Answer:
-150
Step-by-step explanation:
Which of the following sets are subspaces of R3 ?
A. {(x,y,z)|3x+8y-5z=2}
B. {(x,y,z)|-4x-9y+7z=0}
C. {(x,y,z)|x
D. {(-4,y,z)|y,z arbitrary numbers}
E. {(x,0,0)|x arbitrary number}
F. {(-2x,-3x,-8x)|x arbitrary number}
Answer:
The following are the solution to the given points:
Step-by-step explanation:
for point A:
[tex]\to A={(x,y,z)|3x+8y-5z=2} \\\\\to for(x_1, y_1, z_1),(x_2, y_2, z_2) \varepsilon A\\\\ a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)[/tex]
[tex]=3(aX_l +bX_2) + 8(ay_1 + by_2) — 5(az_1+bz_2)\\\\=a(3X_l+8y_1- 5z_1)+b (3X_2+8y_2—5z_2)\\\\=2(a+b)[/tex]
The set A is not part of the subspace [tex]R^3[/tex]
for point B:
[tex]\to B={(x,y,z)|-4x-9y+7z=0}\\\\\to for(x_1,y_1,z_1),(x_2, y_2, z_2) \varepsilon B \\\\\to a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)[/tex]
[tex]=-4(aX_l +bX_2) -9(ay_1 + by_2) +7(az_1+bz_2)\\\\=a(-4X_l-9y_1+7z_1)+b (-4X_2-9y_2+7z_2)\\\\=0[/tex]
[tex]\to a(x_1,y_1,z_1)+b(x_2, y_2, z_2) \varepsilon B[/tex]
The set B is part of the subspace [tex]R^3[/tex]
for point C: [tex]\to C={(x,y,z)|x<y<z}[/tex]
In this, the scalar multiplication can't behold
[tex]\to for (-2,-1,2) \varepsilon C[/tex]
[tex]\to -1(-2,-1,2)= (2,1,-1)[/tex] ∉ C
this inequality is not hold
The set C is not a part of the subspace [tex]R^3[/tex]
for point D:
[tex]\to D={(-4,y,z)|\ y,\ z \ arbitrary \ numbers)[/tex]
The scalar multiplication s is not to hold
[tex]\to for (-4, 1,2)\varepsilon D\\\\\to -1(-4,1,2) = (4,-1,-2)[/tex] ∉ D
this is an inequality, which is not hold
The set D is not part of the subspace [tex]R^3[/tex]
For point E:
[tex]\to E= {(x,0,0)}|x \ is \ arbitrary) \\\\\to for (x_1,0 ,0) ,(x_{2},0 ,0) \varepsilon E \\\\\to a(x_1,0,0) +b(x_{2},0,0)= (ax_1+bx_2,0,0)\\[/tex]
The [tex]x_1, x_2[/tex] is the arbitrary, in which [tex]ax_1+bx_2[/tex]is arbitrary
[tex]\to a(x_1,0,0)+b(x_2,0,0) \varepsilon E[/tex]
The set E is the part of the subspace [tex]R^3[/tex]
For point F:
[tex]\to F= {(-2x,-3x,-8x)}|x \ is \ arbitrary) \\\\\to for (-2x_1,-3x_1,-8x_1),(-2x_2,-3x_2,-8x_2)\varepsilon F \\\\\to a(-2x_1,-3x_1,-8x_1) +b(-2x_1,-3x_1,-8x_1)= (-2(ax_1+bx_2),-3(ax_1+bx_2),-8(ax_1+bx_2))[/tex]
The [tex]x_1, x_2[/tex] arbitrary so, they have [tex]ax_1+bx_2[/tex] as the arbitrary [tex]\to a(-2x_1,-3x_1,-8x_1)+b(-2x_2,-3x_2,-8x_2) \varepsilon F[/tex]
The set F is the subspace of [tex]R^3[/tex]
Can someone please help this is my daughters homework
Answer:
its A
Step-by-step explanation:
A store sells 8-foot boards for $2.40 each. What is the cost per foot?
Answer:
8x≤2.40, x ≤ $0.30
Step-by-step explanation:
Joyce saved $130 on an item that was 35 % off. What was the original price?
Answer:
x=$200
Step-by-step explanation:
cross-multiply
130=0.65x
How many days equal 7344 minutes?
The answer is 5.1 days
60*24= 1440 minutes in one day
7344/1440= 5.093 or 5.1 rounded to the nearest tenth
Elizabeth is a manager at a nursery and is in charge of displaying potted trees in a row Elizabeth has 150 citrus trees and 180 Palm trees she wants to make rows of trees so that each row has the same number of trees and each tree is in the same row. if the citrus trees and the palm trees must not be mixed in the rows what is the largest number of trees she can have in a row
Answer: the greatest number of trees that ElizaBeth can have in a row is 30
Step-by-step explanation:
given data:
citrus trees = 150
palm trees = 180
As we have to find the greatest number of trees that Elizabeth can have in a row, we will find the GCF or greatest common factor.
150 = 2 x 3 x 5 x 5
180 = 2 x 2 x 3 x 3 x 5
Greatest common factor is = 2 x 3 x 5 = 30
Therefore, the largest number of trees that ElizaBeth can have in a row is 30.
302 + 299 + 296 + 293 ... + 2 = _____ what is the sequence using Gauss’s Law
By Gauss's Law the approach of solving sum of a sequence of n terms in arithmetic progression is :
[tex]S_n=\dfrac{n}{2}(a_1+a_n)[/tex] ......1 )
Here, [tex]a_n = 302[/tex] , [tex]a_1=2[/tex] .
We know :
[tex]a_n=a_1+(n-1)d\\\\302=2+3(n-1)\\\\n = 101[/tex]
Putting, all values in equation 1) we get :
[tex]S_n=\dfrac{101}{2}\times (2+302)\\\\S_n=101\times 152\\\\S_n=15352[/tex]
Therefore, the sum of sequence using Gauss's Law is 15352.
Hence, this is the required solution.
A student rolls a fair die 10 times and obtained an even number 10 times. The student believes that the next roll will
be an odd number because "odds are due."
Is this correct?
Yes, if the die is fair, then an odd number is due because the probability will approach 50%.
No, an even number is due based on past experience.
Yes, it is certain that an odd number will be rolled next because it is impossible to roll an even number 11 times in
a row.
No, an even or odd outcome is equally likely for each roll, regardless of what has happened in the past.
Answer:
N0, an even or odd outcome is equally likely for each roll regardless of what happened in the past
Step-by-step explanation:
Answer:
D. No, an even or odd outcome is equally likely for each roll, regardless of what has happened in the past.
Solve this linear system 28x + 44y = 964.40 21x + 33y = 723.30
28x + 44y = 964.40
21x + 33y = 723.30
Let's multiply the first equation by 4 and the second by -4
84x + 176y = 3857.6
-84x - 132y = -2893.2
Add the equations together.
0 + 44y = 964.4
Simplify
44y = 964.4
Divide both sides by 44
y = 964.4/44
Since we have the value of y, let's plug 964.4/44 into y for the first equation.
28x + 44(964.4/44) = 964.40
Simplify the left side
28x + 964.4 = 964.4
Subtract 964.4 from both sides
28x = 0
Divide both sides by 0
x = 0
In conclusion,
y = 964.4/44
x = 0
Dwayne buys 1 loaf of bread and 6 eggs for $4.45. Sheila buys 1 loaf of bread and 1 dozen eggs for $5.65. Let x be the cost, in dollars, of a loaf of bread. Let y be the cost, in dollars, of an egg.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Let x = cost of a loaf of bread ; y = cost of an egg
Dwayne :
1 loaf of bread and 6 eggs :
X + 6y = 4.45 - - - (1)
Sheila :
X + 12y = 5.65 - - - (2)
From (1);
X = 4.45 - 6y
In (2):
(4.45 - 6y) + 12y = 5.65
4.45 + 6y = 5.65
6y = 5.65 - 4.45
6y = 1.2
y = 0.2
From X = 4.45 - 6y:
X = 4.45 - 6(0.2)
X = 4.45 - 1.2
X = 3.25
Cost of a loaf of bread = $3.25
Coat of an egg = $0.2
PLEASE HELP! 40 points!! I've been stuck on this for 30 minutes constantly coming up with all different answers, please help me.
What is the area of rhombus ABCD?
Enter your answer in the box. Do not round at any steps.
______units²
Answer:
36 units^2
Step-by-step explanation:
The area of a triangle is 1/2*base*height. Knowing this is just 2 triangles means you solve for 1 triangle, then multiply that by 2
Answer:
[tex]A=36\text{ units}^2[/tex]
Step-by-step explanation:
The area of a rhombus is given by the formula:
[tex]A=\frac{d_1\cdot d_2}{2}[/tex]
Namely, it is half of one diagonal multiplied by the other diagonal.
So, to find the area, we just need to find the length of AC and BD, multiply them together, and then divide by 2.
To find their lengths, we can use the distance formula. The distance formula is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
So, let's find the lengths of each diagonal:
AC:
Point A is (-1,0) and Point C is (-1,-6). Let (-1,0) be (x₁, y₁) and let (-1,-6) be (x₂, y₂). Substitute this into our formula:
[tex]d=\sqrt{(-1-(-1))^2+(-6-0)^2[/tex]
Simplify:
[tex]d=\sqrt{(-1+1)^2+(-6-0)^2[/tex]
Add or subtract:
[tex]d=\sqrt{(0)^2+(-6)^2[/tex]
Square:
[tex]d=\sqrt{36}[/tex]
Take the square root:
[tex]d=6[/tex]
So, the length of diagonal AC is 6.
BD:
Point B is at (5,-3) and Point D is at (-7,-3). Let (5,-3) be (x₁, y₁) and let (-7,-3) be (x₂, y₂). Substitute this into our formula:
[tex]d=\sqrt{(-7-5)^2+(-3-(-3))^2[/tex]
Simplify:
[tex]d=\sqrt{(-7-5)^2+(-3+3)^2[/tex]
Add or subtract:
[tex]d=\sqrt{(-12)^2+(0)^2[/tex]
Square:
[tex]d=\sqrt{144}[/tex]
Take the square root:
[tex]d=12[/tex]
So, our second diagonal is 12 units long.
Now, to find the area, substitute 6 and 12 into our formula. So:
[tex]A=\frac{d_1\cdot d_2}{2}[/tex]
Substitute 6 for d₁ and 12 for d₂. So:
[tex]A=\frac{(6)(12)}{2}[/tex]
Multiply:
[tex]A=\frac{72}{2}[/tex]
Divide:
[tex]A=36\text{ units}^2[/tex]
So, the area of the rhombus is 36 squared units.
And we're done!
Notes:
Of course, instead of using the distance formula, you can also just count :)
P(n)=4n+1 ; find p(3)
Answer:
13
Step-by-step explanation:
you plug in 3 for n
4n+1
4(3)+1
12+1
13
2 – 1 + 5 x 4 x 11 Solve with PEMDAS
Answer:
221
Step-by-step explanation:
2-1+5*4*11
2-1+20*11
2-1+220
1+220
221
Which linear equation has no solution?
round 355,668 to the nearest hundred thousands
Answer:
400,000
Step-by-step explanation:
The product of 79 and -0.22 is a positive number. True Or False
Answer:
False
Step-by-step explanation:
We know that this statement is false because a positive number times a negative number will produce a negative answer.
Answer:
False
Step-by-step explanation:
You will get a positive number only by multiplying two positive numbers or two negative numbers.
please help! BRAINLIEST to best answer!
Answer:
I'm not sure if I'm right but you should try X = the x value of the vertex.
Sonya has a books. Nick has 3 more books than Sonya. How many books do both children have together?
Answer:
[tex]2a+3[/tex] books
Step-by-step explanation:
Sonya -> [tex]a[/tex] books
Nick -> [tex](a+3)[/tex] books
Total: [tex]a+(a+3)=a+a+3=2a+3[/tex]
The formula d=rt is used to calculate the distance
an object travels over a period of time, t, at a
constant rate, r. Based on this formula, what is the
rate, r, in terms of d and t?
A) r = d/t
B)r = dt
C)r = t/d
D) r = r - t
A basketball player shoots free throws and makes them with probability 1/7. What is the probability of the event the player will miss three in a row?
Answer:
216/343 or 0.6297 (4dp)
Step-by-step explanation:
Anytime the probability of an event occurs more than once in a particular order (one time after another in the same instance), then the probability is multiplied together. If the probability of him making the shot is 1/7, then the probability of him missing it is 6/7. This is because this is the only other possible outcomes and all outcome probabilities must add to 1 (1-1/7 - 6/7).
So, if he misses it three times in a row then the probability is:
6/7 (probability miss this first time) x 6/7 (probability miss second time) x 6/7 (probability miss 3rd time).
6/7 x 6/7 x 6/7 = 216/343
or 0.6297 (4dp)
Hope this helped!
Solve for t.
-3t + 3 – 7t = -90 – 7
Answer:
t = 10Step-by-step explanation:
-3t + 3 - 7t = -90 - 7
Simplify both sides of the equation
That's
- 10t + 3 = - 97
Using the subtraction property subtract 3 from both sides of the equation
We have
- 10t + 3 - 3 = -97 - 3
- 10t = - 100
Divide both sides by - 10
[tex] \frac{ - 10t}{ - 10} = \frac{ - 100}{ - 10} [/tex]
We have the final answer as
t = 10Hope this helps you
Answer:
Step-by-step explanation:
-3t + 3 - 7t = -90 - 7
-10t + 3 = -97
-10t = -100
t = 10
100 POINTS HELP / Which is correct about the graph’s slope?
Its slope is positive.
Its slope is negative.
Its slope is zero.
It has no slope.
Answer:
slope is zero
Step-by-step explanation:
it is a horizontal line which means the slope all points that lie on the line have a -coordinate
[tex]\huge\boxed{No\;slope}[/tex]
There is no rise over run therefore, there is no slope.
You have to have rise over run to be able to have a slope.
Solve all these to be marked the brainlest
3 x² - 2x-1=0
solve using quadratic formula
Answer:
The answer to your question: x is -1/3 or 1
2. Tess picked 12 flowers on Monday morning In the afternoon she picked some more flowers. If Tess picked 27 flowers in all, how many did she pick in the afternoon?
Tom, Kwasi, and Juan purchased a large pizza to share. If Tom ate of
the pizza, Kwasi ate of the pizza, and Juan ate of the pizza, what
fractional part of the pizza was eaten?
find the solution to K+1=3k-1
Answer: k=1
Step-by-step explanation: Isolate the variable by dividing each side by factors that do not contain the variable.
I hope this helps you out! :)
Step-by-step explanation:
the answer would be k=1
Find the difference. (3 • 1,000) - (2• 100)
The value of ( 3 x 1,000 ) - ( 2 x 100 ) is 2,800.
Here,
Given that, ( 3 x 1,000 ) - ( 2 x 100 )
What is subtraction of two number?
Subtraction is the operation of taking the difference of two numbers.
Now,
Firstly the value of 3 x 1000 = 3000
And, 2 x 100 = 200
⇒ 3000 - 200 = 2800
Hence, The value of ( 3 x 1,000 ) - ( 2 x 100 ) is 2,800.
Learn more about the subtraction visit:
https://brainly.in/question/12241794
#SPJ2
Use the graph to estimate the x- and y-intercepts.
Answer:
x- intercept is 6 y- intercept is -18
Step-by-step explanation:
Just use the graph, this graph is hard to get the answer but you just have to estimate.
Please please help me on that.