Answers
The fog(x) of the function will be 6x² -2x - 5 and gof(x) of the function will be 12x² + 62x - 80.
What is the domain of a function?
The collection of values that can be plugged into a function's domain is called its parameters. The x values for a function like f(x) are contained in this collection (x). The collection of numbers that the operator assumes is known as its range.
As per the given information in the question,
f(x) = 2x - 5 and,
g(x) = 3x² - x
fog(x) = 2x - 5 and,
gof(x) = 2x - 5
fog(x) = f(g(x))
= f (3x² - x) = 2(3x² - x) -5
= 6x² -2x - 5
gof(x) = g(f(x))
= g (2x - 5) = 3(2x - 5)² + 2x - 5
= 12x² - 75 + 60x + 2x -5
12x² + 62x - 80.
To know more about Domain:
https://brainly.com/question/28135761
#SPJ1
Related Questions
If a polynomial f\mathopen{}\mathclose{\left(x\right)}f(x) has a remainder of 22 when divided by x-6x−6, what is f\mathopen{}\mathclose{\left(6\right)}f(6)?\
Answers
f\mathopen{}\mathclose{\left(6\right)}f(6) = (6-6)(something) + 22 = 0(something) + 22 = 22 which has a remainder of 22 when divided by x-6x-6. f\mathopen{}\mathclose{\left(6\right)}f(6) = \boxed{22}.
What is the remainder theorem?The remainder theorem states that when a polynomial is divided by a linear term, the remainder equals the value of the polynomial at the root of the linear term. This theorem may be used to determine the roots of a polynomial by dividing it by a linear term and solving for the remainder. For instance, when the polynomial x3+x2-5x+6 is divided by (x2), the result is identical to the polynomial's value at x=2. After finding the remainder, we may determine that the polynomial's root is 2, which we can do by solving for the remainder. This theorem may also be used to discover the roots of higher degree polynomials by combining linear terms.
How to solve?
f\mathopen{}\mathclose{\left(x\right)}f(x) can be written as (x-6)(something) + 22.
f\mathopen{}\mathclose{\left(6\right)}f(6) = (6-6)(something) + 22 = 0(something) + 22 = 22.
Therefore, f\mathopen{}\mathclose{\left(6\right)}f(6) = \boxed{22}.
To learn more about the remainder theorem, visit:
https://brainly.com/question/9160275
#SPJ1
Help please[tex]\sqrt{x-3} -\sqrt{x} =3[/tex]
Answers
Answer: No solution
Step-by-step explanation:
[tex]\sqrt{x-3}=\sqrt{x} +3\\[/tex]
square both sides
x-3=x+9
x=x+12
0=12
0 does not equal 12, and therefor, there is no solution.
4. A seed is planted in a glass pot and its height is measured in centimeters
every day. (Lesson 3-4)
Height (cm)
3
2
5
2
-3
-4
-5
HATH
3 6 9 12 15 18 21 24 27 30
Days
The best fit line is given by the equation y = 0.404x - 5.18, where y
represents the height of the plant above ground level, and x represents the
number of days since it was planted.
a. What is the y-intercept of the best fit line? What does the y-intercept of the line mean in this situation? Is it reasonable?
Answers
The y-intercept of the line of best fit is -5.18cm and it is showing the initial height of the plant immediately it was planted and it is not reasonable because it shows a negative height
The general form of the equation of a line in slope intercept form is expressed as;
y = mx + c
where;
m is slope
c is y-intercept.
Now, we are given the equation of the line of best fit as;
y = 0.404x - 5.18
where;
y represents the height of the plant above ground level.
x represents the number of days since it was planted.
a) From the given equation, we see that the slope is; m = 0.404 and that the y intercept is -5.18.
Now, what the y-intercept means is that the height of the plant is 5.18 cm below the ground and this is not reasonable.
Read more about slope of line at; https://brainly.com/question/3493733
#SPJ1
Graph y = 2/3x
Where do i put the dots
Answers
Answer:
On (3,7) and (-2,7)
Step-by-step explanation:
A 12,000-lb killer whale might eat as much as 14,000 lb of fish per month (assume a 30-day month). If the average weight of a certain type of fish is 2.8oz, estimate how many of these fish a killer whale would eat in a day.† (Round your answer to the nearest whole number.)
Answers
Answer:
2196 fish
Step-by-step explanation:
:)
Answer:
2196 fish
Step-by-step explanation:
your welcome
Each day for three weeks, Kenisha records the number of eggs her chickens lay. The frequency table
shows her data.
On how many days did Kenisha's chickens
lay 5 or more eggs?
?
days
Number of Eggs
3
4
5
6
7
Frequency
!!
11
Answers
Answer:
12
Step-by-step explanation:
add the number of days that the chicken laid 5 or more eggs
5 + 5 + 2 = 12
From the given frequency table, we observe that the chicken lays 5 or more eggs on day 4, 5 and 6, and the eggs laid by the chicken are the greatest on day 4.
What is a frequency table?A frequency distribution table is a tool for structuring the provided data in a way that makes sense and facilitates comprehension. Two or three columns make up a frequency distribution table.
here, we have,
All of the results are shown in the first column as individual values or as class intervals.
The table's second column contains the results' totals, which also display the frequency as vertical lines. It's not required.
The frequency of each result is revealed in the third column.
The frequency table uses lines to depict the number of laid eggs. Here, 5 is represented using a hashed line over four lines. Thus, we see that the maximum number of eggs laid are 6, on day 4.
Also, the chicken lays 5 or more eggs on day 4, 5 and 6.
Learn more about frequency table here:
brainly.com/question/28931302
#SPJ5
I know the answer but I don't know how to solve
In a raffle, 1,500 tickets are sold for $3 each. One ticket will be randomly selected and the winner will receive a laptop computer valued at $1000. What is the expected value for a person that buys one ticket?
e(x)=-2.33
how do you find that answer ?
Answers
The solution to probability problem is the expected value for a person that buys one ticket is -$2.32
What is probability?Probability is a measure of the likelihood or chance that a specific event will occur, expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.
According to the given information:
To find the expected value, you need to multiply each possible outcome by its probability and then add them together.
In this case, there are two possible outcomes: either the person wins the laptop computer (with a probability 1/1500), or they don't win anything (with a probability 1499/1500).
So, the expected value can be calculated as:
E(x) = (1/1500)($1000) + (1499/1500)(-$3)
E(x) = $0.67 - $2.99
E(x) = -$2.32
So the expected value for a person that buys one ticket is -$2.32.
To know more about probability Visit: https://brainly.com/question/11234923
#SPJ1
A cyclist rode 3.85 miles in 0.7 hours. How fast was she going in miles per hour?
A. 3.85 miles per hour
B. 0.18 miles per hour
C. 5.5 miles per hour
D. 1.4 miles per hour
Answers
Whats 5 3/8 - 3 3/4 ?
Answers
let's convert the mixed fractions to improper fractions and the subtract.
[tex]\stackrel{mixed}{5\frac{3}{8}}\implies \cfrac{5\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{43}{8}} ~\hfill \stackrel{mixed}{3\frac{3}{4}}\implies \cfrac{3\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{15}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{43}{8}~~ - ~~\cfrac{15}{4}\implies \cfrac{(1)43~~ - ~~(2)15}{\underset{\textit{using this as the LCD}}{8}}\implies \cfrac{43-30}{8}\implies \cfrac{13}{8}\implies {\Large \begin{array}{llll} 1\frac{5}{8} \end{array}}[/tex]
NO LINKS!! Determine if the figures have line, point, and/or rotational symmetry. Check all that apply. Part 3
Answers
Recall properties of symmetry:
Line - reflection mirror,Rotational - you can rotate it about its center and it will overlap with the initial shape after minimum of 180 degrees rotation,Point - acting as a midpoint of the segment formed by opposite points.Using the properties we can state that:
#9It has no symmetry.#10It has rotational and point symmetry but not line.#11It has a line symmetry.#12It has rotational and point symmetry.Would you use SSS or SAS to prove the triangles are congruent? If there is not enough information to prove the triangles are congruent, write not enough information. Explain your answer.
Answers
We can use both according to the given information.
• In 2 triangles if 2 sides of a triangle and 2 sides of another triangle are equal and if any one angle is equal to the angle in another triangle then we use SAS congruence rule
• In 2 triangles if 3 sides are equal to the 3 sides of another triangle then we use SSS congruence rule
• We can also use RHS (Right angle Hypotenuse Side). It is for 2 right angle triangle.
*Hope It Helps you*°Please Mark Me As Brainliest°Farrah is painting vases to sell in a local craft show. She paints 8 vases in 2 hours. Which is a reasonable estimate of the amount of time it will take her to paint 50 vases?
Responses
A between 13 and 14
B between 14 and 15
C between 12 and 13
D between 11 and 12
Answers
Answer:
C.)
Step-by-step explanation:
1.) Since she does 8 vases in 2 hours, she would do 4 vases in 1 hour.
2.) By using this, we divide 50/4 to figure out the amount of hours. This is equal to 25/2, which is equal to 12.5.
3.) Now, check the options. C.) fits this situation the best. Therefore, C.) is the answer.
I need help asap. please help me..............................................
Answers
The sequence of transformations that show figure A and figure B are congruent is: Translate figure A 4 units right and then reflect the image across the x-axis.
What is translation?Translation refers to a type of transformation that involve a straight line movement.
Movements as seen in translation includes
leftrightupdownThe left and right movements are on the horizontal direction controlled by the x coordinate.
The object moved 4 units right then reflected over the x axis to have the mirror image below the x axis
Learn more on translation:
https://brainly.com/question/29321966
#SPJ1
Find the area of the shaded region. Round to the nearest tenth. All polygons are regular.
Answers
Check the picture below.
let's take a looksie at that, notice, if we split the circle into 6 even pieces, we end up with six 60° angles at the center, namely six equilateral triangles as you see there.
now, if we run a dashed line as you see from a corner to the other to make the flatter triangle which is shaded, we end up cutting the equilateral triangle into two equal halves, each with 30° and 30° angles, because the dashed line intercepts the green line at 90°.
well, the flatter triangle from corner to corner, is spanning over two equilateral triangles, if it's owning half of one, it must be also owning half of the other. What the dickens does that mean? well, it means the area of the flatter triangle that's shaded, is really the same area as a "whole" of one of those equilateral triangles.
so hmmm we have three of those flatter triangles shaded hmm, so let's simply get the area of three of those equilateral triangles and sum them up.
[tex]\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4} ~~ \begin{cases} s=side\\[-0.5em] \hrulefill\\ s=12 \end{cases}\implies A=\cfrac{12^2\sqrt{3}}{4}\implies A=36\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\large area of the shaded region}}{36\sqrt{3}~~ + ~~36\sqrt{3}~~ + ~~36\sqrt{3}}\implies 108\sqrt{3}\qquad \approx\qquad \text{\LARGE 187.1}[/tex]
Given the table below, write a linear equation that defines the
dependent variable, a, in terms of the independent variable, p.
Someone help
Answers
Answer:
a = 4p + 3
Step-by-step explanation:
The general form of a linear equation is y = mx + b
where y is the dependent variable, x the independent variable
m = slope(rate of change)
b = y-intercept which is the value of y when x = 0
In this problem, instead of x we are asked to use p and instead of y we are using a
Therefore we get
a = mp + b
We have to compute m and b
Since b is the value of a when p = 0, we can easily see that a = 3 when p = 0
Therefore:
a = mp + 3
To determine m, take any value of p, find the corresponding a from the table, plug in these values and solve for m
When p = 1, a= 7
So we get
7 = m(1) + 3
7 = m + 3
or
m = 7-3 = 4
So the equation is
a = 4p + 3
You can verify this as correct by plugging in different values for p from the table and checking if you get the corresponding a value
The solution to a(x)-b(x)=0
Answers
Answer:
a = b
b = a
Step-by-step explanation:
A car travels for 7 hours at 55 miles per hour. Use the formula d = r. t, where d =
distance, r = rate, and t = time, to find the distance the car traveled.
The distance traveled is
miles.
The solution is
Answers
The distance traveled is 385miles
Which equation models the line on the graph?
Answers
Answer:
y = 2x - 4
Step-by-step explanation:
(3, 2) (1, -2)
m = y2-y1 / x2-x1
m = -2-2 / 1-3
m = -4/-2
m = 2/1
m = 2
y = 2x + b
2 = 2(3) + b
2 = 6 + b
b = -4
y = 2x - 4
Could you please give me brainliest for this? Thank you!
6x + 45 is less than or equal to 240
Answers
Answer: neither
Step-by-step explanation:
To get rid of the fractions, we pick a useful number and multiply both sides of the equation by that number. The number is useful if multiplying eliminates all fractions.
Divit earned $1,420 each month for 3 months this summer working as a lifeguard he spent $450 on a new bike and put half of the rest of his earnings in a savings account?
Answers
A rectangular room is
5
meters longer than it is wide, and its perimeter is
34
meters. Find the dimension of the room.
Answers
Answer:
Step-by-step explanation:
P = 2(L + W)
P = 34
L = W + 5
34 = 2(W + 5 + W)
34 = 2(2W + 5)
34 = 4W + 10
34 - 10 = 4W
24 = 4W
24/4 = W
6 = W <=== 6 meters wide
L = W + 5
L = 6 + 5
L = 11 <=== 11 meters long
Can anyone help with this two question ? Please
Answers
let's go like the crab, go backwards, start at the last
if you don't have a Unit Circle, this is a good time to get one, there are many online.
Check the picture below.
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{6}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +6}{2}~~~ ,~~~ \cfrac{ y +7}{2} \right) ~~ = ~~\stackrel{midpoint}{(-5~~,~~-5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +6}{2}=-5\implies x+6=-10\implies \boxed{x=-16} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +7}{2}=-5\implies y+7=-10\implies \boxed{y=-17}[/tex]
help meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer:
Step-by-step explanation:
im not in 100th grade yet
tickets for a school play have one price for students, x, and a different price for non-students, y. The system of equations shown is based on two different ticket orders in which the prices x and y are in dollars. 2x + 3y = 49 and x + 2y = 30
A. What is the first step in solving the system by substitution?
B. Solve the system and explain what your solution represents.
Answers
A) x+2y=30
x=30-2y
B) x=8, y=11 and the solutions x and y represent the prices of tickets for students and non students.
What is meant by an equation?An equation in French is defined as having one or more variables, whereas an equation in English is any well-formed formula consisting of two expressions combined with an equals sign.
Solving a variable equation includes determining which variables' values result in equality. Unknowns are the variables for which the equation must be solved, while equation solutions are the unknown values that satisfy the equality. An equation is a mathematical phrase with two equal sides separated by an equal sign. An equation is 4 + 6 = 10. We can see 4 + 6 on the left side of the equal sign and 10 on the right.
Given equations are:
2x + 3y = 49
x + 2y = 30
A) From eq 2,
x+2y=30
x=30-2y
B) x and y represents the prices of tickets for students and non students.
2(30-y)+3y=49
60-4y+3y=49
y=60-49
y=11
x=30-2y
x=30-2(11)
x=30-22
x=8
The solutions x and y represent the prices of tickets for students and non students.
To know more about equation, visit:
https://brainly.com/question/29538993
#SPJ1
100 POINTS
The two-way frequency table contains data about students' preferred exercise.
What is the joint relative frequency of students who like running and swimming?
45%
37%
28%
14%
Answers
Answer:
28
Step-by-step explanation:
hope this helps if its wrong really sorry
Find g(x), where g(x) is the translation 5 units down of f(x)=x2.
Write your answer in the form a(x–h)2+k, where a, h, and k are integers.
Answers
If we want to translate (aka move) [tex]f(x) = x^2[/tex] down 5 units, we need to subtract 5 from the [tex]x^2[/tex].
[tex]g(x) = x^2-5[/tex]
The [tex]k[/tex] in the [tex]a(x-h)^2 +k[/tex] form will always be the vertical translation component. If you translate up, [tex]k[/tex] is positive. If you translate down, [tex]k[/tex] is negative.
Solve for X in graph the solution set label your number line below with at least three numbers
3(x+1)>12
Answers
Answer:
X+1>12/3
X+1>4
X>4-1
X>3
22. Given f(x)=10x & g(x)=2x-4
Find the value of f(1)
Find the value of g(3)
Find the value of f(1)+g(3)
Find the value of f(10)-g(0)
Answers
Answer:
f(1)=10
g(3)=2
f(1)+g(3)=12
f(10)-g(0)=104
Step-by-step explanation:
f(x)=10x
g(x)=2x-4
f(1)=10×1=10
g(3)=2×3-4=2
f(1)+g(3)=10+2=12
f(10)-g(0)=(10×10)-(2×0-4)=100+4=104
10 Find the value of 2x+y for the simultaneous equations.
3x + 5y = 48
2x-y=19
Answers
y=3
x=11
hence answer 25
3x+5y=48
2x-y=19
eliminate x to find y
(3x+5y=48)2
(2x-y=19)3
(6x + 10y. = 96)
- minus direct
(6x - 3y. = 57)
=
13y = 39
Note: (10y -(-3y)=13y)
divide by 13 to remain with y
y =3
substitute to any equation to get x lets pick second one
2x-(3)=19
2x-3=19
2x=19+3
2x/2=22/2. (to remain with x value)
x=11
therefore 2x+ y results to 2(11) +3=25
Answer:
2x + y = 25
Step-by-step explanation:
Given equations:
[tex]\begin{cases} 3x + 5y = 48\\\;\;2x-y=19\end{cases}[/tex]
Rearrange the second equation to isolate y:
[tex]\implies 2x-y=19[/tex]
[tex]\implies 2x-19=y[/tex]
Substitute the found expression for y into the first equation and solve for x:
[tex]\implies 3x+5y=48[/tex]
[tex]\implies 3x+5(2x-19)=48[/tex]
[tex]\implies 3x+10x-95=48[/tex]
[tex]\implies 13x=143[/tex]
[tex]\implies x=11[/tex]
Substitute the found value of x into the equation for y and solve for y:
[tex]\implies y=2x-19[/tex]
[tex]\implies y=2(11)-19[/tex]
[tex]\implies y=22-19[/tex]
[tex]\implies y=3[/tex]
Therefore, the solution of the given system of equations is:
x = 11, y = 3To find the value of 2x + y, substitute the found values of x and y into the expression and solve:
[tex]\begin{aligned}\implies 2x+y&=2(11)+3\\&=22+3\\&=25\end{aligned}[/tex]
Therefore:
2x + y = 25Ryan has a major problem of overspending from each of his paychecks, even though his ultimate goal is to be saving money for college. His friend Sydney says Ryan's problem is that he's too worried about "keeping up with the Joneses." What does Sydney mean by this?
A.Ryan's college savings goals are too lofty, which is why he can't achieve them
B.Ryan is buying too many material things or spending too much on experiences so that he feels on par with his peers
C.Ryan is imitating a famously wealthy family -- the Joneses -- from American history
D.Ryan doesn't know the 50-20-30 rule for budgeting, so he needs to take a financial management class like the fictitious "Jones" family would do in this situation
Answers
Answer: B. Ryan is buying too many material things or spending too much on experiences so that he feels on par with his peers
Idioms
Idioms are phrases or expressions that have a specific meaning that is different from the meaning of the individual words, for example, the idiom "you have bitten off more than you can chew" implies that someone is trying to do something that is too difficult for him/her.
"Keeping up with the Joneses" is an idiom that refers to the urge to keep up with the social status, wealth, or popularity of other people around us. This situation causes someone to constantly compare himself/herself with others and buy the same goods in order to show that he/she has as much money as other people.
Learn more about idioms here: https://brainly.com/question/17956606
#SPJ1