Answer: y=x³+2 or f⁻¹(x)=x³+2
Step-by-step explanation:
To find the inverse of the radical function, we replace y with x and x with y. Then, you solve for y.
[tex]y=\sqrt[3]{x-2}[/tex] [replace y with x and x with y]
[tex]x=\sqrt[3]{y-2}[/tex] [cube both sides to cancel out the cubed root]
[tex]x^3=y-2[/tex] [add both sides by 2]
[tex]x^3+2=y[/tex]
Now that we have switched the variables and solved for y, we know that the inverse function is y=x³+2 or f⁻¹(x)=x³+2.
Answer:
f^-1(x)=x^3+2
Step-by-step explanation:
What is the x-intercept of the graph -4x=20
Answer:
-4x=20
x=20/-4
x=-5
maybe not sure
Johanna rode her bike 7 miles to a lake . She rode 3/4 of distance to the lake before lunch. How many miles did johanna ride before lunch?
Answer:
5.25 miles
Step-by-step explanation:
Total distance = 7 miles
Distance she rode before lunch = 3/4 of the total distance
=> 3/4 of 7
=> 21/4
=> 5.25 miles
So, she drove 5.25 miles before lunch.
What does a “3-mile” radius mean? What does it look like, and how large is it?
Answer:
the radius is halfway across the circle, while diameter is all the way across. for reference, a three mile radius would be equivalent to 52.8 football fields
Step-by-step explanation:
Through a host of various investors, you have finally raised enough capital to begin producing the next summer blockbuster. You have a budget of 279 million dollars, which you must allocate between filming and editing. The general consensus among experts is that filming tends to cost twice as much as editing. How much money should you allocate to filming?
Answer:
$186 million
Step-by-step explanation:
The ratio of costs is ...
filming : editing = 2 : 1
So, the filming cost as a fraction of the total cost is ...
filming : total cost = 2 : (2+1) = 2/3
The allocation to filming is ...
(2/3)($279 million) = $186 million
Find the sum of the first 9 prime numbers.
Answer:
100
Step-by-step explanation:
The first 9 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and 23.
Their sum is 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 100
1/x - 1/y = 1/4
1/x^2 - 1/y^2 = 3/16
x + y = ...
GIVEN:
1/x - 1/y = ¼.1/x² - 1/y² = 3/16.TO FIND:
The value of x + y.ANSWER:
Firstly let us assume ,
p = 1/x .q = 1/y .Now the equⁿ s becomes ,
=> p - q = 4 . ........(1)
Also , given that:
=> 1/x² - 1/y² = 3/16.
=> p² - q² = 3/16.
=> (p+q)(p-q) = 3/16.
From (1),
=> 4 (p+q) = 13/16.
=> (p+q) = 13/16 × 1/4.
=> p+ q = 13/64.
On adding (1) and (2) ,
=> 2p = 4 + 13/64.
=> 2p = 256+13/64.
=> p = 269/64 × 1/2.
=> p = 269/128.
Now lets find q ,
=> q = 13/64 - 269/128.
=> q = 26-269/128.
=> q = -243/128.
Hence
p = 269/128.q = -243/128..°. x = 128/269 , y = -128/243
PLZ HELP ME OUT Is 1.3 rational or irrational? Is 36 rational or irrational Is 3.14 or pi rational or irrational Is 2/3 rational or irrational
A rational number can be made by dividing two integers.
An irrational number cannot be made by dividing two integers.
1.3 is rational
36 is rational
2/3 is rational
Pi is not rational
witch is the simplified form of x-12
the distance from a boy's house to his school is 10km. he left home at 6.30am, cycling at the rate of 4km/h. if he spent 15 minutes on the way waiting for his friend, when did he get to school?
Answer:
9:15 am
Step-by-step explanation:
First you know the speed and you know the distance.
So now we have to find the time it took for him to get to school(ignore the waiting time first)
time=10/4=2.5h
now we add the waiting time,
2.5h+0.25h(15minutes is the same as 0.25h)=2.75h
convert 0.75h to minuts,
0.75*60=45minutes
6.30+2.45=9.15am
The boy arrived at school at 8:15 am after cycling for 2.5 hours and waiting for 15 minutes.
Given Distance from the boy's house to school = 10 km
Cycling speed = 4 km/h
Time spent waiting for his friend = 15 minutes
Now calculate the time it took for the boy to cycle the distance from his house to the meeting point, excluding the waiting time.
Distance = Speed × Time
10 km = 4 km/h × Time
Time = 10 km / 4 km/h
Time = 2.5 hours
Now, we need to convert the waiting time from minutes to hours, so we can add it to the cycling time.
Waiting time = 15 minutes / 60 minutes/hour
Waiting time = 0.25 hours
Add the cycling time and waiting time to determine the total time it took for the boy to reach school.
Total time = Cycling time + Waiting time
= 2.5 hours + 0.25 hours
=2.75 hours
We need to determine the arrival time by adding the total time to the departure time.
Arrival time = Departure time + Total time
Arrival time = 6.30 am + 2.75 hours
To calculate the arrival time, we need to consider the minutes and hours separately:
Minutes: 30 minutes + (0.75 hours × 60 minutes/hour)
= 30 minutes + 45 minutes
= 75 minutes
Since 75 minutes is more than an hour, we need to adjust the hours and minutes accordingly.
Adding the hours: 6 + 2 = 8
So, the boy arrived at school at 8:15 am.
Therefore, the boy arrived at school at 8:15 am.
To learn more on Distance click:
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1.) Which of the following is the correct equation for the Pythagorean Theorem, where a and b are the side lengths and c is the length of the hypotenuse?
a.) (a+b)^2=c^2
b.) a^2+b^2=c^2
c.) a^2-b^2=c^2
d.) (a-b)^2=c^2
3.) Find the distance between the points (9, −7) and (5, −4).(1 point)
a.) 5
b.) 25
c.) √7
d.) √137
4.) To find the distance between (17, 3) and (17, −5), Marcia used the following equation. Is Marcia correct? Explain.
D = | 3 − (−5) | = 8
a.) Marcia is not correct. Since the points are in two-dimensions, the distance formula must be used to find the distance.
b.)Marcia is correct. For any pair of points, the distance between the points can be treated as if they are in one-dimension.
c.)Marcia is correct. Since the x-coordinates are the same, the distance between the points can be treated as if they are in one-dimension.
d.)Marcia is not correct. According to the distance formula, the distance should be D=√(17-17)^2+(3-(-5))^2=√8
Option d for question 4 should be:
d.)Marcia is not correct. According to the distance formula, the distance should be D=√(17-17)^2+(3-(-5))^2=8
Answer:
1. (b) a^2+b^2=c^2
3. (a) 5
4. (d) Marcia is not correct. According to the distance formula, the distance should be D=√(17-17)^2+(3-(-5))^2=8
Step-by-step explanation:
(1) From Pythagoras' theorem, the square of the hypotenuse side of a given right-angled triangle, is equal to the sum of the squares of the other two sides. Now, if the other two sides are a and b, and the hypotenuse is c, then using this theorem, the following holds:
c² = a² + b²
(2) The distance D, between two points (a, b) and (c, d) is given by;
D = √(a-c)² + (b-d)² ----------------(i)
From the question, the points given are (9, -7) and (5, -4):
This means that;
a = 9
b = -7
c = 5
d = -4
Substitute these values into equation (i) and get;
D = √(9-5)² + (-7- (-4))²
D = √(4)² + (-3)²
D = √16 + 9
D = √25
D = 5
Therefore, the distance between these points is 5 units
(4) As explained in question 3 above, Maria is not correct. To find the distance between two points, we use the relation shown in the answer to question 3 above. i.e
D = √(a-c)² + (b-d)²
Since the given points are (17, 3) and (17, -5), it implies that;
a = 17
b = 3
c = 17
d = -5
D = √(17-17)² + (3-(-5))²
D = √(0)² + (8)²
D = √8²
D = 8
plot the x-intercept of the function f(x)=(x+4)squared
Answer:
(-4,0)
Step-by-step explanation:
Hello, we need to find the points so that f(x)=0 as this is the intersection between y = f(x) and y = 0.
[tex](x+4)^2=0<=> x+4=0<=> x =-4[/tex]
Thank you
a ladder 10 m long,leans against a vertical wall at an angle of 70° to the ground.if the ladder slips down the wall 4m,find,correct to 2 significant figure
(a) the new angle which the ladder makes with the ground
(b) the distance the ladder slipped back on the ground from it's original position
Answer:
(a) The new angle the ladder makes with the ground = 32.66°
(b) The distance the ladder slipped back on the ground from it's original position = 5 m
Step-by-step explanation:
The given parameters are;
The length of the ladder = 10 m
Angle of inclination of the ladder = 70°
Length to which the ladder slips down the wall = 4 m
(a) The height of the wall adjacent to the ladder = 10×sin(70°) ≈ 9.4 m
The new height of the wall adjacent to the ladder after the ladder slips down 4 m = 9.4 - 4 = 5.4 m
Therefore, the new angle of inclination of the ladder = sin⁻¹(5.4/10) = 32.66°
The new angle the ladder makes with the ground = 32.66°
(b) The distance the ladder slipped back on the ground from its original position is found as follows
The initial distance of the base of the ladder from the wall = 10 × cos(70°) = 3.42 m
The distance of the base of the ladder from the wall after slipping 4 m down the wall = 10 × cos(32.66°) ≈ 8.42 m.
Therefore, the amount by which the ladder slip back on the ground from its original position = 8.42 - 3.42 = 5 m.
The distance the ladder slipped back on the ground from it's original position = 5 m.
Translate into a variable expression.
the product of a number n and four more than the number
Answer:
(x)n+4
Step-by-step explanation:
x=quantity multiplied by n for a product
n=a number
+4=4 more than the number
HOPE THIS HELPS!!!!!! :)
<3333333333
Determine if ΔABC and ΔFHG are similar. If so, write the similarity statement.
options:
A) The triangles are not similar
B) ΔABC ∼ ΔHFG
C) Impossible to determine.
D) ΔABC ∼ ΔFHG
Answer:
[tex]\Large \boxed{\mathrm{D) \ \triangle ABC \sim \triangle FHG }}[/tex]
Step-by-step explanation:
The two triangles are similar.
The corresponding sides are proportional.
AB ∼ FH
[tex]\displaystyle \frac{72}{12} =6[/tex]
AC ∼ FG
[tex]\displaystyle \frac{48}{8} =6[/tex]
BC ∼ GH
[tex]\displaystyle \frac{84}{14} =6[/tex]
terms and definitions of aphasia
Answer:
loss of ability to understand or express speech, caused by brain damage or loss or impairment of the power to use or comprehend words usually resulting from brain damage (as from a stroke, head injury, or infection) — see motor aphasia — compare amusia, anarthria.
Step-by-step explanation:
Please help me with this
Answer:
7^-3+5 (5 goes up and becomes+5)
so ans is 7^2
Answer:
7^2[tex] \frac{ {7}^{ - 3} }{ {7}^{ - 5} } = {7}^{ - 3 + 5} = {7}^{2} [/tex]
Write the equation of a line with a slope of −1 and a y-intercept of −6. (2 points)
Answer:
y = -1x - 6
Step-by-step explanation:
Hi!
The format of the equation of a line is y = mx + b
m is the slope and b is the y-intercept
We just need to substitute in the values you gave for the variables and we get the answer,
It is known that the birth weights of full-term newborn infants in the U.S. have an approximately normal distribution with a mean weight of 6.8 lbs and a standard deviation of 1.7. Approximately what proportion of newborn babies will have a birth weight between 6 lbs and 8 lbs? Provide all four decimal places in your answer.
Answer: 0.4419
Step-by-step explanation:
Given: The birth weights of full-term newborn infants in the U.S. have an approximately normal distribution with a mean weight of 6.8 lbs and a standard deviation of 1.7.
i.e. [tex]\mu=6.8\ \ \ \text{ and }\sigma= 1.7[/tex]
Let X denotes the birth weight.
Then, the proportion of newborn babies will have a birth weight between 6 lbs and 8 lbs is given by :-
[tex]P(6<X<8)=P(\dfrac{6-6.8}{1.7}<\dfrac{X-\mu}{\sigma}<\dfrac{8-6.8}{1.7})\\\\=P(-0.47<Z<0.71)\ \ \ [Z=\dfrac{X-\mu}{\sigma}] \\\\=P(Z<0.71)-(1-P(Z-0.47))\\\\=0.7611-(1-0.6808)\ \ \ [\text{By z-table}]\\\\= 0.4419[/tex]
Hence, the proportion of newborn babies will have a birth weight between 6 lbs and 8 lbs is 0.4419 .
What’s 4/10i simply ?
Answer:
= 2i / 5
Step-by-step explanation:
4 / 10 i
= 2² / (2 * 5) i
= 2i / 5
Answer:
2i / 5 is the answer.
On a quiz there are four multiple choice questions worth 3 points each
Answer:
12 pts total
Step-by-step explanation:
Answer:
The four multiple choice are worth 12 points total
Use the compound interest formula to compute the balance in the following account after the stated period of time, assuming interest is compounded annually. $5000 invested at an APR of 4.5% for 11 years. What is the balance in account after 11 years?
Answer:
The amount $ 8114.3 is the balance in the account after eleven years
Step-by-step explanation:
From;
A= P(1+r)^n
Where;
A= amount
P= principal
r= interest rate
n= time
A= 5000(1+ 0.045)^11
A= 5000(1.045)^11
A= $ 8114.3
The amount $ 8114.3 is the balance in the account after eleven years.
Solve this equation 7- 4=7 +:
Answer:
what is after the plus sign
Solv for x for all of these 1. 3x+6=21 2. 33=7x-9 3. 28=7+x need to know now please help !!!!!!
Answer:
[tex] \boxed{ \sf{ \bold{1. \: \: \: x = 5}}}[/tex][tex] \boxed{ \sf{ \bold{2. \: \: x = 6}}}[/tex]
[tex] \boxed{ \bold{ \sf{3. \: \: x = 21}}}[/tex]
Step-by-step explanation:
1. [tex] \sf{3x + 6 = 21}[/tex]
Move constant to right hand side and change its sign
⇒[tex] \sf{3x = 21 - 6}[/tex]
Subtract 6 from 21
⇒[tex] \sf{3x = 15}[/tex]
Divide both sides of the equation by 3
⇒[tex] \sf{ \frac{3x}{3} = \frac{15}{3} }[/tex]
Calculate
⇒[tex] \sf{x = 5}[/tex]
--------------------------------------------------------
2. [tex] \sf{33 = 7x - 9 }[/tex]
Swap the sides of the equation
⇒[tex] \sf{7x - 9 = 33}[/tex]
Move constant to right hand side and change it's sign
⇒[tex] \sf{7x = 33 + 9}[/tex]
Add the numbers
⇒[tex] \sf{7x = 42}[/tex]
Divide both sides of the equation by 7
⇒[tex] \sf{ \frac{7x}{7} = \frac{42}{7} }[/tex]
Calculate
⇒[tex] \sf{x = 6}[/tex]
---------------------------------------------------------
3. [tex] \sf{28 = 7 + x}[/tex]
Swap the sides of the equation
⇒[tex] \sf{7 + x = 28}[/tex]
Move constant to right hand side and change it's sign
⇒[tex] \sf{x = 28 - 7}[/tex]
Subtract 7 from 28
⇒[tex] \sf{x = 21}[/tex]
Hope I helped!
Best regards!!
Round 72.163 to the nearest tens place.
Answer:
72.2 is the correct answer
Step-by-step explanation:
Geometry: Find the value of x.
X = [?]°
Answer:
x = 25°
Step-by-step explanation:
The secant- secant angle DGB is half the difference of the intercepted arcs, that is
[tex]\frac{1}{2}[/tex] ( BD - FE) = 55
[tex]\frac{1}{2}[/tex](135 - x) = 55 ( multiply both sides by 2 )
135 - x = 110 ( subtract 135 from both sides )
- x = -25 ( multiply both sides by - 1 )
x = 25°
Convert 330 meters per second (m/s) to kilometers per minute (km/min). A) 1.98 x 10^1 km/min B) 1.98 x 10^-1 km/min C) 1.98 x 10^2 km/min D) 1.98 x 10^-2 km/min
Answer:
A
Step-by-step explanation:
330 m/s=330×60 m/min=19800/1000 km/min=198 km/min=1.98×10^1 km/min
A solid aluminum cube has sides each of length L . A second cube of the same material has sides four times the length of the first cube; i.e., 4 L . Compared to the first cube, the total surface area of the second cube is
Answer:
Compared to the first cube, the total surface are of the second cube is 16 times larger.
Step-by-step explanation:
The first cube has L*L*6=6L²
The second cube has 4L*4L*6=14L²*6=84L²
Compared to the first cube, the total surface are of the second cube is 16 times larger. (6*16=84)
Which equation represents this sentence? SIx times the difference of a number and eight is equal to twelve. A. 6n−8=12 B. 6n+8=12 C. 6(n−8)=12 D. 6(n+8)=12
Answer:
The answer is option CStep-by-step explanation:
Let the number be n
The statement
the difference of a number and eight is written as
n - 8
It's multiplied by 6
That's
6( n - 8)
The result is 12
So we have the final answer as
6( n - 8) = 12Hope this helps you
what is simplifying?
what is simplifying in math?
Answer:
Simplifying means making (something) simpler or easier to do or understand.
Simplification in math is the process of replacing a mathematical expression by resolving it or making it shorter.
Step-by-step explanation:
hope it will help :)
Mountain High Ski Resort offers two “Learn to Snowboard" packages - Package A gives you 5
group snowboard lessons for $200 or Package B gives you 10 group lessons for $350. Which
package is the least expensive per lesson? How much do you save per lesson going with that
package versus the other one? (Section 17.3) (1 point)
Answer: Package B is least expensive; Will save $5
Step-by-step explanation:
Package A
$200 for 5 lesson=$40/lesson
Package B
$350 for 10 lesson=$35/lesson
35<40
Package B is least expensive
-------------------------------------------------------
40 (Package A)- 35 (Package B)
=$5
Answer:
Packages A and C.
Step-by-step explanation: