Answer:
[tex]g(x)=\frac{x}{4}-3[/tex]
Step-by-step explanation:
we have
[tex]f(x)=4x+12[/tex]
Find the inverse
Let
y=f(x)
[tex]y=4x+12[/tex]
Exchange the variables (x for y and y for x)
[tex]x=4y+12[/tex]
Isolate he variable y
subtract 12 both sides
[tex]4y=x-12[/tex]
divide by 4 both sides
[tex]y=\frac{x}{4}-3[/tex]
Let
g(x)=y
[tex]g(x)=\frac{x}{4}-3[/tex] ---> inverse of the function f(x)
A room has dimensions 6.8m x 9.2m. Steven wants to paint the walls of the room. A large tin of paint covers 20m^2 and cost £11.75. Ignoring windows and doors, and allowing for 2 coats of paint, how much will it cost Steven to paint the room.
Answer:
Total cost to paint the room = £73.51
Step-by-step explanation:
Given:
Dimensions of the room = 6.8 m [tex]\times[/tex] 9.2 m
Cost of tin of paint = £11.75
A tin of paint covers an area = 20 [tex]m^2[/tex]
To find the cost of painting the room with two coats of paint.
Solution:
Area of the room = [tex]length\times width=6.8\ m\times 9.2\ m= 62.56\ m^2[/tex]
We will use unitary method to find the amount of paint required for the room.
If [tex]20\ m^2[/tex] of area is covered by 1 tin of paint.
For [tex]1\ m^2[/tex] of area, amount of paint required = [tex]\frac{1}{20}[/tex] of a tin
Then, for [tex]62.56\ m^2[/tex] amount of paint required = [tex]\frac{62.56}{20}=3.128[/tex] tins of paint.
For double coats twice paint must be required.
So, total amount of paint required for painting the room with two coats of paint = [tex]3.128\times 2=6.256[/tex] tins of paints.
Using unitary method to find total cost.
If 1 tin of paint costs = £11.75
6.256 tins of paint will cost = [tex]6.256\times \£11.75=\£73.508\approx\£73.51[/tex]
Total cost to paint the room = £73.51
Tomas is at least 7 years older than Larry. If Tomas is 16 years old, how old is Larry
Answer:
Larry is about 9 years old
Step-by-step explanation:
Subtract
15) Write an equation in slope-intercept form for the line that is parallel to the given line and passes
through the given point ----> (2,7)
y = 4x + 6
Answer:
[tex]\displaystyle y = 4x - 1[/tex]
Step-by-step explanation:
7 = 4[2] + b
8
[tex]\displaystyle -1 = b \\ \\ y = 4x - 1[/tex]
* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], so 4 remains the way it is.
I am joyous to assist you anytime.
Help, I know D2 is the dilation of 2? And I know the rotation is 90 degrees but I’m not to sure on how to find my answer? Help please
Answer:
(-18, 2)
Step-by-step explanation:
To rotate a point by 90°:
R₉₀ (x, y) = (-y, x)
R₉₀ (1, 9) = (-9, 1)
To dilate by 2:
D₂ (x, y) = (2x, 2y)
D₂ (-9, 1) = (-18, 2)
Blueberries cost $4.00 per pound. How many pounds of blueberries can u buy for $1.00
Answer:
Step-by-step explanation:
Blueberries cost $4.00 for 1 pound. The number of blueberries that can be bought $1.00 = (1×1)/4 pounds
= 1/4 pounds
please help me out will mark brainliest :)
Answer:
AOC
Step-by-step explanation:
Angle COX is formed at vertex O with two rays OC and OX.
Angle AOX is formed at vertex O with two rays OA and OX.
Ray OA lies between rays OC and OX.
All three rays have the common vertex O.
The angle addition postulate describes that putting two angles side by side with their vertices together creates a new angle whose measure equals the sum of the measures of the two original angles.
So,
[tex]m\angle AOX+m\angle AOC=m\angle COX[/tex]
what is the sum of 7.09 + 13.95
Answer:
21.04
Step-by-step explanation:
Start by adding the hundredths category. 0.09 + 0.05 = 0.14, this means that your hundredths column will be a 4, and you will carry the 1 over to the tenths.
Now add your tenths. 0.0 + 0.9 + 0.1 = 1.0, which means that your tenths column is a 0. Carry the 1 over to the whole numbers.
Now add your whole numbers. 7 + 13 + 1 = 21. Combine your terms and you get 21.04
Final answer:
21.04
Explanation:
To find the sum of 7.09 and 13.95, we simply add the two numbers together, aligning the decimal points vertically.
Add the hundredths place: 9 (from 7.09) + 5 (from 13.95) = 14. Write down 4 and carry over 1 to the tenths place.Add the tenths place: 0 (from 7.09) + 9 (from 13.95) + 1 (the carryover) = 10. Write down 0 and carry over 1 to the ones place.Add the ones place: 7 (from 7.09) + 3 (from 13.95) + 1 (the carryover) = 11. Hence, write down 1 and carry over another 1 to the tens place.Add the tens place, which is just the carryover: 1 (from the carryover) + 1 (from 13.95) = 2. So, write down 2.Putting it all together, we get 21.04 as the final sum.
How does the value of an expression change when it is expanded
Answer:
The value remains the same.
Step-by-step explanation:
using the expression: [tex](x + 1)^{2}[/tex],
where x = 2
substitute for x in the expression;
[tex](2 + 1)^{2}[/tex]
= [tex](3)^{2}[/tex]
=9
The value of the expression before expansion = 9
Lets expand the expression: [tex](x + 1)^{2}[/tex]
= (x + 1) (x + 1)
= [tex]x^{2}[/tex] + 2x + 1
substitute for x in the expression
= [tex]2^{2}[/tex] + 2(2) + 1
= 4 + 4 + 1 = 9
The value of the expansion after expansion = 9
The value remains the same before and after expansion.
The value of an expression, before and when it is expanded will be always same.
Let us consider that an expression,
[tex]f(x)=(x-1)^{2}[/tex]
Substitute x = 2 in above relation.
[tex]f(2)=(2-1)^{2}=1[/tex]
Now expand,
[tex]f(x)=(x-1)^{2}=x^{2} -2x+1\\\\f(2)=2^{2}-2*2+1\\\\f(2)=4-4+1\\\\f(2)=1[/tex]
Hence, the value of an expression, before and when it is expanded will be always same.
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An airplane has 29 seats. The price for a coach seat is $600 in the price for a first class seat is $1050. The airline collected a total of $21,900 for the flight. How many coach seats were sold
Answer:
19 coach seats
Step-by-step explanation:
let the number of coach seats be C and number of first class seats be F
given that the total number of seats is 29,
C + F = 29 ---------(eq 1)
also given that each coach seat = $600, each 1st class seat is $1050 and a total of $21900 was collected,
600C + 1,050F = 21,900 -------(eq 2)
we have 2 equations and 2 unknowns, we can solve the system of equations by elimination
(eq 1) x 1,050 gives us:
1,050 (C + F) = 1,050(29)
1,050C + 1,050F = 30,450 ----- (eq 3)
by elimination, subtract eq 2 from eq 3
(1,050C + 1,050F) - (600C + 1,050F) = 30,450 - 21,900
1,050C - 600C = 8,550
450C = 8550
C = 855 /450
C = 19
Does Anyone know the answer to this?
Exact form: x= NEGATIVE 6/7
I NEED HELP PLEASE!!
Answer:
t = 51°
Step-by-step explanation:
The total sum of a polygon's exterior angles is always 360°.
Add all of the given angles and equate it to 360°.
40° + 34° + 34° + 46° + (2t - 50°) + (2t - 50°) + 2t = 360° Collect like terms
154° + 2t - 50° + 2t - 50° + 2t = 360° Remove brackets and collect like terms
54° + 6t = 360° Isolate t by doing reverse operations in reverse BEDMAS
6t = 360° - 54° Subtract 54° from both sides
6t = 306° Divide both sides by 6
t = 51° Answer
Please answer the question
Please help, brainliest!!
Write an expression equivalent to 4(6x + 12), and state the property you used to write it.
Answer:
4(6x) + 4(12)
Distributive property
4(6x + 12) = 4(6x) + 4(12)
To see if the answer is correct, we can solve the equations
24x + 12 = 24x + 12
The expressions are equal, so the equivalent expression provided is correct
Hope this helps :)
Answer:
By applying the Distributive Property, I can generate these equivalent expressions: 24x + 48, 24(x + 2), and 12(2x + 4).
During a period of 80 minutes, a music station played 8 minutes of commercials. What is the ratio of music they played to commercials they played?
Answer:
Step-by-step explanation:
80 minutes.......8 minutes played commercials....that means (80 - 8) = 72 minutes played music
so the ratio of music to commercials is : 72/8 which reduces to 9/1...so the ratio is 9:1 <=== ur answer
** pay attention to the wording, because if it would have asked for the ratio of commercials to music, it would have been 8/72....ratio would be 1:9
Given f(x) = 14x + 42, find x when f(x) = 35.
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Form an equation:
14x + 42 = 35
-42
14x = -7
/14
x = -0.5
Have A Nice Day ❤
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Answer:
532
Step-by-step explanation:
14x + 42 = ?
14(35) + 42 = ?
14(35) + 42 =532
You mix 1/3
quart of blue paint for every 1/2
quart of red paint to make 2 1/2
quarts of purple paint. How much blue paint and how much red paint do you use?
Answer:
1 quart blue + 1 1/2 quart red
Step-by-step explanation:
Given:
Ratio of blue paint : red paint = 1/3 : 1/2
simplifying this ratio into whole numbers by multiplying both sides by 2 and 3, we get:
(1/3) x (3x2) : (1/2) x (3x2)
2 : 3
From this we can determine the fractions of red and blue paint used in any total purple mix
fraction of blue paint = 2/(2+3) = 2/5 of purple mix
fraction of red paint = 3/(2+3) = 3/5 of purple mix
we are given that we want to make 2 1/2 (= 5/2) quarts of purple paint
hence
amount of blue paint
= fraction of blue paint in purple mix x total amount of purple paint
= (2/5) x (5/2) = 1 quart
amount of red paint
= fraction of redpaint in purple mix x total amount of purple paint
= (3 /5) x (5/2) = 3/2 quart = 1 1/2 quart
Help Needed!!!..............................
Answer:
I think D.
Step-by-step explanation
Answer:
Part(B) is the correct answer
Step-by-step explanation:
Given functions are
f(x) = [tex]4x^3+5[/tex] and g(x) = [tex]\sqrt[3]{x-5/4}[/tex]
So both are inverse of each other
Since Definition of inverse function is
If a function f(x) is mapping from x to y , then the inverse function of f(x) maps
y back to x.
Solution
suppose
y = f(x)
y = [tex]4x^3+5[/tex]
in order to find inverse of f(x)
interchange the variables x and y
x = [tex]4y^3+5[/tex]
Now solve for y
Subtract 5 from both sides we get
[tex]4y^3[/tex] = x-5
Divide both sides by 4 we get
[tex]y^3[/tex] = (x-5)/4
[tex]y = \sqrt[3]{x-5/4}[/tex]
so this is the inverse of the f(x) and also from this we see that is [tex]g(x) = \sqrt[3]{x-5/4}[/tex]
This is Answer.
Janet's paycheck was $248.60. She put 1/4 of her paycheck into a checking account and 1/5 of what was left to buy dinner for her family. How much money does she have remaining from her paycheck? Show Work!
Janet has remaining $ 149.16 in her paycheck
Solution:Given that Janet's paycheck was $248.60
She put 1/4 of her paycheck into a checking account
Therefore amount put into checking account is given as:
[tex]\text {amount put into checking account }=\frac{1}{4} \times 248.60=62.15[/tex]
So she spent $ 62.15 into checking account
Now the remaining paycheck amount left is:
remaining paycheck amount left = 248.60 - 62.15 = 186.45
Therefore remaining paycheck amount left is $ 186.45
Now she spent 1/5 of what was left to buy dinner for her family
[tex]\text { Amount spend on dinner }= \frac{1}{5} \times 186.45 = 37.29[/tex]
So she spent $ 37.29 on dinner
Now the remaining paycheck amount left is:
remaining paycheck amount left = 186.45 - 37.29 = 149.16
Thus Janet has remaining $ 149.16 in her paycheck
who can solve this exercises pleaseeee i have a exam
Answer:
Step-by-step explanation:
1) Two angles supplementary. So sum of two angles is 180
One angle = x
Other angle = 2x
x + 2x = 180
3x = 180
x = 180/3 = 60
The angles are 60, 120
2)Two angles complementary. So sum of two angles is 90
one angle = x
Other angle = x + 20
x +x +20 = 90
2x + 20 = 90
2x = 90- 20
2x = 70
x = 70/2 = 35
The angles are 35,55
3) one angle =x
Other angle = 3x - 20
x + 3x - 20 = 120
4x = 120 + 20
4x = 140
x = 140/4 = 35
The angles are 35,85
5) x + 4x -20 = 180
5x = 180 + 20
5x = 200
x = 200/5 = 40
x = 40
6) This sum is not clear only half is visible
if a b and c are three different numbers which of the following equations has exactly one solution?
A:ax+b=ax+b
B:ax=bx+c
C:ax+b=ax+c
Option B is correct.
Step-by-step explanation:
We need to identify which of the following equations has exactly one solution.
We will solve each equation to find the answer
A. [tex]ax+b=ax+b[/tex]
Solving and finding value of x:
[tex]ax+b=ax+b\\ax-ax=b-b\\0=0[/tex]
This equation has infinite number of solutions because both sides are equal to 0
B. [tex]ax=bx+c[/tex]
Solving and finding value of x:
[tex]ax=bx+c\\ax-bx=c\\x(a-b)=c\\x=\frac{c}{a-b}[/tex]
This equation has exactly one solution
C. [tex]ax+b=ax+c[/tex]
[tex]ax+b=ax+c\\ax-ax=c-b\\0=c-b[/tex]
This equation has no solution because both sides are not equal.
So, Option B is correct.
Keywords: Solving Equations
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An artist needs to purchase jars of paint. The table shows Which quantity container is the better buy?
different sizes of paint jars and their prices.
2-oz jar
4-oz jar
Paints
Total Price
4OZ jar
8-oz jar
2-oz jar
$1.50
16-oz jar
4-oz jar
$2.92
8-oz jar
$5.68
16-ozjar
$11.62
Answer:8-oz jar
First, we have to find out what is the unit rate of the 2-oz jar. $1.50÷2 is $.75.
Second, we have to find the unit rate of the 4-oz jar. $2.92÷4=$73.
Third, we have to find the unit rate of the 8-oz jar. $5.68=$.71.
Fourth, we have to find the unit rate of the 16-oz jar. The division for this one may be tricky. From dividing $11.62 by 16, is stopped at the 3rd number I got from dividing. I got $.726. This is not a value of cents and the value can't go in the thousandths place. So, I rounded .726. I got $.73. So $11.62÷16=$.73.
Lastly, you have to compare the amounts.
The lowest amount or better buy, is $.71 or 8-oz jar.
Answer:
8-oz
Step-by-step explanation:
had the same question on the same assignment:)
Paul and Cindy own different pizza shops. Paul makes 12 pizzas the first day and 6 pizzas each day after that. Cindy makes 16 pizzas the first day and 4 pizzas each day after that. Who will have made more pizzas after 9 days? How many pizzas will that person have made?
A . Paul. He has made 80 pizzas after 9 days.
B . Cindy. She has made 132 pizzas after 9 days.
C. Paul. He has made 60 pizzas after 9 days.
D . Cindy. She has made 48 pizzas after 9 days.
The right answer is Option C.
Step-by-step explanation:
Given,
Pizzas made by Paul on first day = 12
Pizzas made each day after that = 6
Let,
p represent the number of pizzas made after first day.
Total pizzas = 6p + 12
Number of days = 8 because first day 12 pizzas are made
Total pizzas = [tex]6(8)+12=60[/tex]
Pizzas made by Cindy on first day = 16
Pizzas made each day after that = 4
Total pizzas = 4p + 16
Total pizzas = [tex]4(8)+16=48[/tex]
Paul has made more pizzas after 9 days. He has made 60 pizzas.
The right answer is Option C.
Keywords: comparison, addition
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Answer:
C
Step-by-step explanation:
A system of equations is shown below.
5x + 3y = -6
2x + y = -4.
Which statement about the ordered pair (-6, 8) is true? Show your work.
A. It is the only solution to the system
B. It is not a solution to either equation
C. It is one of many solutions to the system
D. It is a solution to the first but not the second equation
Answer:
Step-by-step explanation:
(-6,8)...x = -6 and y = 8
lets start subbing
5x + 3y = -6
5(-6) + 3(8) = -6
-30 + 24 = -6
-6 = -6
so (-6,8) IS a solution to this equation
2x + y = -4
2(-6) + 8 = -4
-12 + 8 = -4
-4 = -4
so (-6,8) IS a solution to this equation
A. It is the only solution to the system
Determine the product, h (x), of the linear and quadratic factors.
f(x) = (8x – 3)
and
g(x) = (x - 1)2
h(x)=_______
[tex]h(x) =8x^3-19x^2+14x-3[/tex]
Step-by-step explanation:
Given functions are:
[tex]f(x) = 8x-3\\g(x) = (x-1)^2[/tex]
h(x) is the product of g(x) and f(x)
[tex]h(x) = f(x) * g(x)\\= (8x-3)(x-1)^2\\= (8x-3)(x^2-2x+1)\\= 8x(x^2-2x+1)-3(x^2-2x+1)\\= 8x^3-16x^2+8x-3x^2+6x-3[/tex]
Combining like terms
[tex]=8x^3-16x^2-3x^2+8x+6x-3\\=8x^3-19x^2+14x-3[/tex]
Hence,
[tex]h(x) =8x^3-19x^2+14x-3[/tex]
Keywords: Functions, product
Learn more about functions at:
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An electronics store makes a profit of $72.00 for every television sold and $90.00 for every computer sold. The manager’s target is to make at least $360.00 a day on sales from televisions and computers. Let x = the number of televisions sold. Let y = the number of computers sold. Which of the following represents three possible solutions to the problem?
A. 72x+90y>360 (5,2),(3,3) and (1,4)
B. 72x+90y<360 (4,0),(2,2) and (1,1)
C. 72x+90y>360 (3,1),(2,2) and (1,0)
D 72x+90y>360 (4,0),(3,3) and (1,4)
Answer:
Option A, C and D is the three possible solution.Step-by-step explanation:
Each Television earns $72 and each Computer earns $90.
The manager’s target is to make at least $360.00 a day.
It is not clarified the exact number of Televisions and Computers.
Hence, as per the given condition, [tex]72x + 90y \geq 360\\8x + 10y \geq 40\\4x + 5y \geq 20[/tex].
Now we just need to check the given options, whether they satisfy the above equation, or not.
Except the option B, each inequality indicates a value greater than 360.
Hence, option B can not be the possible solution.
To meet the profit target of 72x + 90y ≥ 360, the correct points are listed in Option A: (5, 2), (3, 3), and (1, 4). These points meet the required profit condition.
To solve this problem, we need to find the inequality that represents the manager's profit target and identify the solutions that meet this condition. Given:
The profit per television is $72 (x represents the number of televisions sold).The profit per computer is $90 (y represents the number of computers sold).The manager’s goal is to make at least $360. This can be represented by the equation: 72x + 90y ≥ 360.
We need to check which option lists points that satisfy this inequality. Let's test the points:
Option A: 72x + 90y > 360 (5, 2), (3, 3), and (1, 4)
(5, 2): 72(5) + 90(2) = 360 + 180 = 540 (satisfies ≥ 360)(3, 3): 72(3) + 90(3) = 216 + 270 = 486 (satisfies ≥ 360)(1, 4): 72(1) + 90(4) = 72 + 360 = 432 (satisfies ≥ 360)Option B: 72x + 90y < 360 (4, 0), (2, 2), and (1, 1)
(4, 0): 72(4) + 90(0) = 288 (does not satisfy ≥ 360)(2, 2): 72(2) + 90(2) = 144 + 180 = 324 (does not satisfy ≥ 360)(1, 1): 72(1) + 90(1) = 72 + 90 = 162 (does not satisfy ≥ 360)Option C: 72x + 90y > 360 (3, 1), (2, 2), and (1, 0)
(3, 1): 72(3) + 90(1) = 216 + 90 = 306 (does not satisfy ≥ 360)(2, 2): 72(2) + 90(2) = 144 + 180 = 324 (does not satisfy ≥ 360)(1, 0): 72(1) + 90(0) = 72 (does not satisfy ≥ 360)Option D: 72x + 90y > 360 (4, 0), (3, 3), and (1, 4)
(4, 0): 72(4) + 90(0) = 288 (does not satisfy ≥ 360)(3, 3): 72(3) + 90(3) = 216 + 270 = 486 (satisfies ≥ 360)(1, 4): 72(1) + 90(4) = 72 + 360 = 432 (satisfies ≥ 360)Only Option A lists points that all satisfy the inequality 72x + 90y ≥ 360. Therefore, Option A is the correct answer.
Find x and y
x = ?
y = ?
Answer:
Part 1) [tex]x=1.25\ units[/tex]
Part 2) [tex]y=1.75\ units[/tex]
Step-by-step explanation:
In this problem
the triangles of the figure are similar by AA Similarity Theorem
Remember that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
Applying proportion
Find the value of x
[tex]\frac{5}{5+x}=\frac{8}{10}[/tex]
solve for x
[tex]5(10)=8(5+x)\\50=40+8x\\8x=50-40\\8x=10[/tex]
[tex]x=\frac{10}{8}=1.25\ units[/tex]
Find the value of y
[tex]\frac{7}{7+y}=\frac{8}{10}[/tex]
solve for y
[tex]7(10)=8(7+y)\\70=56+8y\\8y=70-56\\8y=14[/tex]
[tex]y=\frac{14}{8}=1.75\ units[/tex]
janet is going to hire a makeup artist for a fashion show and is comparing prices. Austin charges $54 as a booking fee and an additional $80 per hour. Brad charges $69 per hour, plus a booking fee of $65. Depending on the length of the show, the cost could end up being the same for either artist. How long would the show be? What would the cost be?
Step-by-step explanationF(t)= 24 + 36*t
G(t) = 22 + 38*t
They are the same when 24 + 36t = 22 + 38t
Everything to right side: 0 = 22 + 38t - 24 - 36t
0 = 2t - 2
2 = 2t
t=1
THey are the same at one hour.
Longer than 1 hour, the first one is cheaper.
Here's the table to compare them side by side
t 24 + 36 t 22 + 38t
1/2 42 41
1 60 60
2 96 98
3 132 136
The fashion show needs to be 1 hour long for the cost of hiring either makeup artist Austin or Brad to be the same.
To determine how long the fashion show would need to be for the costs of hiring makeup artists Austin and Brad to be the same, we can set up an equation based on their respective fees. Austin charges a booking fee of $54 plus $80 per hour, while Brad charges a $65 booking fee plus $69 per hour.
Let's let 'h' be the number of hours for which the fashion show will run. For Austin, the total cost will be $54 + $80h. For Brad, the cost will be $65 + $69h. To find the number of hours where the costs are equal, we set the two expressions equal to each other:
54 + 80h = 65 + 69h
Now we solve for 'h':
Subtract 69h from both sides: 54 + 11h = 65
Subtract 54 from both sides: 11h = 11
Divide both sides by 11: h = 1
So, the fashion show needs to be 1 hour long for the cost of hiring either makeup artist to be the same, which would be $134.
plz explain and help me answer this question
Answer:
-637
Step-by-step explanation:
What number divide by -7 gives you 91
Algebra 2! Height is 256.
Answer:make a graph
Step-by-step explanation:
A boat travels 12 Mph in still water. It can travel 18 miles upstream in the same time that it can travel 24 miles downstream. What is the current of the water?
Answer:
[tex]1 \dfrac{5}{7}\ mph[/tex]
Step-by-step explanation:
Let x mph be the current's rate.
Upstream:
Distance = 18 miles
Rate = 12 - x mph
Time [tex]=\dfrac{18}{12-x}[/tex] hours
Downstream:
Distance = 24 miles
Rate = 12 + x mph
Time [tex]=\dfrac{24}{12+x}[/tex] hours
Time is the same, so
[tex]\dfrac{18}{12-x}=\dfrac{24}{12+x}\\ \\18(12+x)=24(12-x)\\ \\216+18x=288-24x\\ \\18x+24x=288-216\\ \\42x=72\\ \\x=\dfrac{12}{7}=1 \dfrac{5}{7}\ mph[/tex]