Answer:
y = -15
Step-by-step explanation:
x-5y=-15x−5
Let x = -5
-5 -5y = -15 * -5 -5
Combine like terms
-5 -5y = 75-5
-5 -5y = 70
Add 5 to each side
-5y = 75
Divide by -5
y = -15
This table shows values that represent an exponential function.
What is the average rate of change for this function for the interval from x = 1
to x = 3?
Answer:
B. 3
Step-by-step Explanation:
To find the average rate of change of the exponential function represented by the table of values above can be calculated using the general formula for average rate of change of a function, which is given as [tex] m = \frac{f(b) - f(a)}{b - a} [/tex]
Where,
[tex] a = 1, f(1) = 7 [/tex]
[tex] b = 3, f(3) = 13 [/tex]
Plug in the above values in the average rate of change formula:
[tex] m = \frac{13 - 7}{3 - 1} [/tex]
[tex] m = \frac{6}{2} [/tex]
[tex] m = 3 [/tex]
Average rate of change is B. 3
Answer:
3
Step-by-step explanation:
What type of model best fits the height of a tree increases by 2.5 feet each growing season
Answer:
Step-by-step explanation:
A linear graph with y values (height of tree) going up 2.5 with each increase of x (growing season)
This is the model that best fits the graph describing a growth of a plant
Need answers ASAP!!!!! (due today)
Answer:
15) 2.08m
Step-by-step explanation:
We kow tanA= p/b
Here, A=33°
b=3.2m
Then,
tan33°=p/3.2
0.65=p/3.2
p=0.65*3.2
p=2.08
So, The height of tree is 2.08m
14) 59.58ft
tan50°=p/b
1.19=p/50
p=59.58ft
So, The height of signpost is 59.58ft
In both of these problems, we will be using trigonometry! Remember, SOH-CAH-TOA.
14. x = 13.5950 ft
Visualization of the problem is attached below.
We want to find out the opposite side to the angle, and we know the adjacent side. Therefore, we should use the tangent function.
tan(50) = x / 50
x = tan(50) * 50
x = 13.5950 ft (round off wherever you need)
15. x = 241.0016 m
The visualization of the problem is already given. We know the same information as we need in the previous problems, an angle and an adjacent side, and we want to find the opposite side. Therefore, we should use the tangent function.
tan(33) = x / 3.2
x = tan(33) * 3.2
x = 241.0016 (round off wherever you need)
Hope this helps!! :)
how do I simplify this (sinx)/(secx+1)
Answer:
Step-by-step explanation:
[tex]\frac{sin~x}{sec~x+1} =\frac{sin~x}{\frac{1}{cos~x}+1 } =\frac{sin~x~cos~x}{1+cos~x} \\=\frac{sin~x~cos~x}{1+cos~x} \times \frac{1-cos~x}{1-cos~x} \\=\frac{sin~x~cos~x(1-cos~x)}{1-cos^2 x} \\=\frac{sin~x~cos~x(1-cos~x)}{sin^2x} \\=\frac{cos~x(1-cos~x)}{sin~x} \\=cos ~x(csc~x-cot~x)\\or\\=cot~x(1-cos~x)[/tex]
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each sequence to its appropriate recursively defined function. f(1) = 13 f(n) = f(n - 1) + 26 for n ≥ 2 f(1) = 13 f(n) = 3 · f(n - 1) for n ≥ 2 f(1) = -24 f(n) = -4 · f(n - 1) for n ≥ 2 f(1) = 28 f(n) = f(n - 1) - 84 for n ≥ 2 f(1) = 28 f(n) = -4 · f(n - 1) for n ≥ 2 f(1) = -24 f(n) = 4 · f(n - 1) for n ≥ 2 Sequence Recursively Defined Function -24, -96, -384, -1,536, ... 28, -112, 448, -1,792, ... 13, 39, 65, 91, ...
Answer:
sequence 3no matching sequenceno matching sequenceno matching sequencesequence 2sequence 1Step-by-step explanation:
Recursively Defined Function Sequence
f(1) = 13 f(n) = f(n - 1) + 26 for n ≥ 2 13, 39, 65, 91, ...
f(1) = 13 f(n) = 3 · f(n - 1) for n ≥ 2
f(1) = -24 f(n) = -4 · f(n - 1) for n ≥ 2
f(1) = 28 f(n) = f(n - 1) - 84 for n ≥ 2
f(1) = 28 f(n) = -4 · f(n - 1) for n ≥ 2 28, -112, 448, -1,792, ...
f(1) = -24 f(n) = 4 · f(n - 1) for n ≥ 2 -24, -96, -384, -1,536, ...
__
The initial values are easily seen. They match f(1). The recursive functions can be tested to see if they match the offered sequences.
sequence 1 has a common ratio of 4 (not -4)
sequence 2 has a common ratio of -4 (it is not arithmetic)
sequence 3 has a common difference of 26 (it is not geometric)
Answer:
1 is sequence 3
5 is sequence 2
6 is sequence 1
(These r not included in the test, so don't use them)
|
\ /
2 is no matching sequence
3 is no matching sequence
4 is no matching sequence
Step-by-step explanation:
PLATO
Which of the following is best described as all the points on a plane that are the same distance from a single point called a center?
A.
Ellipse
B.
Circle
C.
Diameter
D.
Chord
Answer:
It would be B. Circle
The principal of a middle school claims that test scores of the seventh-graders at his school vary less than the test scores of the seventh-graders at a neighboring school, which have variation described by σ = 14.7. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.
Answer:
There is sufficient evidence to support the claim that the standard deviation is less than 14.7.
Step-by-step explanation:
From the question we are told that that the null hypothesis is
[tex]H_o : \sigma < 14.7[/tex]
Now given from the question that this null hypothesis was rejected, it mean, in non technical term that there is sufficient evidence to support the claim that the standard deviation is less than 14.7.
g Suppose that three hypothesis tests are carried out, each using significance level 0.05. What is the worst-case probability of a type I error in at least one of these tests?
Answer:
The worst-case probability is 0.05
Step-by-step explanation:
The given significance level ([tex]\alpha[/tex]) = 0.05
since Probability of a type I error is [tex]\alpha[/tex]
∴ P (type I error) = 0.05
0.05 will be the worst-case probability of a type I error in at least one of the tests.
Solve this inequality. -9x - 3 > 51 A. x -392 C. x -6
Answer:
The answer is option C.
Step-by-step explanation:
- 9x - 3 > 51
Group like terms
- 9x > 51 + 3
- 9x > 54
Divide both sides by -9
x < - 6
Hope this helps you
17. Convert the following measures of liquid measure. a. 3,450 deciliters to cubic decimeters _______ b. 124.3 hectoliters to deciliters _______ c. 9 liters to cubic centimeters _______ d. 32.5 liters to cubic decimeters _______
Step-by-step explanation:
. 345,000 cm³.
b. 124,300 hl.
c. 9,000 cm³.
d. 32.5 dm³.
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
a. 3,450 deciliters to cubic decimeters:
1 deciliter=100 cubic decimeters
(3,450dl)(\frac{100cm^{3}}{1dl})=345,000cm^{3}(3,450dl)(
1dl
100cm
3
)=345,000cm
3
b. 124.3 hectoliters to deciliters:
1 hectoliter=1,000 deciliters
(124,3hl)(\frac{1,000dl}{1hl})=124,300hl(124,3hl)(
1hl
1,000dl
)=124,300hl
c. 9 liters to cubic centimeters:
1 liter=1,000 cubic centimeters
(9L)(\frac{1,000cm^{3}}{1L})=9,000cm^{3}(9L)(
1L
1,000cm
3
)=9,000cm
3
d. 32.5 liters to cubic decimeters:
1 liter=1 cubic decimeter
32.5L=32.5dm^{3}32.5L=32.5dm
3
your answer follow me plzzz
Answer:
The first one is 345,000 cm³.
The second is 124,300 hl.
the Third is 9,000 cm³.
Anddd the fourth one is 32.5 dm³
:)
A quality control inspector has determined that 0.25% of all parts manufactured by a particular machine are defective. If 50 parts are randomly selected, find the probability that there will be at most one defective part.
Answer:
9.941*10^-6
Step-by-step explanation:
Probability of at most 1 means not more than 1 defective= probability of 1 or probability of 0
Probability of 1 = 50C1(0.25)(0.75)^49
Probability= 50(0.25)*7.55*10^-7
Probability= 9.375*10^-6
Probability of 0
= 50C0(0.25)^0(0.75)^50
= 1(1)(0.566*10^-6)
= 0.566*10^-6
Total probability
= 9.375*10^-6+ 0.566*10^-6
= 9.941*10^-6
Compute the least-squares regression line for predicting y from a given the following summary statistics. Round final answers to four decimal places, as needed.
xbar = 8.8 sx = 1.5 sy = 1.8 ybar = 30.3
r = -0.84
Download data
Regression line equation: y = ______ + _______ x
Answer: Regression line equation: [tex]\hat{y}=-1.008x+39.1704[/tex]
Step-by-step explanation:
Equation of least-squares regression line for predicting y :
[tex]\hat{y}=b_1x+b_o[/tex]
, where [tex]\text{Slope} (b_1)=r\dfrac{s_y}{s_x}[/tex] , [tex]\text{intercept}(b_0)=\bar{y}-b_1\bar{x}[/tex]
Given: [tex]\bar{x}=8.8,\ s_x=1.5,\ s_y=1.8,\ \bar{y}=30.3,\ r=-0.84[/tex]
Then,
[tex]b_1=(-0.84)\dfrac{ 1.8}{ 1.5}\\\\\Rightarrow\ b_1=-1.008[/tex]
Now,
[tex]b_0=30.3-(-1.008)(8.8)=30.3+8.8704\\\\\Rightarrow\ b_0=39.1704[/tex]
Then, Regression line equation: [tex]\hat{y}=-1.008x+39.1704[/tex]
The graph below shows a line of best fit for data collected on the number of students who wear a jacket to school and the average daily temperature in degrees Fahrenheit.
Based on the line of best fit, how many students wear a jacket to school when the temperature is 50°F?
A.) 240
B.) 210
C.) 300
D.) 180
Answer:
240
Step-by-step explanation:
You should go to the value 50 °F and see the value that match it
here it's 240 students
Based on the line of best fit, the number of students who wear a jacket to school when the temperature is 50°F is 240.
What is a graph?A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
Given that The graph shows a line of best fit for data collected on the number of students who wear a jacket to school and the average daily temperature in degrees Fahrenheit.
Now, Based on the line of best fit, the number of students who wear a jacket to school when the temperature is 50°F can be found by simply observing the graph when the average daily temperature is 50°F as shown below, and then looking the value of y at that temperature.
Hence, Based on the line of best fit, the number of students who wear a jacket to school when the temperature is 50°F is 240.
Learn more about Graph:
https://brainly.com/question/21608293
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Find the circumference of C in terms of π
radius of c Is 5
Answer:
Given that
radius of circle =5units
So, circumference of circle=2πr
=2×π×5
=10π units
hope it helps u...
plz mark as brainliest...
Answer:
[tex]\boxed{Circumference = 10\pi \ units}[/tex]
Step-by-step explanation:
Circumference = [tex]2\pi r[/tex]
Where r = 5
=> Circumference = 2π(5)
=> Circumference = 10π units
Graph the line y=4/3x +1
The slope would be 4/3 and the y-intercept is 1
Create a table x and y and in x there is -3/4 and 0 and for the y side is 0 and 1. The line would be in the 2 quadrant with 2 points on on the y axis 1 and the other on the x axis 0.9 and that would be the graphed description of the line. Sorry if this is hard to understand i don’t have a access to draw or insert an image.
The graph of the linear equation is on the image at the end.
How to graph the line?To do it, we need to find two points on the line, so let's evaluate it.
When x = 0
y = (4/3)*0 + 1 = 1 ----> (0, 1)
When x = 3
y = (4/3)*3 + 1 = 5 ---> (3 , 5)
Now just graph these two points and connect them with a line, that will be the graph of the linear equation.
Learn more about linear equations at:
https://brainly.com/question/1884491
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Solve the equation: 1/3(y - 2) - 5/6(y + 1) = 3/4(y - 3) - 2
Answer:
y=2.2
Step-by-step explanation:
1: Distribute all numbers to get rid of all parenthesis
2: Solve
Hope this helped :) LET ME KNOW IF YOU NEED THE ANSWER IN A DIFFERENT FORM I CAN GET IT FOR YOU
Question 10 of 10
Which set of polar coordinates are plotted in the graph below?
Answer:
(-2, -(2pi)/3)
Step-by-step explanation:
a p ex
In da pic :)))))))))
Keith biked 26 miles today and 32 miles yesterday. Which equation shows m, the number of miles he biked all together?
Answer:
m = 26+32
Step-by-step explanation:
To determine the total number of miles biked, add the days together
m = 26+32
Answer:
26+32=m
Step-by-step explanation:
That is the general eqaution of this, because u must add both days worth of biked miles together.
Need help with this, I don’t need an explanation.
the answer is x=-2
and y=12
Which graph is defined by the function given below ? y=(x-3)(x-3)
Answer:
Graph B
Step-by-step explanation:
We are looking for a graph with a double root at x=3. In such cases, the function will "touch' the x-axis at x=3. The graph that shows such behavior is Graph B.
Answer:B
X intercepts (3,0) Y intercepts (0,9)
A pair of linear equations which has a unique solution x = 2, y = –3 is
a) x – 4y –14 = 0
5x – y – 13 = 0
b) 2x – y = 1
3x + 2y = 0
c) x + y = –1
2x – 3y = –5
d) 2x + 5y = –11
4x + 10y = –22
Answer:
a)x - 4y -14 =0
5x - y - 13 =0
Step-by-step explanation:
Using substitution method to solve equation above gives:
x - 4y - 14 =0 ....eq1
5x - y -13 =0 ....eqn2
From eqn1, making x the subject formula:
x - 4y - 14 =0
x - 4y =14
x = 14+4y ...eqn3
From eqn2, substitute value of x and solve for y:
5(14+4y)-y-13 =0
70+20y-y-13 =0
70+19y-13 =0
70 - 13 = -19y
57 = -19y
divide both sides by -19
-57/19 = -19y/-19, then
y = -3
From eqn1:
x = 14 + 4y
substitute the value of y in the expression above
x = 14 + 4(-3)
x = 14 + (-12)
x = 14 - 12
x = 2
Solve for x : 2^x+4^x+8^x=−14
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
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Let's solve this step by step.
[tex]2^x + 4^x + 8^x = -14[/tex]
↓
In order to factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).
The number of times that each prime divides the original integer becomes its exponent in the final result.
Prime number 2 to the power of 2 = 4
[tex]2^x + (2^2)^x + (2^3) ^x = -14[/tex]
↓
Prime number 2 to the power of 3 = 8
[tex]2^x + 2^2x + 2^3x = -14[/tex]
↓
We need to exponentiate the power.
The following rule is applied:
[tex](A^B) ^C = A^BC[/tex]
In our example,
A is equal to 2,
B is equal to 2 and
C is equal to x.
[tex]( 2^x + 2^2x + 2^3x ) + 14 = -14 + 14[/tex]
↑
In order to solve this non-linear equation, we need to move all the terms to the left side.
In our example,
- term −14, will be moved to the left side.
Notice that a term changes sign when it 'moves' from one side of the equation to the other.
___________________
We need to get rid of expression parentheses.
If there is a negative sign in front of it, each term within the expression changes sign.
Otherwise, the expression remains unchanged.
In our example, there are no negative expressions.
↓
[tex]2^x + 2^2x + 2^3x + 14 = 0[/tex]
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Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
What is 3/4 improper or proper or mixed
Answer:
proper because the numerator is lower than the denominator
Sixty percent of adults have looked at their credit score in the past six months. If you select 31 customers, what is the probability that at least 20 of them have looked at their score in the past six months
Answer:
The probability is [tex]P(X \ge 20 ) = 0.3707[/tex]
Step-by-step explanation:
From the the question we are told that
The population proportion is p = 0.60
The sample size is n = 31
The mean is evaluated as
[tex]\mu = n * p[/tex]
substituting values
[tex]\mu = 31 *0.60[/tex]
[tex]\mu = 18.6[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{n * p * (1- p )}[/tex]
substituting values
[tex]\sigma = \sqrt{31 * 0.6 * (1- 0.6 )}[/tex]
[tex]\sigma = 2.73[/tex]
The the probability that at least 20 of them have looked at their score in the past six months is mathematically represented as
[tex]P(X \ge 20) = 1- P(X < 20)[/tex]
applying normal approximation we have that
[tex]P(X \ge 20) = 1- P(X < (20-0.5))[/tex]
Standardizing
[tex]1 - P(X < 20) = 1 - P(\frac{X - \mu }{\sigma} < \frac{19.5 - \mu }{\sigma } )[/tex]
[tex]1 - P(X < 20) = 1 - P(Z < \frac{19.5 - 18.6 }{2.73 } )[/tex]
[tex]1 - P(X < 20) = 1 - P(Z < 0.33)[/tex]
Form the standardized normal distribution table we have that
[tex]P(Z < 0.0512)[/tex] = 0.6293
=> [tex]P(X \ge 20 ) = 1- 0.6293[/tex]
=> [tex]P(X \ge 20 ) = 0.3707[/tex]
please Help will mark brainliest !!1!Use the linear combination method to solve the system of equations. Explain each step of your solution. 2x -3y = 13 x+2=- 4
Answer:
work is shown and pictured
I hope u can understand help asap
i think u can see sho T=5n+20
Answer:
T(n) = 5n + 20
Step-by-step explanation:
1 candy has a mass of 5 g.
n candies have a mass of 5n grams.
The box has a mass of 20 grams.
total mass = mass of candies + mass of box
T(n) = 5n + 20
n T(n)
0 20
25 145
50 270
75 395
100 520
Write an expression:
a) 4 less than twice a
number
11
Gra
ine
a)
e
Answer:
2x - 4.
Step-by-step explanation:
4 less than twice a number is the same thing as a number times 2 minus 4. Let's say that the number is represented by x.
2 * x - 4 = 2x - 4.
Hope this helps!
The population, p, in thousands of a resort community is given by P(t)=700t/4t[tex]x^{2}[/tex]+9
Answer:
Step-by-step explanation:
pt=700 is basically evaluate it form the bottom to the top and u must mark me as brainly
The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 51 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.2 pounds, what is the probability that the sample mean will be each of the following? Appendix A Statistical Tables a. More than 61 pounds b. More than 57 pounds c. Between 55 and 58 pounds d. Less than 55 pounds e. Less than 48 pounds
Answer:
(a) The probability that the sample mean will be more than 61 pounds is 0.0069.
(b) The probability that the sample mean will be more than 57 pounds is 0.4522.
(c) The probability that the sample mean will be between 55 and 58 pounds is 0.6112.
(d) The probability that the sample mean will be less than 55 pounds is 0.14686.
(e) The probability that the sample mean will be less than 48 pounds is 0.00001.
Step-by-step explanation:
We are given that the Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year.
A random sample of 51 households is monitored for one year to determine aluminum usage. Also, the population standard deviation of annual usage is 12.2 pounds.
Let [tex]\bar X[/tex] = sample mean
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = average aluminum used by American = 56.8 pounds
[tex]\sigma[/tex] = population standard deviation = 12.2 pounds
n = sample of households = 51
(a) The probability that the sample mean will be more than 61 pounds is given by = P([tex]\bar X[/tex] > 61 pounds)
P([tex]\bar X[/tex] > 61 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{61-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z > 2.46) = 1 - P(Z [tex]\leq[/tex] 2.46)
= 1 - 0.9931 = 0.0069
The above probability is calculated by looking at the value of x = 2.46 in the z table which has an area of 0.9931.
(b) The probability that the sample mean will be more than 57 pounds is given by = P([tex]\bar X[/tex] > 57 pounds)
P([tex]\bar X[/tex] > 57 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{57-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z > 0.12) = 1 - P(Z [tex]\leq[/tex] 0.12)
= 1 - 0.5478 = 0.4522
The above probability is calculated by looking at the value of x = 0.12 in the z table which has an area of 0.5478.
(c) The probability that the sample mean will be between 55 and 58 pounds is given by = P(55 pounds < [tex]\bar X[/tex] < 58 pounds)
P(55 pounds < [tex]\bar X[/tex] < 58 pounds) = P([tex]\bar X[/tex] < 58 pounds) - P([tex]\bar X[/tex] [tex]\leq[/tex] 55 pounds)
P([tex]\bar X[/tex] < 58 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{58-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z < 0.70) = 0.75804
P([tex]\bar X[/tex] [tex]\leq[/tex] 55 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{55-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z [tex]\leq[/tex] -1.05) = 1 - P(Z < 1.05)
= 1 - 0.85314 = 0.14686
The above probability is calculated by looking at the value of x = 0.70 and x = 1.05 in the z table which has an area of 0.75804 and 0.85314.
Therefore, P(55 pounds < [tex]\bar X[/tex] < 58 pounds) = 0.75804 - 0.14686 = 0.6112.
(d) The probability that the sample mean will be less than 55 pounds is given by = P([tex]\bar X[/tex] < 55 pounds)
P([tex]\bar X[/tex] < 55 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{55-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z < -1.05) = 1 - P(Z [tex]\leq[/tex] 1.05)
= 1 - 0.85314 = 0.14686
The above probability is calculated by looking at the value of x = 1.05 in the z table which has an area of 0.85314.
(e) The probability that the sample mean will be less than 48 pounds is given by = P([tex]\bar X[/tex] < 48 pounds)
P([tex]\bar X[/tex] < 48 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{48-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z < -5.15) = 1 - P(Z [tex]\leq[/tex] 5.15)
= 1 - 0.99999 = 0.00001
The above probability is calculated by looking at the value of x = 5.15 in the z table which has an area of 0.99999.
Let v1 = -4
-1
-2
v2 = -3
1
-2
v3= 1
-5
2
and H = Span{v1,v2,v3} . Note that v3 = 2v1 - 3v2.
Which of the following sets form a basis for the subspace H, i.e., which sets form an efficient spanning set containing no unnecessary vectors?
a. {V1, V2, V3}
b. {V1, V2}
c. {V1,V3}
d. {V2,V3}
We're told (and we can confirm) that [tex]v_3=2v_1-3v_2[/tex], so [tex]v_3[/tex] is a linear combination of the other two vectors.
This means H is sufficiently spanned by [tex]\{v_1,v_2\}[/tex]; no need for the third vector.
But this also means we can write either [tex]v_1[/tex] as a linear combination of [tex]\{v_2,v_3\}[/tex], and [tex]v_2[/tex] as a lin. com. of [tex]\{v_1,v_3\}[/tex]. So any set of these three vectors taken two at a time will span the subspace H. Hence all of b, c, and d are acceptable.