Answer:
70/17 hours or 4 2/17 hours
Step-by-step explanation:
The equation we use is 1/7 + 1/10 = 1/x, x being the time it took them together to build. x works out to 70/17 hours
Leah and her apprentice can build the wall together in 4 2/17 hours
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Hours required by Leah to build a wall = 7 hours
So , Leah builds ( 1/7 )th of the wall per hour
Hours required by apprentice to build a wall = 10 hours
So , Apprentice builds ( 1/10 )th of the wall per hour
When they are both building the wall together , they build
( 1/7 )th + ( 1/10 )th of the wall together per hour = 1 / x
Therefore , the equation will be
1/x = 1/7 + 1/10
1/x = 17 / 70
Taking reciprocal on both sides , we get
x = 70/17
x = 4 2/17 hours
Hence , Leah and her apprentice can build a wall together in 4 2/17 hours
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For questions 3 - 6, find F'(x), the inverse of F(x).
3. F(x) = x-10
4. F (x) = x/6 + 3
5. F(x) = 3x + 7
6. F(x) = 8x
Answer:
3) f'(x) = x + 10
4) f'(x) = 6x - 18
5) [tex]\displaystyle\mathsf{f'(x)=\frac{1}{3}x-\frac{7}{3}}[/tex] or [tex]\displaystyle\mathsf{f'(x)=\frac{x - 7}{3}}[/tex]
6) f'(x) = ⅛x or [tex]\displaystyle\mathsf{f'(x)=\frac{x}{8}}[/tex]
Step-by-step explanation:
3. f(x) = x - 10Step 1: In order to find the inverse function of f(x) = x - 10, start by replacing f(x) with y.
y = x - 10
Step 2: Switch x and y:
x = y - 10
Step 3: Add 10 to both sides to isolate y:
x + 10 = y - 10 + 10
x + 10 = y
Step 4: Replace y with f'(x):
f'(x) = x + 10 ⇒ This is the inverse function of f(x).
4. [tex]\displaystyle\mathsf{f(x)=\:\frac{x}{6}\:+\:3}[/tex]Replace f(x) with y:
[tex]\displaystyle\mathsf{y=\:\frac{x}{6}\:+\:3}[/tex]Switch x and y:
[tex]\displaystyle\mathsf{x=\:\frac{y}{6}\:+\:3}[/tex]Subtract 3 from both sides:
[tex]\displaystyle\mathsf{x-3=\:\frac{y}{6}\:+\:3-3}[/tex][tex]\displaystyle\mathsf{x-3=\:\frac{y}{6}}[/tex]Multiply both sides by 6 to isolate y:
[tex]\displaystyle\mathsf{6(x-3)=\:\frac{y}{6}(6)}[/tex]6x - 18 = y
Replace y with f'(x):
f'(x) = 6x - 18 ⇒ This is the inverse function of f(x).
5. f(x) = 3x + 7Replace f(x) with y:
y = 3x + 7
Switch x and y:
x = 3y + 7
Subtract 7 from both sides:
x - 7 = 3y + 7 - 7
x - 7 = 3y
Multiply both sides by ⅓:
⅓(x - 7) = 3y (⅓)
[tex]\displaystyle\mathsf{\frac{1}{3}x-\frac{7}{3}=y}[/tex]
Replace y with f'(x):
[tex]\displaystyle\mathsf{f'(x)=\frac{1}{3}x-\frac{7}{3}}[/tex] or [tex]\displaystyle\mathsf{f'(x)=\frac{x - 7}{3}}[/tex] ⇒ This is the inverse function of f(x).
6. f(x) = 8x
Replace f(x) with y:
y = 8x
Switch x and y:
x = 8y
Multiply both sides by ⅛:
⅛(x) = ⅛(8y)
⅛x = y or [tex]\displaystyle\mathsf{\frac{x}{8}=y}[/tex]
Replace y with f'(x):
f'(x) = ⅛x or [tex]\displaystyle\mathsf{f'(x)=\frac{x}{8}}[/tex] ⇒ This is the inverse function of f(x).
Evaluate - (3 ^ - 5) * (3 ^ 3)
Answer:
1 / 3^2 = 1/9
Step-by-step explanation:
3^-5 = 1/3^5
(1/3^5) * (3^3) = 3^3 / 1/3^5 = 3^3 / 3^5 = 1/3^2
The value of the given expression is 1/9 .
Given,
[tex](3^{-5}) (3^{3} )[/tex]
According to the power rule,
[tex](a^{m}) (a^{n} ) = a^{m + n}[/tex]
Now,
[tex](3^{-5}) (3^{2}) = 3^{-5 + 3}\\ \\ (3^{-5}) (3^{2}) = 3^{-2}[/tex]
[tex](3^{-5}) (3^{2}) = 1/3^{2}[/tex]
[tex](3^{-5}) (3^{2} ) = 1/9[/tex]
Thus with the power rule answer will be 1/9.
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A small town has two local high schools. High School A currently has 250 students and is projected to grow by 50 students each year. High School B currently has 450 students and is projected to grow by 25 students each year. Let A represent the number of students in High School A in t years, and let B represent the number of students in High School B after t years. Graph each function and determine after how many years, t, the number of students in both high schools would be the same.
give me the corrdent plan point i need 2 for example
(5,2) and (4,1) like that on the graph
Answer: ________
students
students per year
years
years of student
Answer:
in 8 years both school will have 650 students
Step-by-step explanation:
HS A (t) = 250+50t
HSB (t) = 450+25t
250 + 50t = 450 + 25t
25t=200
t=8
in 8 years
to graph this:
HSA points (0,250) (2, 350) (4, 450) (8, 650)(10, 750)
HSB points (0, 450) ( 2, 500) (4, 550) (8, 650) (10, 700)
when you graph then you will notice they intercept at 8, which gives you 650 students
Addison plays 6 songs in of an hr. How many
songs can she play for 4 hours?
Answer:
24
Step-by-step explanation:
4x6=12or 2x6=12so then 12+12=24
Answer:
6 songs per hour, so multiply that with the number asked which is four
so four times six is24
so she can play 24 songs in four hours!
~ ...
~ !
~ !
Convert to an exponential equation.
In 17 = 2.8332
Answer:
17 = e^2.8332
Step-by-step explanation:
Mariam only saves quarters and dimes. She has already saved 13 quarters and 5 dimes. She wants to purchase a book that costs 7.75. Not including the money she already has, what combinations of quarters and dimes could Mariam save so she has exactly enough money to buy the book?
Answer: 8 Quarters, 20 Dimes
Quarters:
Current/ 13
13x25= 3.25
Dimes:
Current/ 5
5x10= 50 …. 50 cents
Current price: $3.75
Need $4.00
What you need:
Quarters: +8
4 = 100 x2 is 200 …. $2.00
Dimes: + 20
10 = 100 x2 is 200 … $2.00
Will give brainliest
Answer:
down - up +
Step-by-step explanation:
how long is the shadow the tree casts?
Anwser: 12 feet long
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Answer:
f^-1(x) = [ln (x + 4)]/2
Step-by-step explanation:
f(x) = e^(2x) - 4
y = e^(2x) - 4
x = e^(2y) - 4
x + 4 = e^(2y)
ln (x + 4) = ln (e^(2y))
ln (x + 4) = 2y
y = [ln (x + 4)]/2
f^-1(x) = [ln (x + 4)]/2
you’ll live 100 more years if you help me answer 1 through 5 :D!!!
Answer:
You need to give me a thanks and brainliest: 1. = 16 ; 2. = 100 ; 3. = 64; 4. = 604; 5. Cant see the problem in the screen shot.
Step-by-step explanation:
nesesito ayuda ..........4c`````````````````````````````````````````````````````z#DRsw
Answer: ???
Step-by-step explanation:
A water tank is 50cm by 30cm by 20cm. If 1 litre of water costs 300 taka, what is the total cost to fill up the tank with water?
Answer:
Step-by-step explanation:
The volume of the tank= (50x30X20) cm^3
= 30000cm^3
= 30 l
1 l costs 300 tk
therefore 30 l costs= 30X300 taka
= 90000 taka
5^-x = 6
Help ASAP
STEPS MUST.
We have to Find:
The value of x[tex] \sf \longmapsto5^{ - x }= 6[/tex]
Let's start.
Take Logarithm of both sides[tex] \sf \longmapsto log(5^{-x}) = log(6) [/tex]
Solving Further[tex] \sf \longmapsto - x \: log(5) = log(6)[/tex]
[tex] \sf \longmapsto - x = \dfrac{ log(6) }{ log(5) } [/tex]
Take the minus from (-x) and put in on log(6)[tex] \sf \longmapsto \: x = \dfrac{ -log(6) }{ + log(5)} [/tex]
Done
Find Y if f(x)=g(x),please help me to answer this problem.
If f(x) = g(x)
Then :
(x-4)/(x²+1) = (x² - 4) / (x²+ 1)
We can simplify on both sides by x² + 1 :
x - 4 = x² - 4
x = x²
x - x² = 0
x(1-x) = 0
So either x = 0, or x = 1
S = {0,1}
Good Luck
Answer:
Step-by-step explanation:
( x , y )
( 0 , - 4 )
( 1 , - 1.5 )
[tex]y_{1}[/tex] = - 4
[tex]y_{2}[/tex] = - 1.5
please help me i really need it and NOOOO BOTS
the length of the house is 1,200 feet and 1,100 feet wide. what is the perimiter
Answer:
4,600
Step-by-step explanation:
1,200+1,200+1,100+1,100
Latonya swims 50 meters in 1/2 minute. What is the slope
Answer: 100
Step-by-step explanation: 50 x 1/2=100
what is equation of the line shown in this graph
Since this is a horizontal line, the equation for this is simply
[tex]y = -3[/tex]
Highland Park is located between two parallel streets, Walker street and James Avenue. The park faces Walker Street and is bordered by two brick walls that intersect James Avenue at point C, as shown below. Walker St. Highlands Park brick wall brick wall 60 James Ave. What is the measure, in degrees, of ZACB, the angle formed by the park's two bri walls?
Applying the definition of alternate angles and angles on a straight-line: m<ACB = 84°.
Recall:
Alternate angles are congruent and have equal angle measures.Angles on a straight-line = 180 degrees.The diagram showing the information and sketch of the Highland Park is attached below (see attachment).
Thus:
m<BAC = 36° (given)
m<BCE = 60° (given)
<ACD = <BAC (alternate angles)
Therefore,m<ACD = 36°
m<ACB = 180° - (m<ACD + m<BCE) (angles on a straight-line)
Substitutem<ACB = 180° - (36° + 60°)
m<ACB = 84°
Thus, applying the definition of alternate angles and angles on a straight-line: m<ACB = 84°.
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Can anybody answer this for me?
[tex]\\\text{Given that,}\\\\(x_1 , y_1) = (5,6) ,~~ (x_2, y_2) = (-5,-4)\\\\\text{Slope},~m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{-4-6}{-5-5} = \dfrac{-10}{-10} = 1[/tex]
x^3-3x^2+x-2/10x^4-14x^3-10x^2+6x-10
Answer:
The quotient is 10x+16
The remainder is 28x^2+10x+22
Precalc please help!!
Answer:
Step-by-step explanation:
You accelerate from 5m/s to 60m/s in 11 seconds what is the average acceleration.
Change in acceleration: 60 - 5 = 55 m/s
Average acceleration = 55 m/s / 11 second = 5 meters per second squared ( m/s^2)
Answer: 5 m/s^2
There are 14 girls and 15 boys in a sixth grade math class. What is the ratio of girls to total students?
100 POINTS! show work or i report!
Michael purchases a refrigerator for $4,000. On average, it costs $120 per year in electricity to leave it running 24/7. What is the average yearly cost to own and operate this refrigerator at the end of 6 years?
Answer:
$4,720
Step-by-step explanation:
$4,000 fridge
$120/1 year
[tex]\frac{120}{1} = \frac{x}{6}[/tex]
120 * 6 = 720
720 / 1 = 720
$720 for 6 years
720 + 4,000 = 4,720
$4,720
Answer:
$4,720
Step-by-step explanation:
What is the value of 1027
A. 100
B. 1,000
C. 10,000
D. 100,000
Answer:
huh? this doesn't even make sense or I'm just tripib
Step-by-step explanation:
-xoxo
I need some help math
Answer:
ok I will help you please wait for some time
Answer:
23
Step-by-step explanation:
Add the total number of hours in the given situation
A water tank has volume of 300 m3. If the length and width of the tank is 5 m and 300 cm, find the height of the tank.
Answer:
volume=300m3
length=5m
width=300cm=300/100=3m
To find: height of tank .
so,
volume=l×b×h
300=5×3×h
300/15=h
finally,h=20m
Find the volume of a cylinder either enter. An exact answer in terms of pie or 3.14 please help me
When you have > or <, the solutions are only in the shaded area.
True
or
False
Answer: True
Step-by-step explanation: Because the solutions can not land on the dotted lines.