I bet you're talking about column vectors,
[tex]\begin{bmatrix}-5\\4\\5\end{bmatrix}, \begin{bmatrix}2\\-1\\5\end{bmatrix},\text{ and }\begin{bmatrix}-17\\16\\45\end{bmatrix}[/tex]
If these vectors are linearly independent, this means that
[tex]c_1 \begin{bmatrix}-5\\4\\5\end{bmatrix} + c_2 \begin{bmatrix}2\\-1\\5\end{bmatrix} + c_3 \begin{bmatrix}-17\\16\\45\end{bmatrix} = \begin{bmatrix}0\\0\\0\end{bmatrix}[/tex]
only if [tex]c_1=c_2=c_3=0[/tex].
In matrix form, we can write this as a system of linear equations,
[tex]\begin{bmatrix}-5&2&-17\\4&-1&16\\5&5&45\end{bmatrix}\begin{bmatrix}c_1\\c_2\\c_3\end{bmatrix} = \begin{bmatrix}0\\0\\0\end{bmatrix}[/tex]
This system has a potentially non-zero solution so long as the coefficient matrix is not singular.
Compute the determinant:
[tex]\begin{vmatrix}-5&2&-17\\4&-1&16\\5&5&45\end{vmatrix} = -5 \begin{vmatrix}-1&16\\5&45\end{vmatrix} - 4 \begin{vmatrix}2&-17\\5&45\end{vmatrix} + 5 \begin{vmatrix}2&-17\\-1&16\end{vmatrix} \\\\ \begin{vmatrix}-5&2&-17\\4&-1&16\\5&5&45\end{vmatrix} = -5(-45-80) - 4(90+85) + 5(32-17) \\\\ \begin{vmatrix}-5&2&-17\\4&-1&16\\5&5&45\end{vmatrix} = 0[/tex]
The coefficient matrix is singular, so there is no non-zero solution to the system, and in turn the given vectors are linearly dependent.
is 2 1/3 a rational number
Answer:
it is a rational number.
Step-by-step explanation:
rational numbers are numbers which can be written as a fraction.
What are the coordinates of the point on the directed line segment from (−4,10) to (-2, -2) that partitions the segment into a ratio of 3 to 1? HURRYYYY!!!!
Answer:
(-2.5 , 1)
Step-by-step explanation:
the x- coordinates :
[(3×(-2)) + (1×(-4))] /(3+1)
= (-6 +(-4))/(4)
= -10/4
= -2.5
the y-coordinates :
[(3×(-2)) + (1×10)] / (3+1)
= (-6+10)/(4)
= 4/4
= 1
so, the coordinates are (-2.5 , 1)
Answer:
(-2.5, 1)Step-by-step explanation:
Directed line segment from (−4,10) to (-2, -2).
The ratio = 3/1.
The coordinates are:
x = -4 + 3/4*(-2 - (-4)) = -4 + 3/4*(2) = -4 + 1.5 = - 2.5y = 10 + 3/4(-2 - 10) = 10 + 3/4*(-12) = 10 - 9 = 1Solve by factoring:
3x−17x^1/2+10=0
Answer:x=5,2/3
Step-by-step explanation:
-b plus over minus square root over b squared -4(ac)/2a
17 plus over minus square root (-17) squared -4 x (3 x10)/2 x 3
x= 17 plus minus 13/6
x=5,2/3
Is (1,3) a solution of y = 3x2?
One angle of a triangle measures 102°. The other two angles are congruent.
Enter and solve an equation to find the measure x of the congruent angles.
An equation is_______ = 180.
The congruent angles each measure _______°.
Answer:
if i am rightthe two other angles arre 39
Step-by-step explanation:
if a triganle is 180 degrees and you have already one angle then all you do is subtract 180 and 102
180-102= 78
then since you need the other two angles all you do is divide it by 2
so 78/2= 39 so the two missing anlges are 39
What is the slope of a line perpendicular to the line whose equation is x+y=5x+y=5. Fully simplify your answer.
Answer:
1
Step-by-step explanation:
x+y = 5
Put this equation in slope intercept form y = mx+b where m is the slope
y = -x +5
The slope of the line is -1
Perpendicular lines have slopes that multiply to -1
-1 * m = -1
m = 1
The slope of the perpendicular line is 1
Can someone help me?? 3+3
Answer:
6
Step-by-step explanation:
count your fingers
how to calculate angle which is 25 degree?
How much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 10% antifreeze?
To obtain a 10% antifreeze solution, _ gallon(s) of water should be added.
Answer:
Let x = amount of water to be added with 0% antifreeze
1 = amount of pure antifreeze at 100%
x+1 = amount of the mixture at 60% antifreeze
Step-by-step explanation:
1= .60x + .60
Subtract .60 from each side:
1-.60 = .60x
.40 = .60x
Divide both sides by .60
Check: Total antifreeze = 1 gallon in total mixture of 1 + 2/3 gallon = 5/3 gallons. 1 gallon divided by 5/3 equals 3/5 which is 60%. It checks.
What is the value of x?
A
60°
95-
A. 1550
B. 60°
C. 35°
D. 25°
180° - 95° = 85°
x = 180° - 85° - 60°
x = 35°Lian has $1.00 . She has only nickles and dimes. Lian has twice as many dimes and nickles
Answer:
4 nickels and 8 dimes
Step-by-step explanation:
4 nickels is 0.20 and 8 dimes is 0.80
Answer:
4 nickles 8 dimes
Step-by-step explanation:
4 nickles 8 dimes
The following are all 5 quiz scores of a student in a statistics course. Each quiz was graded on a 10-point scale.
Answer:
I think
Category: Calculus and Above
Satisfied Customers: 18,226
Hope this help! Try my best :)
V=S^3 S=20 please help me lol
Hi there!
»»————- ★ ————-««
I believe your answer is:
V = 8,000
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Evaluating...}}\\\\V=s^3\\-----------\\\rightarrow V=(20)^3\\\\\rightarrow V = 20 * 20 * 20 \\\\\rightarrow V = 8,000[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
How to write 72,932 expanded form?
Answer:
70,000+ 2,000 +900 +30 + 2
in expanded form
Step-by-step explanation:
plsssssssssss helpppppppppppppppppppppppp
Answer:
6ft
Step-by-step explanation:
Just use 11 ft - 5ft = 6 ft
Have a good day
In the figure below, S is between Q and T, and R is the midpoint of QS. If RT = 14 and RS = 6, find QT.
Please Help Quickly!
Answer:
QT = 26
Step-by-step explanation:
QT = RT + QR + RS
QR = RS
QT = 14 + 6 + 6
QT = 20 + 6
QT = 26
plese help me fast I will mark you brainlist
Answer:
x= 70 y= 70
Step-by-step explanation:
In 2004, baseball player Lance Berkman had
172 hits out of 544 at bats. What was Lance
Berkman's Batting Average in 2004 rounded to
the nearest thousandth?
Answer:1 thousandth
Step-by-step explanation:
Dominic earns $14.25 an hour. Last week he worked 28 hours. How much did Dominic earn last week?
Answer:
$399
Step-by-step explanation:
If he earns $14.25 an hour and works 28 hours, we can find out how much he's earned by multiplying the rate per hour by the number of hours,
14.25 × 28 =
399
He earned $399 last week.
Find x and RS if RS = 5x, ST = 3x, and RT =48
Answer:
x = 6, RS = 30
Step-by-step explanation:
5x + 3x = 48
8x = 48
8x/8 = 48/8
x = 6
RS = 5x
RS = 5(6)
RS = 30
is 453 exactly divisible by 2
Answer:
No, for any number to be divisible by 2, the one and only rule is that it's even. This number is odd
Question
In a survey of 50 students about television viewership, 25 reported that they watch program X, 18 reported
that they watch program Y, and 14 reported that they watch neither of these programs. How many of the 50
students reported that they watch both program X and program Y?
O 7
11
O 15
18
Answer:
18....I hope thats righ
Step-by-step explanation:
Help please hurry i need done in 20 minutes
Answer:
OKAY I WAS STRESSING FOR A QUICK MINUTE THINKING I WAS GETTING SOMETHING WRONG BUT THINK THE ANSWER IS CORRECT
So Cos0= 15/64 (SIMPLIFIED) or in decimal form 0.234375
Step-by-step explanation:
7/8² is 49/64 or (in decimal form) 0.765625
1 - 0.765625 = 0.234375
Solve the equation z^4+4z^2+16=0
Answer:
As this is a quartic equation, we should expect four roots (although some may end being repeated). Notice also that the equation is symmetrical, which suggests that there might be an element of symmetry in the answer.
First, as this equation is a quadratic in terms of z2 , we can use our formula for finding the roots of a quadratic equation to give the value(s) of z2 . [If you have a problem seeing this, use the substitution y=z2 , and you get a quadratic in y .]
z2=−4±42−4×1×16√2×1=−4±16−64√2
=−4±−48√2=−2±12−−√i=−2±23–√i
=4(−12±3√2)i
=4(cos(2kπ3)+isin(2kπ3)) , where k∈1,2
=4e2kiπ3
As this is the value of z2 , whereas we want z , we need to take the square roots of both sides
z=4–√ekiπ3+nπ , where n∈0,1
=2e(k+3n)iπ3
=2cis((k+3n)iπ3)
As we have two values of k and two values of n , this gives us four solutions.
Writing these angles in terms of degrees, we have: 60, 120, 240 and 300
Evaluating, we end up with the four solutions
z=1±3–√i∪z=−1±3–√i
You can substitute z^2 = x,
Then you get x^2+4x+16=0
Step-by-step explanation:
z=1±3–√i∪z=−1±3–√i
You can substitute z^2 = x,
Then you get x^2+4x+16=0
Then you can use classical x1,2 = (-b +- √[b^2–4ac])/2a
X1,2=(-4+-√[16–16*4])/2
After you solve that you substitute back z^2 = x
HELP PLS!!! You invested $25,000 in two accounts paying 7% and 8% annual interest, respectively. If the total interest earned for the year was $1900, how much was invested at each rate?
Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $29 monthly fee and charges an additional $0.13 for each minute of calls. The second plan has an $11 monthly fee and charges an additional $0.17 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
A car travels at a constant speed of 20m/s.Work out the distance travelled [in meters] by the car after (a) 4seconds (b) 12seconds (c) 3mins (d) 2hrs
Answer:
This is quite an easy question u should try it yourself
Step-by-step explanation:
The formula is
V= d / t
Therefore the distance is
D = vt
So since they alredy gave u that v = 20m/s
Just put in the time, remember to change it to seconds
1/9 y -5 = - 7 what does Y equal?
⅑y - 5 = -7
⅑y = -7 + 5
⅑y = -2 / · 9
y = -18
8x+9 equals 5X +6 what is the value of X
8x + 9 = 5x + 6
8x - 5x = 6 - 9
3x = -3 / : 3
x = -1 ← the end answer
What is 4 x 2? thank you!
Answer:
8
Step-by-step explanation:
4 + 4 = 8
4 x 2 = 8
hope this helps
Answer:
answer is 8 because 4+4 =8 and 2+2+2+2 =8
