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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XYZ Company
Balance Sheet
Assets
Cash
$45,000
Inventory $41,000
Property $134,000
Total Assets:
Liabilities
Notes
Wages
Equity
Stock
$55,000
$56,000
$50,000
Investment $59,000
Total Liabilities + Equity:
Using the balance
sheet, calculate XYZ
Company's total
assets - liabilities.
Total Assets - Liabilities = $ [?]
Enter
PH
Skip
On solving the provided question, we can say that - by formula of simple interest we have SI = [tex]2200 X 2 X 4/100 = > 17600/100 = > 176[/tex]
what is interest ?Multiplying the principal by the interest rate, time, and other factors yields simple interest. Simple return equals principle times interest times hours is the marketed formula. It is easiest to compute interest using this formula. A percentage of the principle balance is how interest is most commonly computed. For instance, he will only pay his portion of the 100% interest if he borrows $100 from a buddy and promises to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you lend money, you must charge interest. Most of the time, interest is expressed as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.
here,
principal, p = 2200
rate, r = 2%
time, t = 4 rs,
so SI = P X R X T/100
SI -
[tex]2200 X 2 X 4/100\\17600/100\\176[/tex]
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Is the relation shown in the table a function?
Input: 4,8,4,8
Output: 1,3,5,4
keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, Check the picture below.
Given csc 0=17/15, determine the values for “a” and “b” in cos 0=a/b
If cosec (tetha) = 17/15 then cos (tetha) = 8/17
What are trigonometry ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
cosec , sine, cotangent, cosine , secant and tangent are trigonometry function.
cosec( tetha) = 1/sin(tetha)
tangent (tetha) = 1/ cot ( tetha)
sec (tetha) = 1/ cos(tetha)
cosec (tetha) = 17/15
therefore 1/sin ( tetha) = 17/15
sin( tetha ) = 15/17 = opp/ hyp
therefore using Pythagoras theorem adj² = 17²-15²
adj² = 289-225
adj² = 64
adj = √64 = 8
cos ( tetha) = adj/hyp
therefore cos ( tetha) = 8/17
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A pump takes 20 minutes to empty a 200 gallon tank. How long to empty 450 gallon tank? a. 40 minutes, b. 30 minutes, c. 60 minutes, d. 45 minutes
[tex]if \: x = 1 - \sin( \alpha ) \: and \: y = 1 + \cos( \alpha ) \\ [/tex]
Express y in terms of x and alpha only
Answer:
A sample of helium was compressed at 35 °C from a volume of 0.5 L
to 0.25 L where the pressure is 500 mmHg. What was the original pressure?
Step-by-step explanation:
List the data in the following stem-and-leaf plot. The leaf represents the tenths digit.
Separate the numbers in the list by a comma. The list is:
151,154,154,157,165,166,178,183,186,186
The data represented by the steam-leaf plot is 115, 138, 145, 145, 156, 166, 168, 168, 175, and 187.
What is a stem leaf plot?A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.
A stem and leaf plot is shown as a customized table with the first or final digit of each data value divided into a stem and the remaining digit in a leaf.
9 I 0 ⇒ 9 on the stem and 0 on the leaf read as 90.
Given, A stem leaf plot and the leaf represents the tens digit.
As the leaf represents tens digits the data set can be represented by,
115, 145, 145, 175, 156, 166, 187, 138, 168, 168.
Representing the data set in ascending order we have,
115, 138, 145, 145, 156, 166, 168, 168, 175, 187.
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Miguel is playing a game in which a box contains four chips with numbers written on them. two of the chips have the number 1, one chip has the number 3 and the other chip has the number 5. Miguel must choose 2 chips, if both chips have the same number, he wins $2, if the 2 chips he chooses have different numbers he loses $1 (-1).
Let X = the amount of money Miguel will receive or owe.
Miguel only wins $2 in one of the six tournaments, and he only loses $1 in the other five.
what is probability ?Probability theory, a subfield of mathematics, gauges the likelihood of an event or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a large group of equally likely outcomes that result in a certain occurrence compared to the total number of outcomes.
given
We identify the chips so that we can check all six events. Let's say two chips each have a designated 1: R1 and B1 (as if they were red and blue). Let's now consider all possible combinations.
There are 4 options for the first chip, and 3 options remain for the second chip.
There are 12 combinations as a result. There are just six combinations since we don't care about the sequence; for instance, R1, 3 is the same as R1, 3 to us. (R1, B1), (R1, 3), (R1, 5), (B1, 3), and (B1, 5) are the combinations (3,5) Miguel only wins $2 in one of the six tournaments, and he only loses $1 in the other five.
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Given the number 254, 476, 951
What number is in the TEN THOUSAND's SPOT?
Step-by-step explanation: 1 is in the ten thousand places and has a place value of 10,000. 3 is in the thousand's place and has a place value of 3,000. 5 is in the hundreds and has a place value of 500.
Solve x^3 + x - 4 = 0, leaving your answers correct to 2 decimal places.
The solution to the equation x³ + x - 4 = 0 is x = 1.38
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
x^3 + x - 4 = 0
Express the exponents as proper superscript
So, we have the following representation
x³ + x - 4 = 0
Next, we solve the equation using a graph
i.e. we plot the graph of x³ + x - 4 = 0
See attachment for the graph of x³ + x - 4 = 0
The points where the graph of x³ + x - 4 = 0 crosses the x-axis are the solution
In this case, the point is 1.38
Hence, the solution is x = 1.38
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A map has a scale of 1 inch=35 miles. What is the actual distance if the distance on the map is 3.5 inches
Answer:
112.5 miles
Step-by-step explanation:
scale: 1 inch= 35 miles
this means that for every inch on a map, that is 35 miles in real life.
if the distance on a map is 3.5 inches, and you want to find out how much the distant would be in real life, all you have to do is:
3.5 x 35 = 112.5
Compute the MIRR statistic for project I if the appropriate cost of capital is 11 percent.
Cash flow -12,000, 5830, 4680, 2,500
The MIRR statistic for the project I given the cost of capital and the reinvestment rate, is 7. 43 %.
How to find the MIRR statistic ?A monetary indicator of an investment's allure is the modified internal rate of return or MIRR. Ranking equivalent alternative investments is done in capital budgeting.
You can use a spreadsheet to find the MIRR by first ordering the cash flows as shown in the attached image. Then use the = MIRR function.
The cost of capital is the finance charge which is 11 %. The reivestment rate will be the same as the finance charge if not given so it will be 11 % as well.
The MIRR is therefore 7 .43 %.
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Cali made a drawing for her parents for a gift. She wanted to frame it. Her drawing has an area of 96 cm and a width of 8 cm. How many cm of the wooden frame will she need?
Answer: 40 cm
Step-by-step explanation:
The wooden frame needed = perimeter of the drawing
The length of the picture: 96 :8 = 12cm
The perimeter: (12 + 8) x 2 = 40 cm
1. The height of a right triangular prism is 1 5/6 inches. Each side of the triangular base measures 10 inches, and the height of the base is 8 2/3 inches. The triangular prism is placed atop a cube whose side measures 10 inches so that one of the triangular prism’s bases lies completely on one side of the cube.What is the surface area of the solid formed?
100 POINTS!!! IF YOU DRAW AN ACCURATE DIAGRAM TOO, YOU WILL BE AUTOMTIC BRAINLIEST!!!!!!
If the height of a right triangular prism is 1⁵/₆ inches. The surface area of the solid formed is 598.33 in².
What is surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.
First step:-
Right triangular prism=1⁵/₆ inches= 11/6 inches
Height of the base=8²/₃ inches = 26/3 inches
Second step:-
Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)
Surface area = 5(100) +43.33+ 3(18.33)
Surface area = 500) +43.33 + 55
Surface area = 598.33 in²
Therefore the surface area of the solid formed is about 598.33 in²
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please help me thank you so much
Answer:
12(7-3) and 2-0.5
Step-by-step explanation:
All the rest are either terms or equations. The top left one is a term, and all the rest have equal signs, so they're equations. Only the bottom left and bottom right ones are expressions.
Please help will mark Brainly
Answer:
x=4 and y=2
Step-by-step explanation:
You should use graph, point of intersection(for example point M(4,2) ) is solution
And we can conclude that x=4 and y=2
SOMEOINE HELP!!!
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task. (1, 2), (2, 4), (3, 8), (4, 16) Part A: Is this data modeling a linear function or an exponential function? Explain your answer. (2 points) Part B: Write a function to represent the data. Show your work. (4 points) Part C: Determine the average rate of change between station 2 and station 4. Show your work. (4 points)
Answer:
Part A:
This data is modeling an exponential function because the y-values are increasing at an increasing rate. For example, between station 1 and station 2, the time increased by 2 minutes, and between station 2 and station 3, the time increased by 4 minutes. The time between each station is increasing by a multiple of the time between the previous two stations. This indicates that the data follows an exponential curve.
Part B:
To represent this data as a function, we can use the formula y = ab^x, where a and b are constants and x is the input (station number).
Substituting in the values from the first data point, we get: 2 = ab^1
Substituting in the values from the second data point, we get: 4 = ab^2
We can then solve for a and b by dividing these equations:
4/2 = (ab^2)/(ab^1)
2 = b
Substituting this value back into the first equation, we get:
2 = a*2^1
1 = a
Therefore, the function that represents this data is y = 2^x.
Part C:
To find the average rate of change between station 2 and station 4, we can use the formula: (y2 - y1)/(x2 - x1).
Substituting in the values from the data, we get: (16 - 4)/(4 - 2) = 12/2 = 6.
Therefore, the average rate of change between station 2 and station 4 is 6.
draw the graph of y=_3x_4
Answer:
I can’t tell if both number are positive, ones negative ect but here’s the answer if both are negativ, let me know if the numbers are negative or positive and I can come back and give ya the right answer! Xoxo
Step-by-step explanation:
A polynomial function g(x) has a positive leading coefficient. Certain values of g(x) are given in the following table.
x –4 –1 0 1 5 8 12
g(x) 0 3 1 2 0 –3 0
If every x-intercept of g(x) is shown in the table and each has a multiplicity of one, what is the end behavior of g(x)? (5 points)
As x→–∞, g(x)→∞ and as x→∞, g(x)→∞.
As x→–∞, g(x)→–∞ and as x→∞, g(x)→–∞.
As x→–∞, g(x)→ –∞ and as x→∞, g(x)→∞.
As x→–∞, g(x)→∞ and as x→∞, g(x)→–∞.
Examining the polynomial function g(x) as given in the table the end behavior is
As x → –∞, g(x) → –∞ and as x → ∞, g(x) → ∞.What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behavior of polynomial functionThe given table when examined shows that there was three zeros hence the graph is that of odd function
The end behavior of an odd function with positive leading coefficient is
x ⇒ ∞ f(x) ⇒ ∞: as x tends to positive infinity the function tends to positive infinity
x ⇒ -∞ f(x) ⇒ -∞: as x tends to negative infinity the function tends to negative infinity
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You are a post person and deliver 40 letters an hour. You start at 6:45 and have 100 to deliver before your break. What time is your break?
Answer:
9:15
Step-by-step explanation:
Time needed to deliver 100 letters: 100 : 40 = 2,5 hours = 2:30min
Your break: 6:45 + 2:30 = 9:15
How much more interest would be earned on a 100,0000 CD for 9 months than for 6 monthd
There is a $1,000 additional interest earned on a $100,000 CD (Commercial Paper) for 9 months than for 6 months.
How is the additional interest determined?The additional interest earned for a 9-month CD over a 6-month CD can be computed using the subtraction operation.
Firstly, the interests on the 9-month CD and 6-month CD are worked out separately, using the interest formula: Principal x Rate x Time.
The interest for the 6-month CD is subtracted from the interest for the 9-month CD. The result is the difference or additional interest earned.
Commercial Deposit = $100,000
Annual Percentage Rate = 4%
Monthly Percentage Rate = 0.333% (4%/12)
Interest for 9 months = $3,000 ($100,000 x 4% x 9/12)
Interest for 6 months = $2,000 ($100,000 x 4% x 6/12)
The difference in interest earned = $1,000 ($3,000 - $2,000) or ($100,000 x 4% x 3/12)
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Question Completion:APY = 4%
5x-21=-2x+28 given
Prove x=7
i hope this helped you xx
What number is increased by 3 is equal to 16 decreased by 3
Answer:
The answer is 10.
16 - 3 = 13
10 + 3 = 13
Answer:
10
Step-by-step explanation:
Here,10+3=13
and,16-3=13
Mr. Tompkins rode a bus that averaged 30 mph from his home to the airport, and
flew to another city at 250 mph. If his total trip was 670 miles and it took him four
hours of traveling time, how many miles does he live from the airport?
Therefore, Mr. Tompkins lives 240 miles from the airport.
Define acceleration.Acceleration is the rate of change of velocity of an object. It is a vector quantity that has both magnitude and direction. Mathematically, it is the derivative of velocity with respect to time. In simpler terms, it is the change in speed or direction of an object over time.
What is velocity?Velocity is a vector quantity that describes the rate of change of an object's position. It has both magnitude and direction. The magnitude of velocity is the speed of an object, which is the distance covered per unit of time.
We can start solving the problem by using the formula: distance = speed x time.
Let x be the distance from Mr. Tompkins' home to the airport in miles.
Therefore, the distance from the airport to the other city is (670 - x) miles
we know that the total traveling time is 4 hours
so we can set up two equations:
x/30 + (670 - x)/250 = 4
x + (670 - x)/8 = 120
we can solve for x
x = 240 miles
Therefore, Mr. Tompkins lives 240 miles from the airport.
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please help with all 3 questions
will give brainliest to whoever answers them all
Answer:
Question 1: 29
Question 2: 50
Question 3: AD≅BC
Step-by-step explanation:
question 1: Since it's a parallelogram opposite sides are equal.
4x+5=5x-1 add one to both sides
4x+6 =5x subtract 4x from both sides
6 = x
So AD is equal to 5(6) - 1 = 30-1 = 29=AD
Question 2: Since diagonals in a parallelogram bisect each other AE = EC
So...
5x+5 = 8x- 7 add 7 to both sides
5x+12 = 8x subtract 5x from both sides
12=3x divide both sides by 3
4=x
AC= 5(4) + 5 + 8(4) - 7
AC= 20 + 5 + 32 - 7
AC= 50
Question 3: Lines can only be congruent, represented by ≅, not equal which is represented by =. Values can be equal.
By using the elimination method you get the answer line AD ≅ line BC
At a sporting event, the price for 3 cheeseburgers and 2 cups of lemonade is
$19 and the price for 2 cheeseburgers and 4 cups of lemonade is $18. How much
does it cost for 1 cheeseburger and 1 cups of lemonade?
*
By solving system of linear equation we get Cost for 1 cheeseburger $5 and 1 cups of lemonade $2
What is a system of linear equations?A system of linear equations is a collection of two or more linear equations that have the same variables. A linear equation is an equation in which the highest power of the variable is 1. In other words, the equation is a straight line when graphed.
Here is an example of a system of linear equations:
3x + 2y = 19
2x + 4y = 18
This is a system of equations problem, where we can use the information provided to set up two equations and then solve for the unknown variables. Let x be the cost of one cheeseburger and y be the cost of one cup of lemonade.
From the information provided, we know that:
3x + 2y = 19 (the cost of 3 cheeseburgers and 2 cups of lemonade is $19)
2x + 4y = 18 (the cost of 2 cheeseburgers and 4 cups of lemonade is $18)
To find the cost of one cheeseburger and one cup of lemonade, we can solve this system of equations. One way to do this is by substitution.
3x + 2y = 19
we get
[tex]x=\frac{19-2y}{3}[/tex]
substituting x in equation 2x+4y=18
we get
[tex]2(\frac{19-2y}{3})+4y=18[/tex]
[tex]38 - 4y + 12y = 54\\8y = 16\\y = 2[/tex]
substituting y in equation 3x+2y=19
[tex]3x+2(2)=19\\3x=19-4\\3x=15\\x=5[/tex]
The cost of one cup of lemonade is $2
The cost of one cheeseburger is $5
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summarize how you can find the slope of a perpendicular line.
Since "slope" tells us the angle of the line being graphed, the word "slope" is commonly used in mathematics.
Planar geometry states that all lines have slopes. Any slope can be calculated by comparing it to another line, usually the x-axis. A line's slope, or angle, in relation to that x-axis value is how steep it is.
In mathematics, slope is the proportion of the change in the y value to the change in the x value.
Two perpendicular lines have a slope such that the reciprocal of the negative slope of one line equals the slope of the other. The slope of perpendicular lines is -1 as a result.
The relationship between the slopes of parallel lines can be demonstrated using the formula m1.m2 = -1, if the slopes of the two perpendicular lines are m1, m2.
Like a fraction, a slope works by favoring the rise, up-and-down movement, over-the-run, or side-to-side movement. If a line rose up one unit for every rightward unit traveled, the slope would be a positive one.
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Given right triangle JKM, which correctly describes the locations of the sides in relation to ∠J?
Answer:
It is the first answer,
Step-by-step explanation:
The hypotenuse is always the longest side and opposite of the right angel. Side b is the adjacent side to J and c is the opposite side of J.
the mean of 100 nummerical observations is 51.82
If the mean of 100 nummerical observations is 51.82 then the value of all 100 numbers is 5182.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that mean of 100 nummerical observations is 51.82
We need to find the sum of all the observations
The formula to find mean is mean=Sum of observations/ Number of observation
From given mean=51.82
Number of observations =100
Let us take x as sum of all 100 numbers
So 51.82=x/100
Now apply cross multiplication
x=51.82×100
x=5182
Hence, if the mean of 100 nummerical observations is 51.82 then the value of all 100 numbers is 5182.
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any help please — Put the fractions 12,38 and 34 in order from smallest to largest. Find the value of 113+256.
The value of 113+256 is determined by the above fractional formulae. Is 369
Why are fractional equations difficult to solve?An exact number that shows a percentage of a total is called a fraction. You may figure it out by dividing a sum by the quantity of parts. As an example, the number 12 represents one-half of a whole number or an object. Simple subtraction of the smaller numerator from the larger numerator will yield the solution to the problem. To solve, for instance, 6/8 - 2/8, just take 2 out of the answer. The answer, which can be abbreviated to "4/8," is 12, or 12.
Making a fraction simpler by reducing or simplifying it is our goal. In order to do this, we divide the denominator and numerator by the largest integer that can be divided into both integers precisely. That is to say,
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Pls help! Step by step:)
Answer:
tan30° = [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{5}{12}[/tex]
Answer:
[tex]\dfrac{5}{12}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
From inspection of the given right triangle:
θ = 30°O = 5A = 12H = 13Substitute the values into the tan trigonometric ratio:
[tex]\implies \tan(30^{\circ})=\dfrac{5}{12}[/tex]