Step-by-step explanation:
Q1 . (f+g)(x) = f(x) + g(x)
=4x-4 +2x^2 -3x
= 2x^2 + x -4
Q2. (f-g)(x) = f(x) - g(x)
= 2x^2−2 - (4x+1)
= 2x^2 -2 -4x -1
= 2x^2 - 4x -3
Q3. h(x)=3x−3 and g(x)=x^2+3
(h.g)(x) = h(x) × g(x)
= (3x-3) × (x^2 + 3)
=3x^3 -3x^2 + 9x -9
Q4.f(x)=x+4 and g(x)=x+6
(f/g)(x) = f(x) ÷ g(x)
= x+4 / x+6
the domain restriction is x>-6
x<-6
x doesn't equal (-6)
If the two function f(x) and g(x) are to be combined, use basic arithmetic rules,
(f + g)(x) = f(x) + g(x)
(f - g)(x) = f(x) - g(x)
[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]
(f . g)(x) = f(x) × g(x)
Question 1
f(x) = 4x - 4 and g(x) = 2x² - 3x
[tex](f+g)(x)=f(x)+g(x)[/tex]
Therefore, [tex](f+g)(x)=(4x-4)+(2x^2-3x)[/tex]
[tex]=2x^2+x-4[/tex]
Question 2
f(x) = 2x² - 2 and g(x) = 4x + 1
Since, (f - g)(x) = f(x) - g(x)
Therefore, (f - g)(x) = (2x² - 2) - (4x + 1)
= 2x² - 2 - 4x - 1
= 2x² - 4x - 3
Question 3
h(x) = 3x - 3 and g(x) = x² + 3
Since, (h - g)(x) = h(x) - g(x)
Therefore, (h - g)(x) = (3x - 3) - (x² + 3)
= 3x - 3 - x² - 3
= -x² + 3x - 6
Question 4
F(x) = x + 4 and g(x) = x + 6
Since, [tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]
Therefore, [tex](\frac{f}{g})(x)=\frac{x+4}{x+6}[/tex]
Learn more,
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two candles, each initial length of 30cm, are 20cm apart. the thinner candle burns at a rate of 1cm every 8 minutes and the other candle burn at a rate of 1 cm every 10 minutes. find two possible lengths for the distance between the tops of the two candles, if the candles can burn up for 3 hours.
Thinner candle:
y = length of the candle
x = rate it burns at every minute
y = -1/8x + 30
Thicker candle:
y = length of the candle
x = rate it burns at every minute
y = -1/10x + 30
To find the length after 3 hours:
y = -1/8(180) + 30
y = -1/10(180) + 30
Janet deducted $5 on Monday and another $6 on Tuesday from her savings account. How much money did Janet deduct?
pls give me answer fast and thank you
Answer:
1) [tex]\frac{x+3}{2x-5}=\frac{3}{2}[/tex] (x ≠ 2,5)
=> 2(x + 3) = 3(2x - 5)
⇔ 2x + 6 = 6x - 15
⇔ 4x = 6 + 15
⇔ 4x = 21
⇔ x = 5,25
2) [tex]\frac{5y-2}{2y+8}=\frac{5}{6}[/tex] (y ≠ -4)
⇒6( 5y - 2) = 5(2y + 8)
⇔30y - 12 = 10y + 40
⇔ 20y = 52
⇔ y = 2,6
3) the denominator of the rational number is x (x ≠ 0)
because the denominator is greater than the numerator by 6
=> the numerator is x - 6
If the numerator is decreased by 1 and the denominator increased
by 1 , the number obtained is 1/3. so we have:
[tex]\frac{x-7}{x+1}=\frac{1}{3}[/tex]
⇒ 3(x - 7) = x + 1
⇔ 3x - 21 = x + 1
⇔ 2x = 22
⇔ x = 11
with x = 11 => the rational number is 5/11
4) the number we need to find is ab (a ≠ 0)
because Sum of the digits of this number is 8
=> a + b = 8 (*)
When we interchange the digits , it is found that the resulting new number is less than the original number by 18, we have:
ab - ba = 18
⇔ 10a + b - (10b + a) = 18
⇔ 9( a - b) = 18
⇔ a - b = 2 (**)
(*)(**) => a + b = 8
a - b = 2
=> a = 5
b = 3
=> the original number is 53
5) the present Arjun's age is x (years old)( x, y E N*)
the present Shriya's age is y
because now, Arjun is twice as old as Shriya => x = 2y
Five years ago, his age was three times Shriya’s age, we have:
=> x - 5 = 3(y - 5)
⇔ x - 5 = 3y - 15
⇔ 3y - x = 10
but x = 2y => y = 10
=> x = 20
so now, Arjun is 20 years old, Shriya is 10 years old
Step-by-step explanation:
8.4 Sampling on Campus. You would like to start a club for psychology majors on campus, and you are interested in finding out what proportion of psychology majors would join. The dues would be $35 and used to pay for speakers to come to campus. You ask five psychology majors from your senior psychology honors seminar whether they would be interested in joining this club and find that four of the five students questioned are interested. Is this sampling method biased, and if so, what is the likely direction of bias
Answer:
To convert the measurements of metric system into another units of metric system we have to either multiply it by 10, 100, 1000, 10000, 100000, etc or divide by 10, 100, 1000, 10000, 100000, etc.
If we have to convert bigger unit into smaller unit then we have to multiply the unit by the multiples of 10, then the decimal point is shifted to right by 1 or 2 or 3 or 4 , etc. places.
For example, 1.2 kg is converted into g so we have to multiply it by 1000, so decimal point is shifted to right by 3 places, i.e.,
1.2 x 1000 = 1200 g
If we have to convert smaller unit into bigger unit then we have to divide the unit by the multiples of 10, then the decimal point is shifted to left by 1 or 2 or 3 or 4 , etc. places.
For example, 12 cm is converted into m so we have to divide it by 100, so decimal point is shifted to left by 2 places, i.e.,
12 / 100 = 0.12 m
Step-by-step explanation:
What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4)?
O y=
--x-1
Oy=-x+5
O y=-x-1
O y=x+5
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Mark this and retum
The equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4) is y = [tex]-\frac{5}{x} x-1[/tex]
Parallel lines
Parallel lines have the same slope. Therefore, using slope intercept form.
y = mx + b
m = slope
b = y-intercept
Therefore,
5x + 2y = 12
2y = -5x + 12
[tex]y = -\frac{5}{2} x+12[/tex]
The slope of the line is [tex]-\frac{5}{2}[/tex]
Base on parallelism, for the line that passes through (-2, 4)
y = mx + b
4 = [tex]-\frac{5}{2} (-2)+b[/tex]
b = -1
Therefore,
y =
learn more on parallel lines here: https://brainly.com/question/18245473
Graph and Label the Points on the coordinate plane below
पाठका सहायताले तलका उखानहरूको अर्थ लेख्नुहोस् : (क) सपनामा खोले खाएको भनेको यही हो
Answer:
pura na hune kaam hunxa vanera jabarjasti garnu. maybe
Two thirds of a number is 24. Find the number.l
Answer:
36
Step-by-step explanation:
of means multiply and is means equals
2/3 *x = 24
Multiply each side by 3/2
3/2 * 2/3 *x = 24 * 3/2
x = 36
Anwser these questions
Car A costs $10,000 to buy and costs an average of $0.25 per mile to maintain. Car B costs $15,000 to buy and costs an average of $0.15 per mile to maintain. After how many miles would the total cost for each car be the same?
Answer: respuesta A EN 40000 millas
en EN 1000000B
Step-by-step explanation
helpppp quick please!! explanation and answers! thanks:)
Answer:
DO NOT CHEAT
Step-by-step explanation:
IT'S HARAM >:(
Kendra bought 235 donuts for $120. Her profit was $35 once she had sold 100 donuts. Which equation below represents Kendra’s profit P(n), as a function of the number sold, n?
P(n)=0.85n-120
P(n)=-0.85n+120
P(n)=0.35n
P(n)=1.55n-120
-(x)+2)=2(3x-6) awnser
Answer:
[tex] -( x) + 2 = 2(3x - 6) \\ - x + 2 = 2 \times 3x - 2 \times 6 \\ - x + 2 = 6x - 12 \\ x \: terms \: togther \\ - x - 6x = - 12 - 2 \\ - 7x = - 14 \\ x = \frac{ - 14}{ - 7} = 2 \\ x = 2 \\ thank \: you[/tex]
The number of viewers of a television station in 2003 was 640000.
(a) In 2004, the station had 716800 viewers. Calculate the percentage increase in the number of viewers from 2003 to 2004.
Each year, the television station invites it's viewers to vote for their favourite actors and actresses.
(b) In 2005, the number of viewers was 896000. Of those viewers, 108000 voted.
(i) Calculate the percentage of viewers who voted in 2005, giving your answer correct to the nearest whole number.
(ii) The number of viewers who voted in 2005 was 20% more than that in 2004. Calculate the number of viewers who voted in 2004.
__________
__________
__________
State your answers with the method of how you got your answers.
Answer:
see the attachment hope it helps you
Step-by-step explanation:
Friends is an American television sitcom created by David Crane and Marta Kauffman, which aired on NBC from September 22, 1994, to May 6, 2004, lasting ten seasons.[1] With an ensemble cast starring Jennifer Aniston, Courteney Cox, Lisa Kudrow, Matt LeBlanc, Matthew Perry and David Schwimmer, the show revolves around six friends in their 20s and 30s who live in Manhattan, New York City. The series was produced by Bright/Kauffman/Crane Productions, in association with Warner Bros. Television. The original executive producers were Kevin S. Bright, Kauffman, and Crane.
Subtract -2x^2-4x+2 from -6x+2
Answer:
2x(x-1)
Step-by-step explanation:
-6x+2-(-2x^2-4x+2)
-6x+2+2x^2+4x-2
2x^2-6x+4x+2-2
2x^2-2x
2x(x-1)
Answer:
2x² - 2x
Step-by-step explanation:
- 6x + 2 - (- 2x² - 4x + 2) ← distribute parenthesis by - 1
= - 6x + 2 + 2x² + 4x - 2 ← collect like terms
= 2x² - 2x
Please answer both questions and Show Work... I will mark you brainliest and give you five starts
Answer:
Step-by-step explanation:
For each problem you need to make sure that the angles are the same.
So x + 22 = 90
x = 90 -22 = 68 degree
For the second problem
7x + 10 = 8x
10 = 8x -7x
x = 10 degree
In this diagram, BAC~EDF. If the area of BAC=15 in2, what is the area of EDF? 4, 5.
Enter a decimal rounded to the tenths.
Answer:
9.6 square inches.
Step-by-step explanation:
We are given that ΔBAC is similar to ΔEDF, and that the area of ΔBAC is 15 inches. And we want to determine the area of ΔDEF.
First, find the scale factor k from ΔBAC to ΔDEF:
[tex]\displaystyle 5 k = 4[/tex]
Solve for the scale factor k:
[tex]\displaystyle k = \frac{4}{5}[/tex]
Recall that to scale areas, we square the scale factor.
In other words, since the scale factor for sides from ΔBAC to ΔDEF is 4/5, the scale factor for its area will be (4/5)² or 16/25.
Hence, the area of ΔEDF is:
[tex]\displaystyle \Delta EDF = \frac{16}{25}\left(15\right) = 9.6\text{ in}^2[/tex]
In conclusion, the area of ΔEDF is 9.6 square inches.
[tex](x^2+3)^{-1/3} -2/3x^2(x^2+3)^{-4/3}[/tex]
Factor the expression completely.
Answer:
[tex] \frac{ {x}^{2} + 9 }{3 \sqrt[3]{ {x}^{2} } + 3( {x}^{2} + 3)} [/tex]
Step-by-step explanation:
attached
if 1 kg is equivalent to 1.000g then 8.500g is 8.5kg?
Answer:
too
Step-by-step explanation:
hhsihwhsusqioshsisjwk shshsusbsoosjs
359, 352,345,...
{Find the 38th term.}
Answer:
100
Step-by-step explanation:
Here, the series is in A.P.
first term a = 359
common difference d = 352-359 = -7
therefore, 38th term = a + [n-1] d
= 359 + (38 -1) (-7)
= 359 - 259
= 100
Which inequality is true?
C, because π ≈ 3,14 so 9π = 9 · 3,14 = 28,26 > 27
To keep it simple i am confused about this problem what can i do?
*show work
*will give brainlist
Answer:
11. 10, 20,30,40,50,60,70
12. 35, 45,55,65,75,85,95
Step-by-step explanation:
10 dollars per week for 7 weeks in equivalent to 10x7 which equals $70.
If you already had $25 you would do 10x7+25. Using PEMDAS you would multiply first (10x7=70) then add 25 (70+25=95)
Order the number from least to greatest
1. root of seven, 2, root of 8/2
2. root of 220, -10, root of 100, 11.5
A sheet of standard-size copy paper measures 8.5 in. by 11 in. If a ream (500 sheets) of this paper has a volume of 187(to the third power) in. , how thick is the ream.
I need an explanation on how to do it please.
============================================================
Explanation:
The area of any given sheet of paper is 8.5*11 = 93.5 square inches.
Divide the volume over this area to get the height of the stack
187/(93.5) = 2
The stack is 2 inches tall.
Extra info: The thickness of each piece of paper is 2/500 = 0.004 of an inch which approximates to about 0.1016 mm.
4
A study measured the average rainfall in 130 months in the state of Hawaii. The average monthly rainfall was 3.7 inches with a stand
0.3 inches. Assume the data is normally distributed. How many months of rainfall had between 3.4 and 4 inches of rainfall?
130 months
124 months
68 months
112 months
88 months
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1
Answer:
I'm unsure, I've seen questions like this before but not this one
Riley's monthly bank statement showed the following deposits and withdrawals:
-−$105.11, -−$33.75, $113.62, $119.42, $29.64
If Riley's balance in the account was $35.27 at the beginning of the month, what was the account balance at the end of the month?
Answer:
$159.09
Step-by-step explanation:
Math
Find the measure of ABD.
Answer:
ABD=26°.
SEE THE IMAGE FOR SOLUTION
Solve the inequality
3(x-2)>-3
Answer:
x>1
Step-by-step explanation:
m at h w ay
what is 2+34-18+2-5+100-49
Answer:
[tex]2 + 34 - 18 + 2- 5 + 100 - 49 \\ = 36 - 16 + 95 - 49 \\ = 20 + 95 - 49 \\ = 115 - 49 \\ = 66 \\ thank \: you[/tex]
Answer:
The answer is 66.
Step-by-step explanation:
→ 2 + 34 - 18 + 2 - 5 + 100 - 49
→ (2 + 34 - 18 + 2 - 5) + (100 - 49)
→ 15 + 51 = 66
Thus, 66 is the solution.
Please awnser
Find m
Find m
Answer:
x = 37
m∠a = 104°
m∠b = 76
Step-by-step explanation:
Two supplementary angles will add up to 180 degrees. We can create an equation and solve for x.
3x - 7 + 2x + 2 = 180
~Combine like terms
5x - 5 = 180
~Add 5 to both sides
5x = 185
~Divide 5 to both sides
x = 37
~Find the measure of angle A
3(37) - 7
104
~Find the measure of angle B
2(37) + 2
76
Best of Luck!
