Span(x,y) is contained in Span(w,u).
Since Span(w,u) is contained in Span(x,y,z) and Span(x,y) is contained in Span(w,u), we have Span(w,u) = Span(x,y,z) = Span(x,y).
A relationship between Span(y) and Span are definitive statements.
Span(y,z) is contained in Span(x,v).
Since Span(v) is contained in Span(y,z) and Span(y,z) is contained in Span(x,v), we have Span(v) = Span(y,z) = Span(x,v).
a) To determine the relationship between Span(x,y) and Span(w,u), we can express w and u in terms of x and y:
w = 2 - 2x + 2y = 2(1-x+y)
u = 2x + 2y + 2z = 2(x+y+z)
So any linear combination of w and u can be written as a linear combination of x, y, and z:
c1 w + c2 u = c1 (2(1-x+y)) + c2 (2(x+y+z)) = (2c1+c2) + (-c1+c2)x + (c1+c2)y + 2c2z
Therefore, Span(w,u) is contained in Span(x,y,z).
On the other hand, since x = (2/2)x + (3/2)y - (1/2)w and y = (-1/2)x + (1/2)w + (1/2)u, any linear combination of x and y can be expressed as a linear combination of w and u:
c1 x + c2 y = c1(2/2)x + c1(3/2)y - c1(1/2)w + c2(-1/2)x + c2(1/2)w + c2(1/2)u
= (c1-c2)x + (3c1/2+c2/2)y + (-c1/2+c2/2)w + (c2/2)u
Therefore, Span(x,y) is contained in Span(w,u).
Since Span(w,u) is contained in Span(x,y,z) and Span(x,y) is contained in Span(w,u), we have Span(w,u) = Span(x,y,z) = Span(x,y).
b) To determine the relationship between Span(y) and Span(:,c), we need to know the dimensions of the vector space V and the specific value of c. Without this information, we cannot make any definitive statements about the relationship between Span(y) and Span(:,c).
c) To determine the relationship between Span(v) and Span(y), we can express v in terms of x and y:
v = 2x + 2y + 2z = 2(x+y+z) - 2(x-y)
Therefore, any linear combination of v can be expressed as a linear combination of y and z:
c1 v = c1(2(x+y+z)) - c1(2(x-y)) = 2c1y + 2c1z - 2c1x
So Span(v) is contained in Span(y,z).
On the other hand, since y = (-1/2)x + (1/2)w + (1/2)u and z = v/2 - x - y, any linear combination of y and z can be expressed as a linear combination of x and v:
c1 y + c2 z = c1(-1/2)x + c1(1/2)w + c1(1/2)u + c2(v/2 - x - y)
= (c1-c2)x + c1(1/2)w + c1(1/2)u + (c2/2)v
Therefore, Span(y,z) is contained in Span(x,v).
Since Span(v) is contained in Span(y,z) and Span(y,z) is contained in Span(x,v), we have Span(v) = Span(y,z) = Span(x,v).
For such more questions on linear combination
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Answer:
Step-by-step explanation:
Span(z,w) contains Span(y), but it is not equal to Span(y), because it also contains vectors that cannot be expressed as linear combinations of y.
a) To determine the relationship between Span(x,y) and Span(w,u), we can start by expressing w and u in terms of x and y:
w = 2 - 2x + 2y = 2(1-x+y)
u = 2x + 2y
We can see that both w and u are linear combinations of x and y, so they belong to Span(x,y). Therefore, Span(w,u) is a subspace of Span(x,y). However, we cannot conclude that Span(w,u) is equal to Span(x,y), because there may be other vectors in Span(x,y) that cannot be expressed as linear combinations of w and u.
b) To determine the relationship between Span(y) and Span(:,c), where c is a vector, we can start by noting that Span(:,c) is the set of all linear combinations of the vector c. On the other hand, Span(y) is the set of all linear combinations of y.
If c is a scalar multiple of y, then Span(:,c) is contained in Span(y), because any linear combination of c can be written as a scalar multiple of y. Conversely, if y is a scalar multiple of c, then Span(y) is contained in Span(:,c). However, in general, neither Span(y) nor Span(:,c) is contained in the other, because they may contain vectors that cannot be expressed as linear combinations of the other set.
c) To determine the relationship between Span(z,w) and Span(y), we can start by expressing z and w in terms of x and y:
z = 2x + 3y
w = 2 - 2x + 2y
We can see that z can be expressed as a linear combination of x and y, while w cannot be expressed as a linear combination of x and y. Therefore, Span(z,w) contains Span(y), but it is not equal to Span(y), because it also contains vectors that cannot be expressed as linear combinations of y.
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Find the length of the third side. If necessary, write in simplest radical form
Answer:
4^2 + 6^2 = x^2
Step-by-step explanation:
Pythagorean theorem is used. Solve for x.
What are 3 of the 6 essential principles in Jefferson's Inaugural Address?
GIVE ME 3 OF THEM PLEASEEE
Answer:
He said that the nation had "room enough for our descendants to the thousandth and thousandth generation" and that his administration would pursue "honest friendship with all nations, entangling alliances with none." He affirmed that America's future depended upon "the preservation of the General government
Step-by-step explanation:
math is so hard man but can someone help me
Answer:
a
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
No, because
the first function if you further calculate you have
y= 3(x +5) is y = 3x+15 ; since you have to distribute
the second function if you have to translate is y=3x+5 because if you read it out loud the equation now you will say y equals 3 times x plus 5 like was given
Who tryna help me with my work? 10th Grade work btw.....
Answer:
Thanks for the points- but im a duma$s
Step-by-step explanation:
BRO PLS HELP ME I NEED TO TURN IT IN AN HOUR
Answer:
A
Step-by-step explanation:
Multiply all the points by 2.
IMPORTANT!! in a unit circle, what is the relationship between arc length and central angle?
The measure of an arc refers to the arc length divided by the radius of the circle. The arc measure equals the corresponding central angle measure, in radians. That's why radians are natural: a central angle of one radian will span an arc exactly one radius long.
Jessica is bringing cupcakes to school for her birthday. She is placing them in a rectangular box that can fit 4 more cupcakes long that it can wide. They will not all fit in the box, so she is also bringing a bag that can hold 12 cupcakes. The amount of cupcakes she is bringing can be represented as x(x + 4) + 12. Solve for the number of cupcakes wide and long the box will hold. Part A) What does x represent?
Answer:
the amount of cupcakes
Step-by-step explanation:
you said the amount of cupcakes can be represented by
4d = 30 the answer would be c=7.5 right if not plz correct me if im wrong
Answer:
Correct!
Step-by-step explanation:
You did it the correct mathematical way, where you divide 4 by 30. Some people get confused and multiply 30 and 4, so good job!
Answer:
Step-by-step explanation: 4÷30=7.5 D = 7.5
Write your own Algebraic expression with four terms that can simplify to 12x+4
Answer:
11x+1x + 2+ 2
Step-by-step explanation:
How many solutions exist for the given equation?
1/2(x+12) = 4x -1
zero
one
two
infinitely many
Answer:
one answer
x = 2
Step-by-step explanation:
can someone help me
Step-by-step explanation:
40 ÷ 4 ( 4 sides) = 10
So each side measures 10inches
Answer:
10
Step-by-step explanation:
beacue 10x4
Find the distance between the points A and B given below.
Answer:
use formula
Step-by-step explanation:
distance between the points A and B=
√((x2-x1)²+(y2-y1)²)
Factor: k^2 + 7x + 10
A:(k+10)(k+4)
B:(k+2)(k+5)
C:(k+2)(k-5)
D:(k-2)(k-5)
Answer:
the answer is B. (k+2)(k+5)
Answer:
a
Step-by-step explanation:
Graph the function y = 4x4 – 8x2 + 4. Which lists all of the turning points of the graph?
(0, 4)
(–1, 0) and (1, 0)
(–1, 0), (0, 4), and (1, 0)
(–4, 0), (–1, 0), (0, 4), and (1, 0)
in case you are wondering, there is no graph.
Answer:
[tex]4(x + 1)^{2}(x - 1)^{2}[/tex]
Step-by-step explanation:
STEP 1:
The equation at the end of step 1
[tex]((4 (x^4)) - 2^3x^2) + 4[/tex]
STEP 2:
The equation at the end of step 2:
[tex](2^2x^4 - 2^3x^2) + 4[/tex]
STEP 3:
STEP 4: Pulling out like terms
4.1 Pull out like factors:
[tex]4x^4 - 8x^2 + 4 = 4(x^4 - 2x^2 + 1)[/tex]
Trying to factor by splitting the middle term
4.2 Factoring [tex]x^4 - 2x^2 + 1[/tex]
The first term is, [tex]x^4[/tex] its coefficient is 1.
The middle term is, [tex]-2x^2[/tex] its coefficient is -2.
The last term, "the constant", is +1.
Step-1: Multiply the coefficient of the first term by the constant 1 • 1 = 1
Step-2: Find two factors of 1 whose sum equals the coefficient of the middle term, which is -2.
-1 + -1 = -2 That's it
Step-3: Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and -1
x4 - 1x2 - 1x2 - 1
Step-4 : Add up the first 2 terms, pulling out like factors :
x2 • (x2-1)
Add up the last 2 terms, pulling out common factors :
1 • (x2-1)
Step-5 : Add up the four terms of step 4 :
(x2-1) • (x2-1)
Which is the desired factorization
Trying to factor as a Difference of Squares:
4.3 Factoring: x2-1
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 1 is the square of 1
Check : x2 is the square of x1
Factorization is : (x + 1) • (x - 1)
Trying to factor as a Difference of Squares:
4.4 Factoring: x2 - 1
Check : 1 is the square of 1
Check : x2 is the square of x1
Factorization is : (x + 1) • (x - 1)
Multiplying Exponential Expressions:
4.5 Multiply (x + 1) by (x + 1)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+1) and the exponents are :
1 , as (x+1) is the same number as (x+1)1
and 1 , as (x+1) is the same number as (x+1)1
The product is therefore, (x+1)(1+1) = (x+1)2
Multiplying Exponential Expressions:
4.6 Multiply (x-1) by (x-1)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x-1) and the exponents are :
1 , as (x-1) is the same number as (x-1)1
and 1 , as (x-1) is the same number as (x-1)1
The product is therefore, (x-1)(1+1) = (x-1)2
Final result :
4 • (x + 1)2 • (x - 1)2
Suppose ABC and DEF are complementary angles. If ABC = (5x + 7)º
and ABC = (3x + 3)', What are the measures of the two angles?
Answer:
The first will be 16.6
The second will be 29
Step-by-step explanation:
Hope this Helped
[tex]5x + 7 = 90[/tex]
[tex]3x + 3 = 90[/tex]
Amanda bought 4 pairs of jeans for $71.40. How much would she need to pay for 8 pairs of jeans?
==========================================================
Explanation:
To get this answer, we double the 71.40 to get 142.80
You can think of it like an equation and we multiply both sides by 2
4 jeans = 71.40 dollars
2*(4 jeans) = 2*(71.40 dollars)
8 jeans = 142.80 dollars
------------
Or you could solve it like this
(4 jeans)/(71.40 dollars) = (8 jeans)/(x dollars)
4/71.40 = 8/x
4x = 71.40*8
4x = 571.2
x = 571.2/4
x = 142.80
------------
Yet another way to solve is to first find the unit rate
4 jeans cost 71.40, so that must mean 1 pair of jeans cost 71.40/4 = 17.85 dollars. This is the unit rate since "unit" means "one". It's the price per pair of jeans.
Multiply that by 8 to find out how much 8 pairs will cost, and we get 17.85*8 = 142.80
McKenzie earns $15 per lawn mowed she also earned $10 for babysitting she earned 100 total, what does that look like in algebra form? Please help.
Answer:
15a + 10b = 100
Step-by-step explanation:
Given:
Cost of each lawn mowed = $15
Cost of each babysitting = $10
Total money earned = 100
Find:
Algebra form
Computation:
Assume;
Number of lawn mowed = a
Number of babysitting = b
So,
15a + 10b = 100
A grocery store is offering a sale on bread and soup. Kacey buys four cans of soup and three loaves of bread for $12.35. Fernando buys eight cans of soup and one loaf of bread for $13.05.
a. Write equations for both Kacey’s and Fernando’s purchases.
Answer:
Kacey
4x+3y=12.35
Fernando
8x+1y=13.05
have to state if the triangles are similar or not.
2. You have to provide the postulate used if similar.
3. You have to complete the similarity statement. 4. You have to support your answers with work.
Answer:
Step-by-step explanation:
10). 1). Both the triangles are not similar.
2). For the similarity of two triangles, corresponding sides of the triangles should be proportional and the included angles should be equal in measure.
Although the angle given is equal but the corresponding sides of the triangles are not proportional, triangles are not similar.
[tex]\frac{UW}{HF}= \frac{UV}{GF}[/tex] (For similar triangles)
[tex]\frac{9}{21}= \frac{18}{42}[/tex]
[tex]\frac{3}{7}=\frac{6}{7}[/tex]
But [tex]\frac{3}{7}\neq \frac{6}{7}[/tex] therefore, both the triangles are not similar.
11). In ΔTUV and ΔCDE,
If the given triangles are similar, their corresponding sides will be proportional and the included angle will be equal in measure.
∠C ≅ ∠T [Given]
[tex]\frac{TU}{CD}= \frac{UV}{DE}[/tex]
[tex]\frac{30}{10}=\frac{27}{9}[/tex]
3 = 3
True.
Therefore, ΔTUV ~ ΔCDE (By SAS postulate of similarity]
PLS HELP!!
Which expressions simplify to a rational answer?
Select each correct answer.
Della has $575.38 in her checking account. What is the balance after she makes a deposit of $50.00 and a withdrawal of $85.45?
A)
$539.93
B)
$558.45
C)
$561.63
D)
$603.73
Answer:
A) 539.93
Step-by-step explanation:
575.38 + 50 - 85.45 = 539.93
Answer: A
$539.93
Step-by-step explanation:
Balance is $575.38 so add (+) $50 for her deposit and subtract (-) $85.45 to get the answer
Pls help me ASAP pls
For the equation: 4x+y=10 what does x equal if y=-6?
Answer:
x = 4
pls mark as brainliest...
Answer:
x=4
Step-by-step explanation:
4x+y=10 then, plug in y
4x+(-6)=10 then, isolate x by adding 6to both sides,
+ 6 +6 then, divide by 4 on each side
4x/4=x
16/4=4
x=4
Kirk is getting a raise of 5% due to inflation. His normal salary is $56,000 per year. Which of the following calculations gives Kirk's new salary, in dollars? A. 56,000 +5 B. 56,000 + 56,000(0.05) C. 56,000 + 56,000(0.50) D. 56,000 + 56,000(5) E. 56,000(.05)
Answer:
The answer is B. 56,000 + 56,000(0.05) because 5% or expressed in decimals 0.05 multiplied by the quantity 56,000 gives us 5% of Kirk's normal salary and added to his normal salary will give us his new salary.
(His new salary is 58,800 and 5% of his normal salary is 2,800)
1. A hammock is suspended between two trees. The curve the hammock makes can be modelled by the equation, y = 0.2x2 – 0.4x – 0.6, where x and y are measured in meters. (Application)
a. What do the x-intercepts tell you?
b. Does the y-intercept have any meaning in this situation.
Answer:
Step-by-step explanation:
Given that:
The modeled equation y = 0.2x² - 0.4x - 0.6
To find x- intercepts
y = 0.2x² - 0.4x - 0.6
y = 0.2(x² - 2x - 3)
y = 0.2(x - 3)(x + 1)
Suppose the upward parabola cuts x axis at x = 3 and x = - 1
Then, the length of the intercepts will be = 3 -(-1)
=4
We can say that the trees will be 4 unit apart.
To find y-intercepts;
y = 0.2(0)² - 0.4(0) -0.6
y = -0.6 meters
hola me ayudan pliss como saco el resultado de 584 × (?) =179288 y (?) ÷ 143 = 572
Answer:
1)307
2)81796
Step-by-step explanation:
584 × (?) =179288
[tex]\frac{179288}{584}[/tex] =307
(?) ÷ 143 = 572
572x143 =81796
¡Espero que esto sea de ayuda! :)
Philippe will read One-half of the number of pages that Rafael reads. How many pages will Rafael read?
Answer: I cannot answer it because it needs more details. For ex say how much day he/she needs and how much pages he/she will read.
Step-by-step explanation: Unknown
The hypotenuse of a right angle triangle is 4 metres. If its other sides are equal find the length of each side.
Answer:
[tex] \sqrt{8} [/tex]
or
[tex]2 \sqrt{2} [/tex]
Step-by-step explanation:
Since the legs are equal this is a 45-45-90 triangle.
The ratio of side length for a 45 45 90 triangle
[tex](1)(1)( \sqrt{2} )[/tex]
where 1 is the legs length and sqr root of 2 is the length of the hypotenuse.
Since we are trying to find the length of the legs side we can set up a proportion.
We know the hypotenuse is 4 so our proportion looks like
[tex] \frac{1}{x} = \frac{1}{x} = \frac{ \sqrt{2} }{4} [/tex]
Let see how far sqr root of 2 goes into 4.
[tex] \sqrt{2} \times x = 4[/tex]
[tex] \sqrt{2} \times x = \sqrt{16} [/tex]
[tex]x = \sqrt{8} [/tex]
so that means the answer for the legs length is
[tex] \sqrt{8} [/tex]
or
[tex]2 \sqrt{2} [/tex]
Answer:
Step-by-step explanation:
hello :
use phtagor - rule: let x the length of each side
x² +x² =4²
2x² =16
x² = 8
x = √8
but : 8 = 4×2 = 2²×2
x = √(2²×2) = √2²× √2 =2√2 ...... √2² =2
x = 2√2 metres.
What is the measure of
Angles are not necessarily drawn to scale.
Answer: 58
Step-by-step explanation:
180-114= 66
66+56=122
180-122= 58
A light house worker is tracking a boat that is 5 km south of her. She is also tracking a boat
that is 6 km from the tower located 70° east of north. To the nearest kilometer, how
far apart are the two boats?
A. 7 km
B. 9 km
C. 8 km
D. 16 kM
Answer:
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