Answer:
i think you have to multiply
Step-by-step explanation:
Lydia graphed ΔXYZ at the coordinates X (0, −4), Y (2, −3), and Z (2, −6). She thinks ΔXYZ is a right triangle. Is Lydia's assertion correct?
Check the picture below.
so hmmm if Lydia is correct, then there's one angle in the triangle that is 90°, hmmm well, looking at the picture, we can pretty much forget about angle Z or Y, they're both acute, hmm how about angle X? is it 90°?
well, if angle X is indeed a right-angle, the lines XZ and XY are perpendicular, but are they? if that's so then the slopes of XZ and XY are negative reciprocal of each other, let's check
[tex]X(\stackrel{x_1}{0}~,~\stackrel{y_1}{-4})\qquad Z(\stackrel{x_2}{2}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-6}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{0}}} \implies \cfrac{-6 +4}{2 +0}\implies -1[/tex]
now, the negative reciprocal of that will be
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{-1\implies \cfrac{-1}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-1}\implies 1}}[/tex]
well, let's see if XY has a slope is 1 then
[tex]X(\stackrel{x_1}{0}~,~\stackrel{y_1}{-4})\qquad Y(\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{0}}} \implies \cfrac{-3 +4}{2 +0}\implies \cfrac{1}{2}[/tex]
OMG!!! Lydia needs to go get a nice Latte with cinnamon and to recheck her triangle.
answer this fully! i need to know what x equals
answer this fully! i need to know what x equals
X equal minus 0.5
1 ounce granulated sugar is equivalent to _____ tablespoons.
Answer:
2
Step-by-step explanation:
find the length for point a to point
b
The equation y - 2 = 3(x + 1) is in point-slope
form. Which is the slope-intercept form?
0
y = 3x + 1
y = 3x - 3
y = 3x + 5
Answer:
y=3x+5
Step-by-step explanation:
See attached image
Answer:
D.) y = 3x + 5
Step-by-step explanation:
The general structure for an equation in slope-intercept form is:
y = mx + b
In this form, "m" is the slope and "b" is the y-intercept.
To convert the given equation into slope-intercept form, you need to do some expanding and rearranging.
y - 2 = 3(x + 1) <----- Given equation
y - 2 = 3x + 3 <----- Multiply 3 by every term in the parentheses
y = 3x + 5 <----- Add 2 to both sides
(5√3-√27)^3
how do you prove that this is an integer?
Keys:
[tex]\left(a\cdot \:b\right)^n=a^nb^n[/tex]Step-by-step explanation:
[tex]\left(5\sqrt{3}-\sqrt{27}\right)^3\\\5\sqrt{3}-\sqrt{27}^3=\left(2\sqrt{3}\right)^3\\= 2\sqrt{3}\\\left(2\sqrt{3}\right)^3=2^3\left(\sqrt{3}\right)^3\\=2^3\left(\sqrt{3}\right)^3\\2^3=8\\=8\left(\sqrt{3}\right)^3\\=8\cdot \:3\sqrt{3}\\8\cdot \:3=24\\=24\sqrt{3}[/tex]
Answer:
It is not an integer.
Step-by-step explanation:
[tex](5\sqrt{3} -\sqrt{27} )^3\\\\=(\sqrt{3} *(5-3))^3\\\\=8*3*\sqrt{3} \\\\=24\sqrt{3} \\[/tex]
Solve below functions word problem ASAP
The revenue function when the assumed values and parameters are used is F(x) = (60 + 8x)(250 - 30x)
The assumed valuesTicket price = $60 per ticketPeople = 250Increase in price = 8Decrease in people = 30The revenue functionLet the number of people be x, and the revenue function be F(x).
Using the assumed values, the revenue function is:
F(x) = (60 + 8x)(250 - 30x)
The maximum fundsWe have:
F(x) = (60 + 8x)(250 - 30x)
Expand
F(x) = 15000 - 1800x + 2000x - 240x²
Differentiate the function
F'(x) = -1800 + 2000 - 480x
Evaluate
F'(x) = 200 - 480x
Set to 0
200 - 480x = 0
This gives
480x = 200
Divide both sides by 480
x = 0.42
Substitute x = 0.42 in F(x)
F(x) = (60 + 8 * 0.42)(300 - 30* 0.42)
Evaluate
F(x) = 18210
Hence, the maximum revenue is $18210, at a rate of $0.42 per person.
Would they raise $5000?We start by setting F(x) to 5000.
So, we have:
15000 - 1800x + 2000x - 240x² = 5000
Evaluate the like terms
10000 + 200x - 240x² = 0
Using a graphing tool, we have:
x = 6.89
Hence, they would reach their goal at a rate of $6.89 per ticket.
The cost function
We have:
People = x
Cost per person = 20
So, the cost function is:
C(x) = 20x
The profit functionProfit is calculated using:
P(x) = F(x) - C(x)
So, we have:
P(x) = 15000 - 1800x + 2000x - 240x² - 20x
Evaluate
P(x) = 15000 + 180x - 240x²
The break even priceThis is the point where P(x) = 0.
So, we have:
15000 + 180x - 240x² = 0
Using a graphing tool, we have:
x = 8.29
Hence, the break even price is $8.29
Read more about profit, cost and revenue at:
https://brainly.com/question/25623677
#SPJ1
Volume of a triangular prism with numbers 3 4 5 6
Answer:
Step-by-step explanation:
V=14h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4aBase sidebBase sidecBase sidehHeight
Express cos K as a fraction in simplest terms.
9
M
15
Answer: cos K=
K
Submit Answer
Answer:
4/5
Step-by-step explanation:
In a right triangle such as this one
cos (angle) = adjacent leg / hypotenuse
cos(k) = KL / 15
You will need to find the leg length KL using Pythagorean Theorem
15^2 = 9^2 + (KL)^2 KL = 12
then cos k = 12/15 = 4/5
f(x) = x^2. What is g(x)?
Answer:
-x²-2
Step-by-step explanation:
x² = the curve faces upwards
but
-x² the curve faces downwards.
also
the downward curve touches -2 on the y axis.
therefore gx = -x²-2
a scientist notes that the number of bacteria in a colony is 50.3 hours later, she notes that the number of bacteria has increased to 80. if this rate of growth continues, how much more time will it take for the number of bacteria to reach 1119?
Answer:
16.8 hours
Step-by-step explanation:
An exponential population increase can be modeled by the function ...
p(t) = a·b^(t/p)
where 'a' is the initial value (at t=0), b is the multiplier in time period p.
__
setupThe colony increased by a factor of b = 80/50 = 1.6 in p = 3 hours. Since we want to find the additional time to reach a population of 1119, the initial population we're working with is 80, not 50.
p(t) = 80·1.6^(t/3)
1119 = 80·1.6^(t/3)
__
solutionSolving this for t, we find ...
1119/80 = 1.6^(t/3) . . . . . . . . . . . . divide by 80
log(1119/80) = (t/3)log(1.6) . . . . . take logarithms
t = 3·log(1119/80)/log(1.6) . . . . . divide by the coefficient of t
t ≈ 16.8 . . . . hours
It will take about 16.8 more hours for the population to increase from 80 to 1119.
what is three and 2 fourths and minus two and three fourths
Answer:
The answer is 0.75
Hope this helps!
Given f(x) = -x + 5, find f(-3).
Answer:
[tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]
Given f(x)=-x+5, find f(-3).
[tex]\rule{50}{1}\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]
We have the function
[tex]\longmapsto\sf{f(x)=-x+5}[/tex]
We need to find
[tex]\longmapsto\sf{f(-3)=}[/tex]
What we need to do:-Replace x with -3:-[tex]\longmapsto\sf{f(x)=-(-3)+5}[/tex]
Simplifying,
[tex]\longmapsto\sf{f(x)=3+5}[/tex]
(which is the exact same thing as 5-3)
Henceforth, We conclude that the answer is
[tex]\longmapsto\sf{f(-3)=8}[/tex]
Good luck with your studies. [tex]\ddot\smile[/tex]#TogetherWeGoFar ~
[tex]\rule{300}{1}[/tex]
Hey there!
Find f(-3) :
Answer :f(-3) = 8 ✅
Explanation :f(x) = -x + 5
>> Substitute -3 for x in f(x) :
f(-3) = -(-3) + 5
f(-3) = 3 + 5
f(-3) = 8
Therefore, your answer is f(-3) = 8
Similar question :
↣ https://brainly.com/question/20922457
Help. I wil give credit
Write an equation and solve the problems below.
1) Angle 1 and angle 2 are complementary angles. If angle 1 measures (3x + 2), what is the measure of angle 2?
2) Angle A and angle b are supplementary angles. Angle A measures (2m – 10) degrees and angle b measures (m + 25) degrees. Find the measure of angle A and angle b.
3) Three angles are supplementary angles. If one angle measures 25 degrees, the second angle measures m + 15. The third angle measures 2m degrees. What is the value of m?
Answer:
Step-by-step explanation:
1) Angle 1 and angle 2 are complementary angles. If angle 1 measures (3x + 2), what is the measure of angle 2? 3x+2 + y = 90
2) Angle A and angle b are supplementary angles. Angle A measures (2m – 10) degrees and angle b measures (m + 25) degrees. Find the measure of angle A and angle b.
3) Three angles are supplementary angles. If one angle measures 25 degrees, the second angle measures m + 15. The third angle measures 2m degrees. What is the value of m?
How do I write 3x3x3x3 in Standard Form
Answer:
3 to the fourth power, which equals 81.
Step-by-step explanation:
Do these two statements contradict
each other?
aurt is scalene
and aurt is obtuse.
yes
no
11. 7b + (4b - 6)
12. 8d2 + (6d2 - 4d)
13. (5x2 + 4) + (-3x2 - 4)
14. [-4x + (10 - 5x)] + 5x
15. 8 + [5 + (6 + x)]
16.
+3c - 7d
- 2c + 5d
- c + 8d
+4c - 6d
17.
3a + 8b - 5c
6a - 9b + 4c
-7a + b + 2c
18.
+6p - 3q + z
- 3p + 2q - z
- p + 00q___
Answer: 11. [tex]11b-6[/tex]
12. [tex]14d^2-4d[/tex]
13. [tex]2x^2[/tex]
14. [tex]-4x+10[/tex]
15. [tex]19+x[/tex]
16. [tex]4c[/tex] (all together, the problems aren't entered correctly)
17. Nothing further can be done with these equations. Please check the expression entered.
18. [tex]2p-q[/tex] (All together, the problems aren't entered correctly)
Step-by-step explanation:
11.[tex]\quad \:a+\left(b+c\right)=a+b+c[/tex]
[tex]7b+\left(4b-6\right)=7b+4b-6[/tex]
[tex]=7b+4b-6[/tex]
[tex]7b+4b=11b[/tex]
[tex]=11b-6[/tex]
12.[tex]2d*(7d-2)=14d^2-4d[/tex]
[tex](8 * (d^2)) + ((2*3d^2) - 4d)[/tex]
[tex]2^3d^2 + (6d^2 - 4d)[/tex]
[tex]14d^2 - 4d = 2d * (7d - 2)[/tex]
13.[tex]((5*(x^2))+4)+((0-3x^2)-4)[/tex]
[tex](5x^2 + 4) + (-3x^2 - 4)[/tex]
[tex]=2x^2[/tex]
14.[tex]-4x+10-5x+5x[/tex]
[tex]-4x-5x+5x+10[/tex]
[tex]-4x-5x+5x=-4x[/tex]
[tex]=-4x+10[/tex]
15.[tex]8+5+6+x[/tex]
[tex]\:8+5+6=19[/tex]
[tex]=19+x[/tex]
Answer: 2a + c is the answer for #17 and #18 is 2p.
17.
3a + 8b - 5c
6a - 9b + 4c
-7a + b + 2c =
2a + c
18.
+6p - 3q + z
- 3p + 2q - z
- p + q =
2p
Step-by-step explanation:
Problem 9
Leon drives a long distance to attend a family reunion. At 12:00 PM, his gas tank is completely filled with
12 gallons of gas. Leon's car uses gas at a constant rate, and after two hours of driving, Leon notices that
his car used five gallons of gas.
Leon will stop to get gas when his tank is one fourth of the way full. If Leon's car continues to use gas at
the same constant rate and Leon makes no other stops on his trip, at what time will Leon stop to get gas?
Be sure to include AM or PM in your answer.
Answer:
3:36PM
Step-by-step explanation:
Leon starts at 12PM with 12 gallons of gas, and after 2 hours he has used 5 gallons of gas. This means that every 2 hours he uses 5 gallons of gas.
Next we will find at what point Leon will stop to get gas. Since he will stop when the tank is at [tex]\frac{1}{4}[/tex] capacity, we can use the equation:
[tex]\frac{1}{4} * 12 = \boxed{3}[/tex]
This shows [tex]\frac{1}{4}[/tex] of his tank's capacity ([tex]12[/tex]) is equal to [tex]3[/tex] gallons. This means he will stop for gas when [tex]3[/tex] gallons are remaining.
Now we need to find how many gallons of gas he uses, but as a unit rate. (This will allow us to find what time Leon will stop to get gas.) To find the unit rate, we will need to find how many gallons of gas he uses per hour.
[tex]\frac{\mbox{5 gallons}}{\mbox{2 hours}} = \frac{\mbox{2.5 gallons}}{\mbox{1 hours}}[/tex]
This is a simple proportion, and now we know he uses [tex]2.5[/tex] gallons of gas per hour.
Now we can how many hours of gas Leon has left.
He has [tex]7[/tex] gallons of gas left at 2PM, so we can divide to find how many hours left of gas he has.
[tex]\frac{7-3}{2.5} = 1.6[/tex]
The [tex]7-3[/tex] is because Leon doesn't stop when his tank is empty, he stops [tex]3[/tex] gallons earlier. We are dividing by [tex]2.5[/tex] because that is how much gas he uses per hour, meaning the result of this division ([tex]1.6[/tex]) is how many hours he has left.
Now we can solve for what time Leon will stop to get gas.
12PM + [tex]2[/tex] hours of driving + the remaining [tex]1.6[/tex] hours = 3:36PM
([tex]1.6[/tex] hours is equal to 1 hour and 36 minutes)
Therefore, Leon will stop for gas at 3:36PM
Solve the equation by completing the square.
0 = 4x2 − 64x + 192
A.
x = -12, -4
B.
x = 4, 12
C.
x = -8, 24
D.
x = -24, 8
Answer:
A
Step-by-step explanation:
Given the following f(x) = 3x² + 7x³ + 8x^4; g(x) = -3x + 12x² - 5x³; and h(x) = 12x +
6
Complete the following: (f.h)(x)
96x5 +132x4+78x³ + 18x²
96x +132x4+78x³ + 18x²
96x5 + 122x + 78x³ + 18x²
96x5 +132x4+84x³ + 18x²
The value of the function (f.h)(x) is 96x⁵ + 132x⁴ + 78x³ + 18x²
How to solve function?f(x) = 3x² + 4x³ + 8x⁴
g(x) = -3x + 12x² - 5x³
h(x) = 12x + 6
Therefore,
(f.h)(x) = f(x).h(x)
Hence,
f(x).h(x) = (3x² + 7x³ + 8x⁴)(12x + 6)
f(x).h(x) = 36x³ + 18x² + 84x⁴ + 42x³ + 96x⁵ + 48x⁴
(f.h)(x) = 96x⁵ + 84x⁴ + 48x⁴ + 36x³ + 42x³ + 18x²
(f.h)(x) = 96x⁵ + 132x⁴ + 78x³ + 18x²
learn more on function here: https://brainly.com/question/7783704
#SPJ1
Perform the indicated operation
Answer:
Step-by-step explanation:
(sqrt2-sqrt3+sqrt6)(sqrt6-sqrt3)
Answer: [tex]-6\sqrt{2}+2\sqrt{3}-\sqrt{6}+9[/tex]
=======================================================
Explanation
Let:
[tex]x = \sqrt{2}\\\\y = \sqrt{6}-\sqrt{3}\\\\[/tex]
We can then say:
[tex](\sqrt{2}-\sqrt{3}+\sqrt{6})(\sqrt{6}-\sqrt{3})\\\\(\sqrt{2}+\sqrt{6}-\sqrt{3})(\sqrt{6}-\sqrt{3})\\\\(x+y)(y)\\\\xy+y^2\\\\2\sqrt{3}-\sqrt{6}+9-6\sqrt{2}\\\\-6\sqrt{2}+2\sqrt{3}-\sqrt{6}+9\\\\[/tex]
Check out the screenshot below for the scratch work on how I computed the [tex]xy[/tex] and [tex]y^2[/tex] terms.
In circle B below, diameter RT, radius BE, and chord RE are drawn.
If m2TRE = 15° and BE = 9, then the area of sector EBR is
The area of sector EBR in the given diagram attached below is: 33.75π units².
What is the Area of a Sector?Area = θ/360º × πr²
Given the following:
m∠TRE = 15° BE = 9Measure of arc TE = 2(m∠TRE) = 2(15) [inscribed angle theorem]
Measure of arc TE = 30°
Arc RE = 180 - arc TE = 180 - 30 [semicircle]
Arc RE = 150°
m∠EBR = Arc RE = 150°
Area of sector EBR = m∠EBR/360 × π(BE²)
Area of sector EBR = 150/360 × π(9²)
Area of sector EBR = 33.75π units²
Learn more about the area of sector on:
https://brainly.com/question/22972014
#SPJ1
First photo question: Given this net of a right circular cone. Find the volume and surface area of the cone.
Second photo question: Given this right circular cone. Find the volume and surface area of the cone. Make a sketch of this net of this cone including the measurements of the radii of the circle and sector and give the central angle of the sector.
Problem 1
Ignore the smaller circle for now. We'll be focusing on the portion on the right.
It's a partial circle with central angle theta = 150 degrees and radius r = 24 inches. The 24 inches also happens to be the slant height of the cone when we form the 3D figure.
Let's compute the arc length based on those inputs.
L = arc length
L = (theta/360)*2*pi*r
L = (150/360)*2*pi*24
L = 20pi
This is the distance along the green curve of this portion.
Now imagine we rolled up that partial circle on the right. We'd form the curved slanted roof of the cone. The green curve wraps around to help match up with the circular base. The 20pi calculated earlier is the circumference of this circular base. Use this to find r.
C = 2pi*r
20pi = 2pi*r
r = (20pi)/(2pi)
r = 10
-------------------------
So far we found that this cone has:
radius = r = 10slant height = s = 24Now compute the height (h) perpendicular to the base
[tex]h^2+r^2 = s^2\\\\h = \sqrt{s^2-r^2}\\\\h = \sqrt{24^2-10^2}\\\\h = \sqrt{476}[/tex]
-------------------------
We can now compute the volume
[tex]V = (1/3)*\pi*r^2*h\\\\V = (1/3)*\pi*10^2\sqrt{476}\\\\V \approx 2284.7153\\\\[/tex]
The units of which are cubic inches.
The surface area is of this cone is:
[tex]SA = \pi*r*s + \pi*r^2\\\\SA = \pi*10*24 + \pi*10^2\\\\SA \approx 1068.1415\\\\[/tex]
The units are in square inches.
For each case, I used the calculator's stored value of pi to get the most accuracy possible. Round the decimal values however you need to, or however your teacher instructs.
-------------------------
Answers:
Volume = 2284.7153 cubic inches approximatelySurface Area = 1068.1415 square inches approximately============================================================
Problem 2
Use the pythagorean theorem to find the slant height
[tex]h^2+r^2 = s^2\\\\s = \sqrt{h^2+r^2}\\\\s = \sqrt{15^2+8^2}\\\\s = \sqrt{289}\\\\s = 17\\\\[/tex]
This slant height will act as the radius of the partial circle that results when forming the net of the unrolled cone.
The process used in the previous problem was to use the slant height and central angle to find the circumference of the base.
We'll follow that process in reverse to use the circumference and slant height to find the central angle.
But first, we need to find the circumference of the base.
C = 2*pi*r
C = 2*pi*8
C = 16pi
This is the arc length similar to the green arc shown in the previous problem (the figure on the right side of that diagram)
This means we'll plug in L = 16pi and r = 17 (not to be confused with the previous radius of 8 inches) to determine theta
L = (theta/360)*2*pi*r
16pi = (theta/360)*2*pi*17
16pi = theta*(34pi/360)
theta = 16pi*(360/(34pi))
theta = 169.4118 degrees approximately
This is the central angle of the unrolled net. The diagram is basically the same as the previous drawing, where we have a circle on the left to represent the base of the cone. The other portion forms the roof of the cone.
-------------------------
Let's compute the volume (V) and surface area (SA)
[tex]V = (1/3)*\pi*r^2*h\\\\V = (1/3)*\pi*8^2*15\\\\V \approx 1005.3096\\\\[/tex]
and,
[tex]SA = \pi*r*s + \pi*r^2\\\\SA = \pi*8*17 + \pi*8^2\\\\SA \approx 628.3185[/tex]
-------------------------
Answers:
Diagram: Copy the diagram shown in problem 1. However, you'll change the "24 inches" to "17 inches". Also, the central angle is roughly 169.4118 degrees.Volume = 1005.3096 cubic inches approximatelySurface Area = 628.3185 square inches approximatelyThe temperature inside of a storage building in degrees Fahrenheit can be modeled using the equation f(t)=-8.3cos((pi/5)•t+63.7 where t is the number of hours since midnight
The temperature at midnight is 55.4 degrees Fahrenheit
How to determine the temperature at midnight?The information that completes the question is "At what temperature is the building at midnight?"
The function is given as:
f(t) = -8.3cos(π/5)t + 63.7
At midnight, t = 0.
So, we have:
f(0) = -8.3cos(π/5) * 0 + 63.7
Evaluate the product
f(0) = -8.3cos(0) + 63.7
Evaluate the expression
f(0) = 55.4
Hence, the temperature at midnight is 55.4 degrees Fahrenheit
Read more about functions at:
https://brainly.com/question/4025726
#SPJ1
Help me out please….
Answer:
There two images below,
one is the final product and one of how it was reflected
If you draw all of the diagonals from one vertex of a regular hexagon, how
many triangles do you make?
If you draw all of the diagonals from one vertex of a regular hexagon we make 5 triangles. This is further explained below.
What is a hexagon?Generally, the hexagon is simply defined as the hexagon is a polygon with six sides. to be considered a hexagon, the form must have six sides, all of which must be closed.
In conclusion, We get five triangles if we draw the diagonals of a regular hexagon starting at a single vertex.
Read more about Trigonometry
https://brainly.com/question/8120556
#SPJ1
What is the approximate length of minor arc JH? Round to the nearest tenth of a centimeter.
3.5 cm
6.9 cm
21.6 cm
46.8 cm
The length of the arc is 3.5 cm
How to determine the arc length?The attached image completes the question
The given parameters are:
Diameter, d = 16Central angle, x = 25The length of the arc is calculated as:
[tex]L = \frac{x}{360} * \pi d[/tex]
So, we have:
[tex]L = \frac{25}{360} * 3.14 * 16[/tex]
Evaluate the product
L = 3.5cm
Hence, the length of the arc is 3.5 cm
Read more about arc lengths at:
https://brainly.com/question/2005046
#SPJ1
Answer:3.5
Step-by-step explanation:
i can figure out
12 is greater than four times a number g
Answer:
"Find g to make this statement true".
12 > 4 • g
The answer of the given expression is 1 & 2.
Concept:Firstly, convert word form into numerical expression.Then Simplify the given expression.How to solve the given question?Convert word form into numerical expression.Thus, the answer of the given expression is 1 & 2.
Learn more about expressions here:
https://brainly.com/question/723406
#SPJ2
Suppose f(x)=6x-2 and g(x)=2x+4. Find each of the following functions.
a. (f+g)(x)
b. (f-g)(x)
Answer:
a) (f + g)(x) = 8x + 2
b) (f - g)(x) = 4x - 6
Step-by-step explanation:
Given:
f(x) = 6x - 2g(x) = 2x + 4a) Find (f + g)(x):
a. (f + g)(x) = f(x) + g(x)
⇒ (f + g)(x) = (6x - 2) + (2x + 4)
⇒ (f + g)(x) = 6x + 2x - 2 + 4
⇒ (f + g)(x) = 8x + 2
b) Find (f - g)(x):
b. (f - g)(x) = f(x) - g(x)
⇒ (f - g)(x) = (6x - 2) - (2x + 4)
⇒ (f - g)(x) = 6x - 2x - 2 - 4
⇒ (f - g)(x) = 4x - 6
Learn more about adding and subtracting functions here:
brainly.com/question/16287318
brainly.com/question/27797089