I need the answer for 9 and 10
1. Let
U = {(x, y, z) = R³ | x+y=2z = 0 = x - y},
and let
V = span {(1, 0, -1), (3, 1, 2)}.
Determine the dimensions of both U and V, proving your results.
Note that to prove the dimension, you should use the definition, which
means you need to find a basis. It is not enough to just state a basis,
you must explain why it is a basis.
The dimension of V is 2, and it is spanned by the basis vectors (1, 0, -1), (3, 1, 2).
The dimension of a vector space is the number of vectors in a basis for the space. To find a basis for a subspace of R³, we need to find a set of linearly independent vectors that span the subspace.
First, let's consider U. The subspace U is defined by the equations x + y = 2z and x - y = 0.
Solving these equations for x and y, we can express them in terms of z: x = 2z and y = -2z. Therefore, every vector in U can be written as (x, y, z) = (2z, -2z, z) = z(2, -2, 1).
Since z is a scalar, the vector (2, -2, 1) is the only vector needed to span the subspace U, which means that it is a basis for U.
Therefore, the dimension of U is 1, and it is spanned by the basis vector (2, -2, 1).
Now let's consider V. The subspace V is defined by the set of vectors that can be written as a linear combination of the vectors (1, 0, -1) and (3, 1, 2). We can start by showing that these vectors are linearly independent. Suppose that there are scalars a and b such that a(1, 0, -1) + b(3, 1, 2) = (0, 0, 0). Then we have:
a + 3b = 0
b = 0
-a = 0
Since a and b are real numbers, the above equation only holds if a = 0 and b = 0. This shows that (1, 0, -1) and (3, 1, 2) are linearly independent, and a basis of V.
Therefore, the size of V is 2, and it is traversed by the basis vectors (1, 0, -1), (3, 1, 2).
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What is the value of ſIg(5)) if f(x) = * +2 and g() = x2 – 27
Answer:
[tex]f(g(5)) = 0[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x+ 2[/tex]
[tex]g(x) = x^2 - 27[/tex]
Required
[tex]f(g(5))[/tex]
First, calculate [tex]f(g(x))[/tex]
We have:
[tex]f(x) = x+ 2[/tex]
Substitute [tex]g(x)[/tex] for x
[tex]f(g(x)) = g(x) + 2[/tex]
Substitute [tex]g(x) = x^2 - 27[/tex]
[tex]f(g(x)) = x^2 -27+ 2[/tex]
[tex]f(g(x)) = x^2 -25[/tex]
Substitute 5 for x
[tex]f(g(5)) = 5^2 -25[/tex]
[tex]f(g(5)) = 25 -25[/tex]
[tex]f(g(5)) = 0[/tex]
A boat is purchased for $51,000 and has a resale value of $42,000 after a useful life of 6 years. Using a book value depreciation chart, calculate the number of years until the book value of the boat is $48,000.
The number of years until the book value of the boat is $ 48, 000, can be found to be 2 years
How to find the number of years ?To find the number of years till the book value of the boat is $ 48, 000, you first need to find the depreciation rate per year by the formula :
= ( Purchase price of boat - Resale value ) / Useful life
= ( 51, 000 - 42, 000 ) / 6
= 9, 000 / 6 years
= $ 1, 500 per year
In the first year, the value of the boat would depreciate to:
= 51, 000 - 1, 500
= $ 49, 500
In the second year, the value would depreciate to:
= 49, 500 - 1, 500
= $ 48, 000
It therefore takes 2 years for the book value to be $ 48, 000.
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help please I need help as soon as possible
Answer:
y = 1/2 x + 3.
In the diagram below AH, AD, and DH are each tangent to circle Q.AT=9,AH=13, and AD= 15 what is HD
Answer: 10
Step-by-step explanation:
I’m positive
Please help I will give brainliest.
Answer:
Hello,
Step-by-step explanation:
m∠DHG=(11x-36)°
m∠GHF=(x+12)°
(11x-36)°+(x+12)°=180°
12x-24=180
x=17
m∠arc DG=(11*17-36)°=151°
how large a sample should be surveyed to estimate a true proportion of college students who do laundry once a week is within 3% with 95% confidence
He learned an average of 130130130 new words per month when he lived in Portugal and an average of 150150150 new words per month when he lived in Brazil. In total, he learned 192019201920 new words.
How long did Wolfrich live in Portugal, and how long did he live in Brazil?
Answer:
He take 5 months in Brazil and 9 months in Portugal.
Step-by-step explanation:
Let us assume the number of months in Portugal be P
And, the number of months in Brazil be B
So, the following equations are made
P + B = 14 ..............(1)
130P + 150B = 1920 .........(2)
We can easily write as
P = 14 - B
Now put the value of P in the second equation
So,
130(14 - B) + 150B = 1920
20B = 100
B = 100 ÷ 20 = 5
P = 14 - 5 = 9
Hence, He take 5 months in Brazil and 9 months in Portugal.
A bag contains 27 balls. The ratio of red to blue to yellow balls is 6:1:2 find how many red, blue and yellow balls there are
Answer:
18 red balls, 3 blue balls, 6 yellow balls.
Step-by-step explanation:
Ratios:a ratio helps us understand the relationship between two or more values (in this case three values). More specifically it tells us how much of one item is present, for every amount another item is also present.
In this example, the ratio of red:blue:yellow is given to be: 6:1:2, which means, for every 6 red balls, there is one blue ball and two yellow balls.
In some cases, a ratio can be simplified, similar to a fraction, by dividing each number by some common factor, but in this case, the ratio cannot be simplified any further.
Solving the Problem:Instead of directly trying to find how many red, yellow, or blue balls there are first, we can instead try solving for how many group of sixes are there in the total number of red balls. It helps to think of it this way, since for every group of six red balls there are, there is one blue ball and two yellow balls, which means we can just multiply this number by one and two to find the number of blue and yellow balls in their respective orders. For simplicity, let's assign this to the unknown "G".
Using this logic, we can set up the following equation:
[tex]6G+1G+2G=27[/tex]
For every group of six red balls... there is 6 red balls, 1 blue ball, and 2 yellow balls, adding all these together should give us the total number of balls, which was given to be 27 balls. Now we can just combine the stuff on the left into one term, by adding the coefficients.
[tex]9G=27[/tex]
Now divide by 9
[tex]G=3[/tex]
Now that we know the number of group of six red balls there are, we can multiply six, one, and two to find the red, blue, and yellow balls.
[tex]\text{red balls} = 3 * 6 = 18\\\\\text{blue balls} = 3 * 1 = 3\\\\\text{yellow balls} = 3 * 2 = 6[/tex]
and you can all this together, to double check, which gives us 27.
Answer:
18,3,6
Step-by-step explanation:
Given ,
A bag contains 27 ballsThe ratio of red to blue to yellow balls is 6:1:2To Find : The number of red,blue and yellow balls present in the bag
Let us take the variable as 'x' to represent the number of balls in the bag
When we Put the values in a equation,
6x+x+2x = 27
9x = 27
x = [tex]\frac{27}{9}[/tex]
x = 3
Hence the number of,
Red Balls = 6x = 6 x 3 = 18
Blue Balls = x = 3
Yellow Balls = 2x = 2 x 3 = 6
All of the quadrilaterals in the shape below are squares. Find the area of the shaded
region.
Answer: I don't remember how to solve, but, I figured out the lengths of each side in the shaded region:
11, 11, 7, 7, 4, 4
Step-by-step explanation:
Hope this helps!! :D
Eric picks 5/8 basket of strawberries. Kiki picks 1/5 basket of strawberries. Which answer is the most accurate estimate for how many more baskets of strawberries Eric picks than Kiki?
Eric picks 17/40 baskets of strawberries more than Kiki.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
Eric picks 5/8 basket of strawberries.
And, Kiki picks 1/5 basket of strawberries.
Hence, After subtraction we get;
Number of baskets of strawberries more than Kiki = 5/8 - 1/5
= (25 - 8) / 40
= 17/40
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Write ✓ –28 in simplest radical form.
[someone help] The speed of the object 7 seconds after it is dropped is ___m/sec
9514 1404 393
Answer:
68.6 m/s
Step-by-step explanation:
The speed at a given time is the derivative of the height at that time.
dh/dt = -9.8t
At t=7, the speed is ...
-9.8(7) = -68.6 . . . . . meters per second (downward)
The speed is 68.6 meters per second.
_____
Additional comment
Height is considered to be positive in the up direction, so velocity and acceleration are also positive in the up direction. The derivative of height will be the velocity. Its negative sign in this case indicates the object is moving in the downward direction. The speed is the magnitude (absolute value) of the velocity.
Which integer in the set has the greatest value (4, -4, -3, 3)?
A. 4
B. 3
C. -3
D. -4
Answer:
A. 4
Step-by-step explanation:
4 is a positive number which is larger to 3 and bigger than negative numbers.
Answer:
Step-by-step explanation:
i\
i \
i \
i /
i /
what is the area of this figure? 20 pts and brainliest!!!! neeed help asap!!!!!! due today!!!!
18 yd2
54 yd 2
72 yd2
90 yd2
Answer:
72yd^2
Step-by-step explanation:
Answer:
87
Step-by-step explanation:
14*3 + 9*5
Gain and his three friends want to share 1/3 of a cake equally. Gavin says that each friend will get 1/9 of the cake. Use the drop-down menus to explain wether or not Gavin is correct.
Gavin is incorrect. To find how much cake each person gets, divide 1/3 by 4 or multiply 1/3 by one-fourth. Therefore, each of the friends gets one-twelfth of the cake.
Good Luck!
A railroad crossing arm that is 20 feet long is stuck with an angle of elevation of 35". Find x and y in the illustration below.
Round to the nearest tenth as needed.
Note: The red line is NOT needed to solve this problem.
20 ft
35
yft
Select the correct response
Ox-32.9 feet; y=12.0 feet
x-11.5 feet, y-16.4 feet
x-12.0 feet, y-32.9 feet
x=16.4 feet, y=11.5 feet
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The angle of elevation of a 20-foot railroad crossing arm is fixed at 35 degrees. As necessary, round up to the next tenth. 20 ft, 35 ft, x -11.5 feet, y- 16.4 feet .
What is angle of elevation ?Between the horizontal line and the line of sight, an angle called the angle of elevation is created. The angle of elevation formula tan =QR/PR can be used to calculate the building's height (QR). Therefore, the building has 8 units of height. When it lies between the line of sight and the horizontal line, the angle of elevation is generated. The angle created, known as the angle of elevation, occurs when the line of sight is above the horizontal line. However, in the depression angle, the line of sight is downward and parallel to the ground.
When we multiply in algebra, we come before a variable with a number. In the same way, xy means to multiply variable x by variable y, while 7xy means to multiply variable x by variable y and then to multiply the entire expression by seven. Due to the complexity of how train-based questions are frequently presented, it is always advisable to read the question thoroughly before responding. After reading the question, try to use a formula in it; this may lead to a direct solution and save you time.
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1 +*
*+1
*+1
I + X
24
Answer:
i
Step-by-step explanation:
what a question answer to the questions
An apple farmer finds that he has to throwout 30 bad apples from the 250 he has picked. What is the experimental probability that the next apples he picks will be good
Answer:
0.88 = 88% probability that the next apples he picks will be good
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In an experimental probability, we have the number of outcomes a priori, that is, before the trial.
What is the experimental probability that the next apples he picks will be good?
250 apples, 250 - 30 = 220 good.
[tex]p = \frac{220}{250} = 0.88[/tex]
0.88 = 88% probability that the next apples he picks will be good
if june 13 was on monday what day will it be on june 13 math
Answer:
Monday??????
SteP-by-step explanation:
The number of paid days off (e.g., vacation, sick leave) taken by 9 employees at a small local business is compared to the national average. You are hired by the new business owner to help her determine whether her employees take less days off than the national average, which is determined to be 13 days. The data for the 9 local employees during the last fiscal year are: 10, 11, 8, 14, 13, 12, 12, 11, 13. What is the effect size for these data and how should it be interpreted
Answer:
-0.80, is a large effect
Step-by-step explanation:
From the given information:
The mean of the sample = [tex]\dfrac{10+ 11+ 8+ 14+ 13+ 12+12+11+13}{9}[/tex]
= 11.556
Using Excel Formula:
The standard deviation = 11.8105
We are told that the population mean = 13
Thus, the effect size can be determined by using the formula:
[tex]Effect \ size = \dfrac{sample\ mean \ ( \bar x) - population \ mean \ \mu }{standard deviation (\sigma)}[/tex]
[tex]Effect \ size = \dfrac{11.5556 -13 }{1.8105}[/tex]
Effect size = -0.80
Thus, -0.80, is a large effect
Martin flips a standard coin three times, what is the probability it lands on tails all three times?
Answer:
thirty-three percent
There are 10 counters in a bag: 3 are red, 2 are blue and 5 are green. The contents of the bag are shaken before Maxine randomly chooses one counter from the bag. What is the probability that she doesn't pick a red counter
Answer:
Step-by-step explanation: total number of counters = 10
number of red counters= 3
number of blue counters= 2
number of green counters = 5
p(of getting a red counter) =3/10
p(of not getting a red counter) = 1-3/10= 10-3/10=7/10
What fraction is equivalent to half
Answer:
1/2 is a half for example u can do 4/8 and it is equal to a half does not matter how big like 50/100 is also correct. Hope this helps :)
PLEASE HELP ME PLEASE!
Answer:
Sample
Population
Step-by-step explanation:
Explain regent? its a term I've never heard of
Write the following expression in expanded form:9 to power of 3× 7to the power of 4
Exponential Expressions into Expanded Form into Answer:
[tex]9^{3}[/tex] = 9⋅9⋅9 = 729
[tex]7^{4}[/tex] = 7⋅7⋅7⋅7 = 2401
I hope this helps, have a good day!
Answer:
= 9⋅9⋅9 = 729
= 7⋅7⋅7⋅7 = 2401
Step-by-step explanation:
will mark u brainliesst
Answer:
- 7√10
Step-by-step explanation:
Step 1 : Take √10 common
2√10 - 5√10 - 4√10
= √10 ( 2 - 5 - 4 )
Step 2 : Subtract the numbers separately.
2 - 5 - 4
= 2 - 9
= - 7
Step 3 : Multiply √10 and - 7
√10 * - 7 = - 7√10
Complete the sentence. __is 6 times as much as 2.
Answer:
1/3
Step-by-step explanation:
2 divided by 6 is 1/3 and 1/3 times 6 is 2
It's all in the picture & please help!
~Rules~
a. SHOW WORK
b. NO LINKS/FILES
c. NO SILLY ANSWERS!
I will give out BRAINLIEST!
~Hocus Pocus
Answer:
Step-by-step explanation:
hi!
area:
both 7 by 4 sides: (7*4)2=56
both 3 by 7 sides: (3*7)2=42
both 3 by 4 sides: (3*4)2=24
add em up=56+42+24=122
i hope this answered your question. let me know if i missed something and ill fix it!