To prove that W = {au + Bula,8 € R} is a subspace of vector space V, we need to show that W satisfies the three conditions for being a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector.
Closure under addition: Let x, y be arbitrary vectors in W. We can write x = au + Bula and y = cu + Cvla, where a, b, c, d are scalars. Now, let's consider the sum of x and y: x + y = (au + Bula) + (cu + Cvla).
By applying the distributive property, we can simplify this to
(a + c)u + (b + d)ula. Since (a + c) and (b + d) are scalars, we see that x + y is also in the form of au + Bula, which means it belongs to W. Therefore, W is closed under addition.
Closure under scalar multiplication: Let x be an arbitrary vector in W and k be a scalar. We have x = au + Bula. Now, let's consider the scalar multiple of x: kx = k(au + Bula). Applying the distributive property, we get kx = (ka)u + (kbl)a. Since (ka) and (kbl) are scalars, we can see that kx is also in the form of au + Bula, indicating that it belongs to W. Thus, W is closed under scalar multiplication.
Contains the zero vector: The zero vector can be expressed as 0 = 0u + 0ula. Since 0 and 0 are scalars, we can see that the zero vector is in the form of au + Bula and therefore belongs to W.
Since W satisfies all three conditions for being a subspace, we can conclude that W is a subspace of V.
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Someone help me plz hurry
-51/7
Answer:
-51/7
Step-by-step explanation:
-51/7 cannot be simplified
Answer:
-7.28571428571
Step-by-step explanation:
This is the answer, mark brainliest if it helped and/or worked!
COuld yall awnsser
-1/5x-18=2
Answer:
x = -100
Hope this helps!
Answer:
x=−100 hope this helps :)
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
Step 2: Add 18 to both sides.
Step 3: Multiply both sides by 5/(-1).
What would be the best first step to use to solve this equation? 7/12=5/6x
Answer: The first step would be to divide both sides by 5/6 to isolate x.
Answer:
Your answer is: x = 7/10
Solve for x by simplifying both sides of the equation, then isolating the variable.
Step-by-step explanation:
Hope this helped : )
An equilateral triangle is shown below. What is the value of x?
Answer:
2
Step-by-step explanation:
Complete the statement.
3 1/4÷ ? =1
Answer:
3 1/4
Step-by-step explanation:
The general rule of thumb is that if the solution is 1 and the operation is division, the the dividend (in this case 3 1/4) should be equal to the divisor (represented with the question mark; ?).
Answer:
3 1/4
Step-by-step explanation:
3 1/4
3 1/4 = 1 :)
will this answer count?
help? this is geometry
what is the equation of a line that passes through the point -(6,6) and has a slope of 1/3
Answer:
Step-by-step explanation:
y-y = m(x - x)
I couldn't tell if the point was negative, so I'll do both
Positive Negative
(6,6) m= 1/3 -(6,6) m= 1/3
y-6 = 1/3(x - 6) y+6 = 1/3(x +6)
y-6 = 1/3x - 2 y+6 = 1/3x + 2
y = 1/3x +4 y = 1/3x - 4
GONZALEZ
Problem 3.3
In order to scale figure F back to figure E, what scale
factor should you use?
20
Submit and Explain
21
20
Answer:
Step-by-step explanation:
Katherine drove 13 miles in 1/5 hour. On average, how fast did she drive, in miles
per hour?
Answer:
65 miles per hour
Step-by-step explanation:
r = d/t
1 : 5 = 0.2
r = 13 : 0.2 = 65
E is the midpoint of AB. If
AE = 4x +6 and EB = 10x - 12,
what is AB?
Answer:
36
Step-by-step explanation:
Since E is the midpoint, AE and EB are equal. We can write this as such,
4x+6=10x-12 if we solve from here we get 6x=18. Simplify to get x=3. sub in three for x in the AE equation, 4(3)+6 and solve. You'd get 18 as your answer. Double that to get the solution since AE= 1/2AB. 18*2= 36
AB=36
Solve for v.
-V + 1 = 3
What is, 3 to the power of 2, times, 3 to the power of 5.
A. 3 to the power of 7
B. 3 to the power of 10
C. 9 to the power of 7
D. 9 to the power of 10
Answer:
3^7
Step-by-step explanation:
3^2 * 3^5
a^b * a^c, since the bases are the same, we can add the exponents
a^ ( b+c)
3^(2+5)
3^7
Answer:
ha
Step-by-step explanation:
please
A + B/ C = D, Solve for B
Answer:
B = DC - A
Step-by-step explanation:
A + B / C = D Multiply C
A + B = CD Subtract A
B = CD - B
PLEASE HELP I DONT WANNA FAIL, THIS IS TOO HARD AND STRESSFUL
Answer:
That is hard. What grade are you in.
Step-by-step explanation:
round 0.0625 to the nearest thousandth
Answer:
0.0630
Step-by-step explanation:
hope this helps
In the diagram below, AB is parallel to CD. What is the value of y?
Answer:
b. 30
Step-by-step explanation:
Answer:
The ans is 30 .
Step-by-step explanation:
y + 150= 180 ( being co-interior angle)
y = 180-150
y= 30
A $40,000 was bought in 2010. The value is depreciating at a rate of 4.5%. How much is the car worth in 2020?
approximately 38,200..... i think ?
Solve to the nearest tenth
[tex] \sqrt{18} [/tex]
which expression is equal (x+4)(-3x^2-4x+2)
Answer:
-3x^3-16x^2-14x+8
Step-by-step explanation:
[tex](x+4)(-3x^2-4x+2)\\\\Distribute\:parentheses\\\\=x\left(-3x^2\right)+x\left(-4x\right)+x\times\:2+4\left(-3x^2\right)+4\left(-4x\right)+4\times \:2\\\\Apply\:minus-plus\:rules\\+\left(-a\right)=-a\\\\=-3x^2x-4xx+2x-4\times\:3x^2-4\times\:4x+4\times\:2\\\\Simplify\\-3x^2x-4xx+2x-4\times\:3x^2-4\times\:4x+4\times\:2:\\\\\quad -3x^3-16x^2-14x+8\\\\=-3x^3-16x^2-14x+8[/tex]
In △ABC, the sides AB and AC are produced to ∠P and ∠Q respectively. If the bisectors of ∠PBC and ∠QCB intersect at A point O. Prove that ∠BOC = 90 - ½ ∠A.
Answer:
in △abc, the sides ab and ac are produced to ∠p and ∠q respectively. if the bisectors of ∠pbc and ∠qcb intersect at a point o. prove that ∠boc = 90 - ½ ∠a.
A. -9
B. -1
C.1
D. 9
Answer:
C. 1
Step-by-step explanation:
Start at (0,3)
Slope is -3/1
X intercept would be 1
Answer:
i think the answer is A. -9
Step-by-step explanation:
i really hoped this helped
Whats the domain and range??
Answer:
Domain: 0 ≤ x ≤ 5
Range: 0 ≤ x ≤ 300
Step-by-step explanation:
Domain is the set of x-values that can be inputted into function f(x).
Range is the set of y-values that are outputted by function f(x).
We see that our x-values span from 0 to 5. Since both are closed dots, they are included in our domain:
[0, 5] or 0 ≤ x ≤ 5
We see that our y-values span from 0 to 300. Since both are closed dots, they are included in our range:
[0, 300] or 0 ≤ x ≤ 300
4 (32 - 139)
Simplify
Answer:
-428
Step-by-step explanation:
32-139=(-107)
4*(-107)=(-428)
No I will mark brain
Answer:
C
Step-by-step explanation:
You can estimate to assume that it is about 512 gallons
*A number consisting of two digits is three times the sum of its digits. If 45 is added
to the number, the digits will be interchanged. Find the number.
Please make an equation and solve it.
Answer: The number is 27
The system of equations is: 7x - 2y = 0
-9x + 9y = 45
Step-by-step explanation:
Let x represent the number in the tens place and y represent the number in the ones place. x y
Then 10x + y = 3(x + y)
When the digits are reversed: 10y + x = 10x + y + 45
Simplify each of the above equations and then create a system of equations:
10x + y = 3x + 3y → 7x - 2y = 0
10y + x = 10x + y + 45 → -9x + 9y = 45
9( 7x - 2y = 0) → 63x - 18y = 0
2(-9x + 9y = 45) → -18x + 18y = 90
45x = 90
x = 2
Input x = 2 into either equation to solve for y:
7x - 2y = 0
7(2) - 2y = 0
14 = 2y
7 = y
Answer:
27
Step-by-step explanation:
Let's say that the number is 10x + y
Accordingly the number consists of digits three times the sum of it's digits, so 10x + y = 3(x + y)
10x + y = 3(x + y) -> Distribute the "3"
10x + y = 3x + 3y -> Combine like terms
7x = 2y -> Isolate "x"
x = 2y/7 --- (1)
With the information provided, the number (10x + y) when added to 45, equals the "interchanged" digits. In this case x and y represents digits, so interchanging them would be 10y + x;
10x + y + 45 = 10y + x -> Combine like terms
9x = 9y - 45 --- (2)
Substitute the first equation into the second, and solve for x and y. Given the digits we can determine the number =>
9(2y/7) = 9y - 45 -> Simplify
- 45y/7 = - 45 -> Multiply either side by 7
- 45y = - 315 -> Divide either side by - 45
y = - 315/ -45 = 7 (second digit)
x = 2(7)/7 = 14/7 = 2 (first digit)
Solution: The number is 27
Can someone help with these problems?
Answer:
First, you have to substitue 3 into x
20 - 5(3)
20 - 15
= 5
so the first one is 5
the next one we will do the same but with 4
20 - 5(4)
20 - 20
= 0
Step-by-step explanation:
Answer:
20-5(3)
20-15
=5
than
20-5(4)
20-20
=0
and there is your answer
Step-by-step explanation:
What the distance between 17 and -8
it's on the picture but please answer it because I don't know how
Answer:
I aso don't know yrr what can i do yrr
simplify 12x^7y^4/6x^2y^5
Answer:
2x⁵/y
Step-by-step explanation:
divide 12/6 to get 2
7-2=5
8 less than the product of 2 and a number is 16. What is the number?
The answer is 24 when using like terms and the order of operations.
The number would be -4 which is 8 less than the product of 2 and a number is equal to 16.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
Let the number would be n
Given that 8 is less than the product of 2 and a number is equal to 16.
According to the statement of the question,
⇒ 8 - (n*2) = 16
⇒ -(n*2) = 16 - 8
Apply the subtraction operation,
⇒ -2n = 8
⇒ n = -8/2
Apply the division operation,
⇒ n = -4
Hence, the number would be -4 which is 8 less than the product of 2 and a number is equal to 16.
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