Answers
The domain of the function is (-∞,∞) and the simplified expression is x²-6x-40 .
A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A B exists that maps every element of A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R. The set of images is the function's range.
The given functions are
f(x)=6x+24
g(x)=x²-16
Now we have to find (g-f)(x) .
(g-f)(x)=x²-16-6x-24
or,(g-f)(x)=x²-6x-40
or,(g-f)(x)=x²-10x+4x-40
or,(g-f)(x)=x(x-10)+4(x-10)
or,(g-f)(x)=(x-10)(x+4)
So the domain of the function (g-f)(x) are the values for which the function exists. we can see that the function exists for all values of x.
Domain in set builder notation={x|x∈R}
Domain in interval notation=(-∞,∞)
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Related Questions
Which sequence of transformations on preimage ∆ABC will NOT produce the image ∆A'B'C'?
Graph shows 2 triangles plotted on a coordinate plane. First triangle is at A(minus 3, 0), B(minus 2, 3), C(minus 1, 1). Second triangle is at A prime (0, minus 3), B prime (3, minus 2), C prime (1, minus 1).
A.
reflection across the line y = x
B.
reflection across the x-axis followed by a reflection across the y-axis
C.
reflection across the line y = -x followed by a rotation 180° counterclockwise about the origin
D.
reflection across the y-axis followed by a rotation 90° clockwise about the origin
E.
rotation 180° clockwise about the origin followed by a reflection across the line y = -x
Answers
The geometric transformation which will not produce the image ∆A'B'C' is an option (B) reflection across the x-axis followed by a reflection across the y-axis
In this question, we have been given a triangle ABC and the transformed triangle A'B'C'
Also, in the graph the first triangle is at A(-3, 0), B(-2, 3), C(- 1, 1) and the Second triangle is at A prime (0, -3), B prime (3, -2), C prime (1, -1).
Consider the graph as shown below.
From the coordinates of vertex of triangle ABC and triangle A'B'C' we can observe that,
A(-3, 0) -> A'(0, -3)
B(-2, 3) -> B'(3, -2)
C(-1, 1) -> C'(1, -1)
For each vertex,
x coordinate of triangle ABC = y coordinate of triangle A'B'C'
and y coordinate of triangle ABC = x coordinate of triangle A'B'C'
This means, the geometric transformation of triangle ABC is reflection across the line y = x
But the reflection across the x-axis followed by a reflection across the y-axis.
Therefore, the geometric transformation which will not produce the image ∆A'B'C' is an option (B) reflection across the x-axis followed by a reflection across the y-axis
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The Lopez family buys 4 dinners at the market. The total cost is $5 above or below $50. Write an equation that models the cost x, in dollars of a single dinner?
answer: |_-_x|-_=0
Answers
==================================================
Explanation:
x = cost of one dinner
4x = cost of four dinners
50-4x = the difference in the cost of $50 vs 4x dollars
To ensure this difference is never negative, we use absolute value to form the expression |50-4x|
Set this equal to 5 since we want this distance or difference to be 5 units above or below 50
|50-4x| = 5
|50 - 4x| - 5 = 0
Answer:
l 50 - 4x l - 5 = 0
Step-by-step explanation:
Find the slope of the line if it exists.
Answers
The slope of the line is 1.
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount
To calculate the slope of the graph, we use the formula below.
Formula:
Slope (S) = (y₂-y₁)/(x₂-x₁)............ Equation 1From the question,
Given:
y₁ = 0y₂ = 4x₁ = -6x₂ = -2Substitute these values into equation 1
S = (4-0)/[-2-(-6)]S = 4/4S = 1Hence, the slope of the line is 1.
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Simplify the expression √48
Answers
4√3
Decimal Form:
6.92820323
Help, I don’t know how to solve this
Answers
Answer:
a=A/8
Step-by-step explanation:
This MIGHT be the answer, I am 99% sure!
78/99 simplified to the smallest form
Answers
Answer:
The simplest form of
78/99
is
26/33
.
Roy has $253.97 in his bank account. He loans his friend $81.19. How much money does he have in his
account?
Answers
Answer:
172.78
Step-by-step explanation:
HELP ASAP I WILL GIVE 30 points to whoever can show their work!
Answers
Answer:
Step-by-step explanation:
sin(A)=2/5
[tex]cos^2(A) +sin^2(A)=1\\cos^2(A)+[\frac{2}{5}]^2=1\\cos^2(A)+\frac{4}{25}=1\\ cos^2(A)=1-\frac{4}{25}\\ cos^2(A)=\frac{21}{25}\\ cosA=\frac{\sqrt{21} }{5}[/tex]
a certain ceiling is made up of tiles.every square mater of ceiling requries 10.75 tiles.fill in table with the missing values
Answers
Table is attached below-
1) 1 m² = 10.75 tiles
2) 10 m² = 107.5 tiles
3) 9.3 m² of tiles = 100 tiles
4) a m² = 10.5a tiles
We have been given that
Every square meter of ceiling requires 10.75 tiles.
we have find missing values in the table.
We know,
1 square meter of ceiling = 10.75 tiles. ...(i)
1. Therefore, the number of tiles corresponding to 1 square meter of ceiling is 10.75.
Multiply both sides by 10.
10×1 square meter of ceiling = 10×10.75 tiles.
10 square meter of ceiling = 107.5 tiles.
2. Therefore, the number of tiles corresponding to 10 square meter of ceiling is 107.5.
Divide both sides by 10.75 in (i).
(1/10.75) square meter of ceiling = 1 tile.
Multiply both sides by 100.
(100/10.75) square meter of ceiling = 100 tiles.
On approximating the value, we get
9.3 square meter of ceiling = 100 tiles.
3. Therefore, the square meters of ceiling corresponding to 100 tiles is about 9.3.
Multiply both sides by a in (i).
a×1 square meter of ceiling = a×10.75 tiles.
a square meter of ceiling = 10.75a tiles.
4. Therefore, the number of tiles corresponding to a square meter of ceiling is 10.75a.
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Find the perimeter of the rectangle. Then, find the area of the rectangle. Round your
answer to the nearest tenth, if necessary.
(Lesson 2-3)
Answers
Solution :
solve by considering data :
The perimeter of a rectangular pool is 56 meters. If the length of the pool is 16 meters, then find its width.
Here the perimeter and the length of the rectangular pool are given. We have to find the width of the pool.
The perimeter P of a rectangle is given by the formula, P=2l+2w, where l is the length and w is the width of the rectangle.
Given that, the perimeter is 56 meters and the length is 16 meters. So, substitute these values into the formula.
56=2(16)+2w
Simplify.
56=32+2w
Subtract 32 from both sides.
24=2w
Divide each side by 2 .
12=w
Therefore, the width of the rectangular pool is 12 meters.
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Which inequality does this graph match?
−19 + 7k< −6(−4−k)
−7 (4−x) + 4 > −18 + 7x
−4 (4+7x) + x < −6x + 5
−2n − 40 < 5 (6+n) + 7n
Answers
Answer:
I think it is -5
Step-by-step explanation:
Help me plsss this is my last oneeeree
Answers
Answer:
For the first question:
The fraction that comes after 0/3 is 1/3The fraction that comes after 1/3 is 2/3For the second question:
The fraction that comes after 0/6 is 1/6The fraction that comes after 1/6 is 2/6The fraction that comes after 2/6 is 3/6The fraction that comes after 3/6 is 4/6The fraction that comes after 4/6 is 5/6Step-by-step explanation:
Hope it helps! =D
Help me with this problem please
Answers
step by step explanation
Answers
The sum of the given infinite geometric series is; 32
What is the sum of the geometric series?The general formula for finding the sum of an infinite geometric series is s = a₁/(1 - r)
where;
s is the sum
a₁ is the first term of the series
r is the common ratio.
To find the common ratio, use the formula: r = a2⁄a1
where a2 is the second term in the series and a1 is the first term in the series.
Thus;
r = 2²/4²
r = 1/2
Thus;
S = 4²/(1 - 1/2)
S = 16/(1/2)
S = 32
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PLEASE HELP ME. DUETODAY. NEED ANSWER ASAP!!!!!!
Answers
Answer: 120 ==> scale
8.4 m==> longer side
Step-by-step explanation:
6 m=
6*100 cm=600 cm
600/5=120 ==> scale
7*120=840 cm
840 cm=
840/100 m=8.4 m ==> longer side
Howard's pawn shop bought an antique clock at the wholesale price of $725. Howard marked up the price of the clock 30%. What was the list price of the clock?
Answers
The list price of the clock is $375.50.
How to calculate the costFrom the information, Howard's pawn shop bought an antique clock at the wholesale price of $725. Howard marked up the price of the clock 30%.
The new price will be:
= $725 + (30% × $725)
= $275 + $82.5
= $357.5
Therefore, the list price of the clock is $375.50.
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You are buying a new car. There are 7 body styles, 3 colors, and 7 models. How many different choices of car are there?
Answers
Answer:
147 different choices.
Step-by-step explanation:
(7)(3)(7) = 147
Hope this helps
A large water container has a leak. It loses 40 drops of water every minute. If 50 drops of water is equivalent to half of a teaspoon. At what rate
Is the water leaking?
O 48 teaspoons per hour
24 teaspoons per hour
O 80 teaspoons per hour
O 12 teaspoons per hour
O 20 teaspoons per hour
Answers
explanation:
container loses 40 drops of water per min so per hour,it loses (40x60=2400)per hour
2400/50=48 so it loses 48 teaspoons per hour
-3x+6=-24bwhat is the value of 2x-17
Answers
The value of the expression 2x - 17 is 3
How to evaluate the expression?The expression is given as
-3x + 6 = -24
Subtract 6 from both sides
-3x = -30
Divide both sides by -3
x = 10
Multiply by 2
2x = 20
Subtract 17 from the sides
2x - 17 = 3
Hence, the value of the expression 2x - 17 is 3
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Layla has $680 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $319.28.
She buys 3 bicycle reflectors for $4.90 each and a pair of bike gloves for $37.94.
She plans to spend some or all of the money she has left to buy new biking outfits for $77.02 each.
Use the drop-down menu below to write an inequality representing oo, the number of outfits she can buy while staying within her budget.
Answers
Layla should by not more than 4 outfits in order not to exceed her budget
The inequality expression is n ≤ 4
Given data
price of a new bicycles = $319.28
3 bicycle reflectors = $4.90
a pair of bike gloves = $37.94.
new biking outfits = $77.02 each
Layla's total money to spend at a bicycle store = $680
How to write the required inequality equationLayla's expenses will not be more than her total amount to spend at the bicycle store therefore will use less than or equal to sign, before the sum of the other items
The expression is written as follows
$680 ≤ $319.28 + 3 * $4.90 + $37.94 + n * $77.02
where n represents the number of the new biking outfits
$680 - ( $319.28 + 3 * $4.90 + $37.94 ) ≤. + n * $77.02
( $680 - ( $319.28 + 3 * $4.90 + $37.94 ) ) / $77.02 ≥ n
( $680 - $371.64 ) / $77.02 ≥ n
( $308.36) / $77.02 ≥ n
4 ≥ n
Layla should by not more than 4 outfits in order not to exceed her budget
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A bicycle-sharing station on Main Street has 5 times as many bicycles as a station on Park Avenue. There are 24 bicycles at the two stations. How many bicycles are at the Main Street station?
Answers
There are 20 bicycles at the Main Street station.
According to question statement, A bicycle-sharing station on Main Street has 5 times as many bicycles as a station on Park Avenue. There are 24 bicycles at the given two stations.
We are supposed to know the number of bicycles at the Main Street station.
Let us assume that the number of bicycles at the Park Avenue station is "x". Then, number of bicycles at the Main Street station will be "5x".
We will have to form a Linear Equation of single variable "x" as per the conditions based in the question statement, and solving for x, we will obtain our desired answer.
As there are 24 bicycles at the two stations therefore,
[tex]x + 5x = 24[/tex], will be our equation.
Solving the equation for x, we get
[tex]x + 5x = 24\\6x = 24\\x=\frac{24}{6} \\or x=4[/tex]
Therefore the number of bicycles at the Park Avenue station is 4.
And the number of bicycles at the Main Street station will be 5x i.e., [tex]5*4 = 20[/tex].
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Determine if each statement is TRUE or FALSE.
15. LAGF and LBGE are vertical angles..
Answers
Answer:
TRUE
Step-by-step explanation:
na sa inyo na answer
Answer:
Add your questions
Step-by-step explanation:
find the average of 1/8, 1/6, and 3/4
Answers
Answer:
Average= [tex]\frac{25}{72}[/tex]
Step-by-step explanation:
o find the average add up the values and divide the sum by the number of values.
Rewriting all values as fractions, rewriting any negatives if necessary and, setting up as an addition problem
= [tex]\frac{1}{8}[/tex] + [tex]\frac{1}{6}[/tex] +[tex]\frac{3}{4}[/tex]The least common denominator (LCD) is: 24.
Rewriting as equivalent fractions with the LCD:
= [tex]\frac{3}{24\\}[/tex] + [tex]\frac{4}{24}[/tex] + [tex]\frac{18}{24}[/tex]Rewriting numerators over the common denominator,
= [tex]\frac{3 + 4 + 18}{24}[/tex]Totaling the numerator:
= [tex]\frac{25}{24}[/tex]
Dividing by the number of values: 3
[tex]\frac{25}{24}[/tex] ÷3 =[tex]\frac{25}{24}[/tex] ×[tex]\frac{1}{3}[/tex] = [tex]\frac{25}{72}[/tex]
Average of the fractions is:
Average= [tex]\frac{25}{72}[/tex]
Sue has a 8 cups of flour and needs to fill it equally in containers that hold 3/4 of a cup each. How many containers can she fill?
Answers
Answer: 10
Step-by-step explanation: First you decide that each container can fill 3/4 of a cup. You have 8 cups so you need to divide 8 by 3/4 which will give you the answer of 10.666 repeating so the answer is you can only fill up 10 containers.
Perform the indicated operation & simplify. Express the answer as a complex number. ( 12 − 11 i ) 2
Answers
The answer is 24 - 22i
The answer we got is a complex number.
We are asked to find out the multiplication of a complex number and a real number.
The general form of a complex number is a + bi.
If we need to find the product of a complex number and a real number,
then, we need to multiply the real and imaginary parts by the real number and write down the answer.
The real number given is 2.
And the complex number given is 12 - 11i.
The real part of the complex number is 12.
And the imaginary part of the complex number is -11.
When the real part of the complex number is multiplied by the real number, we get 12 × 2 = 24.
When the imaginary part of the complex number is multiplied by the real number, we get (-11) × 2 = -22
Therefore, the required complex number is 24 - 22i
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The student council is selling popsicles to raise money for prom. Each box contains 10
popsicles and each box costs $4.50. How much does the school need to charge per
popsicle to make a profit of $6 per box?
Answers
Answer:
1.05 dollars per popsicle
Step-by-step explanation:
x is the price per popsicle. In order for you to make 6 dollars of profit, each box is going to cost 10.50 dollars because 4.50 is your amount of expenses.
Profie= revenue-expenses
6= revenue-4.5
revenue=10.5
If you charge 10.5 per box, and each box has 10 popsicles, then one popsicle is 10.5/10=1.05 dollars per popsicle.
Sixty-three and six-teen-thousandths
Answers
Answer:
63 and 16,000
Step-by-step explanation:
There are 8 adults in line for a ride. The line has 4 fewer children than adults. How many people are in line? Explain your answer.
Answers
Answer:
12 People
Step-by-step explanation:
To start you have 8 people for sure. Then you know that there are 4 fewer children. So then you subtract 4 from 8 and get four. Four plus eight is twelve!
The number of people in line will be 12.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
There are 8 adults in line for a ride. The line has 4 fewer children than adults. Then the number of children will be
⇒ 8 - 4
⇒ 4 children
Then the number of people in line will be
⇒ 8 + 4
⇒ 12
The number of people in line will be 12.
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Last year, Abdul opened an investment account with $8600. At the end of the year, the amount in the account had decreased by 7.5%. How much is this decrease in dollars? How much money was in his account at the end of last year?
Answers
The amount that decreased in dollars is equal to $ 645 and the money left in the account at the end of the year is $ 7955.
The amount of investment that Abdul opened an account with = $ 8600
The amount decreased by 7.5 %.
So, the amount left will be calculated by first using the percentage to find the amount that decreased.
Amount decreased = 7.5 % of 8600
Amount decreased = 0.075 × 8600
Amount decreased = $ 645
Amount left at the end of the year = $ 8600 - $ 645
Amount left at the end of the year = $ 7955
Therefore, the amount that decreased in dollars is equal to $ 645 and the money left in the account at the end of the year is $ 7955.
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Graph the numbers -0.2, 7/10, -1, √2, and -4 on a number line.
-8 -7, -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Answers
Answer:
Step-by-step explanation:
