The surface area of the interior of the box is the total area of the interior walls of the box.
This can be calculated by subtracting the area of the 5 unit square removed from the total area of the original 20 by 30 unit rectangular sheet of cardboard. This gives us an area of 450 units. To calculate the area of the interior walls, we need to multiply the length and width of the remaining rectangle. This gives us a length of 15 units and a width of 25 units, which gives us a total area of 375 units. Therefore, the surface area of the interior of the box is 375 square units. We can calculate this using the formula A = L x W, where A represents the area, L represents the length and W represents the width.
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Guys pls help me fast rapidly is of math:
For the given equation, the binomial factor is (5x² + 3).
In mathematics, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero. The greatest common divisor of two numbers x and y
How do binomial factors work?Factors in polynomial equations with exactly two terms are called binomial factors. Because binomials are simple to solve and their roots are the same as the polynomial's roots, binomial factors are fascinating. Finding a polynomial's roots begins with factoring it.
5x³ - 25x² + 3x - 15
Taking 5x² and 3 as common factors -
⇒ 5x² (x - 5) + 3 (x - 5)
GCF of 1 step is 5x²
⇒ (5x² + 3) (x - 5)
GCF of 2 step is 5x² + 3
Common binomial factor is (5x² + 3)
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solve for an unknown quantity in a two-variable linear equation, given one of the values. determine a two-variable linear equation that represents a scenario, identifying constraints on the variables in terms of the context.
A two variable linear equation means an equation having two variables. It is usually represented as ax+by =c. We can solve a two variable linear equation in many ways.
If the linear equation is only given, to solve it we have to calculate the x-intercept and y-intercept. It is one way of solving a two variable linear equation. Lets look into an example.
2x+5y = 19
The x intercept is when y=0,
then, 2x+ (5×0) = 20
2x = 20, x=10
y intercept is when x=0, then
2×0 + 5y = 20
5y = 20, y= 20/5 =4
So, by solving the equation, we get x=10 at x intercept and y=4 at y intercept.
If one the values are given , we can substitute it in the equation to calculate the other variable.
In the equation, 2x+3y= 12, if y=2, we can calculate by substituting.
2x + (3×2) = 12
2x = 12-6
2x = 6
x =3
So when y=2 then x=3.
Constraints are the restrictions on the domain of a linear equation, like a number of days or students should be a positive integer.
So, we can solve a two variable linear equation through different ways.
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.An artist sells his paintings at a gallery. He charges a set price for each small painting K and
each large painting he sells. Last month, the artist sold 6 small paintings and 8 large
paintings and earned $670 in all. This month, he sold 12 small paintings and 10 large
paintings and earned $950 in all. How much does the artist charge for a small painting?
How much does he charge for a large painting?
I need this in system of equation form please.
The artist charges $25 for a small painting and $65 for a large painting.
How to substitute two equations?
To substitute one equation into another, you can replace one of the variables in the second equation with the expression from the first equation.
Let K be the price of small painting and L be the price of large painting.
From the information given, we know that:
Last month:
6K + 8L = $670 (1)
This month:
12K + 10L = $950 (2)
We have two equations and two unknowns, so we can use a system of equations to find the values of K and L.
Solving the system of equations:
From (1) equation, we have:
6K + 8L = $670
From (2) equation, we have:
12K + 10L = $950
Now we can solve for K (small painting) by multiplying equation (1) by 2 and equation (2) by -1 and adding the two equations together:
12K + 16L = $1340
-12K - 10L = -$950
0K + 6L = $390
Therefore, L = $390 / 6 = $65
Now we can substitute this value of L back into the first equation (1) and solve for K:
6K + 8($65) = $670
6K = $670 - 8($65) = $670 - $520 = $150
K = $150 / 6 = $25
So, the artist charges $25 for a small painting and $65 for a large painting.
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HELP ME ASAP! i need help rn
Answer: yes
Step-by-step explanation:
It's right angled if and only if A^2 + B^2 = C^2
- a^2 = (11-3^2 + 11-5^2) = (64 + 36) = 100
- b^2 = (6-3^2 + 1-5^2) = (9 + 16) = 25
a^2 + b^2 = 125 = sqrt(125)^2
In 2015, as part of its 10th high school reunion, the class of 2005 held a reception at the high school. In an informal survey, the principal of the high school asked 50 of the attendees about their income. The principal computed the mean income of the 50 attendees to be $148,535. In an article published by the local newspaper, the principal was quoted as stating, "The members of our class of 2005 enjoyed resounding success. Last year, they had a mean income of $148,535!"
Part A: What is a statistical advantage of using the median of the reported incomes, rather than the mean, as the estimate of the typical income? (4 points)
Part B: The principal felt the individuals who attended the reception may be different from the class as a whole. A more detailed survey of the class was planned to determine a better estimate of income. The staff developed two methods based on the available funds to carry out the survey.
Method 1: Send out an e-mail to all 2,476 members of the class and ask them to complete an online form. The staff estimates that at least 500 members will respond.
Method 2: Select a simple random sample of members of the class and contact the selected members directly by phone. Follow up to ensure all responses are obtained. Because method 2 requires more time than method 1, the staff estimates only 100 members of the class can be contacted using method 2.
Which of the two methods would you select for estimating the average yearly income of all 2,476 members of the class of 2005? Explain your reasoning by comparing the two methods and by describing the effect of each method on the estimate.
Method 2 is the best option for estimating the average yearly income of the class of 2005.
What type of sampling technique is used?I would select Method 2 for estimating the average yearly income of all 2,476 members of the class of 2005. Method 2 involves selecting a simple random sample of members of the class and contacting them directly by phone. This method guarantees that the sample will be representative of the entire population and thus provides the best estimate of the average income of the class. By randomly selecting the sample, we can be sure that the sample will be unbiased and the results will be more reliable. Method 1, on the other hand, involves sending an e-mail to all 2,476 members of the class and asking them to complete an online form. Although this method is easier and less time-consuming, it does not guarantee a representative sample. If only 500 people respond, it is possible that the sample will not be representative of the entire population and thus, the results will not be accurate. Overall, It will ensure that the sample is representative of the entire population and that the results are unbiased and reliable.To learn more about the sampling theory refer to:
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Pls help, OR ELSE a grotesque Dung Beatle will find its way into your coffee ☕
Question
In this figure, GH=10, GP=16, and FP=4.
What is EF?
Enter your answer in the box.
EF =
Answer: EF = 12 is the correct answer.
Step-by-step explanation: EF = GP - FP = 16 - 4 = 12Given that GH=10, GP=16, and FP=4. We have to find the value of EF. We can use this formula to find it:EF = GP - FP = 16 - 4 = 12So the value of EF is 12. In the given figure, ABCD is a rectangle and GP and GH are the diagonals. EF is the length of the rectangle.Therefore, EF = 12 is the correct answer.
Answer:Well i think EF would be 10 since it looks like the same length as GH
Step-by-step explanation:
two expressions that are equivalent to 3f
The two expressions are written as :
3f + 2f + 4s 5f + 4sHow to solve for the expressions that are equivalent to 3f+4s+2f3f+4s+2f this expression that we have here is a mathematical expression that we can combine by making use of the commutative addition.
We would have the first expression when we write the equation as:
3f+4s+2f = 3f + 2f + 4s
We would have the second expression when we write the equation as
5f + 4s
This is the solution of the expression.
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two expressions that are equivalent to 3f+4s+2f ?
Patricia is making homemade snacks. Each snack requires 2.25 cups of almonds. Patricia buys 6 cans of almonds that each contain eight 1/3 cup servings. What is the maximum number of snack bags that Patricia can make with the almonds?
Answer: 7
Step-by-step explanation:
Patricia has 6 cans of almonds that each contain eight 1/3 cup servings, meaning that Patricia has a total of
6 cans x 8 servings x 1/3 cup = 16 cups of almonds
If she needs 2.25 cups of almonds, that would be equal to
16/2.25 = around 7.1
since you can't have a fraction of a snack bag, Patricia just has 7 snack bags.
Evaluate the expression using the given value of the variable:[ y + z - z ]; use [y = 6], and [z = 5] .
Answer:
( y + z - z )
given, y= 6 z=5
(6 + 5 - 5 )
Use DMAS rule
D=division M= multiplication A= addition S=subtraction
(11-5)
6 (ans)
graph an equation of the form y=kx+1 which includes point m. m(2,-7)
The linear equation y = - 4 · x + 1 includes point (x, y) = (2, - 7).
How to graph a linear function on Cartesian plane
In this problem we need to plot a linear equation on Cartesian plane, linear equations are first polynomials of the form:
y = m · x + b
Where:
x - Independent variabley - Dependent variablem - Slopeb - InterceptIf we know that b = 1 and (x, y) = (2, - 7), then the equation of the line is:
- 7 = 2 · k + 1
- 8 = 2 · k
k = - 4
y = - 4 · x + 1
Now we proceed to graph the line. First, find two points of the line:
x = 0
y = - 4 · 0 + 1
y = 1
x = 1
y = - 4 · 1 + 1
y = - 3
Second, plot the points on Cartesian plane.
Third, construct the line that passes through the two points.
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State if the three numbers can be the measures of the sides of a triangle. 7, 10, 10
Yes, these numbers meet the triangular inequalities, then these can be the measures of the sides of a triangle.
Can be the measures of the sides of a triangle?Remember that if A, B, and C are the sides of a triangle, then the triangle inequality says that:
A + B > C
A + C > B
C + B > A
As long as 3 values are solutions of the inequalities, then these can be the sides of a triangle.
if we use:
A = 7
B = 10
C = 10
Then we get:
7 + 10 > 10 ---> 17 > 10
7 + 10 > 10 ---> 17 > 10
10 + 10 > 7 ---> 20 > 7
All the ienqualities are true, thus, these can be the measures of the sides of a triangle.
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In ABCD, CD = 12, DB = 10, and BC = 6. Which list has the angles of ABCD in order from largest to smallest?
A, C, B, and D make up the list of ABCD's angles, from largest to smallest, with 90°, 54°, 24°, and 12°, respectively.
What's an angle?The sides of a triangle, or angle, are two rays that make up the figure. The Law of Cosines can be used to find Angle A. We can solve for the angle A by using the formula
c² = a² + b² - 2abcos(C).
Since we know the lengths of all sides, we can substitute in the values.
c² = 122 + 102 - 2(12)(10)cos(A)
Cos(A) = (144 + 100 - 120)/240
= 24/240
= 0.1
In the end, we use the inverse cosine to determine the angle A, which is roughly 74 degrees.
The same formula can be used to determine Angle D.
c² = 62 + 102 - 2(6)(10)cos(D)
Cos(D) = (36 + 100 - 60)/120
= 76/120
= 0.63 .
When we take the inverse cosine, we get the angle D, which is about 27.3 degrees.
The same formula can be used to determine Angle C.
c² = 122 + 62 - 2(12)(6)cos(C)
Cos(C) = (144 + 36 - 72)/144
= 108/144
= 0.75
When we take the inverse cosine, we get the angle C, which is about 36.9 degrees.
The same formula can be used to determine Angle B.
c² = 122 + 102 - 2(12)(10)cos(B) .
Cos(B) = (144 + 100 - 120)/240
= 24/240
= 0.1
We obtain the angle B, which is roughly 74 degrees, by applying the inverse cosine.
Therefore, ABCD's angles, from largest to smallest, are as follows: angle C (36.9°), angle B (74°), and angle D (27.3°)
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What is the measure of n?
28
m
7
n = [?]
Give your answer in simplest form.
The measure of the side length n is equal to 14 for the right triangle.
How to evaluate the length of n in the right triangleConsidering the larger acute angle, if we represent it by θ then for the bigger right triangle with adjacent m and hypotenuse 28+7= 35;
cosθ = m/35
for the smaller right triangle with adjacent 7 and hypotenuse m
cosθ = 7/m
m/35 = 7/m
m² = 245 {cross multiplication}
m = √245 = 7√5 {take square root of both sides}
(√245)² = 7² + n² {by Pythagoras rule for the smaller right triangle}
245 = 49 + n²
n² = 245 - 49 {collect like terms}
n² = 196
n = √196 {take square root of both sides}
n = 14
Therefore, the measure of the side length n is equal to 14 for the right triangle
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The top selling brand of vape machines sold 10000 units at $89 per unit in 2018. what is their market share if the vape machine market had sales of $1.4M?
The market share of the vape machine market had sales of $1.4M is given as 63.57%.
How to solve for the market share of the vape machineTo calculate the brand's market share, you would need to divide the brand's sales by the total sales of the market and then multiply by 100 to get the percentage.
In this case, the brand's sales are 10000 units x $89/unit = $890,000.
So the market share would be:
$890,000 / $1,400,000 x 100 = 63.57%.
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Debbie shipped 2 packagesone weighed 2 pounds10 ounces the other weighed 4 pounds and12 ounces what is the total weight of The 2 packages
The combined weight of the two parcels, one of which weighs 2 pounds 10 ounces and the other 4 pounds and 12 ounces, is 7 pounds 10 pounces.
what is unitary method ?The unit tactic is a strategy for addressing issues that entails first figuring out the value of a particular unit, then increasing that value to figure out the needed value. Simply put, the unit method is employed to obtain a minimum unit value from a multiple that is supplied. For example, 40 pens may cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its homologue and reciprocal are equal in terms of mathematics, algebra, linear algebra, applied mathematics, or mathematics for matrices or operators.
given
1 pound = 16 ounces
for 2 packages
2 pounds 10 ounces + 4 pounds 12 ounces
6 pounds and 22 ounces
= 7 pounds 10 pounces
The combined weight of the two parcels, one of which weighs 2 pounds 10 ounces and the other 4 pounds and 12 ounces, is 7 pounds 10 pounces.
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use theorem 2.1.13 to prove that if $f$ and $g$ are continuous functions with open domains $u f$ and $u g$, and if $g(u g)\subseteq u f$, then $f \circ g$ is continuous on $u g$
Since function f andg are continuous and u g subseteq u f, Theorem 2.1.13 states that f circ g is continuous on u g.
In accordance with Theorem 2.1.13, if two functions,f andg, are continuous on open domains [tex]$u f$[/tex]and [tex]$u g$[/tex] respectively, and $g(u g)subseteq u f, then $ circ g is continuous on u g. This is the case since the domain of f, which is u g is a subset of the domain of f, which is u g, and the composition of continuous functions is continuous. The composition of these two functions will be continuous onu g because both of these functions are continuous and u g subseteq u f.
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I NEED HELP ASAP, I PROMISE WHOEVER IS CORRECT IS GOING TO GET BRAINLIST!
The numbers that correctly complete the two-way table are 100,70, 170, 80, 130, 210, 180,200, and 380 as shown in the attached chart.
How to calculate the number of sweatshirts per color and style?Total of sweatshirts= 380
Total with no hood= 210
Green sweatshirts= 180
Purple sweatshirts with no hood= 70
Based on this information we can conclude:
There are 170 sweatshirts with no hood (380-210= 170)There are 200 purple sweatshirts (380 - 180 = 200)There are 130 purple sweatshirts (200-70 = 130)There are 100 green sweatshirts with hood (170-70= 100)There are 80 green sweatshirts with hood (180-100 = 80)Learn more about two-way tables in https://brainly.com/question/29766382
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Please help! Systems of equation/matrix problem
5. TELEVISION During t
ring the summer, Manuel watches television M hours per day, Monday through Friday. Harry watches television H hours per day, Friday and Saturday. Ellen watches television E hours per day, Friday through
Sunday. Altogether, they watch television 37 hours each week. On Fridays, they watch a total of 11 hours of television.
If the number of hours Ellen spends watching television on any given day is twice the number of hours that Manuel
spends watching television on any given day, how many hours of television does each of them watch each day?
Answer:
see attached
Step-by-step explanation:
X^2 - y^2
—————-
3x - Зу
Step-by-step explanation:
x² - y² = (x + y)(x - y)
3x - 3y = 3(x - y)
(x + y)(x - y) / (3(x - y)) = (x + y)/3
Answer:
x^2 - y^2
_______
3x - 3y
(x+y) (x-y)
_______ { (x-y) (x-y) cancels out}
3(x-y)
(x+y)
____
3
Hope this will help you...!!!!
State the critical values for a one-sample t test given the following conditions:
1. Two-tailed test, a = .05, n = 12
2. One-tailed test, lower-tail critical, a = .01, df = 15
3. Two-tailed test, a = .01, df = 26
4. One-tailed test, upper-tail critical, a = .05, n = 30
Use the values listed in the table; do not round. Be sure to include the appropriate signs in your answers:
• if positive --> + and the value
. if negative --> - and the value
if both --> +/- and the value
(Privitera, 2019, p. 250, #14)
The critical values for a one-sample t test given the following conditions are +1.796, -1.796 2. -2.60 3. +2.576, -2.576 4. +1.729.
What is value?Value is a term used in many different contexts to refer to the worth or importance of something. It is used to describe the worth of an item or service in terms of its utility, its ability to satisfy a need or desire, or its usefulness in exchange. Value can also refer to the worth of an individual or group in terms of their contribution to society or their inherent worth. Value is subjective and can vary greatly from one person or group to another.
1. +1.796, -1.796
2. -2.60
3. +2.576, -2.576
4. +1.729
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Angelina spent less than 15 hours practicing for her surfing competition. How many hours could she have spent surfing?
If a rock is thrown upward on the planet Mars with a velocity 16 m/s, its height in meters t seconds later is given by y = 16t − 1.86t2. (Round your answers to two decimal places.)
(a)Find the average velocity (in m/s) over the given time intervals:
A. [1,2]
B. [1,1.5]
C. [1,1.1]
D. [1,1.01]
E. [1,1.001]
The average velocity (in m/s) over the given time intervals is [1,2]
Part A.
Keep in mind that the formula for average velocity is
(Y2 - Y1)/V avg = displacement/time interval (t2 - t1)
Given that the rock's position at time t is determined by:
y = 16t - 1.86*t^2
Part 1
for the time period [1, 2]
Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.
Y2 = 16*2 - 1.86*22 = 24.56 m when t2 = 2 sec.
So
average Velocity = (24.56 - 14.14)/(2 - 1) (2 - 1) = 10.42 m/s V avg
Part 2.
for the time period [1, 2]
Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.
Y2 = 16*1.5 - 1.86*1.52 = 19.815 m when t2 = 1.5 sec.
So,
average Velocity = (19.815 - 14.14)/(1.5 - 1) (1.5 - 1) = 11.35 m/s V avg
Part 3.
During the period [1, 1] .1]
Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.
Y2 = 16*1.1 - 1.86*1.12 = 15.3494 m when t2 = 1.1 sec.
So,
average Velocity = (15.3494 - 14.14)/(1.1 - 1) (1.1 - 1)
average Velocity = 12.094 m/s and equals 12.09 m/s (In two decimal places)
Part 4.
During the period [1, 1] .01]
Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.
Y2 = 16*1.01 - 1.86*1.012 = 14.262614 m when t2 = 1.01 sec.
So,
average Velocity = (14.262614 - 14.14)/(1.01 - 1) (1.01 - 1)
12.26 m/s and V avg = 12.2614 m/s (In two decimal places)
Part 5.
During the period [1, 1] .001]
Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.
Y2 = 16*1.001 - 1.86*1.0012 = 14.15227814 m when t2 = 1.001 sec.
So,
average Velocity = (14.15227814 - 14.14)/(1.001 - 1) (1.001 - 1)
12.28 m/s V avg = 12.27814 m/s (In two decimal places)
Part B.
Rock's immediate velocity will be determined by:
d[16t - 1.86t2]/dt = V= dy/dt
Velocity = 16*1 - 2*1.86*t
time = 1 second,
Velocity = 16 - 2*1.86*1
average velocity at time t is equal to V = 12.28 m/s.
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a = 47.4 rounded to 1 DP
b = 0.19 rounded to 2 DP
Find the minimum of a - b
Answer:
47.21
Step-by-step explanation:
Subistitute:-47.4-0.19
Calculate the sum or difference:-47.21
Can anyone help??
Which line is parallel to y=-4x+11 and goes through (2,1)? Hint: use point slope form
A)y-1=-4x(x-2)
B)y-1=-1/4(x-2)
C)y-1=4(x-2)
D)y-2=-4(x-1)
(I’m trying to do test corrections :c )
A line that is parallel to y = -4x + 11 and goes through the point (2, 1) in point slope form is: A. y - 1 = -4(x - 2).
What is the point-slope form?Mathematically, the point-slope form of a line is modeled by this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.From the given linear equation y = -4x + 11, the slope is given by:
y = -4x + 11
m₁ = -4
In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂ (m represents the slope.)
At point (2, 1), an equation of this line can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = -4(x - 2)
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Solve the system of linear equations by graphing.
y equals negative one half times x plus 3
y equals one half times x minus 2
one half comma negative 5
one half comma 5
5 comma one half
negative 5 comma one half
The solution to the simultaneous equations is; 5 comma one half
How to solve Simultaneous Linear Equations?The simultaneous equations are;
y = -¹/₂x + 3 -------(1)
y = ¹/₂x - 2 -------(2)
Substitute ¹/₂x - 2 for y in eq 1 to get;
¹/₂x - 2 = -¹/₂x + 3
Add -¹/₂x to both sides using addition property of equality to get;
¹/₂x + ¹/₂x - 2 = 3
Add 2 to both sides using addition property of equality to get;
x = 3 + 2
x = 5
Thus;
y = ¹/₂(5) - 2
y = ¹/₂
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Answer:
Solve the system of linear equations by graphing.
y equals negative one half times x plus 3
y equals one half times x minus 2
Step-by-step explanation:
the figure at the right is a regular octagon with the sign length s. Write two algebaric
The expression of the side length is 6y - 5
How to determine the expression of the side lengthThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Perimeter = 48y - 40
Number of sides = 8
The side length s can be calculated as
s =(48y - 40)/8
Evaluate the quotient
s = 6y - 5
Hence, the side length expression is 6y - 5
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6= 1/v+2
Solve for V
simplify your answer as much as possible
Answer:
your question is 6=1/v+2
Step-by-step explanation:
6-2=1/v
4v=1
v=1/4
If angle A=−170∘, what is the radian measure of A? Enter an exact fraction that contains the π symbol.
The radian measure of A = 170° as an exact fraction that contains the π symbol is; ¹⁷/₁₈π
How to convert degrees to radians?When we want to convert the value of an angle in degree, to its equivalent radians, what we need to do is to multiply the given value with π/180. For example, the value of 180 degrees is π in radians.
Thus, since we want to find the radian measure of 170 degrees, it means that;
If 180° = π radians,
then; 170° = (170 * π)/180
= ¹⁷/₁₈π
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According to the United States Department of Health and Human Services, the mean height for Americans is 1.757m for men and 1.618 m for women3. The standard deviation is 0.074m for men and m for women.
1)
What -score corresponds to a man who is 1.853m tall?
A man who is 1.853m tall would have a z-score of 1.297.
What is the z-score?Generally, To find the z-score for a man who is 1.853m tall, we need to use the formula for a z-score:
= (x - mean) / standard deviation.
In this case, the mean height for men is 1.757m and the standard deviation is 0.074m, so the z-score for a man who is 1.853m tall would be:
(1.853 - 1.757) / 0.074 = 1.297297297
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determine if one of the given vectors is in the span of the other vectors. (hint: check to see if the vectors are linearly dependent, and then appeal to this theorem.) u=[1,7,8,3] v=[-1,3,5,3]
w=[4,8,6,0]
a. None of the vectors is in the span of the other vector.
b. One of the vectors is in the span of the other vector
Out of the given vectors is in the span of the other vectors, b. One of the vectors is in the span of the other vector. Since u and v have the same last component, they are linearly dependent, so u is in the span of v and w.
If a set of vectors is linearly dependent, then one of the vectors can be expressed as a linear combination of the other vectors. This means that one vector is in the span of the other vectors. In this case, u can be expressed as a linear combination of v and w, so u is in the span of the other vectors.
To check for linear dependence, we can first check for a zero row in the matrix formed by the vectors. If there is a zero row, then the vectors are linearly dependent. In this case, the last row of the matrix formed by the vectors is [3,3,0], which is a zero row, so the vectors are linearly dependent. We can also check for linear dependence by computing the determinant of the matrix formed by the vectors.
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