Given:
The two functions are
[tex]f(x)=3x+1[/tex]
[tex]g(x)=x^2-6[/tex]
To find:
The function (f+g)(x).
Solution:
We know that,
[tex](f+g)(x)=f(x)+g(x)[/tex]
Putting the values of given functions, we get
[tex](f+g)(x)=3x+1+x^2-6[/tex]
[tex](f+g)(x)=x^2+3x+(1-6)[/tex]
[tex](f+g)(x)=x^2+3x-5[/tex]
Therefore, the required function is [tex](f+g)(x)=x^2+3x-5[/tex].
Find the 18h term of the arithmetic sequence whose common difference is d=4 and whose first term is a, =3.
Answer:
the 18th term is 71
Step-by-step explanation:
The general form for any term "n" in an arithmetic sequence is:
a(n) = a1 + (n-1) * d
where "d" is the common difference.
So, in our case we have:
a(n) = 3 + (n-1) *4
Therefore, the 18th term will be:
a(18) = 3 + (18 - 1) 4 = 3 + 17 * 4 = 71
Please show work :) thanks for the help.
Answer:
-3f
0
f1
Step-by-step explanation:
(x = -3) f x -3 -3f
(x = 0) f x 0 = 0
x = 1) f x 1) f1
write in exponential notation (-3)^6/ (-3)
Answer:
-3⁵
Step-by-step explanation:
3⁶ / -3 = -3⁶ * -3⁻¹ = -3⁶⁻¹ = -3⁵
Answer:
(-3)⁶/(-3) = {(-3)×(-3)×(-3)×(-3)×(-3)×(-3)}/(-3) = (-3)⁵
-3⁵ is the right answer.On Monday Sylvia spent 5/12 of a day driving to her cousins house. On Friday she spent the same amount of time driving home. What fraction of day did Sylvia spent driving to her cousin’s house and back? Explain
Answer:
10
Step-by-step explanation:
Which quadrants are (-4,5) in
Answer:
Quadrant 2
Step-by-step explanation:
Take a look at the picture I added it should help you on futures questions like this :)
Find the number that makes the ratio equivalent to 12:1.
?:6
The TV you bought was $900 and the sales tax was 10%, what was the total cost of the TV.
A line includes the points (8,5) and (9, – 5). What is its equation in point-slope form?
Answer:
Step-by-step explanation:
slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]=\frac{-5-5}{9-8}\\\\=\frac{-10}{1}\\\\=-10\\[/tex]
Point-slope form:
y - y1 = m(x - x1)
y - 5 = -10(x - 8)
which inequality is the solution to 20+2
Answer:
is there supposed to be answer choices?
Step-by-step explanation:
Answer:
2.11
Step-by-step explanation:
In order to factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).
The number of times that each prime divides the original integer becomes its exponent in the final result.
In our example,
Prime number to the power of equals .
Prime number to the power of equals .
Find 9079 + 1232 + 9786.
Kyle wants to wrap the box in wrapping paper.
A rectangular prism with a length of 18 inches, width of 6 inches, and height of 3 inches.
What is the minimum amount of paper needed to cover the entire box?
180 inches squared
324 inches squared
360 inches squared
648 inches squared
Answer: 360 in. squared
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
I did it and got it right
Michael drove from home to work at an average speed of 50 mph. His return trip home took 30 minutes longer because he could only drive at 40 mph. Find the distance from his home to his work. A. [3 pts) Define variables to represent the unknowns and setup the necessary equations to answer the question. B. [4 pts) Algebraically solve the equation you created and express your final answer using a complete sentence and appropriate units. (You will not receive full credit if a trial and error method is used in place of an algebraic method.)
Answer:
100 miles
Step-by-step explanation:
Given :
To work :
speed = 50mph
Let time taken = x
From work :
speed = 40mph
30 minutes = 30/60 = 0.5
Time taken = x + 0.5
Distance from home to work :
Distance = speed * time
To work distance = from work distance
This can be algebraically expressed as :
50 * x = 40(x + 0.5)
50x = 40x + 20
50x - 40x = 20
10x = 20
x = 20/10
x = 2
Hence,
Distance = 50 * 2 = 100
The the distance from home to work = 100 miles
The distance from Michael home to work is 100 miles
SpeedSpeed is the ratio of the total distance travelled to the total time taken. It is given by:
Speed = distance / time
Let d represent the distance from Michael home to work. Hence:
50 = d/tt = d / 50He took 30 minutes (0.5 hours) longer when driving at 40 mph, hence:
40 = d/(t + 0.5)t = (d - 20)/40d/50 = (d - 20) / 40
40d = 50d - 1000
10d = 1000
d = 100 miles
The distance from Michael home to work is 100 miles
Find out more on speed at: https://brainly.com/question/4931057
help plz
can someone simplify 3 to the power of 2 times 3 to the power of 3
Answer:
(9)(27) also 243
Step-by-step explanation:
So, 3^2=9, and 3^3=27, so (3^2)(3^3) is equal to (9)(27) or 243
Suppose that 65\ee, percent of the 310{,}000310,000310, comma, 000 citizens in a county are registered to vote. A not-for-profit organization takes an SRS of 100100100 of these citizens and finds that 67\gg, percent of those sampled are registered to vote. The organization plans on taking repeated samples like this. What are the mean and standard deviation of the sampling distribution of the proportion of citizens who are registered to vote
Answer:
mean= 0.65
standard deviation=[tex]\sqrt{\frac{0.65(0.35)}{100}[/tex]
Step-by-step explanation:
The mean of the sampling distribution is 0.65 and the standard deviation is approximately 0.004779.
What is the standard deviation?The standard deviation mathematical and statistical analysis tool used to explain the diversity of treatments or values around the Mean is the standard deviation, which is also known as the square root of variance.
The mean of the sampling distribution of the proportion of citizens who are registered to vote is equal to the proportion of all citizens who are registered to vote, which is 65% = 0.65.
The standard deviation of the sampling distribution is equal to the standard error of the proportion, which can be calculated as follows:
standard error = √((65% × 35%) / 100)
= √((0.65 × 0.35) / 100)
= √(0.0227 / 100)
= √(0.0000227)
= 0.004779
Therefore, the standard deviation is approximately 0.004779.
Learn more about the standard deviation here:
brainly.com/question/14747159
#SPJ5
One lap around the lake is 710 mile.
Dasha runs 9 laps around the lake.
Use the drop-down menus to complete the equation.
100 points if u help
The answer is 87.12
Just check it once
Answer:
87.92
that is the answer
3.14(4^2+12)
this is how it looks in normal form without a and b
4^2 is going to be 16
16+12= 28
3.14 times 28= 87.92
Step-by-step explanation:
Plz answer correctly
Answer:
B) -1,-4,-7,-10,........
The first five terms
-1,-4,-7,-10,........
Step-by-step explanation:
Explanation:-
Given that the explicit rule
[tex]a_{n} = -3n +2[/tex]
Put n=1
⇒ a₁ = -3(1) +2
a₁ = -1
Put n=2
⇒ a₂ = -3(2)+2
a₂ = -6+2
a₂ = -4
Put n=3
a₃ = -3(3)+2
a₃ = -9+2
a₃ = -7
Put n=4
a₄ = -3(4)+2
a₄ = -12+2
a₄ =-10
The first five terms
-1,-4,-7,-10,........
PLEASE HELP ME!!!! 20 POINTS!!!!!!!
What is the correct expanded form and value of 4/5?
A. 4/5+4/5+4/5=12/5
B.4/5•4/5•4/5=64/125
C. 4+4+4+4/5=12/5.
D. 5/4•5/4•5/4=125/64
Help me with my math **50 pts** I mark brainliest**
Answer:
2)
[tex]2x + 6x + 8 = 32[/tex]
collect like terms
[tex]8x + 8 = 32[/tex]
move the constant to the right hand side and change its sign.
[tex]8x = 32 - 8[/tex]
Subtract the numbers
[tex]8x = 24[/tex]
Divide both sides of the equation by 8
[tex]x = 3[/tex]
PLEASE HELP I WILL MAKE YOU BRAINLIEST!!!!! A rectangular prism has a volume of 198 cm³. A rectangular pyramid has the same height as the rectangular prism and a base that is congruent to the base of the rectangular prism.
What is the relationship between the volume of the rectangular prism and the rectangular pyramid?
(A) The volume of a rectangular pyramid is 2 times the volume of a rectangular prism. The volume of the rectangular pyramid is 396 cm3.
(B) The volume of a rectangular pyramid is 13 the volume of a rectangular prism. The volume of the rectangular pyramid is 66 cm3.
(C) The volume of a rectangular pyramid is 3 times the volume of a rectangular prism. The volume of the rectangular pyramid is 594 cm3.
(D) The volume of a rectangular pyramid is 12 the volume of a rectangular prism. The volume of the rectangular pyramid is 99 cm3.
Answer:
(B) The volume of a rectangular pyramid is 1/3 the volume of a rectangular prism. The volume of the rectangular pyramid is 66 cm3.
Step-by-step explanation:
Volume of a rectangular prism:
The volume of a rectangular prism is given by:
[tex]V_R = A_{b}*h[/tex]
In which [tex]A_b[/tex] is the base area and h is the height.
Volume of a pyramid:
[tex]V_P = \frac{A_{b}*h}{3}[/tex]
Relation:
From this, given the same base and the same height, the volume of the pyramid will be a third of the rectangular prism.
A rectangular prism has a volume of 198 cm³
So the volume of the pyramid is 1/3 of this, that is, 198/3 = 66 cubic centimers.
The correct answer is given by option B.
Two similar triangles have a scale factor of 3:5. Determine whether the
following statement about the triangles is true or false.
The ratio of their perimeters is 3:5
Answer:
That is statement is true
Choose a random number between 1 and 25. What is the probability that it is an even number
Answer:
6/25
Step-by-step explanation:
its a probability out of all the odd numbers such as 1,3,5,7,9,11,13,15,17,19,21,23,25
Find the area of the trapezoid.
1 1/2cm
4 cm
3 1/2 cm
9x + 1x =
Need answer asap
toby has already cycled 6 kilometers this year, plus he plans to cycle 14 kilometers during each trip to work. after 3 trips to work, how many kilometers will toby have cycled?
Answer:
48 kilometers
Step-by-step explanation:
If Toby has traveled to work 3 times, and each time he traveled 14 kilometers, to find out how many kilometers he's traveled total, all you have to do is multiply 14 x 3, which equals 42. To find out how many kilometers he's traveled in all this year, just add the amount of kilometers he has already traveled. (42+6)
What is the remainder of 96÷7
Answer:
13 reminder 7.
Step-by-step explanation:
i’m confused on this- can someone help me?
Answer: great adventure theme park is more expensive
Step-by-step explanation:
7.13 g =
cg what is the answer
Answer: 713 cg
Step-by-step explanation:
1 g = 100 cg
----------------------------------------------------------
Given
7.13 g = ? cg
Solve
7.13 × 100 = 713 cg
Hope this helps!! :)
Please let me know if you have any questions
A cell phone company charges $40 per month plus a $35 activation fee.Write an expression for the total cost for m months.
40m+35=
Step-by-step explanation:
I'm not sure but I think it is this
40m+35=
Is (4, 2) a solution to the equation y = x2 − 7x?
Answer:
not rlly
Step-by-step explanation:
you need more information to solve that type of equation
Answer: NO
Step-by-step explanation:
Given
y=x²-7x
Substitute the [solution] into the equation
y=x²-7x
2=(4)²-7(4)
2=16-28
2=-12
2≠-12
Therefore, (4, 2) is not a solution
Hope this helps!! :)
Please let me know if you have any questions