The inverse of the function h(x) = ³√x - 3 is h⁻¹(x) = (x + 3)³.
What is termed as the inverse of the function?An inverse function is one that reverses the action of another function. A function g has become the inverse of a function f when and only when y=f(x) and x=g (y). In other words, using f and then g is equivalent to doing nothing. This can be written as g(f(x))=x in terms of the combination of f and g.The given function is-
h(x) = ³√x - 3
Put y = h(x);
h(x) = y = ³√x - 3
Make x the subject;
x = (y + 3)³
Replace x with h⁻¹(y) = (y + 3)³
Restate with x instead of y.
h⁻¹(x) = (x + 3)³
Thus, the inverse of the function h(x) = ³√x - 3 is h⁻¹(x) = (x + 3)³.
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with explanation needed. a and b
a)
Solution,
According to fuel gauge,the petrol left is exactly between 1/2 and 3/4 part of the 40 litres.
i.e. Left fuel = (1/2 + 3/4)/2 litres
Here,
1/2 of 40l = 1/2×40l
= 20l
3/4 of 40l = 3/4×40l
= 30l
Then,
Left fuel = (20l + 30l)/2
= 50l/2
= 25l
Consumed fuel = 40l - 25l
= 15l
Therefore,15 litres of petrol is used to travel 240km
b)
Solution,
Consumed fuel = 15l
Distance covered = 240km
Then,
Fuel consumption rate = 240km/15 l
= 16km/l
Therefore,the rate of petrol consumption is 16km/l of his car for this journey
find the measure of each lettered angle. a=, b=, c=, d=, e=
Answer:
a= 20
b= 70
c= 20
d=70
e=110
Step-by-step explanation:
a + the 70 degree angle have to equal 90 degrees (the right angle marking) and the same with b + a. So to ind a, you do 90-70 and to find b, because you now have the value of a, you do 90-20.
a+b+c+70 is equal to a 180 degree angle, so since you know the value of a and b, now you can figure out c by doing 180-(70+20+70).
d and the 70 degree angle are vertical angles so they are equal to each other.
lastly for e, d+e is equal to 180 degrees so since you know the value of d, you just do 180-70 to find e.
Answer:
a = 20°
b = 70°
c = 20°
d = 70°
e = 110°
Step-by-step explanation:
Angle A is complementary with 70°, so they add together to = 90° (as indicated by the 90° mark).
90° - 70° = 20°
Angle A = 20°
Angle B is complementary with angle A, 20°, so they also add together to = 90°.
90° - 20 = 70°
Angle B = 70°
Although not indicated by a 90° mark, Angle C and Angle B are complementary since they share a straight line with the complementary angles A and 70°. This means Angles C + B = 90°
90° - 70° = 20°
Angle C = 20°
Angle D is vertical to 70°, so Angle D = 70°
Angle E is supplementary to 70°, so they should combine to = 180°
180° - 70° = 110°
Angle E = 110°
What is this type of polynomial?
13x² + 17x +3
Answer:
This is a quadratic (second-degree) polynomial.
A 1,600 deposit for 15 years at a compound interest rate of 12%
Answer:
$8,758
I hope this helps!
Kiara and Donovon attend different middle schools. They both went to their schools’ winter carnivals. Kiara paid a $5 entrance fee and bought several tickets costing $0.75 each for games and rides. Donovon paid a $7 entrance fee and bought several tickets costing $0.50 each for games and rides. How many tickets, x , must Kiara and Donovan each buy in order for the cost of attending their school carnivals to be the same?
A. 8 tickets
B. 10 tickets
C. 28 tickets
D. 48 tickets
Answer:B
Step-by-step explanation:
what is the problem 10.5-9.67
Answer:
0.83
Step-by-step explanation:
10.5-9.67 the answer is 0.83
Answer:The answer is 0.83
Step-by-step explanation:Please give brainliest if right.I hope this helps.
. If the lesser of two consecutive even integers is five more than half the greater,
what are the two integers?
Answer:
12 and 14
Step-by-step explanation:
You want two consecutive even integers such that the lesser is five more than half the greater.
SetupLet x represent the lesser of the integers. Then x+2 is the greater, and we can write the given relation as ...
x = (x+2)/2 +5 . . . . . lesser is 5 more than half the greater
SolutionMultiplying by 2 gives ...
2x = x +2 +10
x = 12 . . . . . . . . subtract x
x+2 = 14
The two integers are 12 and 14.
Find missing length.
The area of a rhombus is 168 square centimeters. If one diagonal is three times as long as the other, what are the lengths of the diagonals?
Given the area, the lengths of the diagonals p and q of the rhombus are 4√7 cm and 12√7 cm respectively.
What are the lengths of the diagonals of the rhombus?A rhombus which is called an equilateral quadrilateral is simply a quadrilateral whose all four sides have the same length.
The area of a rhombus is expressed as;
A = ( p × q )/2
Where p and q are the diagonals
Given the data in the question;
Let one of the diagonal be x.
Area of the rhombus = 168cm²Diagonal p = xDiagonal q = 3xPlug in the given values into the equation above and solve for x.
A = ( p × q )/2
168 = ( x × 3x )/2
168 = ( 3x² )/2
3x² = 168 × 2
3x² = 336
Divide both sides by 3
x² = 112
Take the square root of both sides
x = ±√112
x = ±4√7
Since the dimension of the rhombus cannot be negative,
x = 4√7
Hence, the length of the diagonals are;
Diagonal p = x = 4√7 cm
Diagonal q = 3x = 3( 4√7 ) = 12√7 cm
Given the area, the lengths of the diagonals p and q of the rhombus are 4√7 cm and 12√7 cm respectively.
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The end points of ab are A (-7,3) and B (1,0) find the coordinates of the midpoint M.
Answer: M(-3,1.5)
Step-by-step explanation:
A(-7,3) B(1,0)
[tex]\displaystyle\\M(x,y)=(\frac{x_A+x_B}{2} ,\frac{y_A+y_B}{2} )\\\\M(x,y)=(\frac{-7+1}{2},\frac{3+0}{2} )\\\\M(x,y)=(\frac{-6}{2},\frac{3}{2} )\\\\M(x,y)=(-3,1.5)\\\\Thus,\\\\M(-3,1.5)[/tex]
[tex]3x+6=4x+7[/tex]
which of these equations are shown on the graph?
The equation shown on the graph is y = 2x + 3. The correct answer is C. y = 2x +3
Equation of a lineFrom the question, we are to determine the equation that represent the given line
To determine the equation, we will pick two points on the line and determine the equation of the line
Picking the points (0, 3) and (3, 9)
Using the formula for the finding the equation of a line with two given points
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
x₁ = 0
y₁ = 3
x₂ = 3
y₂ = 9
Then,
(y - 3)/(x - 0) = (9 - 3)/(3 - 0)
(y - 3)/x= 6/3
(y - 3)/x= 2
y - 3 = 2x
y = 2x + 3
Hence, the equation shown on the graph is y = 2x + 3. The correct answer is C. y = 2x +3
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is this statement true or false? the imaginary line which passes through the north and south poles, upon which the earth rotates once every 24 hours is called the prime meridian.
It is False that the imaginary line which passes through the north and south poles, upon which the earth rotates once every 24 hours is called the prime meridian. .
Where is prime meridian located?In a geographic coordinate system, a prime meridian is any line of longitude when longitude is defined to be 0°. A great circle is formed by a prime meridian and its anti-meridian (the 180th meridian in a 360° system).
A spheroid, like the Earth, is divided into two hemispheres by this vast circle: the Eastern Hemisphere and the Western Hemisphere (for an east-west notational system).
Different conventions have been used or supported for Earth's prime meridian throughout history in various places. The IERS Reference Meridian is the current international prime meridian for the Earth. It is developed from the former Greenwich Meridian, however it is somewhat different.
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the product of two consecutive integers is 272. which quadratic equation can be used to find x, the smaller number? x2 1
Quadratic equation which is x² + x - 272 = 0 can be used to find the product of two consecutive integers.
What is a quadratic equation?An algebraic equation of a second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
Let one number be x,
second number will be - (x+1)
so, the product of two numbers will be -
x(x+1) = 272
x² + x = 272
x² + x - 272 = 0
The quadratic equation, used to find the numbers is x² + x - 272 = 0.
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Please help please I’m in desperate need
Answer:
ok I will help u don't worry
How many three-digit numbers may be formed using elements from the set {1,2,3,4,5,6,7,8}. if no element may be used more than once in a number and the number must be even?
126 three-digit numbers may be formed using elements from the set {1,2,3,4,5,6,7,8}. if no element may be used more than once in a number and the number must be even
For given question,
We need to find number of three-digit numbers formed using elements from the set {1,2,3,4,5,6,7,8} if no element may be used more than once in a number and the number must be even.
3-digit even numbers are to be formed using the given six digits,1 ,2,3,4,6,7, and 8 without repeating the digits.
Then, units digits can be filled in 4 ways by any of the digits, 2,4, 6 or 8.
Since the digits cannot be repeated in the 3-digit numbers and units place is already occupied with a digit (which is even), the hundreds and tens place is to be filled by the remaining 7 digits.
So, the number of ways in which hundreds and tens place can be filled with the remaining 7 digits is the permutation of 7 different digits taken 2 at a time.
[tex]\Rightarrow ~^7P_2=\frac{7!}{(7-2)!} \\\\\Rightarrow ~^7P_2=42[/tex]
Thus, by multiplication principle, the required number of 3-digit numbers is 3 × 42 = 126
Therefore, 126 three-digit numbers may be formed using elements from the set {1,2,3,4,5,6,7,8}. if no element may be used more than once in a number and the number must be even
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Both lines on the graph represent proportional relationships. What is the constant
of proportionality for each relationship? Explain how you know.
Each relationship's proportionality constants are k=3 and k=1, respectively.
What is the proportionality constant?The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.
Given that the relationship is proportional,
the equation linking the quantities is y = k x k, where k is the proportional constant.
Divide both sides by x to determine k
k = y/x
For graph a use the point (2, 6 ), then
k = 6/2
= 3
For graph b use the point (4, 4 ), then
k = 4/4
= 1
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PLEASE HELP ME ASAP THIS NEEDS TO BE DONE TODAY.
Answer:
#1
[tex]{ \tt{119 \degree + 34 \degree + b = 180 \degree}} \\ { \tt{b = (180 - 34 - 119) \degree}} \\ { \tt{b = 27 \degree}}[/tex]
#2
[tex]{ \tt{ \red{❗ \: image \: not \: clear}}}[/tex]
18 12 over 7 minus 2
Answer: whats the answer choices
Step-by-step explanation: i dont get it
Answer:
1,798/7
Step-by-step explanation:
1812/7-2 (or it can be written as 14/1 because you getting rid of two sevenths)
= f(x)= 4 -x, for what input is the output 7
Answer:
-3
Step-by-step explanation:
Rewrite as follows and solve for x:
7 = 4 - x
Add x to both sides to get positive x
x + 7 = 4
Subtract 7 from both sides to get x by itself
x = -3
Charlotte is driving at 61.4 mi/h and receives a text message. she looks down at her phone and takes her eyes off the road for 3.93 s. how far has charlotte traveled in feet during this time?
The distance travelled by Charlotte in feet is 354 feet. This is obtained by using the concept of speed and distance on the given problem.
What is speed?
Speed is defined as the distance per unit of time. It is the numerical quantity that specifies how fast an object is moving. The basic unit of speed is given by m / s.
Calculation of the distance travelled by Charlotte in feet
Given:
Speed = 61.4 mi / h
Time = 3.93 s
The basic step to solve this problem is to convert miles per hour to feet per second
(61.4 mi / hr) * (5280 feet / mi) * (1 hr / 3600 sec) = 90.0533 feet / sec
Now, multiply the speed by the number of seconds to find the value of distance in feet
(90.0533 feet / sec) * (3.93 sec) = 353.909 feet.
Hence, the distance travelled by Charlotte in feet is 354 feet.
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Assignment
Find the midpoint of the line segment with the given endpoints
1) (7,2), (-7, -9)
belinda received a 3+ points on a problem on a quiz what is the absolute value of the number of points she received
Answer:
3
Step-by-step explanation:
the absolute value is distance of a number from 0 so +3 absolute value is 0
Rewrite in simplest terms: -10(-5f +7f+2) - f
Answer:
-21f - 20
Step-by-step explanation:
Rewriting in the simplest terms,
→ -10(-5f + 7f + 2) - f
→ 50f - 70f - 20 - f
→ -20f - 20 - f
→ -21f - 20
Hence, simplest term is -21f - 20.
Please Help!! Find the sum. In your final answer, include your calculations.
−3.45 + 5.1
8.55
Here's a video that could explain
https://youtu.be/WwKLA-6S-e0
Also when doing the math ignore the - sign, the larger number will determine if the answer will be a whole or a minus , let me explain, so as you see in the question the 5.1 is the largest so that means the answer will be a whole.
Jen was the leading scorer on her soccer team. She scored 120 goals and had 20 assists in her high school career. a. The number of points awarded for goals is given by 2g where g is the number of goals scored. How many points did Jen earn for goals? b. The point total is given by n + a where a is the number of assists. Use your answer from part (a) to find Jen's point total. mirum
a. The number of points that Jen earned will be 240 points.
b. The point total where a is the number of assists is 260 points.
How to compute the function?The number of points that Jen earned will be:
= 2g
where g = number of goals scored
= 2 × 120
= 240
b. The point total is given by n + a where a is the number of assists.
Therefore, the point total will be:
= Goals + Assist
= 240 + 20
= 260 points.
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Given that f(x)=6x+5 and g(x)=2x−7, what would be the composite function (f∘g)(x)?
Answer:
f ◦ g is the composition function that has f composed with g. ... Find (f ◦ g)(x) for f and g below. f(x)=3x + 4. (6) g(x) = x2 +. 1 x. (7).
Step-by-step explanation:
Melinda has 5 cousins. She called each one on the phone 4 times this month. How many phone calls did she make to her cousins this month
Answer:20
Step-by-step explanation:5*4=20 hope this helps
how can you represent 0.721 without using hundredths?
0.721 can be written in scientific notation as 7.21 x [tex]10^{-1}[/tex]
What is scientific notation?Scientific notation is used to compress large numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
For example:
1 x 10² is equivalent to 100
1 x [tex]10^{-1}[/tex] is equivalent to 0.1
To convert 0.721, multiply and raise 10 to the power of -1
by 10 = 7.21 x [tex]10^{-1}[/tex]
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5 less than 10 times a number is 2 times than number plus 6
Group of answer choices
11/8
11
8
6
4. (40 Pts) The Vacation Times website rates recreational vehicle campgrounds
using integers from 0 to 15. Last year they rated over 1,000 campsites. The
ratings were normally distributed with mean 7.6 and standard deviation 1.7.
a. How high would a campsite's rating have to be for it to be considered in
the top 10% of rated campsites? Round to the nearest hundredth.
b. Find the z-score for a rating of 5. Round to the nearest hundredth.
Using the normal distribution, it is found that:
a) The rating would have to be of at least 9.78.
b) The z-score for a rating of 5 is of -1.53.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given by:
[tex]\mu = 7.6, \sigma = 1.7[/tex]
For item a, we have to find the 90th percentile, which is X when Z = 1.28, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
1.28 = (X - 7.6)/1.7
X - 7.6 = 1.28 x 1.7
X = 9.78.
The rating would have to be of at least 9.78.
For item b, we have to find Z when X = 5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (5 - 7.6)/1.7
Z = -1.53.
The z-score for a rating of 5 is of -1.53.
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