Z × Z → Z, where f(x,y) = |x + y|.
g: Z × Z → Z, where g(x,y) = |x| +| y|.
These are different, if x = 1 and y = -1
f(1, - 1) = |1 - 1| = 0
g(1, -1) = |1| + |-1| = 2
c) B = {0, 1}
f: B × B → B × B, where f(x,y) = (1-y, 1-x)
g: B × B → B × B, where g(x,y) = (x,y)
This is clearly false, when x and y are 0 and 0 we have:
f(0, 0) = (1 - 0, 1 - 0) = (1, 1)
While g gives:
g(0, 0) = (0, 0)
These functions are different.
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NEED HELP WILL GIVE BRAINLIEST IF I GET FULL HELP ON BOTH QUESTIONS
The inverse of the function is y = (-3x + 50)/4.
The domain of the inverse function are {4, 5, 6, 10}.
The range of the inverse function are {5, 8, 9, 13}.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At point (5, 10), an equation of the line f(x) can be calculated by using the point-slope form:
y - 10 = (6 - 10)/(8 - 5)(x - 5)
y - 10 = -4/3(x - 5)
y = -4x/3 + 20/3 + 10
y = -4x/3 + 50/3
y = (-4x + 50)/3
In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;
x = (-4y + 50)/3
3x = -4y + 50
4y = -3x + 50
y = (-3x + 50)/4
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What is the area of the trapezoid? ___ units 2
The area of the trapezoid is 176 square units.
What is a trapezoid?
A trapezoid, which is also referred to as a trapezium, is a flat, closed shape with four straight sides and one set of parallel sides.
A trapezium's parallel bases and non-parallel legs are referred to as its bases and legs, respectively. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.
The altitude is the length of the parallel sides measured perpendicularly.
The height of the trapezoid is 4 units.
The parallel sides of the trapezoids are 17 units and (5+17+5) = 27 units.
The area of a trapezoid is half of the product of the height and the sum of parallel sides.
The area of the trapezoid is
1/2 × 4 ×(17+27)
= 176 square units
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85 POINTS!!! With brainiest 5th grade please complete this page below you can print it or do it online please just do it
Answer:
1. 8
2. 24
3. 15
4. 135
b. 135 x 1/9
5. the answer is 24
construct a quadratic equation of -2 +3
[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +2 )( x -3 ) = \stackrel{0}{y}}\hspace{4em}\stackrel{\textit{now, assuming that}}{a=1}\hspace{5em}1( x +2 )( x -3 ) =y \\\\\\ ~\hfill {\Large \begin{array}{llll} x^2-x-6=y \end{array}}~\hfill[/tex]
Suppose I am rolling a standard 6-sided dice. Let A be the event I roll a prime number, Let B be the event I roll a number less than or equal to 4. I ran a trial 10 times and got the results 2, 4, 3, 1, 5, 6, 1, 3, 2, 1
What is the experimental P(B)
The experimental probability of rolling a number less than or equal to 4 is 0.7.
How is conditional probability calculated? What does it mean?The likelihood that an event (A) will occur given the occurrence of another event (B) is known as conditional probability. P(A|B), which stands for "the probability of A given B," is used to express it. You must first determine P(A and B) by multiplying the odds of A and B happening together. Next, you may compute P(A|B). The conditional probability of A given B is then obtained by dividing the result by P(B).
Several situations in everyday life, including medical diagnosis, industrial quality control, and risk assessment in insurance, call for the usage of conditional probability.
Given that, the trial was run 10 times.
Thus,
P(B) = (number of times B occurred) / (total number of trials)
= 7 / 10
= 0.7
Therefore, the experimental probability of rolling a number less than or equal to 4 is 0.7.
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A rancher has 600
feet of fencing to put around a rectangular field and then subdivide the field into 3
identical smaller rectangular plots by placing two fences parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms.
The dimensions of the rectangular field that maximize the enclosed area are 150 feet by 75 feet.
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
Let's call the length of the rectangle "l" and the width "w".
We can write two equations based on the given information -
Perimeter equation: 2l + 4w = 600 (since there are two sets of parallel sides, we have to add an extra "w" to the perimeter equation)
Area equation: A = 3lw (since the field is divided into 3 equal parts)
We want to maximize the enclosed area, which means we want to find the values of "l" and "w" that make the area as large as possible.
We can use the perimeter equation to solve for one of the variables in terms of the other -
2l + 4w = 600
2l = 600 - 4w
l = 300 - 2w
Now we can substitute this expression for "l" into the area equation -
A = 3lw
A = 3(300 - 2w)w
A = 900w - 6w²
To find the maximum area, we can take the derivative of this equation with respect to "w" and set it equal to zero -
dA/dw = 900 - 12w = 0
12w = 900
w = 75
So the width of each of the smaller rectangular plots is 75 feet.
We can use the perimeter equation to find the length -
2l + 4w = 600
2l + 4(75) = 600
2l = 300
l = 150
Therefore, the dimensions value are obtained as 150 feet by 75 feet.
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A rectangular corral of 117 square meters is to be fenced off and then divided by a fence into two sections, as shown in the figure to the right. If the cost of fencing for the boundary is $10 per meter and the dividing fence costs $6 per meter, find the dimensions of the corral that minimize the cost of the fencing.
Answer:
the dimensions of the corral that minimize the cost of the fencing are approximately 17.91 meters by 6.54 meters.
Step-by-step explanation:
Let the length of the corral be x, and the width be y. We know that the area of the corral is 117, so:
xy = 117
We also know that the corral is divided by a fence into two sections. Let the length of one section be L, and the width be y. Then, the length of the other section will be x - L, and the width will still be y. The total fencing cost will be:
10(2x + 2y) + 6(L + 2y)
Simplifying this expression, we get:
20x + 32y + 6L
Using the area equation, we can rewrite this as:
20x + 32(117/x) + 6L
To minimize the cost, we need to take the derivative of this expression with respect to L, and set it equal to zero:
d/dL [20x + 32(117/x) + 6L] = 6 = 0
Solving for L, we get:
L = x/2
Therefore, the two sections of the corral will have equal length. Substituting this value of L into the expression for total fencing cost, we get:
20x + 32y + 3x
Simplifying this, we get:
23x + 32y
Using the area equation to substitute for y, we get:
23x + 32(117/x)
Taking the derivative of this expression with respect to x, and setting it equal to zero, we get:
23 - 3744/x^2 = 0
Solving for x, we get:
x = sqrt(3744/23) ≈ 17.91
Substituting this value of x into the area equation, we get:
y = 117/x ≈ 6.54
Therefore, the dimensions of the corral that minimize the cost of the fencing are approximately 17.91 meters by 6.54 meters.
(b). A competitive market has the demand schedule p=420-2q and the supply schedule p= 60+ 4q where p is measured in naira. (i) Find the equilibrium values of p and q. (ii) What will happen to these values if the government imposes a tax of N24 per unit on q?
1. The equilibrium quantity = 60, the equilibrium price = 300
2. If the government imposes the tax of 24, the quantity supplies would fall to 56, and the price would rise to 308
How to solve for equilibriumAt equilibrium we have P = Q
that is price is equal to quantity. Such that we would have:
420-2q = 60+ 4q
take the like terms
420 - 60 = 4q + 2q
360 = 6q
q = 360 / 6
q = 60
The equilibrium quantity = 60 then equilibrium price =
420-2q
420 - 2 * 60
300
The equilibrium price is 300
2. If the government imposes 24 dollar per unit
420-2q = 60+ 4q + 24
420 - 2q = 84 + 4q
420 - 84 = 4q + 2q
336 = 6q
56 = q
420-2 * 56
p = 308
If the government imposes the tax of 24, the quantity supplies would fall to 56, and the price would rise to 308
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The total cost of producing a type of boat is given by C(x)=21000−40x+0.1x^2
, where x is the number of boats produced. How many boats should be produced to incur minimum cost?
Using differentiation, 200 boats should be produced to incur minimum cost
What is meant by differntiation?A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable in mathematics. A crucial calculus technique is the derivative.
Differentiation is a technique for determining a function's derivative. In mathematics, the technique of differentiation is used to determine the instantaneous rate of change in a function dependent on one of its variables. The most typical illustration is the velocity, or rate of change of displacement with respect to time.
Minimum boats can be found by differentiating the given function,
[tex]C(x)=21000 - 40x+0.1x^2[/tex]
Differentiating with respect to x,
0 = 0.2x - 40
0.2x = 40
x = 200
∴ 200 boats should be produced to incur minimum cost.
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Prove the following: In a semigroup (written multiplicatively) multiplication of subsets is associative?
Therefore , the solution of the given problem of unitary method comes out to be x = (ab)c = a(bc) .
An unitary method is what?The job can be finished by multiplying the variable information obtained using this kind of nanosection alongside the results of the two people who used the unilateral approach. In essence, this mean that whenever a desired item happens, either the chosen entity is described or the tone of both commercial manufacturing is skipped. A varying fee of Inr ($1.01) might have been necessary for forty pens.
Here,
We must demonstrate that the following formula holds for any subsets A, B, and C of S in order to demonstrate that multiplication of subsets is associative:
=> (AB)C = A(BC)
where AB and BC stand for the sets created by increasing all of the elements in A by all of the elements in B, and vice versa.
We must demonstrate that every element on the left-hand side is also an element on the right-hand side and vice versa in order to demonstrate that (AB)C = A(BC).
Let x represent any one of the (A*B)C elements. If a, b, and c are all in A, then x can be expressed as
=> x = (ab)*c by definition. * being associated with S gives us:
=> x = (ab)c = a(bc)
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I will mark you brainiest!
Please do it in steps
What is the base of a parallelogram with an area of 36 units2 and a height of 9 units?
The base length of the parallelogram found using the area formula is 4 units.
What is a parallelogram?
A basic quadrilateral with two sets of parallel sides is known as a parallelogram. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. A parallelogram has adjacent angles that add up to 180 degrees. 360 degrees is the sum of all interior angles.
A parallelogram's area is the area that it takes up in a two-dimensional plane. The parallelogram's area is calculated by multiplying the base length by the height.
Each shape's perimeter can be defined as either the entire length or total distance encircling the object. The entire distance between a parallelogram's boundaries is also known as the parallelogram's perimeter.
Given,
The area of the parallelogram A =36 sq. units
The height of the parallelogram h = 9 units
We are asked to find the base length b.
Now the formula for the area of the parallelogram is:
A = b * h
36 = b * 9
b = 36/9 = 4 units.
Therefore the base length of the parallelogram, found using the area formula is 4 units.
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A customer purchased 10 items at a rummage sale. The prices paid are given in the table. What amount of change should the customer have received given that the customer paid with a $20 bill?
The amount of change that the customer will be given when payment is made with a $20 bill would be = $7.15. That is option G.
How to calculate the cost balance of the customer?The total number of items purchased by the customer = 10
The cost for 5 items = $1.60× 5 = $8
The cost of 3 items = $1.25×3 = $3.75
The cost of 2 items = $0.55×2 = $1.1
The total cost = 8+3.75+1.1 = $12.85
Therefore, the change of the customer when $20 bill is used = 20-12.85
= $7.15.
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A flower bed is in the shape of a triangle, with a base of 15 feet and a height of 9 feet. What is the area of the flower bed? (4 points)
The area of the flower bed is 67.5 square feet.
An area in mathematics is what?The area of an object is the space that is enclosed by its boundaries. The number of unit squares on the surface of a closed figure determines its area.
The following formula provides the area of a triangle:
(1/2) * Base * Height = Area
Inputting the values provided yields:
Area equals (1/2) * 15 * 9
Dimensions: 67.5 square feet
The flower bed therefore has a 67.5 square foot space.
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Simplify: 5/6-17/12-5/3 A. -19/12 B.-17/12 C.1/4 D.23/12
HELP ASAP pls!!!
Answer:
The simplified expression is -13/12. (are you sure you don't have a typo somewhere), double checked.
Step-by-step explanation:
First, let's simplify the expression inside the absolute value bars:
5/6 - 17/12 = 10/12 - 17/12 = -7/12
Next, we can simplify the expression outside the absolute value bars:
| -7/12 | - | 5/3 |
= 7/12 - 5/3 (since the absolute value of -7/12 is 7/12)
= 7/12 - 20/12
= -13/12
The simplified expression is -13/12.
_______________________
Simplify the following:
abs(5/6 - 17/12) - abs(5/3)
Put 5/6 - 17/12 over the common denominator 12. 5/6 - 17/12 = (2×5)/12 - 17/12:
abs(((2×5)/12 - 17/12)) - abs(5/3)
2×5 = 10:
abs(10/12 - 17/12) - abs(5/3)
10/12 - 17/12 = (10 - 17)/12:
abs(((10 - 17)/12)) - abs(5/3)
10 - 17 = -7:
abs((-7)/12) - abs(5/3)
Since 5/3 is a non-negative constant, abs(5/3) = 5/3:
abs(-7/12) - 5/3
Since -7/12 is a negative constant, abs(-7/12) = 7/12:
7/12 - 5/3
Put 7/12 - 5/3 over the common denominator 12. 7/12 - 5/3 = 7/12 + (4 (-5))/12:
7/12 - (5×4)/12
4 (-5) = -20:
7/12 + (-20)/12
7/12 - 20/12 = (7 - 20)/12:
(7 - 20)/12
7 - 20 = -13:
Answer: (-13)/12
If the length and breadth of a rectangle are 12 cm and 5 cm respectively, what will be the length of its diagonal?
Please help . A burglar alarm system has six fail-safe components. The probability of each failing is 0.05. Find the probability that fewer than three will fail. Round to the nearest thousandth.
Answer:
Answer:
0.050
Rounded to the nearest 0.001 or
the Thousandths Place.
Step-by-step explanation:
Explanation
0.05__
You rounded to the nearest thousandths place. The _ in the thousandths place rounds down to 0 because the digit to the right in the ten thousandths place is _.
0.050
When the digit to the right is less than 5 we round toward 0.
0.05 was rounded down toward zero to 0.050
On a menu, there are 5 beef options, 3 pork options, 6 chicken options, and 4 vegetarian options. One of the options is selected at random. Determine the theoretical probability of selecting a meat option. Express your answer as a fraction in simplest form. HELP!
Answer: The theoretical probability of selecting a meat option is 7/9.
Step-by-step explanation:
5 beef + 3 pork + 6 chicken + 4 veggie = 18 options total
meat options = 18 (total) - 4 veggie = 14 meat options
14/18 = 7/9
Jillian measures two line segments. Segment A is 12.4 centimeters long and segment B is
4 centimeters in length. Which best represents the ratio of the length of segment A to the length
of segment B?
4
1
3.1
3.1
3.1 best represents the ratio of the length of segment A to segment B.
What is ratio?
By comparing two amounts of the same unit and finding the ratio, one can determine how much of one quantity is included in the other.
We are given that Jillian measures two line segments.
The length of Segment A is measured as 12.4 centimeters and the length of Segment B is measured as 4 centimeters.
So, on comparing both the lengths, we get
⇒12.4 : 4
⇒124 : 40
⇒3.1
Hence, 3.1 best represents the ratio of the length of segment A to segment B.
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Calculate the size of one exterior angle and one exterior angle of a regular ten-sided shape (decagon)
Answer:
36∘
Step-by-step explanation:
Decagon has ten sides and ten angles. All these sides and angles are equal to each other. Therefore, the measure of each exterior angle of a regular decagon is 36∘
A recipe for bread calls for 4 cups of flour for every 1/2 cup of water. Using the same recipe, how much
water will you need for 5 cups of flour?
Answer:
According to the recipe, the ratio of flour to water is 4:0.5 or 8:1 (since 1/2 can be simplified to 0.5).
To determine how much water is needed for 5 cups of flour, we can use this ratio:
8:1 = 5:x
where x represents the amount of water needed.
To solve for x, we can cross-multiply:
8x = 5 * 1
8x = 5
x = 5/8
Therefore, you will need 5/8 cup of water for 5 cups of flour, using the given recipe.
Step-by-step explanation:
HELLLPPPPP me please
The length and the width of the model are Length = 2 and Width = 3x² + 5x + 6
Why 6x cant be the lengthThe expression 6x cant be the length because 12 cannot divide 6x without becoming a radical expression
Calculating the length and the widthWe have
Area = 6x² + 10x + 12
Factor out 2
Area = 2(3x² + 5x + 6)
This means that
Length = 2 and Width = 3x² + 5x + 6
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The equivalent expression
The equivalent expression is (x -2)/(x+4)(x + 6)
How to determine the equivalent expressionIt is important to note that algebraic expressions are defined as expressions composed of coefficients, terms, variables, constants and factors.
They are also made up of arithmetic operations.
Also, equivalent expressions are defined as expressions that have the same solution but differs in the arrangement of the terms.
From the information given, we have the expression;
(x - 2)/x² + 10x + 24
Now, let's factorize the denominator, we have;
x² + 10x + 24. Find the pair factors of 24 that add up to 10, we get;
x² + 4x + 6x + 24
Factorize in pairs
x(x + 4) + 6(x + 4)
Then, substitute the expressions;
(x -2)/(x+4)(x + 6)
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12 1/2 4 7/10 = ? Select one answer. show your work A 7 6/8 B 7 8/10 C 8 6/8 D 8 8/10
According to the question the option C is the correct answer that is 8 6/8 or 8 ¾ calculated by simplifying the fraction.
what is fraction?To represent a whole, every number of equal parts or fractions can be utilised. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of a whole. In mathematics, numbers are stated as a ratio of a numerator to the denominator. They can all be expressed as simple fractions as integers. A fraction appears in a complex fraction's numerator or denominator. The numerators of true fractions are smaller than the denominators. A sum that is a fraction of a total is called a fraction. You can analyse something by dissecting it into smaller pieces. For instance, the number 12 is used to symbolise half of a whole number or object.
To add mixed numbers, we need to first convert any fractions to a common denominator. In this case, we can use 10 as the common denominator.
12 1/2 = 12 + 1/2 = 12 + 5/10 = 12 5/10
4 7/10 = 4 + 7/10
Now we can add the two mixed numbers:
12 5/10 + 4 7/10 = 16 12/10
Simplifying the fraction by dividing the numerator and denominator by their greatest common factor of 2, we get:
16 12/10 = 16 6/5
Therefore, the answer is C) 8 6/8 or 8 3/4.
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what is the measure of MN
Answer:
45 degrees I think
Step-by-step explanation:
sorry if wrong
You have four fun things in a bag (scorpion, tarantula, centipede, and wasp). You reach into the bag and randomly grab two fun things, one after the other, keeping both. Create a tree diagram, table, or list that models the sample space for this event.
Answer: Here is a table that models the sample space for this event:
Scorpion Tarantula Centipede Wasp
First S1 T1 C1 W1
Second S2 T2 C2 W2
Each combination of two fun things is represented by a two-letter code. For example, "S1T2" represents grabbing the scorpion first and the tarantula second.
Here is the list of all possible outcomes:
S1S2
S1T2
S1C2
S1W2
T1S2
T1T2
T1C2
T1W2
C1S2
C1T2
C1C2
C1W2
W1S2
W1T2
W1C2
W1W2
And here is a tree diagram that shows the same information:
|----S2
|----T2
First --|----C2
|----W2
|
|----S2
|----T2
Second--|----C2
|----W2
The branches on the left represent the first fun thing that is grabbed, and the branches on the right represent the second fun thing that is grabbed.
Step-by-step explanation:
Find the area of the triangle.
Easy points!
Answer:
53.06 ft^2
Step-by-step explanation:
Calculate semi perimeter and use Scalence triangle area formula
Semi perimeter: a+b+c/2
Area of Scalence triangle: √s(s-a)(s-b)(s-c). {where s=semi perimeter}
Answer: I don't know
Use appropriate method to solve the following. 1. If twice the age of a son is added to age of a father, then the sum is 56. If twice the age of the father is added to the age of son, then the sum is 82. Find the ages of father and son. 2. In a two-digit number, the sum of the digits is 13. Twice the tens digit exceeds the units digit by one. Find the numbers. 3. I am thinking of a two-digit number. If I write 3 to the left of my number, and double this three digit number, the result is 27 times my original number What is my original number?
Answer:
Step-by-step explanation:
Let the age of the son be $s$ and the age of the father be $f$. From the first equation, we have $2s + f = 56$, and from the second equation, we have $f + 2s = 82$. Solving this system of equations, we get $s = 12$ and $f = 32$, so the son is 12 years old and the father is 32 years old.
Let the two-digit number be $10t+u$, where $t$ is the tens digit and $u$ is the units digit. We are given that $t+u=13$ and $2t-u=1$. Solving this system of equations, we get $t=7$ and $u=6$, so the two-digit number is $76$.
Let the two-digit number be $10x+y$, where $x$ is the tens digit and $y$ is the units digit. We are given that $2(10+x+y) = 27(10x+y)$, or $20+2x+2y = 270x+27y$. Simplifying this equation, we get $268x-25y = 10$. Since $y$ is a digit, we know that $0 \leq y \leq 9$. We can check that $x=1$ is too small, so we try $x=2$. Plugging in $x=2$, we get $536-25y=10$, which gives $y=21/5$, which is not a digit. Thus, there is no solution for a two-digit number.
Marty has a piece of rope with exactly 7 knots tied at equal intervals as shown. using the rope, he wants to make triangles so that each vertex of the triangle occurs at a knot. how many triangles can Marty make?
(a) 4
(b) 1
(c) 2
(d) 3
Using algebra, Marty can make 4 triangles from a rope with 7 knots.
What do you mean by algebra?Algebra, a branch of mathematics, facilitates the representation of situations or issues as mathematical expressions. Mathematical operations like addition, subtraction, multiplication, and division are combined with variables like x, y, and z to produce a meaningful mathematical expression.
All branches of mathematics, such as trigonometry, calculus, and coordinate geometry, employ algebra. Algebraically, 2x + 4 = 8 is a simple expression.
Now here in the question,
3 knots form the vertices of a triangle.
Remaining 4 knots out of the 7 can be distributed as:
4+0+0 .......(on 3 sides)
3+1+0
2+2+0
2+1+1
Therefore, Marty can make 4 triangles from the rope with 7 knots.
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