To show that {u1, u2} is an orthogonal basis for R2, we need to verify that u1 and u2 are orthogonal and that they span R2.
First, let's verify orthogonality. Two vectors are orthogonal if their dot product is zero. So we need to calculate the dot product of u1 and u2 and verify that it is zero:
u1 · u2 = [2, 1] · [-1, 2] = (2 × -1) + (1 × 2) = 0
Since the dot product is zero, u1 and u2 are orthogonal.
Next, let's verify that u1 and u2 span R2. This means that any vector in R2 can be expressed as a linear combination of u1 and u2.
Let x = [1, 8]. We want to find coefficients c1 and c2 such that x = c1u1 + c2u2.
We can solve for c1 and c2 using the following system of equations:
2c1 - c2 = 1
c1 + 2c2 = 8
Multiplying the first equation by 2 and adding it to the second equation, we get:
5c1 = 10
c1 = 2
Substituting c1 = 2 into the first equation, we get:
2(2) - c2 = 1
c2 = 3
Therefore, x = 2u1 + 3u2.
So {u1, u2} is indeed an orthogonal basis for R2, and we have expressed x as a linear combination of u1 and u2 without row reduction:
x = 2u1 + 3u2 = 2[2, 1] + 3[-1, 2] = [4, 2] + [-3, 6] = [1, 8].
Learn more about orthogonal here:
https://brainly.com/question/2292926
#SPJ11
Lori works as a cartoonist for a teen magazine. The time she spends sketching is given by the equation m = 12s, where m is the number of minutes and s is the number of sketches.
If Lori made
3
4
of a sketch
If Lori made a fraction of 3/4 of a sketch, then she spent 9 minutes of sketching.
What is fraction?A fraction is a portion of something. Mathematics refers to a number as a quotient when the numerator and denominator are divided. Both are integers in a simple fraction. There is a fraction in the numerator or denominator of a complex fraction. The numerator and denominator of a proper fraction are different sizes.
Given the equation
m = 12s,
where
m is the number of minutes, and
s is the number of sketches.
Lori made 3/4 of a sketch i.e.
m = 12(3/4)
m = 9 mins
Thus, If Lori made 3/4 of a sketch, she spent 9 minutes sketching.
Learn more about fraction
https://brainly.com/question/12220774
#SPJ1
Is triangle FHK similar to triangle GHJ? If so, which postulate or theorem proves these two triangles are similar?
The postulate or theorem that proves that the two triangles are similar is: ΔFHK is similar to ΔGHJ by the SSS Similarity Theorem.
Properties of similar triangles.When the corresponding sides or measure of angles of two or more triangles have common properties, the triangles are said to be similar. This can be deduced on comparing the corresponding length of sides or measure of angles.
In the given question, comparing the corresponding sides of the triangle. We have;
HG/ HF = 10/ 22
= 0.4545
Also,
HJ/ HK = 15/ 33
= 0.4545
Since the two ratios are the same, it implies that the third sides of the two triangles would give the same answer. Thus they are similar.
Therefore, the postulate or theorem that proves that the two triangles are similar is: ΔFHK is similar to ΔGHJ by the SSS Similarity Theorem.
Learn more about properties of similar triangles at https://brainly.com/question/16553249
#SPJ1
What is the center theorem?
The central law expresses that even if a group is not normally distributed, the means of sufficiently large samples drawn from that group will be normally distributed.
A key conclusion of graph theory is known as the Center Theorem, which asserts that in a connected graph, the minimal degree of a vertex's degree is equal to the most significant number of vertices that can be removed from the graph while maintaining connectivity.
Generally, it is the collection of vertices with the lowest eccentricity that constitutes the centre of a connected graph, where the eccentricity of a vertex is defined as the most significant distance between that vertex and any other vertex in the graph. The radius of a graph is the number of vertices that make up its centre.
Read more about the centre theorem on:
https://brainly.com/question/18403552
#SPJ4
Maths sucks and this got my brain scramble
Answer:
Step-by-step explanation:
this is how I do it in Vietnam, if you don't understand, ask me
Answer:
x = 70°-----------------------------
According to the picture we have:
∠BAK ≅ ∠CBD as corresponding angles,∠BDC ≅ ∠PDK as vertical angles.Find the measure of angle PDK, using sum of angles of ΔPDK:
m∠PDK + 60° + 70° = 180° -m∠PDK = 180° - 130° m∠PDK = 50°Find x, using sum of angles of ΔBDC:
x + 60° + 50° = 180°x = 180° - 110°x = 70°A number is increased by 7, twice the result is 41.what is the number?
Answer:
After increasing it by 7, it becomes = 2x + 7. => x = 82/2 = 41. Hence, the original number = 41.
Is 2 3 4 5 6 6 a function or not?
No, 2 3 4 5 6 6 is not a function.
A function is a set of ordered pairs (x, f(x)) where each input value x corresponds to exactly one output value f(x). In other words, for any given input value x, there should be only one corresponding output value f(x).
2 3 4 5 6 6 is a list of integers, but it does not represent any ordered pairs. It is not clear which integers correspond to input values and which correspond to output values. Therefore, it cannot be considered a function.
It's important to note that in order to identify if a set of ordered pairs is a function or not, you must check if there's any value that is repeated as an input value, if so then it's not a function.
To learn more about the integer, visit:
brainly.com/question/15276410
#SPJ4
Question 7
SPORTS The Fan Cost Index (FCI) tracks the average costs for attending sporting events, including tickets, drinks, food, parking, programs,
and souvenirs. According to the FCI, a family of four would spend a total of $592.30 to attend two Major League Baseball (MLB) games and
one National Basketball Association (NBA) game. The family would spend $691.31 to attend one MLB and two NBA games.
a. Write a system of equations to find the family's costs for each kind of game according to the FCI. Let x be the cost of MLB games and y be
the cost of NBA games.
MLB: $
x+
NBA: $
y=592.30
b. Solve the system of equations to find the cost for a family of four to attend each kind of game according to the FCI.
y=
Answer: a. To write a system of equations to find the family's costs for each kind of game according to the FCI, we can use the information provided in the problem. According to the FCI, a family of four would spend a total of $592.30 to attend two MLB games and one NBA game, and the family would spend $691.31 to attend one MLB and two NBA games. Let x be the cost of MLB games and y be the cost of NBA games. Then we can write the following system of equations:
x + y = 592.30 equation 1 represents the cost of attending two MLB games and one NBA game
2y + x = 691.31 equation 2 represents the cost of attending one MLB and two NBA games
b. We can solve the system of equations to find the cost for a family of four to attend each kind of game according to the FCI.
We can substitute equation 1 into equation 2
2y + (592.30 - y) = 691.31
2y + 592.30 - y = 691.31
2y = 691.31 - 592.30 = 99.01
y = 49.51
we know y represents cost of NBA games so 49.51 is cost of one NBA game for a family of four
x = 592.30 - y = 592.30 - 49.51 = 542.79
x represents cost of MLB games so 542.79 is the cost of one MLB game for a family of four
So, according to the FCI, a family of four would spend $542.79 to attend one MLB game, and $49.51 to attend one NBA game.
Step-by-step explanation:
xena runs halfway across a field in 1 minute. the next fourth of the field takes her 2/3 of a minute to cross, the next eighth takes 4/9 of a minute, and so on, with each half of the previous distance taking 2/3 of the previous time. how many minutes does it take xena to cross the field?
it would take 3 minutes for Xena to finish the run.
What is the geometric sequence?A geometric sequence is a sequence of numbers that follows a pattern where the next term is found by multiplying by a constant called the common ratio, r.
From the general formula of the nth term of the geometric sequence:
Aₙ = A rⁿ⁻¹
Given, every stop Xena makes is diminished by half of the distance she covers from the preceding. And she takes 2/3 of the time she used from the previous stop.
The problem above is a WORDED PROBLEM that involves INFINITE GEOMETRIC PROGRESSION.
As we all know, a worded problem just basically needs a thorough understanding of what is happening on the problem to translate words and phrases into algebraic phrases and equations.
Meanwhile, a geometric progression is a type of progression in which the proceeding value is greater or smaller than the previous by a ratio. Typical geometric progression problems involve ratios of greater than 1.
The above problem is an “infinite geometric progression” in which the ratio is less than 1.
Refer to the illustration below.
We first take elimination of the given.
Since both the distance and the time have infinite number of stops to complete the run, the SUM OF INFINITE GEOMETRIC PROGRESSION is
S = (A₁)/(1-r)
a1 = first term
r = ratio
Substituting the values, we have
S = (1min) / (1- (2/3))
S = 1 / (1/3)
S = 3 minutes
Therefore, it would take 3 minutes for Xena to finish the run.
Learn more about geometric sequence here:
https://brainly.com/question/13008517
#SPJ1
Billy bought a lamp that costs $13.00 the tax is 5% what is the amount of tax he will have to pay
Answer:
0.65
Step-by-step explanation:
[tex]13.00*5%=0.65[/tex]
Answer:
Price before tax: $ 13.00
+ Sales tax (5%): $ 0.65
Total price including tax: $ 13.65
Good luck <33
Help fast please help
As the difference between the output values, the rate of change of the linear equation is 4/3.
what is linear equation ?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
given
The specified points' coordinates should be found.
The difference between the output values = 4
The difference between the input values = 3
Find the expression for the ratio of the change in y to the change in x: yx.
= 4/3
As the difference between the output values, the rate of change of the linear equation is 4/3.
To know more about linear equation visit:
https://brainly.com/question/11897796
#SPJ1
at 6:00 am and the wind is blowing 32 mph with the increase of 2mph. it is currently 9:00am .how fast is the wind blowing
party city is selling a helium tank for inflating balloons for $38. Mark has two coupons that he could use. one coupon is for $5 off, and the other coupon is for 10% off. Which coupon should he use to get the better deal?
He should use $5 off coupon to get the better deal. This will make the price of helium tank $33 which is less than $10% off i.e $34.2.
What is a coupon?"Coupon" is a term used when bonds were printed on paper. The bondholder would receive a certificate serving as a representation of the bond. On the side of the document would be tear-off coupons that the bondholder could present to the company that issued the bond to receive the coupon payment.
The coupon rates are set by the governments or corporations that issue the bonds, and they can differ significantly depending on the term of the bond and/or the stability of the issuing entity. In order to compensate for the holder's longer wait for the final payment, a 30-year-term bond, for example, might have a higher rate than a note with a 1-year term.
Price when $5 off = 38 - 5
= $33
Price when 10% off = 38 - (38 × 5/100)
= $34.2
Thus, He should use $5 off coupon to get the better deal.
Learn more about Coupon
https://brainly.com/question/30177801
#SPJ1
Do the sides 7cm 24cm and 25cm form a right-angled triangle give reasons?
The sides 7 cm, 24 cm and 25 cm can form a right-angled triangle. The Pythagorean theorem can be used to verify this.
From Pythagorean theorem, it can be said that, the square of hypotenuse side is equal to the sum of other two sides of a right angles triangle.
Let AB, CA and BC be the sides of a right triangle. CA is the hypotenuse side, AB and BC are the base and height sides of the right triangle. The equation can then be expressed as,
CA² = AB² + BC²
Now, let us check this rule for the above given sides of the triangle.
Longest side² = Sum of squares of other two sides
25² = 24² + 7²
625 = 625
Thus, the sides 7 cm, 24 cm and 25 cm can form a right-angled triangle.
To know more about Pythagoras theorem:
brainly.com/question/343682
#SPJ4
the ___ is the line through the vertices of an ellipse.
Answer: The major axis is the line segment that passes through the foci of the ellipse. The endpoints of this axis are called the vertices of the ellipse. The segment passing through the center and perpendicular to the major axis is called the minor axis.
if f(x)=x^5 and g(x)=-2x-3x^2, which is f(g(x))?
Therefore , the solution of the given problem of function comes out to be
f(g(x)) = (-2x-3x2)⁵
What exactly do composite functions do?When the result of one function is used as the input for another, this is known as a composite function. The function f g (x) fg(x) fg(x) fg(x), also known as "f of g of x" or "f g fg fg of x," is the composition of the two functions if we have a function f and another variable function g.
Here,
Given,
f(x) = x5
g(x)=-2x-3x₂
f(g(x)) = (-2x-3x2)⁵
Therefore , the solution of the given problem of function comes out to be
f(g(x)) = (-2x-3x2)⁵
To know more about function visit:-
brainly.com/question/12431044
#SPJ1
Product
3². 3³
5¹ 52
●
8³. 84
76.72
Expanded Form
(33) (333)
●
(5) (5.5)
(888)
(7 7 7 7 7 7) (77)
●
●
(8 8 8 8)
•
●
Exponential Form
A way to multiply a number and display it several times. by creating a basis using the number and the repeats.
What is meant by expanded form?A method of displaying several times of the same number multiplied. by forming a base with the number of repeats and the number. Its upper right has a little number written on it.
A number is typically written in exponential notation as a coefficient between 1 and 10 times the exponent, which is an integral power of 10. Write a number in the form: c 10n, where c is a number between 1 and 10 (for example, 1, 2.5, 6.3, 9.8) and n is an integer, to represent it in exponential notation (e.g. 1, -3, 6, -2).
When we expand a number to show the value of each digit, we do so by dividing it into its place values.
To learn more about expanded form refer to:
https://brainly.com/question/102887
#SPJ1
-2y - 5 > 5/2 problem 4 Record Practice Journal (red)
On solving the provided question, we can say that the inequality equation is -2y - 5 > 5/2 => -4y - 10 > 5 => -4y > 15 +. y > -15/4
What is inequality?An inequality in mathematics is a relationship between two expressions and or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
here,
the inequality equation is
-2y - 5 > 5/2
-4y - 10 > 5
-4y > 15
y > -15/4
To know more about inequality visit:
https://brainly.com/question/29914203
#SPJ1
Find the area of the polygon with the given vertice. N(-2,1), P(3,1), Q(3,-1), R(-2,-1)
The area of polygon is 10 units.
To find the area of the polygon with the given vertices, we can use the shoelace formula, which is a method for finding the area of a polygon when given its vertices in a certain order.
The shoelace formula is:
Area = (1/2) * |(x1y2 + x2y3 + x3y4 + ... + xn-1yn + xny1) - (y1x2 + y2x3 + y3x4 + ... + yn-1xn + ynx1)|
where (x1, y1), (x2, y2), (x3, y3), ..., (xn, yn) are the vertices of the polygon in a certain order.
For the given vertices, we have:
N(-2,1), P(3,1), Q(3,-1), R(-2,-1)
So the area of the polygon is:
Area = (1/2) * |(-21 + 3-1 + 3*-1 + -21) - (13 + 13 + -1-2 + -1*-2)|
Area = (1/2) * |(-2 - 3 - 3 + 2) - (3 + 3 + 2 + 2)|
Area = (1/2) * |-8 - 12|
Area = (1/2) * 20
Area = 10 square units
So the area of the polygon is 10 square units.
To learn more about polygons visit: brainly.com/question/28276384
#SPJ4
What is the y-intercept of the line given by the equation below y =- 10x 14?
The y-intercept of the line given by the equation y = -10x + 14 is (0, 14)
We know that the y-intercept of the line is nothing but the point at which the line intersects the y-axis.
To find the y-intercept, we substitute x = 0 in given equation of line and solve it for y.
In this question we have been given an equation of line y = -10x + 14
to find y-intercept substitute x = 0 in given equation.
y = -10x + 14
y = -10(0) + 14
y = 0 + 14
y = 14
This means, a line y = -10x + 14 intersects the y-axis at point (0, 14)
Learn more about y-intercept here:
https://brainly.com/question/29140020
#SPJ4
what is angle LOM equal to?
Answer:
90 degrees
Step-by-step explanation:
True or False: To solve an inequality means to get the variable by itself on one side of the inequality.
Answer:
True
That is the formula to solve an inequality
Assume an exponential function has a starting value of 16 and a decay rate of 44%. Write an equation to model the situation.
16 x 0.56^x
where 16 is the sfadtin value
0.56 is how much the amount is decreasing by each time
x= number of hours/days etc
Before jude broke his right arm, he was able to type 19 words per minute on his phone. After he broke his arm, he had to use his left hand for a while, and he could only type 12 words per minute. What is the difference between the number of words he could type in 5 minutes before and after he broke his arm
30 words in 5 minutes following the arm break.
What is unitary method?This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.
A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.
We typically utilize this technique for math calculations.
This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc
According to our question-
45 words in five minutes before to breaking his arm
9*5=45 6*5=30
learn more about unitary method click here:
brainly.com/question/24587372
#SPJ1
What is the sign of a^{72}\cdot \left(\dfrac{-3}{7}\right)a
72
⋅(
7
−3
)a, start superscript, 72, end superscript, dot, left parenthesis, start fraction, minus, 3, divided by, 7, end fraction, right parenthesis when aaa is a negative number?
Answer:
Welcome to Gboard clipboard, any text that you copy will be saved here.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Tap on a clip to paste it in the text box.
The product is positive since [tex]a^{(72)}[/tex] is positive (without a question control), the division is negative, and 'a' is negative.
What is the sign of right parenthesis when aaa is a negative number?Let's analyze the expression step by step:
[tex]a^{72}:[/tex] This term talks to a raised to the control of 72.
left(dfrac{-3}{7}right): This term talks to -3/7, a division with a negative respect.
a: This term talks to the variable "a".
To select the sign of the expression, we have to consider the person parts:
[tex]a^{72}[/tex] can be a positive number since any positive base raised to an without-a-question control comes around in a positive respect.
left(dfrac{-3}{7}right) may be a negative division.
a may be a negative number concurring with the address.
By and by, let's put it all together:
a^{72} cdot left(dfrac{-3}{7}right) cdot a
Since a^{72} is positive, left(dfrac{-3}{7}right) is negative, and "a" is negative, the extraordinary product will be positive:
Positive number[tex](a^{72})[/tex] × Negative number left(dfrac{-3}{7}right) × Negative number (a) = Positive number.
In this way, the expression will result in positive respect when "a" may be a negative number.
Learn more about negative numbers here:
https://brainly.com/question/13831313
#SPJ2
Nick and Chloe left their campsite by canoe and paddled
downstream at an average speed of 12 km/h. They
paddled downstream for 2 km. How much time did the
campers take to get downstream? (include formula)
To find out how much time the campers took to get downstream, we can use the formula:
time = distance / speed
where distance is the distance they paddled downstream (in this case, 2 km) and speed is their average speed (in this case, 12 km/h). So we can substitute in the values we know to get:
time = 2 km / 12 km/h
To solve for the time, we can divide the distance by the speed:
time = 2/12 hours = 0.17 hours or approximately 10.2 minutes
So it takes 10.2 minutes for Nick and Chloe to get downstream.
A factory produces 350 smartphones per hour. How many smartphones can it produce in 4 days, given 24 hours in a day?
A day has 24 hours, so 4 days have 4 * 24 = 96 hours.
The factory produces 350 smartphones per hour, so in 96 hours it can produce 350 * 96 = 33600 smartphones.
Therefore the factory can produce 33600 smartphones in 4 days.
100 points, please help:)
Given the graph below, state the parabola's vertex and the equation of the axis of symmetry.
1.(2, –3); x = 2
2.(2, –3); x = –3
3.(2, –3); y = 2
4.(2, –3); y = –3
5. none of the above
Answer:
1. (2, –3); x = 2---------------------------------
According to the graph, the vertex is at (2, - 3).
The axis of symmetry passes through the vertex, so its x-coordinate determines the vertical line:
x = 2The matching answer choice is 1.
Answer:
1. (2, –3); x = 2
Step-by-step explanation:
The vertex of a parabola is its turning point. This is:
the minimum point of a parabola that opens upwards, or the maximum point of a parabola that opens downwards.From inspection of the given graph, the vertex of the parabola is (2, -3).
The axis of symmetry is the vertical line that passes through the vertex and divides the parabola into two equal (symmetrical) halves.
The axis of symmetry is the x-value of the vertex.
Therefore, the axis of symmetry of the graphed parabola is x = 2.
5) You invest in 200 shares of Lerner Windows stock and receive a semiannual dividend of
$0.78 a share. At that rate, what will be your annual income from the investment?
Answer:
your annual income from the investment would be $312.
Step-by-step explanation:
If you invest in 200 shares of Lerner Windows stock and receive a semiannual dividend of $0.78 a share, your annual income from the investment would be:
$0.78 x 200 shares = $156 in semiannual dividends
To find the annual income, you would multiply the semiannual dividends by 2:
$156 x 2 = $312
So, your annual income from the investment would be $312.
The total cost y of an amusement park membership and the number of months x can be represented with the equation y = 15x + 20. Find
and interpret the rate of change and initial value. The rate of change is so the cost per month is $ . The initial value is .so the initial membership fee is $
The rate of change in the equation y = 15x + 20 is 15. This means that for every increase of 1 unit in x (1 month), the total cost y will increase by 15. So the cost per month is 15 dollars.
The initial value in the equation y = 15x + 20 is 20. This means that when x = 0 (i.e. no months have passed), the total cost y is equal to 20 dollars. So the initial membership fee is 20 dollars.
Answer:
Through from posted good new dts day utilities january home tub just further january kg has last jan free k be page with questions 2:5
If segments DE and AB are parallel, which of the following expressions will help Eshaal determine the length of segment BC
The expression that will help Eshaal determine the length of segment BC is: BC = DE - AB
Since segments DE and AB are parallel, we can use the following expression to calculate the length of segment BC: BC = DE - AB. This expression states that the length of BC is equal to the length of DE minus the length of AB.
If segments DE and AB are parallel, we can use a simple expression to find the length of segment BC. This expression is: BC = DE - AB. This expression states that the length of BC is equal to the difference of the length of DE and the length of AB. In other words, if we know the lengths of segments DE and AB, we can calculate the length of segment BC by subtracting the length of segment AB from the length of segment DE. This expression is a useful tool for finding the length of segment BC when we know the lengths of segments DE and AB. It is a simple and efficient way to calculate the length of segment BC without having to measure it directly.
the complete question is : If segments DE and AB are parallel, which of the following expressions will help Eshaal determine the length of segment BC?If segments DE and AB are parallel, what expression can Eshaal use to determine the length of segment BC?
Learn more about expression here
https://brainly.com/question/14083225
#SPJ4