Rational functions v and w both have a point of discontinuity at x = 7. which equation could represent function w?
The correct option is C.
The formula that could be used to represent a function w is
= w(x)=v(x-7)+7
What is Rational function?A polynomial divided by another polynomial can be used to represent a rational function. Since polynomials are defined everywhere, the set of all numbers excluding the zeros in the denominator constitutes the domain of a rational function.
Example 1. x = f(x) (x - 3). The denominator, x = 3, only contains one zero. When the denominator is zero, rational functions are no longer defined.
According to the given Information:
Rational functions whose point of discontinuity is at x=7.
When a point of discontinuity exists for a rational function,
It occurs when:
q(x) = r(x-a), x=a
In this instance, we are required to notice the following relationship, which is a union of a parent rational function and a vertical translation:[tex]w(x)=v(x-a)+k\\ \forall k \in \mathbb{R}[/tex], (2)
If we are aware of a=7 and k=7 .
The equation that could be used to represent a function w is. w(x)=v(x-7)+7
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I understand that the question you are looking for is:
Rational functions v and w both have a point of discontinuity at x = 7. Which equation could represent function w?
A. w(x)=v(x-7)
B. w(x)=v(x+7)
C. w(x)=v(x-7)+7
D. w(x)=v(x)+7
Please help me with this polynomial based questions
Answer:
Hello,
Step-by-step explanation:
All is in the following picture:
Write an equation to represent the following statement.
51 divided by 3 is k
Solve for k.
Answer:
K = 17
Based on the given conditions, formulate:
51 / 3 = k
Swap the sides : k = 51 / 3
Cross out the common factor: k = 17
Help with this!! Thank you
Answer:
Step-by-step explanation:
1) The equation of circle having center at origin:
x² + y² = r²
Where 'r' is the radius.
diameter = 36
r = 36 ÷ 2 = 18
Equation of circle :
x² + y² = 18²
x² + y² = 324
Option d.
2) Find the discriminant D.
If D > 0, then the quadratic equation has two distinct real roots.
If D= 0, then the quadratic equation has two identical real roots.
If D < 0, then the quadratic equation has no real roots.
D = b² - 4ac
x² - 6x + 9 = 0
a = 1 ; b = -6 ; c = 9
D = (-6)² - 4*1*9
= 36 - 36
D = 0
As D = 0, the quadratic equation has two identical real roots
Option a.
3) The axis of symmetry of a parabola is the vertical line passing through the vertex. It will be middle of the x-intercepts.
X- intercepts are -8 , 2
( -8 + 2 ) ÷ 2 = -6 ÷ 2 = -3
x = - 3
Option d.
please answer these correctly i will mark u brainliest pleaseee.
1) Find the general term of the sequence 5,6,7,8,9,.........
2) Find the midpoint of the line segment A (3,5) B (4,5)
3) Work out and write ur answer in the simplest form :- 3 1/4 + 2 5/6
4) work out the 30th term of 10,13,16,19, .......
5) the ratio of the width to height of a wall is 20cm. what is it's height in meters?
6) Find the mean of 2.1, 4, 6.2, 7, 3.3,
7) Work out and write the answer in the simplest form :- 1 1/2 + 1 5/9
Answer: 1. an = n + 4, 2. ( 3 1/2, 3.5, 5), 3. 6 1/12, 4. 97, 5. 0.2 meters, 6. 4.52, 7. 3 1/18
Step-by-step explanation:
Nani needs to buy 8 cups of fresh pineapple for a fruit cocktail. the table shows the unit prices of pineapple at different stores. if nani only has $4, from which stores could she purchase her pineapple?
Nani could purchase her pineapple from stores A, D, and E.
Given Information
It is given that Nani needs to purchase 8 cups of pineapple.
The unit prices of pineapple at each store is as follows,
Store A : 0.49
Store B : 0.51
Store C : 0.55
Store D : 0.48
Store E : 0.45
Amount that Nani has = $4
Reason Behind Purchasing From Either A, D, or E
Since Nani has amount of $4, she can purchase pineapple only from the stores where the total cost of 8 pineapple cups adds up to less than $4. The purchase of 8 pineapple cups at each store would be given as,
Store A : 0.49(8) = $3.92
Store B : 0.51(8) = $4.08
Store C : 0.55(8) = $4.40
Store D : 0.48(8) = $3.84
Store E : 0.45(8) = $3.60
As it can be seen, Nani can purchase from the store A, D, and E as it falls within her budget of $4.
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The interior angles of a polygon are; (3x + 30), x, 2x, (x + 20) and 3x. find the value of x
Answer: 49
Step-by-step explanation:
This polygon has 5 sides, meaning its interior angles add to [tex]180(5-2)=540^{\circ}[/tex].
[tex]3x+30+x+2x+x+20+3x=540\\\\10x+50=540\\\\10x=490\\\\x=49[/tex]
(‼️‼️I WILL MARK BRAINLIEST PLEASE HELP‼️‼️)Dilate the figure by the scale factor. Then enter
the new coordinates.
K = 5
(-3,-1)
A
(-1,-4) C
B(2,-2)
A' ([?], [ ])
B' ([ ], [ ])
C' ([ ], [ ])
Answer:
A' (-15, -5)
B' (10, -10)
C' (-5, -20)
Answer:
A ' (-15, -5)
B ' (10, -10)
C ' (-5, -20)
Step-by-step explanation:
The scale factor is [tex]K=5[/tex]. This tells us to multiply each coordinate, of each point, by the scale factor (5) to get the dilated points.
Point A is at [tex](-3,-1)[/tex] and moves to [tex]A ' (-15, -5)[/tex] after multiplying the x and y coordinates by 5. The same applies to points B and C as well.
Point B moves from [tex](2,-2)[/tex] to [tex]B' (10,-10)[/tex] because [tex]2*5=10[/tex] and [tex]-2*5=-10[/tex]. This also means that Point C moves from [tex](-1,-4)[/tex] to [tex]C' (-5,-20)[/tex] because [tex]-1*5=-5[/tex] and [tex]-4*5=-20[/tex].
The dilation rule can be written as [tex](x, y)[/tex] → [tex](5x, 5y)[/tex]
As a result of the dilation, triangle A'B'C' has sides that are 5 times longer compared to the corresponding sides of triangle ABC.
2sin^2(x)+sin(2x)=2
please help!!
[tex]2sin {}^{2} (x) + sin(2x) = 2 \\ 2sin {}^{2} (x) + 2sin(x)cos(x) = 2 \\ sin {}^{2} (x) + sin(x)cos(x) - 1 = 0 \\1 - cos {}^{2} (x) + sin(x)cos(x) - 1 = 0 \\ - cos {}^{2} (x) + sin(x)cos(x) = 0[/tex]
[tex]cos(x)( - cos(x) + sin(x)) = 0[/tex]
[tex]cos(x) = 0 \\ x = \frac{\pi}{2} + k\pi \\ \\ sin(x) = cos(x) \\ x = \frac{\pi}{4} + k\pi[/tex]
Help me with this question please
Answer:
x- axis , quadrant 2 , quadrant 3
Step-by-step explanation:
(9.5, 0 ) ← is located on the x- axis
(- 4, 7 ) ← is located in Quadrant II
(- 1, - 8 ) ← is located in Quadrant III
If both cars in Exercise 62 are on one side of the plane and if the angle of depression to one car is 38∘ and that to the other car is 52∘, how far apart are the cars?
The two cars lying on one side of the plane are 50 meters apart.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
let us assume that the height is 100 m. Let d represent the horizontal distance. For depression of 38°, Ф = 90 - 38 = 52°, hence:
tan(52°) = d / 100
d = 128 m
For depression of 52°, Ф = 90 - 52 = 38°, hence:
tan(38°) = d / 100
d = 78 m
Distance apart = 128 - 78 = 50 m.
The two cars lying on one side of the plane are 50 meters apart.
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help me with this pls asap
Answer:
your picture is blank if you can fix it i will be glad to help you
Step-by-step explanation:
Answer:
First option
Step-by-step explanation:
The line corresponds to the f(x).
Hope this helps
POSSIBLE OUTCOMES!!!
A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles.
Use a tree diagram to list all the possible outcomes for tossing a coin and then drawing a marble from the bag.
The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL
How to determine the possible outcomes?The given parameters are:
Coin = Head (H) and Tail (T)
Marble = W, B, B, B, R, R
See attachment for the tree diagram
From the tree diagram, we have the following possible outcomes
WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL
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The table shows your height on a water slide at various time intervals
1. Find the average rate of change in a riders height between 1 and 3 seconds
2. Find the average rate of change in a riders height between 0 and 5 seconds
3. What is another word for rate of change in this situation?
Time(s) Height (ft)
0 120
1 90
2 60
3 30
4 0
5 0
1. The average rate of change in a riders height between 1 and 3 seconds -30 ft/s
2. The average rate of change in a riders height between 0 and 5 seconds -24 ft/s
3. Another word for rate of change in this situation is speed
What is speed?Speed is defined as the rate of change of the distance travelled with time. Mathematically, it can be expressed as:
Speed = distance / time
With the above idea, we can obtain the answers to the question given above.
1. How to determine the rate of change between 1 and 3 secondsChange in height = 30 - 90 = -60 ftChange in time = 3 - 1 = 2 sRate of change =?Rate = Change in height / change in time
Rate = -60 / 2
Rate = -30 ft/s
2. How to determine the rate of change between 0 and 5 secondsChange in height = 0 - 120 = -120 ftChange in time = 5 - 0 = 5 sRate of change =?Rate = Change in height / change in time
Rate = -120 / 5
Rate = -24 ft/s
3. what is another word for rate of change?From the definition of speed given above, we can say that: another word for rate of change is speed
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What is the length of an edge of a cube whose total surface area is equal to 150 square feet?
The length of an edge of a cube is 5 feet.
What is cube?In Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Total surface area of a cube = 6[tex]l^{2}[/tex]
Given that,
Total surface area of a cube = 150 square feet
Total surface area of a cube = 6[tex]l^{2}[/tex]
[tex]\Rightarrow[/tex] 150 = 6[tex]l^{2}[/tex]
[tex]\Rightarrow[/tex] [tex]l^{2}[/tex] = [tex]\frac{150}{6}[/tex]
[tex]\Rightarrow[/tex] [tex]l^{2}[/tex] = 25
[tex]\Rightarrow[/tex] l [tex]=\sqrt{25}[/tex]
[tex]\Rightarrow[/tex] l = 5 feet
Hence, the length of an edge of a cube is 5 feet.
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PLEASE HELP!! This graph shows the bird population of a large lake. Note that the
number of birds at the lake in the month of December is zero. What
does this extreme drop between November and December MOST
likely represent?
Select one:
O a. The beginning of duck hunting season.
O b. A reflection of the migratory nature of the birds at the lake.
O c. An inaccurate collection of data, and so, invalid results.
Od. A reflection of the hibernation patterns of the birds at the
lake.
The extreme drop can be said to most likely represent: b. A reflection of the migratory nature of the birds at the lake.
What is Bird Migration?Bird migration is a natural process which can be described as a the movement of different birds by flight across thousands of kilometers in search of ecological conditions and habitats that favors breeding, feeding, and raising of their young.
Migratory birds have well built physiology and morphology that make them better equip to fly fast and across long distances in search of the best ecological conditions, which is dependent on seasons.
Like in the graph given, like we see that at the beginning of January, number of birds were few in the lake until sudden increase occurred. It can be said that during those period of increase, the ecological conditions favored the survival of the bird until November and December. This extreme drop can be said to most likely represent: b. A reflection of the migratory nature of the birds at the lake.
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determine which two of the three given triangles are similar. Find the scale factor for the pair.
Type the correct answer in each box.
Find the elements of matrix A.
help PLS!!
Answer:
a = 2
b = 11
c = 11
d = -2
Step-by-step explanation:
[tex]\sf \left[\begin{array}{cc}a&b\\c&d \end{array}\right] *\left[\begin{array}{ccc} 22&11&7\\ 6&-9&-15 \end{array}\right] =\left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \end{array}\right][/tex]
[tex]\sf \left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \\ \end{array}\right] =\left[\begin{array}{ccc} 110&-77&-151\\230&139&107 \\ \end{array}\right][/tex]
On comparing to right side, we get,
22a + 6b = 110
Divide the entire equation by 2
11a + 3b = 55 ------------(I)
11a - 9b = -77 -------------(II)
Subtract equation (II) from (I)
11a + 3b = 55
11a - 9b = -77
- + + {Now subtract}
12b = 132
b = 132/12
[tex]\sf \boxed{\bf \ b = 11}[/tex]
Substitute the value of b in eqaution (I)
11a + 3*11 = 55
11a + 33 = 55
11a = 55 - 33
11a = 22
a = 22/11
[tex]\sf \boxed{\bf \ a = 2}[/tex]
22c + 6d = 230
Divide by 2
11c + 3d = 115 -----------------(III)
11c - 9d = -139 ------------------(IV)
Subtract (IV) from (III)
11c + 3d = 115
11c - 9d = 139
- + -
12d = -24
d = -24/12
[tex]\sf \boxed{\bf \ d = -2}[/tex]
Plugin d = - 2 in equation (III)
11c + 3*(-2) = 115
11c - 6 = 115
11c = 115 + 6
11c = 121
c = 121/11
[tex]\sf \boxed{\bf \ c = 11}[/tex]
Kawan buys some protein bars at $0.90 each and bottled water at $0.70 each for a group hike. He buys twice as many bottles of water as protein bars. If he spends $46 in total, how many bottles of water and protein bars does he buy? Let x= the number of protein bars
Answer:
he buts 20 protein bars and 40 water bottles
Step-by-step explanation:
so first u set up an equation like this
46=.90x+.70(2x)
next you multipy
46=.90x+1.4x
Then add
46=2.3x
then divide by 2.3 to solve for x
x=20 so u have 20 protein bars
and 20 times 2 to find the amount of water bottles
Answer:
20 Protein bars and 40 waters.
Step-by-step explanation:
Let x = protein bars and y = waters
y = 2x .9x + .7 y = 46
Looking at the second equation, I would rather not work with decimals, so I will multiple the whole equation through by ten. That now gives m
9x + 7y = 460 Substitute in 2x for y (from my first equation above)
9x + 7(2x) = 460
9x +14x = 460 Combine 9x and 14x
23x = 460 Divide both sides by 23
x = 20 This is the number of protein bars. To find y plug 20 into the first equation above.
y = 2x
y =20(2)
y = 40
Rule 1: Multiply by 2 then add 1 starting from 1.
Rule 2: Divide by 2 then add 4 starting from 40.
I need to make a sequence and I need help :)
PLease dont delete my question :(
Rule 1:
1, 3, 7, 15, 31, 63, 127, 255, 511, 1023 etc
Rule 2:
40, 24, 16, 12, 10, 9, 8.5, 8.25, 8.125, 8.0625 etc
Hope this helps!
x/2+y=4/5. x+y/2=7/10
Answer:
x = 2/5
y = 3/5
Step-by-step explanation:
**Disclaimer** Hi there! I assumed the question to be a system of equations. The following answer is a method for solving a system of equations. Thus, if it is not, please let me know and I will modify my answer.
Given information:
[tex]\frac{x}{2}+y=\frac{4}{5}[/tex]
[tex]x+\frac{y}{2} =\frac{7}{10}[/tex]
Eliminate fractions by multiplying 10 on both sides of the first equation:
[tex]10*\frac{x}{2}+10*y=10*\frac{4}{5}[/tex]
[tex]5x+10y=8[/tex]
Eliminate fractions by multiplying 10 on both sides of the second equation:
[tex]10*x+10*\frac{y}{2} =10*\frac{7}{10}[/tex]
[tex]10x+5y=7[/tex]
Current system:
[tex]5x+10y=8[/tex]
[tex]10x+5y=7[/tex]
Multiply the second equation by 2:
[tex]5x+10y=8[/tex]
[tex]20x+10y=14[/tex]
Subtract the first equation from the second equation:
[tex](20x+10y)-(5x+10y)=14-8[/tex]
[tex]20x+10y-5x-10y=6[/tex]
[tex](10y-10y)+20x-5x=6[/tex]
[tex]0+15x=6[/tex]
[tex]\boxed{x=\frac{2}{5} }[/tex]
Substitute the x value back to one of the equations to get the y value:
[tex]x+\frac{y}{2} =\frac{7}{10}[/tex]
[tex](\frac{2}{5}) +\frac{y}{2} =\frac{7}{10}[/tex]
[tex](\frac{2}{5}) +\frac{y}{2}-\frac{2}{5} =\frac{7}{10}-\frac{2}{5}[/tex]
[tex]\frac{y}{2} =\frac{3}{10}[/tex]
[tex]\frac{y}{2}*2 =\frac{3}{10}*2[/tex]
[tex]\boxed{y=\frac{3}{5} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The answer is x = 2/5, y = 3/5 or (2/5, 3/5)
First, in order to avoid fractional values during calculation, multiply both equations by 10 to simplify.
10 (x/2 + y) = 10 (4/5) ⇒ 5x + 10y = 810 (x + y/2) = 10 (7/10) ⇒ 10x + 5y = 7Multiply the 1st equation by 10 and 2nd equation by 5.
3. 10 (5x + 10y) = 10 (8) ⇒ 50x + 100y = 80
4. 5 (10x + 5y) = 5 (7) ⇒ 50x + 25y = 35
Subtract : 3rd equation - 4th equation
50x + 100y - 50x - 25y = 80 - 3575y = 45y = 3/5Now, substitute for x in the 1st equation to find y.
x/2 + 3/5 = 4/5x/2 = 1/5x = 2/5Select the correct answer from each drop-down menu.
Consider the function f(x) = 3x + 1 and the graph of the function g(x) shown below.
A coordinate plane linear graph function shows a line intersecting Y-axis at minus 5 and X-axis at 1.5.
The graph g(x) is the graph of f(x) translated
units
, and g(x) =
.
there are two correct options:
A translation of 6 units down: g(x) = f(x) - 6A translation of 2 units to the right: g(x) = f(x - 2).How to relate the function g(x) to the function f(x)?
We know that:
f(x) = 3x + 1
Now, if we look at the graph of f(x), we can see that the y-intercept is at y = -5, and for each increase in one unit in the x-variable, there is an increase of 3 units in the y-variable.
Then the equation of g(x) is:
g(x) = 3*x - 5
Then g(x) is a translation downwards of 6 units, such that:
g(x) = f(x) - 6 = (3x + 1) - 6 = 3x - 5
And we also could write it as a horizontal translation of 2 units to the right:
g(x) = f(x - 2) = 3*(x - 2) + 1 = 3*x - 3*2 + 1 = 3x - 5
So there are two correct options:
A translation of 6 units down: g(x) = f(x) - 6A translation of 2 units to the right: g(x) = f(x - 2).If you want to learn more about translations:
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Please help its confusing meeeeee
Answer:
p = 21.4 cm
∠P = 44°
Step-by-step explanation:
Apply the Pythagorean Theorem to solve for the length of p.
p² + 21² = 30²p² = 900 - 441p² = 459p = √459[tex]\fbox {p = 21.4 cm}[/tex]Now, take the inverse sine function to find angle P :
sin⁻¹ (opposite side / hypotenuse)sin⁻¹ (21/30)sin⁻¹ (0.7)[tex]\boxed {44^{o}}[/tex] (approximately)Answer:
a) 21.4 cm
b) 45.6°
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationships between trig functions and sides of a right triangle. Here, two relevant function are ...
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
b) Angle PThe hypotenuse of the triangle, and the side adjacent to angle P are given, so we have ...
cos(P) = (21 cm)/(30 cm)
The angle value can be found using the inverse cosine function:
P = arccos(21/30)
P ≈ 45.6°
a) Side pNow, we know angle P and the side adjacent to it. We want to find the measure of side p, which is opposite the angle. This can be done using either the sine function or the tangent function. Here, we choose to use the tangent function.
tan(P) = p/21
p = 21×tan(P) = 21·tan(45.573°)
p ≈ 21.4 . . . . cm
__
Additional comment
In the attached, part of the calculator keypad is shown so you can see that the inverse cosine function is the 2ND function of the Cos key. The calculator mode is set to DEG (lower left of display) so that angles are in units appropriate to this problem.
Of course, you can always use the Pythagorean theorem to find the length of side p. More calculations are involved, so we used trig functions instead. Note that the angle P must be found first using the approach here, and its value must be retained with enough significant digits to ensure accuracy in the 'p' calculation.
The relationship between distance travelled, d, and time, t, can be represented by a linear relation. In 56 minutes, a person
runs 6 miles. In 104 minutes, the same person runs 10 miles. An equation that represents this linear relation is?
Answer:
[tex]d=\frac{t}{12}+\frac{4}{3}[/tex]
Step-by-step explanation:
The average rate of change is (10-6)/(104-56) = 1/12.
So, the equation is of the form d = t/12 + c for some constant c.
Substituting in d=6 and t=56 gives that c=4/3.
So, the equation is
[tex]d=\frac{t}{12}+\frac{4}{3}[/tex]
Hi! I’ve tried at this question many times and still do not understand why the answer isn’t B but A. Please explain as best as you can! Thanks! (The question is below in the picture)
Answer:
Graph B is not linear.
Step-by-step explanation:
This question asks for a linear relationship. Graph B is not linear.
Please look closely at the attached images where I gave graphed these points.
I hope this helps. Please let me know if you have questions.
Jenny made $120 for 8 hours of work. How much would jenny make for 40 hours of work? Use a proportion to show your work in the space provided.
Answer:
$600
Step-by-step explanation:
For 8 hours she makes $120
For 1 hour she makes $120÷8 = $15
For 40 hours she makes $15 × 40 = $600
Our final answer is $600
Hope this helped and have a good day
In a carnival drawing, a green ticket wins $1, a yellow ticket wins $5, and a blue ticket wins $10. There are 100 green tickets, 25 yellow tickets and 5 blue tickets. In simplest form, what are the odds in favor of winning $5 or more?
A. 1:4
B. 1:5
C. 1:25
D. 3:10
The odds in favor of winning $5 or more is 3 : 13
What are the odds in favor of winning $5 or more?The odds of winning $5 or more can be determined by finding the ratio of the total value of tickets that have a value of $5 or greater to the total value of tickets.
Total number of the tickets that have a value of $5 or more = 25 + 5 = 30
Total number of ticket = 25 + 5 + 100 = 130
Ratio : 30 : 130
3 ; 13
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prove that if r is a matrix in echelon form, then a basis for row(R) consists of the nonzero rows of R
Let [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex] be the nonzero rows of [tex]$R$[/tex] starting from the 1st row to the [tex]k[/tex]th row.
Step 1: We want to show that
R(R)= span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]
For any vector [tex]v $$\in \mathcal{R}(R)$$[/tex], We may write
v= [tex]$$c_{1} \boldsymbol{r}_{1}+c_{2} \boldsymbol{r}_{2}+\cdots+c_{k} \boldsymbol{r}_{k}+c_{k+1} \mathbf{0}+\cdots+c_{m} \mathbf{0}$$[/tex]
Then v= [tex]$$c_{1} r_{1}+c_{2} r_{2}+\cdots+c_{k} r_{k}$$[/tex]
So [tex]v[/tex] belongs to span{ [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]}
Thus R(R)[tex]\leq[/tex] Span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]
But trivially,
span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]≤ span{[tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex], 0, . . . , 0} = R(R),
span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]=R(R)
Step 2: We want to show that [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]are linearly independent. Suppose otherwise,
then we can write
[tex]$$c_{1} \boldsymbol{r}_{i_{1}}+\cdots+c_{\ell} \boldsymbol{r}_{i_{\ell}}=\mathbf{0}$$[/tex]
From Steps 1 and 2, we have proven that the nonzero rows of R form a basis for the row space.
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If a wall is built in a room at a 36 degree angle. The angle formed in the other room by the wall is 144 degrees. What kind of angles are formed when they are added together
They form supplementary angles when they are added together.
Reason for Being Called Supplementary Angles
It is given that the angle made by the wall in one room is 36° and the angle formed by the same wall in the other room is 144°.
This implies that,
∠1 = 36°
∠2 = 144°
∠1 and ∠2 are adjacent angles and,
∠1 + ∠2 = 36° + 144°
⇒ ∠1 + ∠2 = 180°
Hence, these two adjacent angles make a straight-line angle. Hence, they are supplementary angles.
What are supplementary angles?
Two angles that form a straight line angle, that is, angle equal to 180°, when they are added together are said to be a pair of supplementary angles.
Learn more about supplementary angles here:
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bob baked 60 cookies and brownies. the number of cookies he baked was 4 less than 3 times the number of brownies he baked. how many cookies did bob bake
Answer:
Cookies = 44
Step-by-step explanation:
universal U=60
let the number of cookies be C,
n(C)=(3*b)-4
and the number of brownies be b,
n(b)=?
n(buc)=60
b+c=60
then, c=60-b
substitute for c=60-b.
60-b=3b-4
60+4=3b+b
64=4b
b=16
c=60-b
c= 60-16
c=44