If f(n) = 4n + 7 and g(n) = 2n + 3, find (g - f)(n).2(n-4)4- 2n-2n - 42n + 4
Answers
The question provides two functions:
\(\begin{gathered} f(n)=4n+7 \\ g(n)=2n+3 \end{gathered}\)We are then told to find (g - f)(n).
Using the Operation of functions we can solve this problem.
\((g-f)(n)=g(n)-f(n)\)Since we know what g(n) and f(n) are, we can find (g - f)(n).
This is done below:
\(\begin{gathered} (g-f)(n)=g(n)-f(n) \\ g(n)=2n+3 \\ f(n)=4n+7 \\ \\ \therefore(g-f)(n)=g(n)-f(n)=(2n+3)-(4n+7) \\ (g-f)(n)=2n+3-4n-7 \\ \\ \text{Collect like terms} \\ \\ (g-f)(n)=2n-4n-7+3 \\ \therefore(g-f)(n)=-2n-4 \\ \\ \end{gathered}\)Therefore, the final answer is:
-2n - 4
Related Questions
An eagle flew for 2 hours at 105 miles per hour, and then it
flew for 4 hours at 115 miles per hour. How far did the eagle
miles
Answers
Answer:
670
Step-by-step explanation:
2×105=210
4×115=460
460+210=670
Which shows the most reasonable way to estimate 3 4/7 (-2 1/12) using compatible fractions
Answers
Answer:
B). 3 1/2(-2) = -7
Step-by-step explanation:
Let's evaluate the expression so as to be able to get the right estimate.
3 4/7 (-2 1/12)
=3 4/7 (-25/12)
= 25/7 * -25/12
= 25/7 * -25/12
= -625/84
= -7 37/84
Approximately it's equal to ,-7
Answer:
b
Step-by-step explanation:
got it right on edge
Sally can paint 90 ft2 of wall per hour. Write a linear function that describes how many square feet of wall she can paint over time. Then make a graph to show how many square feet she can paint over the first 4 hours.
Answers
Answer:
Hello...
Hello...Sally can paint a house in 4 hours; Which means in 1 hour she can paint 1/4th of the house.
Hello...Sally can paint a house in 4 hours; Which means in 1 hour she can paint 1/4th of the house.John can paint the same house in 6 hours. Which means in 1 hour she can paint 1/6th of the house.
Hello...Sally can paint a house in 4 hours; Which means in 1 hour she can paint 1/4th of the house.John can paint the same house in 6 hours. Which means in 1 hour she can paint 1/6th of the house.Together in 1 hour they can paint: - 1/4 + 1/6 = 5/12th of the house.
Hello...Sally can paint a house in 4 hours; Which means in 1 hour she can paint 1/4th of the house.John can paint the same house in 6 hours. Which means in 1 hour she can paint 1/6th of the house.Together in 1 hour they can paint: - 1/4 + 1/6 = 5/12th of the house.Total Hours for painting the house together will be 12/5 = 2.4 Hours.
hope it helps
The linear function that describes how many square feet of wall she can paint over time is y = 90x.
What are linear equations?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Both linear equations with one variable and those with two variables exist.
Given the area painted by Sally in one hour = 90 square feet
so from the given data, we can find that the area painted by Sally is directly proportional to the time,
let she paint for x hours and the area she painted be y,
the equation for the condition is y = 90x,
where x is in hours and y is in square feet,
Table for the area she painted in first 4 hours
x(hours) 1 2 3 4
y ( sq. feet) 90 180 270 360
The graph for the first four hours is attached.
Hence the equation is y = 90x.
Learn more about linear equation;
https://brainly.com/question/29739212
#SPJ2
Which ordered pairs make both inequalities true? Select two options.
y One-halfx + 1
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (negative 2, 0) and (0, 1). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 3) and (0, 2). Everything to the right of the line is shaded.
(–1, 3)
A. (0, 2)
B. (1, 2)
C. (2, –1)
D. (2, 2)
Answers
Answer:
d
Step-by-step explanation:
i took the test
Answer:
I just did this test, its 1,2 and 2,2
Step-by-step explanation:
help with rewriting polynomial in standard form
Answers
The polynomial -6x⁵ - 1/8 - x³ in standard form is -6x⁵ - x³ - 1/8
Rewriting the polynomial in standard formFrom the question, we have the following parameters that can be used in our computation:
-6x⁵ - 1/8 - x³
To rewrite polynomial in standard form, we order the powers in decreasing order
Using the above as a guide, we have the following:
-6x⁵ - x³ - 1/8
Hence, the polynomial in standard form is -6x⁵ - x³ - 1/8
Read more about polynomial at
https://brainly.com/question/4142886
#SPJ1
This statement is justified by which property of equality?
"If
x = y and y= 3, then x= 3"
A Transitive property
B Reflexive property
C Identity property
D Symmetric property
Answers
Answer:
symmetric property
Step-by-step explanation:
with symmetric property if x=y then both values on either side of the equal sign will be equal
The graph shows information about the
height of the tide over 12 hours.
How fast is the depth changing at 11:00?
Give your answer as a fraction in its
simplest form.
Answers
According to the information we can infer that the change between 11 and 12 is 1.3 m/hr
How much does the height of the wave change between 11 and 12?To establish the value of the change in height between 11 and 12 we must look at the values of the y axis. According to this information we can establish that 11 o'clock coincides with 5.2 and 12 o'clock coincides with 3.9. So we must subtract these two values:
5.2 - 3.9 = 1.3According to the above, we can infer that the change between these two hours is 1.3 m/hr.
Learn more about time in: https://brainly.com/question/33137786
#SPJ1
Instructions: Find the missing side. Round your answer to the nearest tenth.
22
58°
Answers
Answer:
x = 19.2
Step-by-step explanation:
tan(58)=x/12
x=12×tan(58)
x=19.2
Answered by GAUTHMATH
A carpenter purchased 50 ft of redwood and 70 ft of pine for a total cost of $280. A second purchase, at the same prices, included 100 ft of redwood and 60 ft of pine for a total cost of $440. Find the cost per foot of redwood and of pine.
Answers
The cost per foot of redwood and of pine is $3.5 and $1.5 respectively.
How to solve simultaneous equation?let
cost of redwood = xcost of pine = y50x + 70y = 280
100x + 60y = 440
Multiply (1) by 2
100x + 140y = 560
100x + 60y = 440
subtract to eliminate x
80y = 120
y = 120/80
y = $1.5
substitute y = 1.5 into (1)
50x + 70y = 280
50x + 70(1.5) = 280
50x + 105 = 280
50x = 280 - 105
50x = 175
x = 175 / 50
x = $3.5
Learn more about equation:
https://brainly.com/question/2972832
#SPJ1
Convert 34.6 centimeters to inches. Use 1 in=2.54 cm.
Answers
Alexandra invested $20,000 in an account paying an interest rate of 6.2%
compounded annually. Assuming no deposits or withdrawals are made, how long
would it take, to the nearest tenth of a year, for the value of the account to reach
$27,200
Answers
Answer:
5.1
Step-by-step explanation:
Compounded Annually:
A=P(1+r)^t
A=P(1+r)
t
A=27200\hspace{35px}P=20000\hspace{35px}r=0.062
A=27200P=20000r=0.062
Given values
27200=
27200=
\,\,20000(1+0.062)^{t}
20000(1+0.062)
t
Plug in values
27200=
27200=
\,\,20000(1.062)^{t}
20000(1.062)
t
Add
\frac{27200}{20000}=
20000
27200
=
\,\,\frac{20000(1.062)^{t}}{20000}
20000
20000(1.062)
t
Divide by 20000
1.36=
1.36=
\,\,1.062^t
1.062
t
\log\left(1.36\right)=
log(1.36)=
\,\,\log\left(1.062^t\right)
log(1.062
t
)
Take the log of both sides
\log\left(1.36\right)=
log(1.36)=
\,\,t\log\left(1.062\right)
tlog(1.062)
Bring exponent to the front
\frac{\log\left(1.36\right)}{\log\left(1.062\right)}=
log(1.062)
log(1.36)
=
\,\,\frac{t\log\left(1.062\right)}{\log\left(1.062\right)}
log(1.062)
tlog(1.062)
Divide both sides by log(1.062)
5.1116317=
5.1116317=
\,\,t
t
Use calculator
t\approx
t≈
\,\,5.1
5.1
The time it will take for the value of the account to reach
$27,200 is 21.9 years to the nearest tenth of a year.
Calculation of interest periodThe amount invested(P) = $20,000
The interest paying rate (R)= 6.2%
The simple interest (SI)= $27,200
Therefore time of interest (T)= X
Using the formula,
SI = P×T×R/100
Make T the subject of formula,
T = SI×100/P×R
T = 27,200× 100/20,000×6.2
T = 2,720,000/124000
T = 21.9 to the nearest tenth of a year.
Learn more about simple interest here:
https://brainly.com/question/25793394
#SPJ2
Represent the following sentence as an algebraic expression, where "a number" is the
letter x. You do not need to simplify.
Twice the difference of 1 and a number.
Answers
Answer:
2(1 - x)
Step-by-step explanation:
Twice the difference of 1 and a number
a number = x
The difference of 1 and a number is expressed as :
1 - x
Twice this difference, means the difference of (1-x) multiplied by 2
2 * (1 - x) = 2(1 - x)
PLZ HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
tell me about your hobbies?
can you profit from the ?
do you learn from them? What do they teach you?
do your family members have hobbies?
explain to me?
Does your parents country have any particular customs/hobbies?
what is a hobby you could see developimg?
What do you think are some of the qualities that hobbies teach us?
WRITE 2 PARagraph
Answers
Answer:
Hobbies give teenagers a chance to meet new people, discover new passions, develop skills outside of school, and do something all kids (yes, teens are part kid) should do: have fun. ... That's where hobbies come in. Hobbies are a great way for teens to form an identity outside their family.
Step-by-step explanation:
Answer:
ok ok ok ok ok ok ok ok
Step-by-step explanation:
i don't know
Pls help what do I write in box pls.
Answers
The simplified expression can be written as:
\((-\sqrt{6} )*(-2*\sqrt{-42} ) = \sqrt{-1,008}\)
How to completely simplify the given expression?
Here you need to remember the property:
\(\sqrt{x} *\sqrt{y} = \sqrt{x*y}\)
Now we have the expression:
\((-\sqrt{6} )*(-2*\sqrt{-42} )\)
First, we can cancel the two first negative signs to get:
\((\sqrt{6} )*(2*\sqrt{-42} )\)
Now we can write the 2 as the square root of 4.
\((\sqrt{6} )*(\sqrt{4} *\sqrt{-42} )\)
Finally, we can use the above property to get:
\((\sqrt{6} )*(\sqrt{4} *\sqrt{-42} ) = \sqrt{6*4*(-42)} = \sqrt{-1,008}\)
If you want to learn more about square roots:
https://brainly.com/question/98314
#SPJ1
What is the radius of this circle? *
180 ft
180 ft
18.0 ft
9 ft
90ft
Please help
Answers
The radius of the circle with a diameter of 180 ft is 90 ft.
Option E is the correct answer.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is πr².
We have,
Diameter of the circle = 180 ft ____(1)
The diameter of a circle is = 2radius ______(2)
Now,
From (1) and (2) we get,
180 = 2 radius
Divide both sides by 2.
Radius = 90
Thus,
The radius of the circle is 90 ft.
Learn more about circle here:
https://brainly.com/question/11833983
#SPJ2
Solve for R: 16 + 8(R-6) = 5R + 50.
Answers
Answer:
82/3
Step-by-step explanation:
Hi! I'm back!
16+8r-48=5r+50
8r-32=5r+50
3r=82
r=82/3
Answer:
R = 82/3
Step-by-step explanation:
16 + 8(R - 6) = 5R + 50.
16 + 8 × R - 8 × 6 = 5R + 50
16 + 8R - 48 = 5R + 50
8R - 5R = 50 + 48 - 16
3R = 82
R = 82/3
R = 82/3
Thus, the value of R is 82/3
enter the range of values for x:
Answers
12x because you multiply it
The length of a rectangle is twice its width. Find its lenght and width, if its perimeter is 7 1/3 cm.
Answers
The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.
Let's assume the width of the rectangle is "b" cm.
According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.
The formula for the perimeter of a rectangle is given by:
Perimeter = 2 * (length + width)
Substituting the given perimeter value, we have:
7 1/3 cm = 2 * (2b + b)
To simplify the calculation, let's convert 7 1/3 to an improper fraction:
7 1/3 = (3*7 + 1)/3 = 22/3
Rewriting the equation:
22/3 = 2 * (3b)
Simplifying further:
22/3 = 6b
To solve for "b," we can divide both sides by 6:
b = (22/3) / 6 = 22/18 = 11/9 cm
Therefore, the width of the rectangle is 11/9 cm.
To find the length, we can substitute the width back into the equation:
Length = 2b = 2 * (11/9) = 22/9 cm
So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.
For more information on the Perimeter of the Rectangle, click:
https://brainly.com/question/13757874
Write this number in standard form 3 thousands, 16 tens,7 ones
Answers
What should be the third row in the following series of shapes
Answers
Answer:
The answer is number 2
find the general solution for: cos(x+30)=-1
Answers
The required, general solution for x that satisfies the equation cos(x + 30) = -1 is x = (2n + 1)π - 30.
To find the general solution for the equation cos(x + 30) = -1, we can start by considering the general form of the cosine function. The cosine function has a period of 2π, meaning it repeats every 2π radians.
In this equation, we have cos(x + 30) = -1. Since the cosine function has a maximum value of 1 and a minimum value of -1, the only way for cos(x + 30) to equal -1 is if x + 30 is an odd multiple of π. We can write this as:
x + 30 = (2n + 1)π
Here, n is an integer representing the number of periods of the cosine function. To find the general solution, we can solve for x by subtracting 30 from both sides:
x = (2n + 1)π - 30
This equation gives us the general solution for x that satisfies the equation cos(x + 30) = -1. We can see that for each integer value of n, we have a different solution.
Learn more about trigonometric functions here:
https://brainly.com/question/25618616
#SPJ1
Identify two angles that are marked congruent to each other on the diagram below.
(Diagram is not to scale.)
please help as soon as possible
Answers
Answer:
angle W and T are congruent to one another
Step-by-step explanation:
the markings show that they are congruent
9514 1404 393
Answer:
angles PWV and RTU
Step-by-step explanation:
Angles marked with the same arc symbol are identified as congruent. There are only two marked angles on the diagram, and the same symbol is used for both. These are the angles you're looking for.
angles PWV and RTU
suppose the integers from 1 to 25 are arranged in consecutive order. How many different pairs of integers may be selected if there are at least four integers between the selected integers?
Answers
find the value of x please help
Answers
Answer:
16
Step-by-step explanation:
15 --> 20 = /3 then X4
12/3=4
4X4=16
Tell whether -2 is a solution of the inequality n-5<8
Answers
Answer:
-2 is a solution
Step-by-step explanation:
-2-5<8
-7<8
Answer:
-2 is a solution.
Step-by-step explanation:
negative 2 minus 5 is less than 8
negative 7 is less than 8
Andy has $310 in his account. Each week, w, he withdraws $30 for his expenses. Which expression could be used if he wanted to find out how much money he had left after 8 weeks?
1) 310-8w
2) 280+30(w-1)
3) 310w-30
4) 280-30(w-1)
Answers
Hey you man what are you doing here go to there
EXPLANATION - we read the questions and create 310-30w as an equation, but we have to find another way that is equivalent to A B C or D. If you take D-280-30(w-1) and distribute to get 280-30w+30 then you have to combine like terms to get 310-30w.
2.6 X 16 fourth grade answers
Answers
Answer:
41.6 lol
Step-by-step explanation:
Use the figures below to evaluate the indicated derivative, or state that it does not exist. If the derivative does not exist, enter dne in the answer blank. The graph to the left (in black) gives f(x), while the graph to the right gives g(x) (which is constant for values of x greater than 80). f(x) g(x) ddxf(g(x))|x=60= (If the derivative does not exist, enter dne.)
Answers
\(\frac{d}{dx}f(g(x)) |_{x=60}\) = Derivative does not exist.
What is a function?A function contains input and output.
It describes the relationships between them.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The graph of f(x) and g)(x) is given,
We see that g(x) at 60 is increasing.
And f(x) at 60 is decreasing.
So,
\(\frac{d}{dx}f(g(x)) |_{x=60}\) does not exist.
Thus,
\(\frac{d}{dx}f(g(x)) |_{x=60}\) = dne
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ9
If there is an 80% chance of rain for 10 days, how many days should it rain?
Answers
Answer:
10 shouldn't it be 10 days
Step-by-step explanation:
hope it helps
Factor the expression using the GCF.
7 + 14 =
Answers
Answer:
1+2
Step-by-step explanation: