In linear algebra, a subspace of a vector space is a subset of vectors that satisfies certain properties.
(a) To show that {(x1, x2)T | x1 + x2 = 0} forms a subspace of R2, we need to show that it satisfies the three conditions for a subspace:
i. The zero vector is in the set: (0,0)T is in the set because 0 + 0 = 0.
ii. The set is closed under addition: Let (a,b)T and (c,d)T be in the set. Then a + b = 0 and c + d = 0. We need to show that (a + c, b + d)T is also in the set. (a + c) + (b + d) = (a + b) + (c + d) = 0 + 0 = 0, so (a + c, b + d)T is in the set.
iii. The set is closed under scalar multiplication: Let (a,b)T be in the set and let c be a scalar. We need to show that c(a,b)T is also in the set. c(a,b)T = (ca, cb)T, and ca + cb = c(a + b) = c(0) = 0, so c(a,b)T is in the set.
Since the set satisfies all three conditions for a subspace, we can conclude that {(x1, x2)T | x1 + x2 = 0} forms a subspace of R2.
(b) To show that {(x1, x2)T | x21 = x22} does not form a subspace of R2, we only need to show that it fails one of the conditions for a subspace.
Take (1, -1)T and (1, 1)T, which are both in the set since 12 = (-1)2. However, their sum (2, 0)T is not in the set since 22 ≠ 0. Therefore, the set is not closed under addition and does not form a subspace of R2.
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Which expression is equivalent to the following complex fraction?
1 + StartFraction 1 Over y EndFraction divided by 1 minus StartFraction 1 Over y EndFraction
StartFraction (y + 1) (y minus 1) Over y squared EndFraction
StartFraction y + 1 Over y minus 1 EndFraction
StartFraction y minus 1 Over y + 1 EndFraction
StartFraction y squared Over (y + 1) (y minus 1) EndFraction
The equivalent expression of [tex](1 + \frac{1}{y}) \div (1-\frac 1y)[/tex] is [tex]\frac{y + 1}{y-1}[/tex]
How to determine the equivalent fraction?The fraction is given as:
[tex](1 + \frac{1}{y}) \div (1-\frac 1y)[/tex]
Take the LCM
[tex]\frac{y + 1}{y} \div \frac{y-1}y[/tex]
Express as products
[tex]\frac{y + 1}{y} \times \frac{y}{y-1}[/tex]
Evaluate the product
[tex]\frac{y + 1}{y-1}[/tex]
Hence, the equivalent expression of [tex](1 + \frac{1}{y}) \div (1-\frac 1y)[/tex] is [tex]\frac{y + 1}{y-1}[/tex]
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(-4, 8) and (6, 2). Slope
Answer:
In order to go from the first point to the second, we need to rise from 4 to 7, i.e. by 3. We also need to run from -4 to -2, i.e. by 2. Therefore the slope is 32 .
Step-by-step explanation:
Solve for the unknown measure of this equation in degrees.
< X in 15^(2) = 13^(2) + 10^(2) -2(13)(10) cos X
Also a question down below.
Answer:
12
Step-by-step explanation:
Well they are similar I assume so 5 / 3.5 = roughly 1.43 and 8.4 x this number gives you 12 so I would say 12
PLEASE ANYONE: The tennis club has 5 new members each member buys a racet and a tube of balls. If 6 racket cost $186.00 and 6 tubes of balls cost $27.00 how much do the 5 people pay for rackets and balls?
Answer:
Total cost is $177.50.
Step-by-step explanation:
Rackets:
Divide the cost for racket by 6 to find the cost per racket.
186÷6=31
Multiply 31 by 5 to find the cost for 5 rackets.
31×5=155
$155
Tubes of balls:
Divide 27 by 6 to find the cost per a tube of balls.
27÷6=4.50
Multiply 4.50 by 5 to find the cost for 5 tubes of balls.
4.50×5=22.50
$22.50
Add the amounts for rackets and tubes of balls to find the total cost.
155+22.50=177.50
The total cost is $177.50.
Hope this helps!
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Find the measure of the angle indicated.
53°
44°
127°
52°
Answer:
53 degrees
Step-by-step explanation:
If the two lines intersected by a transversal are parallel then the same side interior angle should add up to 180 degrees.
180-127 = 53 degrees
Which equation can be used to find y, the year in which both bodies of water have the same amount of mercury? 0.05 – 0.1y = 0.12 – 0.06y 0.05y 0.1 = 0.12y 0.06 0.05 0.1y = 0.12 0.06y 0.05y – 0.1 = 0.12y – 0.06
The equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y. Hence, the 3rd option is the right choice.
In the question, we have been asked for the equation that can be used to find y, the year in which both bodies of water have the same amount of mercury.
First, we will find the equations showing the level of mercury in each body of water.
For the first water body:
Initial measure of mercury = 0.05 ppb.
Rate of rising = 0.1 ppb each year.
Number of years = y.
Thus, the equation showing level of mercury = 0.05 + 0.1y.
For the second water body:
Initial measure of mercury = 0.12 ppb.
Rate of rising = 0.06 ppb each year.
Number of years = y.
Thus, the equation showing level of mercury = 0.12 + 0.06y.
We are looking for the equation, to find y, the year in which both bodies of water have the same amount of mercury.
As they will have the same amount of mercury, their respective equations showing the level of mercury should be equal, that is:
0.05 + 0.1y = 0.12 + 0.06y, which is the required equation.
Thus, the equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y. Hence, the 3rd option is the right choice.
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For the complete question, refer to the attachment.
Explain all of the steps needed to simplify the equation 8(x+2) = 4(2x+9) using the order of operations.
Answer:
First, use the distributive property and distribute 8 to the [tex](x,2)[/tex] in the first part of the equation to get [tex]8x + 16[/tex].
Next, also use the distributive property to distribute the 4 to the [tex](2x+9)[/tex] in the second part of the equation to get [tex]8x+36[/tex].
The simplified equation looks like this: [tex]8x+16=8x+36[/tex].
sin (x+y)/sin (x-y) =
No directions given here. What exactly do you need to be done with this trigonometric function?
Consider trapezoid LMNO.
Trapezoid L M N O is shown. Sides L M and O N are parallel.
What information would verify that LMNO is an isosceles trapezoid? Check all that apply.
LN ≅ MO
LM ≅ ON
LO ≅ MN
∠L ≅ ∠N
∠L ≅ ∠M
The side LO is congruent to the side MN, the diagonal LN is congruent to the diagonal MO, and the angle L is congruent to the angle M in an isosceles trapezoid, denoted by the symbols LMNO.
What are the conditions for an Isosceles Trapezoid?
The conditions listed below demonstrate that any trapezoid is an isosceles trapezoid:
The length of both legs is the same.2nd condition: The base angles are of equal proportion.The length of the diagonals is the same.When these conditions are met by the given trapezoid LMNO, it will be referred to as an isosceles trapezoid. Hence, the following conditions of trapezoid LMNO need to be fulfilled,
LN ≅ MO
LO ≅ MN
∠L ≅ ∠M
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✔ (A.) LN ≅ MO
✔ (C.) LO ≅ MN
✔ (E.) ∠L ≅ ∠M
5
Sample Space and Venn Diagrams: Mastery Test
Type the correct answer in each box. If necessary, use / for the fraction bar.
A bag contains 5 blue marbles, 2 black marbles, and 3 red marbles. A marble is randomly drawn from the bag.
The probability of not drawing a black marble is
. The probability of drawing a red marble is
m. All rights reserved.
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The probability of not drawing a black marble is 4/5
The probability of drawing a red marble is 3/10
What are the probabilities?Probability determines the odds of the occurrence of a random event. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability of not drawing a black marble = total marbles that are not black / total number of marbles
(5 + 3) / (5 + 3 + 2) = 8/10 = 4/5
The probability of drawing a red marble = total number of red marbles / total number of marbles
= 3/10
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Answer:
See image
Step-by-step explanation:
Plato
Select the correct answer from each drop-down menu.
The general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0.
The equation of this circle in standard form is. The center of the circle is at the point, and its radius is units
Step-by-step explanation:
the equation in the standard form is :
( x - 2 ) 2+ ( Y + 3 ) 2 = 18
the center is at the point ( 2, - 3 ).
its radious is : /18 = 3/ 2 units
Help! asap!
As shown in the figure below, a || b and c is the transversal, m∠1= 40°, m∠2= 70°.
Question: m∠3= ?
The measure of angle 3 from the figure is 110 degrees
Lines and anglesAn angle is the intersection between two lines. From the given figure, we have the following parameters
m∠1= 40°,
m∠2= 70°.
Required
Measure of angle 3
The sum of the interior angles of the triangle is equal to the exterior
Sum of interior = <1 + <2
Sum of interior = 40 + 70
Sum of interior =110 degrees
Hence the measure of angle 3 from the figure is 110 degrees
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Compare the theoretical probability to the experimental probability of landing on H.
The correct statement comparing the theoretical and experimental probabilities is given as follows:
[tex]\frac{1}{4} < \frac{7}{25}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The theoretical probability is taken before any experiment. Since the four sections are equal, the theoretical probability is:
T(H) = 1/4.
The experimental probability is taken considering previous experiments. Out of 100 tosses, 28 landed on H, hence:
E(H) = 28/100 = 7/25.
Hence the correct statement is:
[tex]\frac{1}{4} < \frac{7}{25}[/tex].
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Find the surface area of the composite figure. Round to the nearest tenth if necessary.
By definition of surface area, the composite figure reports an area of 233.6 square centimeters.
How to calculate the surface area of a composite figure
In this question we need to determine the surface area of a composite figure, which is the sum of all the areas of the faces, which are combinations of triangles and quadrilaterals. Now we proceed to calculate the surface area:
A = 2 · (6 cm) · (3 cm) + 2 · (8 cm) · (6 cm) + 2 · (8 cm) · (3.6 cm) + 2 · (8 cm) · (2 cm) + 4 · (1/2) · (3 cm) · (2 cm)
A = 233.6 cm²
By definition of surface area, the composite figure reports an area of 233.6 square centimeters.
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Can somebody please help me I have exam tomorrowwww
Answer:
3x²y (2x²-3y²+ 4y)
Step-by-step explanation:
Factor the expression 6x^4y-9x²y³+12x²y².
First, check if there is a GCF. The GCF is 3x²y.
3x²y (2x²-3y²+ 4y).
This equation cannot be factored further. Therefore, the answer is
3x²y (2x²-3y²+ 4y).
Hope this helps!
Answer:
3x²y(-3y²+4y+2)
Step-by-step explanation:
6x⁴y-9x²y³+12x²y²
solution:
first common
3x²y(2x²-3y²+4y)
3x²y(-3y²+4y+2)
A group of birds are flying, they meet another group of birds. They ask 'hello hundred.' They replied we are not 100. we need half of us plus you to be hundred. How many birds are needed?
Answer:
Step-by-step explanation:
You answer
Select the correct answer.
Choose the system of inequalities that best matches the graph below.
Considering the linear functions on the graph, the inequality that matches the situation is:
B.
[tex]y \geq \frac{1}{2}x + 2[/tex][tex]y \leq 2x + 1[/tex]What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The lower bound of the interval is a linear function with y-intercept of b = 2, that also passes through (2,3), hence the slope is:
m = (3 - 2)/(2 - 0) = 1/2.
Hence the inequality is:
[tex]y \geq \frac{1}{2}x + 2[/tex]
The upper bound of the interval is a linear function with y-intercept of b = 1, that also passes through (2,5), hence the slope is:
m = (5 - 1)/(2 - 0) = 2.
Hence the inequality is:
[tex]y \leq 2x + 1[/tex]
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Which expression is equivalent to (2 Superscript one-half Baseline times 2 Superscript three-fourths Baseline) squared?
RootIndex 4 StartRoot 2 cubed EndRoot
StartRoot 2 Superscript 5 EndRoot
RootIndex 4 StartRoot 4 cubed EndRoot
StartRoot 4 Superscript 5 EndRoot
Answer:
D
Step-by-step explanation:
A 2-column table with 3 rows. Column 1 is labeled x with entries 2, 4, 5. Column 2 is labeled y with entries 5, 10, 12.5.
Use the information in the table to find the constant of proportionality and write the equation.
The constant of proportionality is
.
The equation that represents this proportional relationship is
.
The constant of proportionality is 2.5.
First, There is a proportional relationship
Two values x and y are said to be in a proportional relationship if y=kx, where x and y are variables and k is a constant.
y = kx
The constant k is the constant of proportionality
As shown that ,
A 2-column table with 3 rows.
Column 1 is labeled x with entries 2, 4, and 5.
Column 2 is labeled y with entries 5, 10, and 12.5.
According to the Above statement, the calculation is as follows:
5/2 = 2.5 , here we get is 2.5
10/ 4 = 2.5 so Here we get 2.5 and so on
Hence, The constant of proportionality is 2.5.
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helppppppp please help help
The y-value of the terminal point of the vector is 3.
How to determine the resulting vector by applying rotation about the origin
In this question we must apply a matricial form of rotation, which is a kind of rigid transformation. This transformation is defined by the following formula:
[tex]\vec A' = \vec T\cdot \vec A[/tex], where [tex]\vec A' , \vec A \in \mathbb{R}_{1 \times 2}[/tex], [tex]\vec T \in \mathbb{R}_{2 \times 2}[/tex]
If we knw that [tex]\vec A = \left[\begin{array}{c}- 4\\3\end{array}\right][/tex] and [tex]\vec T = \left[\begin{array}{cc}-1&0\\0&1\end{array}\right][/tex], then the transformed vector column is:
[tex]\left[\begin{array}{cc}x\\y\end{array}\right] = \left[\begin{array}{cc}-1&0\\0&1\end{array}\right] \cdot \left[\begin{array}{cc}-4\\3\end{array}\right][/tex]
[tex]\left[\begin{array}{cc}x\\y\end{array}\right] = \left[\begin{array}{cc}4\\3\end{array}\right][/tex]
The y-value of the terminal point of the vector is 3.
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The triangles are similar. Find the value of the variable.
Answer:
y = 27
Step-by-step explanation:
The given are two similar triangles.
We can use the following equation to find the variables:
[tex]\frac{y-3}{32} = \frac{18}{24}[/tex]
Cross multiply fractions
32*18 = 24(y-3)
576 = 24y - 72
add 72 to both sides
648 = 24y
divide both sides by 24
27 = y
7/11 = x/9
Round your answer to the nearest tenth.
The solution to the given fraction 7/11 = x/9 to the nearest tenth is 5.7
Fraction7/11 = x/9
cross product7 × 9 = 11 × x
63 = 11x
divide both sides by 11x = 63/11
x = 5.72727272727272
Approximately,
x = 5.7
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A sequence of transformations maps Triangle ABC onto triangle ABC prime prime. The type of transformations that maps triangle ABC onto Triangle prime ABC is a _____. When Triangle prime ABC is reflected across the line x=2 to form triangle triangle prime prime ABC vertex _____ of triangle ABC will have the same coordinates as B prime.
The type of transformations that maps triangle ABC onto Triangle prime ABC is a Reflection across the line y=x ; translation 10 units to the right and 4 units up.
What is the reflection about?Note that: Triangle ABC has vertices at points which are:
A(-6,2), B(-2,6) and C(-4,2).
Therefore, the reflection across the line y=x has the rule of"
(x, y) ---(y, x).
Hence:
A(-6,2) -- A''(2,-6);
B(-2,6)--- B''(6,-2);
C(-4,2)----C''(2,-4).
2. The translation 10 units to the right and 4 units up is:
(x, y)----(x+10,y+4).
Hence
A''(2,-6)----A'(12,-2);
B''(6,-2)----B'(16,2);
C''(2,-4)----C'(12,0).
Therefore, Points A'B'C' are said to be exactly of the vertices of that of triangle A'B'C'.
Hence, The type of transformations that maps triangle ABC onto Triangle prime ABC is a Reflection across the line y=x ; translation 10 units to the right and 4 units up.
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To calculate accurate ____________________ (vital/hospital) statistics rates to represent the entire United States, the quotient is multiplied by an appropriate factor such as 1,000 or 100,000 to represent the larger population.
To calculate accurate vital statistics rates to represent the entire United States, the quotient is multiplied by an appropriate factor such as 1,000 or 100,000 to represent the larger population.
What are vital statistics?The term "vital statistics" refers to the collection of data on live births, deaths, migration, fetal deaths, marriages, and divorces. Civil registration, an administrative system used by governments to record vital events that occur in their populations, is the most prevalent method of gathering information on these events. Efforts to increase the quality of vital statistics will thus be inextricably linked to the growth of countries' civil registration systems. Since the nineteenth century, civil registration has followed the practice of churches keeping such records. To compute accurate vital statistics rates for the full United States, multiply the quotient by a suitable factor, such as 1,000 or 100,000 to represent the greater population.As it is given in the description itself, to compute accurate vital statistics rates for the full United States, multiply the quotient by a suitable factor, such as 1,000 or 100,000 to represent the greater population.
Therefore, to calculate accurate vital statistics rates to represent the entire United States, the quotient is multiplied by an appropriate factor such as 1,000 or 100,000 to represent the larger population.
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If the class sizes in a school from 18 to 24 what is the range?
Answer:
18 students
Step-by-step explanation:
Answer:
the range between 18 and 24 is 6
Step-by-step explanation:
24-18=6
The length of the rectangle is 10.4cm. the perimeter of the rectangle is 28cm. calculate the area of the rectangle.
Answer:
37.44 cm²
Step-by-step explanation:
To find the width, follow these steps.
10.4*2=20.8
28-20.8=7.2
7.2/2=3.6
The width is 3.6.
To find the area, multiply the width and the length together.
10.4*3.6=37.44
The area of the rectangle is 37.44 cm²
Hope this helps!
On a number line, point D is at -6, and point E is at 8. Point F lies between points D and E. If DF: FEis 3: 1, where does point F lie on the
number line?
F is located on the number 4.5 on the number line.
Where does point F lie on the number line?We know that point D is at -6
Point E is at 8.
Point F is between D and E, such that the ratio:
DF:FE is 3:1
So if we divide the distance between D and E in 4 parts, 3 of these parts are DF, and one of these parts is FE.
First, the distance between E and D is:
distance = 8 - (-6) = 14 units.
Now, if we divide that by 4, we get:
14/4 = 3.5
Then we have:
DF = 3*(3.5) = 10.5
This means that F is at 10.5 units to the right of D, then:
F = D + 10.5 = -6 + 10.5 = 4.5
F is located on the number 4.5 on the number line.
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Answer:
4.5 is the answer :D
Step-by-step explanation:
The vertices of a quadrilateral on the coordinate plane are (2, 4), (-4, -2), (-2, 4), and (4, -2). What type of quadrilateral has these vertices
Answer: Isosceles Trapezoid
Step-by-step explanation:
See the graph of the quadrilateral.
May someone please explain to me how exponents can be used to represent fractions between 0 and 1???
The fraction m/n that lies between 0 and 1 is equivalent to the real number m · n⁻¹, where m, n > 0 and m < n.
How can rational numbers between 0 and 1 be represented in terms of exponents?
By algebra, we know that fractions, a kind of rational numbers, are real numbers of the form m/n, where m and n are integers and n ≠ 0.
In addition, the operator "/" means division, an operator derived from the existence of multiplicative inverse and fundamental operation of multiplication in the real field.
Thus, the rational number m/n is equivalent to the number m · n⁻¹. If the rational number is between 0 and 1, then m, n > 0 and m < n.
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Kimo went into a bakery where they sell cookies for $0.75 each and brownies for $1.25 each. Kimo has $15 to spend and must buy no less than 12 cookies and brownies altogether.
a. Define the variables. (4 pts)
b. Write the system of inequalities that could be used to solve the situation. DO NOT SOLVE. (4 pts)
a) The variables are:
x = number of cookies bought.y = number of brownies bought.b)
x + y ≥ 12
x*$0.75 + y*$1.25 ≤ $15
How to write the system of inequalities?a) First we need to define the variables, in this case we have:
x = number of cookies bought.y = number of brownies bought.b) Now we want to write the system, we know that he must buy at least 12 items, then:
x + y ≥ 12
And he can spend, at most, $15, then:
x*$0.75 + y*$1.25 ≤ $15
These two inequalities conform the system of inequalities:
x + y ≥ 12
x*$0.75 + y*$1.25 ≤ $15
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