The set (x1,x2)+(y1,y2)=(x1-x2, y1+y2) is not a vector space.
A set is a vector space if it satisfy all the addition operation axiom and scalar multiplication axiom.
Addition operation:
Commutativity -
(x1, x2) + (y1, y2) equals (x1 - x2, y1 + y2) equals (y1, y2) + (x1, x2)
Associativity -
(x1, x2) plus ((y1, y2) plus (z1, z2)) = (x1, x2) + (z1 + y1, z2 + y2) = (x1+ y1 + z1, x2 + y2 + z2) =
((x1, x2) + (y1, y2)) + (z1, z2)
Zero element -
(0, 0) → (x1, x2) + (0, 0) = (x1, x2)
Inverse element -
(x1, x2) adding (-x1, -x2) = (0, 0)
Scalar multiplication:
Compatibility -
a(b (x, y)) = a(bx, 0) = (abx, 0) = b(ax, 0) = b(a(x, y))
Identity element -
1(x, y) = (x, 0) ≠ (x, y) [Identity element doesn’t exist for this operation.)
Distributivity law -
a((x1, x2) + (y1, y2)) = a(x1 + y1, x2 + y2) = (a(x1 + y1), 0) = a(x1, x2) + a(y1, y2)
Distributivity law -
(a + b)(x, y) = ((a + b)x, 0) = (ax, 0) + (bx, 0) = a(x, y) + b(x, y)
The scalar multiplication postulate is not fulfilled in this space (this operation does not have the identity element). It is therefore not a vector space.
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Someone do this please
Answer: 102 degrees
Step-by-step explanation:
The remote angle theorem is that two remote angles are equivalent to the exterior angle. Both 51 degrees are remote angles, and angle 4 is the exterior.
51 + 51 = Angle 4
Angle 4 = 102 degrees
Find the area of the convex polygon with vertices (0,5), (-1,2), (4,4), (-3,-4) and (2,0).
The area of the convex polygon is 21.5 square units
How to determine the area of the convex polygon?The vertices are given as:
(0,5), (-1,2), (4,4), (-3,-4) and (2,0)
The area is then calculated as:
A = 0.5 * |x1y2 - x2y1 +x2y3 - x3y2 + ....... |
So, we have:
A = 0.5 * |-1 * 5 - 2 * 0 + 0 * 4 - 5 * 4 + 4 * 0 - 4 * 2 +2 * -4 - 0 * -3 - 3 * 2 + 4 * 1|
Evaluate
A = 0.5 * |-43|
Remove the absolute bracket
A = 0.5 * 43
This gives
A = 21.5
Hence, the area of the convex polygon is 21.5 square units
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Solve for this equation:
x(x+3)(x+3)=0
Answer:
x^3+6x^2+9x
if you are trying to find the original function
if not, and you are trying to find the zeros is
x=-3
x=0
Step-by-step explanation:
multiply x(x+3)
x^2+3x
then multiply that by x+3 and that should give you the answer
Answer:
x = 0 or x = -3 or x = -3
Step-by-step explanation:
set up factors as:
x = 0
x + 3 = 0
x + 3 = 0
the first will remain as x = 0 while the others become x = -3 once subtracted
i hope this helped!
Find the coefficient of t to the 4th power in the expansion of (-9t-9) to the 7th power select one: a. -25,515 b. -100,442,349 c. -167,403, 915 d. -4,782, 969
The coefficient of t to the 4th power in the given expansion is -167403915.
Option (c) is the correct answer.
What is an expansion?An expansion of a product of sums uses the fact that multiplication distributes across addition to represent it as a sum of products. A polynomial expression can be expanded by repeatedly substituting equivalent sum of products for subexpressions that multiply two other subexpressions, at least one of which is an addition, up until the expression becomes a sum of (repeated) products. Simplifications like grouping similar terms or canceling terms may also be used during the expansion.
Given expansion=[tex](-9t-9)^{7}[/tex]
Coefficient of the 4th power of t in the expansion,
=[tex]_{7} {C} _{7-4} (-9t)^{4}(-9)^{7-4}[/tex]
=[tex]_{7}C_{3}(-9)^{4}t^{4}(-9)^{3}[/tex]
=[tex]_{7}C_{3}(-9)^{7}t^{4}[/tex]
=[tex]35t^{4}(-9)^{7} \\[/tex]
=[tex]35t^{4}(4782969)[/tex]
= -167403915[tex]t^{4}[/tex]
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100 POINTS!!! PLEASE HELP ASAP EXPERTS! PLEASE I'M BEGGING!!
The function H(t) = −16t2 + 64t + 12 shows the height H(t), in feet, of a baseball after t seconds. A second baseball moves in the air along a path represented by g(t) = 10 + 10.4t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 1 through 4 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)
Part B: Explain what the solution from Part A means in the context of the problem. (4 points)
Answer:
A)
[tex]\begin{array}{|c|c|c|}\cline{1-3} t & H(t) & g(t)\\\cline{1-3} 1 & 60 & 20.4\\\cline{1-3} 2 & 76 & 30.8\\\cline{1-3} 3 & 60 & 41.2\\\cline{1-3} 4 & 12 & 51.6\\\cline{1-3} \end{array}[/tex]
Between 3 and 4 seconds.
B) The baseballs will collide between 3 and 4 seconds.
Step-by-step explanation:
Given functions:
[tex]H(t)=-16t^2+64t+12[/tex]
[tex]g(t)=10+10.4t[/tex]
Part ASubstitute the values of t = 1, 2, 3 and 4 into the two functions:
[tex]H(1)=-16(1)^2+64(1)+12=60[/tex]
[tex]H(2)=-16(2)^2+64(2)+12=76[/tex]
[tex]H(3)=-16(3)^2+64(3)+12=60[/tex]
[tex]H(4)=-16(4)^2+64(4)+12=12[/tex]
[tex]g(1)=10+10.4(1)=20.4[/tex]
[tex]g(2)=10+10.4(2)=30.8[/tex]
[tex]g(3)=10+10.4(3)=41.2[/tex]
[tex]g(4)=10+10.4(4)=51.6[/tex]
Create a table with the found values:
[tex]\begin{array}{|c|c|c|}\cline{1-3} t & H(t) & g(t)\\\cline{1-3} 1 & 60 & 20.4\\\cline{1-3} 2 & 76 & 30.8\\\cline{1-3} 3 & 60 & 41.2\\\cline{1-3} 4 & 12 & 51.6\\\cline{1-3} \end{array}[/tex]
The solution to H(t) = g(t) is between 3 and 4 seconds as:
When t = 3, H(t) > g(t)
When t = 4, H(t) < g(t)
To prove this, equate the equations and solve for t:
[tex]\implies -16t^2+64t+12=10+10.4t[/tex]
[tex]\implies -16t^2+53.6t+2=0[/tex]
Using the Quadratic Formula to solve for t:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]\implies t=\dfrac{-53.6 \pm \sqrt{53.6^2-4(-16)(2)} }{2(-16)}[/tex]
[tex]\implies t=\dfrac{53.6 \pm \sqrt{3000.96}}{32}[/tex]
[tex]\implies t=3.39, -0.04\:\:(\sf 2\:d.p.)[/tex]
As time is positive, t = 3.39 s (which is between 3 and 4 seconds).
Part BWhen the two baseballs are at the same height they will collide.
Therefore, the baseballs will collide between 3 and 4 seconds (when t = 3.39 s).
HALP URGENT PLS im dum
x =x=x, equals
^\circ
∘
Answer:
x = 55°
Step-by-step explanation:
That square box indicates a right angle.
A right angle is 90°.
We know that angle x and the 35° angle are making up this 90° angle together.
So, the equation to show what this ship looks like is the following:
[tex]x+35=90[/tex]
This is a simple equation, that if we solve, we get:
[tex]x=55[/tex]
So, x is 55°.
Considering the angle of the ray, it is found that the value of x is of x = 55º.
What is the angle of the ray?The ray has an angle of 180º. It is composed by:
Angle x.An angle of 35º.An angle of 90º.Hence:
x + 35 + 90 = 180
x = 180 - 125
x = 55º.
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All the students in a science class complete a 15-point extra-credit assignment to raise their test scores the new test score is 15 points more than the original score let x = original score let y = new score ehich equation represents this situation?
The equation that represents the situation is,
y = x + 15
Given Information
It is given that the students complete a 15-point extra-credit assignment in order to raise their test scores.
The new test score is 15 more than the old test score.
We have to find an equation for this situation. A mathematical equation is a formula that uses the equals sign to connect two expressions in order to express their equality.
Forming Equation
Original Score = x
New Score = y ................... (1)
Thus, after the test, the score is raised by 15 points.
⇒ New score = x + 15 .................... (2)
The following equation can be deduced from (1) and (2)
y = x + 15
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3. A gardener uses 2 packages of lettuce seeds for 3 garden rows, each 5 feet long. How many packages of seeds does the gardener need to plant 45 feet of lettuce rows? Use the table to help.
Seeds (pkg) 2,4
Lettuce (rows) 3, 6
A 27
B 16
C 6
D 80
I need this with explanation please:(
Answer:
C) 6
Step-by-step explanation:
3 garden rows = 3*5 = 15 feet
we know we need 2 packages per each 15 feet
45/15=3 so 3 15 in 45, we just multiply 3 and 2 to get 6 packages
Question 12 of 20
Subtract.
(2x²+5)-(4x-3)
OA. 2x²-4x+2
OB. -2x² +8
OC. 2x2²-4x+8
OD. -2x²+2
Answer:
C
Step-by-step explanation:
Distribute the negative, (2x^2 + 5) + (-4x+3)
Add like terms, 2x^2 - 4x +(5+3)
2x^2-4x+8
The sum of a number and its reciprocal is 122/11. Find the
number.
O -11
09
O 11
Answer:
11
Step-by-step explanation:
if the some of a number is an restrocal is 122 upon 11 find the integers value of x let the number bees two values of x i e 11 and 1 upon 11 are possible hence required in future value of x is 11
x - 3y = 9, complete the ordered pair (12, ).
Answer:
(12,1)
Step-by-step explanation:
We know that ordered pairs are in the format of (x,y).
This means in that (12, __) 12 is our x coordinate. Plugging 12 into the equation as x we get:
[tex]12-3y=9\\-3y=9-12\\-3y=-3\\y=1[/tex]
Therefore our answer is (12,1) as we plug y back into our coordinate (x,y).
Answer:
(12,1)
Step-by-step explanation:
In the ordered pair, x=12
plug 12 back in the equation
12-3y=9
-3y=-3
3y=3
y=1
Write an absolute value inequality for each of the following. Then graph the
solution set on a number line.
all numbers less than 7and greater than -7
An absolute value inequality for "all numbers less than 7 and greater than -7" is given by |x| < 7.
How to write an absolute value inequality?Based on the information provided, we can logically deduce that the statement describes an intersection of set because the word "and" was used.
This ultimately implies that, we would use the less than (<) symbol to write an absolute value inequality for the given statement:
|x| < 7
Therefore, this can be translated as follows:
-7 < x < 7 or x < 7 and x > -7.
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Find the odds against hitting the ball if you have made 3 out of 19 attempts
We conclude that the odds of hitting the ball are 0.158
How to find the odds?
The odds (like the probability) are given by the quotient between the number of attempts in which you hit the ball and the total number of attempts.
Here we know that out of 19 attempts, in 3 you hit the ball. Then the odds of hitting the ball are:
P = 3/19 = 0.158
We conclude that the odds of hitting the ball are 0.158
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The revenue earned from tourists in Florida was:
2018 – $4 381 million
2019 – $3 607 million
What is the percentage decrease in revenue from tourists to Florida?
Select one answer
A) 17.67%
B) 21.46%
C) 82.33%
D) 121.46%
which of the following is equivalent to the logarithmic equation below?
Answer:
A
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex] , then
[tex]log_{2}[/tex] 8 = 3 ⇒ 2³ = 8
Answer:
A
Step-by-step explanation:
loga(b)=x
a^x=b
since the answer to log2(8)=3
a^3=8
b=8
a=2
so 2^3=8
I hope this helped!
There are 86,400, frames of animation in 1 hour of anime.
How many frames are there per second?
There are 3,600, seconds in 1 hour.
Answer:
There are 24 frames of animation in 1 second of anime. Step-by-step explanation: There are 60 seconds in 1 minute, and 60 minutes in 1 hour. 60×60=3600, so there are 3600 seconds in 1 hour.Since 3600 seconds and 1 hour is the same, there are 86400 frames of animation in 3600 seconds of anime. To find out how many frames are in one second of anime, divide 86400 by 3600.86400 ÷ 3600 = 24There are 24 frames of animation in 1 second of anime.
20pts and brainliest !! please help quick
Answer:
y = -1.3x + 10
Step-by-step explanation:
x_avg = (-2 + -1 + 1 + 2 + 3 + 4)/6 = 1.166666...
y-avg = (21 + 8.6 + 1 + 1 + 5 + 14.3) = 8.48333...
x y x-x_avg y-y_avg (x-x+avg)² (x-x_avg)(y-y_avg)
-2 21 -3.1666 12.51666 10.02777 -39.63611
-1 8.6 -2.1666 0.11666 4.69444 -0.252777
1 1 -0.1666 -7.48333 0.02777 1.247222
2 1 0.83333 -7.48333 0.69444 -6.236111
3 5 1.8333 -3.48333 3.3611111 -6.386111
4 14.3 2.8333 5.81666 8.02777 16.480555
sum of (x-x_avg)(y-y_avg) = -34.858
sum of (x+x_avg)² = 26.8333
slope = [(x-x_avg)(y-y_avg)/[(x+x_avg)²]
slope = -34.858/26.8333
slope = -1.29907
y = mx + b
y_avg = m(x_avg) + b
8.48333 = -1.3(1.1666) + b
b = 9.9989
y = -1.3x + 10
The formula d=1/2n+26 relates the nozzles pressure n (in pounds per square inch) of a free hose and the maximum horizontal distance the water reaches d (in feet). How much pressure is needed to reach a fire 50 feet away?
The pounds of pressure needed to reach a fire 50 feet away is 48 pounds
Formulad = 1/2n + 26
where
n = nozzle pressure in pounds per square feetd = distance the water reachesIf d = 50 feet
d = 1/2n + 26
50 = 1/2n + 26
50 - 26 = 1/2n
24 = 1/2n
n = 24 ÷ 1/2
n = 48 pounds
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A machine in a candy company creates 9,328 pieces of candy each hour. if a box holds 98 pieces of candy, how many boxes can be filled in one hour?
Answer:
Step-by-step explanation:
9,328 and you would divide that by 98 and the answer would be 95.18367347 boxes
Use a triple integral to find the volume of the wedge bounded by the parabolic cylinder yx and the planes zy and z0.
The volume of wedge is 4/15 by use of Triple integral.
According to the statement
we have to find the volume of wedge which is bounded by the parabolic cylinder.
So, because of the given shape of z=√y
the plane y=0 is a boundary, in addition to the given x = 0, z = 0.
so we are in the first octant for all of this. and the further constraint is the plane x + y = 1
Triple integrals are 3 successive integrations, used to calculate a volume, or to integrate in a 4th dimension, over 3 other independent dimensions.
but as a triple integral you would write:
∫x=0 ∫y=0∫z=0 dz dy dx
And after put the values in it and solving it we get the
[−4/15(1−x)^5/2] at x=0
Then after that the answer will become 4/15.
So, The volume of wedge is 4/15 by use of Triple integral.
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Juan bought a sweater for $15.95 and two shirts for $9.00 each. how much did juan spend on clothes?
Answer:
Step-by-step explanation:
Well first you have:
$15.95 for one sweater
$9.00 each for two shirts
You would double the amount $9.00 which would be:
9 + 9 = 18 or Multiply 9 x 2 = 18
So this would total to 15 + 18 = $33
mel cuts a slice of cake if her slice is 4/15 of the cake, what is the central angle of her slice, please give answer in degrees
Answer:
Below in bold.
Step-by-step explanation:
That would be 4/15 * 360 as there are 360 degrees in a circle
= 96 degrees.
Explain why the standard deviation of a set of data is always given as a positive number, but data points can have a negative overall standard deviation.
The reason why the standard deviation of a set of data is always given as a positive number is because the individual values are squared.
What is the standard deviation?The term standard deviation is used to express how much numbers depart from the mean value. Now we know that the standard deviation for each of the data points is the square of the difference between the score and the mean.
Given that the value that is extracted from each data point is squared, the standard deviation of a set of data is always given as a positive number, but data points can have a negative overall standard deviation.
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The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as
1
L-10log where lo-10-12
and is the least intense sound a human ear can hear. What is the approximate loudness
of a dinner conversation with a sound intensity of 10-7?
[tex]\\ \rm\dashrightarrow B=10log\dfrac{I}{I_o}[/tex]
[tex]\\ \rm\dashrightarrow B=10\log\dfrac{10^{-7}}{10^{-12}}[/tex]
[tex]\\ \rm\dashrightarrow B=10log10^5[/tex]
[tex]\\ \rm\dashrightarrow B=10\times 5log10[/tex]
[tex]\\ \rm\dashrightarrow B=10(5)[/tex]
[tex]\\ \rm\dashrightarrow B=50dB[/tex]
Answer:
50 Db
Step-by-step explanation:
Given:
[tex]L=10 \log \dfrac{I}{I_0}[/tex]
[tex]I_0=10^{-12}[/tex]
where:
L is the loudness measured in decibels (Db)I is the sound intensity measured in w/m²To find the approximate loudness of a dinner conversation with a sound intensity of [tex]I=10^{-7}[/tex], substitute the values of I and I₀ into the given equation and solve for L:
[tex]\implies L=10 \log \dfrac{10^{-7}}{10^{-12}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies L=10 \log 10^{-7-(-12)[/tex]
[tex]\implies L=10 \log 10^5[/tex]
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies L=5 \cdot 10 \log 10[/tex]
[tex]\implies L=50 \log 10[/tex]
As the given log does not have a specified base, assume the base is 10.
[tex]\implies L=50 \log_{10} 10[/tex]
[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]
[tex]\implies L=50 (1)[/tex]
[tex]\implies L=50\:\:\sf Db[/tex]
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Are the triangles similar? If so, state the similarity and the postulate or theorem that justifies your answer.
The triangles are similar by SAS principle.
How to know similar triangles?Similar triangles have the same shape but may have different sizes.
In similar triangles, corresponding sides are always in the same ratio.
The corresponding angles are congruent.
Therefore, using SAS ratio,
6 / 8 = 8 × 3 / 32
6 / 8 = 24 / 32 = 3 / 4
Therefore, the corresponding sides are a ratio of each other.
Therefore, the triangles are similar by SAS principles because the two triangles have two pairs of sides in the same ratio and the included angles are also equal
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A package weighs P pounds, P being a whole number. To ship this package by express costs $1.65 for the first five pounds and 12c for each additional pound. The total shipping cost was $3.45. How many pounds did the package weight
The total weight of the package was 20 pounds, given the total shipping cost was $3.45, using the total cost function, C(P) = 1.65 + 0.12(P - 5), where P is the weight of the package in pounds.
In the question, we are given that a package weighs P pounds, P being a whole number. To ship this package by express costs $1.65 for the first five pounds and 12c for each additional pound. The total shipping cost was $3.45.
We are asked for the package weight in pounds.
First, we design a general cost function.
The cost is given to be $1.65 for the first 5 pounds, and 12c for each additional pound.
The weight of the package is given to be P pounds.
We assume the total cost function to be C(P), a function of the weight of the package, P pounds.
Thus, the total cost function can be shown as the sum of $1.65 and 12c or $0.12 multiplied with (P - 5), as it is the cost for additional pounds after 5 pounds.
Thus, the total cost function, C(P) = 1.65 + 0.12(P - 5).
Now, we are given that the total shipping cost was $3.45.
Thus, to find the weight of the package, we equate the total cost function, C(P) to 3.45, to get:
1.65 + 0.12(P - 5) = 3.45,
or, 1.65 + 0.12P - 0.6 = 3.45,
or, 0.12P + 1.05 = 3.45,
or, 0.12P = 3.45 - 1.05,
or, 0.12P = 2.40,
or, P = 2.40/0.12 = 20.
Thus, the total weight of the package was 20 pounds, given the total shipping cost was $3.45, using the total cost function, C(P) = 1.65 + 0.12(P - 5), where P is the weight of the package in pounds.
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Two fishing boats leave the same dock at the same time. One boat heads northeast and is travelling at a speed of 15 km/h while the other is travelling northwest at 18 km/h. After 45 minutes, the boats are 14.0 km apart. Assuming that both boats are travelling in straight paths, what is the angle between their paths to the nearest degree?
The boat speeds of 15 km/h and 18 km/h, directions, and the time of travel of 45 minutes gives the angle between their paths as approximately 68°.
How can the angle between the paths of the boats be found?The given parameters are;
Direction of the first boat = Northeast
Speed of the first boat = 15 km/h
Direction of the second boat = Northwest
Speed of the second boat = 18 km/h
Distance between the boats after 45 minutes = 14.0 km.
45 minutes = 0.75 × 1 hour
Distance traveled by the first boat in 45 minutes, d1, is therefore;
d1 = 15 km/h × 0.75 hr = 11.25 km
For the second boat, we have;
d2 = 18 km/h × 0.75 hr = 13.5 km
Using cosine rule, we have;
14² = 11.25² + 13.5² - 2 × 11.25 × 13.5 × cos(A)
Where A is the angle between the paths of the two boats.
Which gives;
[tex]cos(A) = \frac{361}{972} [/tex]
[tex] A= \mathbf{ arccos\left(\frac{361}{972} \right) }\approx 68^\circ [/tex]
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Sofa co is selling sofas with a 33% discount off the original price to reduce its stock. Calculate the discounted price of a sofa originally selling for £999.00. Please show your working.
Jagrit is looking at two computer repair stores.
Store 1: Data-Fix
The total cost charged by Data-Fix is represented by the graph
as shown.
a) Write an equation to model the relation of total cost, C, and
number of hours, n as shown in the graph.
b) One of the points on the graph is (3, 60). Explain the
meaning of this point, in the context of this scenario.
Store 2: Comput-Repair
It charges a fixed cost of $10 plus $15 per hour for repair
services.
c) Write an equation to model the relation of total cost, C, and
number of hours, n, in Comput-Repair.
d) On the grid provided, graph the line that describes the fee structure for Compu-Repair.
e) What are the coordinates of the point of intersection?
f) What does it mean in this scenario?
g) Based on the point of intersection, how would you advise Jagrit when trying to choose between the two
computer repair stores? Fully explain your answer supported by the information from the graph.
PLEASE I DON'T HAVE TIME
See below for the solution of each question
The equation of the modelThe points are given as:
(3,60) and (5, 80)
The equation is calculated as:
[tex]C(n) = \frac{C_2 -C_1}{n_2 -n_1} * (n - n_1) + C_1[/tex]
This gives
[tex]C(n) = \frac{80- 60}{5-3} * (n - 3) + 60[/tex]
Evaluate the quotient
C(n) = 10 * (n - 3) + 60
Expand
C(n) = 10n - 30 + 60
Evaluate
C(n) = 10n + 30
Hence, the relation of total cost, C, and number of hours, n is C(n) = 10n + 30
Explain the points on (3, 60)The point (3, 60) means he paid $60 for 3 hours
The equation of the model for Comput-RepairHere, we have:
Fixed = $10
Hourly rate = $15
The equation is calculated as:
C(n) = Fixed + Rate * Number of hours
This gives
C(n) = 10 + 15n
Hence, the relation of total cost, C, and number of hours, n is C(n) = 10 + 15n
The graph of the fee structure for Compu-RepairThe equation is represented as:
C(n) = 10 + 15n
See attachment for the graph
The coordinates of the point of intersectionThis is the point where the two lines intersect.
From the graph, we have the point of intersection to be:
(n, C(n)) = (4, 70)
The meaning in this scenarioThis means that the charges for Comput-Repair and Data-Fix are the same after 4 hours
Advice JargitBased on the point of intersection, it is best that Jargit uses Compu-Repair because they have a lesser hourly rate
Read more about linear functions at:
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Can someone help me please
Answer:
D. (4,0) and (-4,0)
C. there is one discontinuity at x=3
Step-by-step explanation:
Roots can be found by setting f(x)=0:
f(x)=(x^2-16)/(x^2-2x-3)
0=(x^2-16)/(x^2-2x-3), multiply both sides by x^2-2x-3 to get rid of the denominator
0=x^2-16, use difference of squares to factor it
0=(x+4)(x-4)
x=4,-4
Therefore the roots are (4,0) and (-4,0)
Discontinuities are when f(x) is undefined, and f(x) is undefined when something is divided by 0
Set the denominator equal to 0:
0=x^2-6x+9, use the form a^2 - 2ab + b^2 to factor
0=(x-3)^2
x=3
Therefore, there is a discontinuity at x=3