Final Answer:
The inverse function is [tex]\( f^{-1}(x) = x^2 + 5 \)[/tex] and the range of [tex]\( f^{-1} \)[/tex] is [tex]\( y \geq 5 \)[/tex] or [5, ∞].
Explanation:
To find the inverse function, [tex]\( f^{-1} \)[/tex], for the function [tex]\( f(x) = \sqrt{x-5} \)[/tex], we'll need to follow these steps:
1. Write the function as an equation: [tex]\( y = \sqrt{x-5} \)[/tex].
2. To find the inverse, we exchange the roles of x and y. The equation now reads [tex]\( x = \sqrt{y-5} \)[/tex].
3. Our next task is to solve this equation for y. To do so, we need to eliminate the square root by squaring both sides of the equation:
[tex]\[ x^2 = (\sqrt{y-5})^2 \\\\\[ x^2 = y - 5 \][/tex]
Now, we add 5 to both sides in order to isolate y:
[tex]\[ y = x^2 + 5 \][/tex]
This is our inverse function: [tex]\( f^{-1}(x) = x^2 + 5 \)[/tex].
Regarding the range of [tex]\( f^{-1} \)[/tex], we need to consider the domain of the original function f(x). The original function [tex]\( f(x) = \sqrt{x-5} \)[/tex] is only defined for [tex]\( x \geq 5 \)[/tex], because you cannot take the square root of a negative number in real numbers.
Since the domain of f(x) becomes the range of [tex]\( f^{-1}(x) \)[/tex], the range of the inverse function must be [tex]\( y \geq 5 \)[/tex], because the smallest value of x is 5, which when inputted into the inverse gives us [tex]\( 5^2 + 5 = 25 + 5 = 30 \)[/tex], and it only grows larger for larger values of x.
So the inverse function is [tex]\( f^{-1}(x) = x^2 + 5 \)[/tex] and the range of [tex]\( f^{-1} \)[/tex] is [tex]\( y \geq 5 \)[/tex].
How many days would it take a loan of $18,889 to earn $500 exact interest at a 3.3% interest rate?
the thickness of a deep dish pizza is approximately 2 x 10^-1 feet. the thickness of a thin crust pizza is approximately 5 x 10^-2 feet. how many times smaller is the thickness of a thin crust pizza compared to the thickness of a deep dish pizza?
A. 0.25
B.0.4
C4
D25
The thickness of a thin crust pizza is 4 times smaller than the thickness of a deep dish pizza.
The question asks us to compare the thickness of a deep dish pizza to that of a thin crust pizza and determine how many times smaller the thin crust is. The deep dish pizza has a thickness of 2 x 10⁻¹ feet and the thin crust pizza has a thickness of 5 x 10⁻² feet. To find how many times smaller the thin crust is, we divide the thickness of the thin crust by the thickness of the deep dish pizza:
(5 x 10⁻² feet) / (2 x 10⁻¹ feet) = 0.25
A constant is a value in a formula that doesn't change. _______________
PLEASE ANSWER ALL, IF YOU CANNOT ANSWER ALL THEN PLEASE DO NOT COMMENT A ANSWER!!! (YOU GET 22 POINTS!!)
1. What is 193.492 rounded to the nearest hundredth?
2. Compare the decimals 9,135.40 and 9,135.4.
Which comparison is correct?
A.9,135.40 < 9,135.4
B. 9,135.40 > 9,135.4
C. 9,135.40 = 9,135.4
Which is the best estimate for the product of 3,826.301 × 175.6?
A. 8,000,000
B. 800,000
C. 80,000
D. 8,000
Which is the best estimate for the quotient of 198.32 ÷ 9.001?
A. 2,000
B. 200
C. 20
D. 2
TYSM IF YOU ANSWER!!
Find the area of the following circle. (Round answer to the nearest whole number.) Circumference = 280 cm. (Hint: Find r from C = 2πr (round r to tenths); then find area). 1) 89 2)560 3)1,989 4)6,246
Answer:
4)6,246
Step-by-step explanation:
First we will find the value of r.
The formula for circumference is C = 2πr:
280 = 2(3.14)r
280 = 6.28r
Divide each side by 6.28:
280/6.28 = 6.28r/6.28
44.6 ≈ r
The formula for the area of a circle is
A = πr²
Using our value for r, we have
A = 3.14(44.6)² = 6245.9624 ≈ 6246
Area of circle is,
⇒ 11493.2 cm²
What is mean by Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
Circumference of circle = 280 cm.
Now, We know that;
Circumference = 2πr
Hence, We get;
⇒2πr = 280
⇒ 2 × 3.14 r = 380
⇒ 6.28 r = 380
⇒ r = 380 / 6.28
⇒ r = 60.5
Hence, Area of circle is,
⇒ πr²
⇒ 3.14 × 60.5²
⇒ 11493.2 cm²
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Which of the following are opposite rays?
A. TV and TS
B. TX and TL
C. TS and TX
D. TL and TV
The correct answer is:
B. TX and TL
Explanation:
Opposite rays are rays that have the same endpoint and extend in opposite directions. The ones in the diagram that fit this description are TX and TL.
The natural history museum has a 1:75 scale model of an apatosaurus dinosaur. the length of the model is 30 centimeters. find the actual length x (in meters) of an apatosaurus.
Answer:
22.5 meters is the correct answer.
Step-by-step explanation:
In a paddock there are emus and wombats. If there are 52 heads and 148 feet, how many emus are in the paddock?
A plane requires 3300 gallons of fuel and 75 minutes to make a round trip to Prague, and it takes 5700 gallons of fuel and 130 minutes to make a round trip to Stockholm. A pilot is asked to use at least 94500 gallons of fuel and spend at least 2400 minutes to make round trips to Prague and Stockholm in his plane. Let P denote the number of round trips to Prague and S the number of round trips to Stockholm. Write an inequality that represents the condition based on the number of gallons of fuel. Write an inequality that represents the condition based on the number of minutes.
Answer: The inequality that represents the condition based on the number of gallons of fuel will be:
[tex]3300P +5700S \geq94500[/tex]
The inequality that represents the condition based on the number of minutes will be:
[tex]75P +130S\geq2400[/tex]
Step-by-step explanation:
Let P denote the number of round trips to Prague and S the number of round trips to Stockholm.
Since the plane requires 3300 gallons of fuel and 75 minutes to make a round trip to Prague and 5700 gallons of fuel and 130 minutes to make a round trip to Stockholm.
Then the inequality that represents the condition based on the number of gallons of fuel will be:
[tex]3300P +5700S \geq94500[/tex]
The inequality that represents the condition based on the number of minutes will be:
[tex]75P +130S\geq2400[/tex]
Write an expression to represent: One more than the quotient of a number x and 4.
9514 1404 393
Answer:
x/4 +1
Step-by-step explanation:
The quotient of a number (x) and 4 is written ...
x/4
One more than that is ...
x/4 +1
What are the zeroes of the function? What are their multiplicities?
= x4 – 4x3 + 3x2 (1 point)
helppppppppppppppppppppppp
Starting at home, Jessica traveled uphill to the toy store for 12 minutes at just 10 mph. She then traveled back home along the same path downhill at a speed of 30 mph. What is her average speed for the entire trip from home to the toy store and back?
Answer: 15 mph
Step-by-step explanation:
Given: Time taken to travel uphill to the toy store= 12 minutes[tex]=\frac{12}{60}=0.2\ hour[/tex]
Let d be the distance(in miles) between the home and toy store.
Also, [tex]Speed=\frac{Distance}{Time}[/tex]
[tex]\\\Rightarrow10=\frac{d}{0.2}\\\Rightarrow\ d=0.2\times10=2[/tex]
Thus, distance from home to toy store= 2 miles
When she turn back, to home distance remains same.
The time taken by her to come back at 30 mph speed=
[tex]Time=\frac{Distance}{speed}=\frac{2}{30}=\ hour[/tex]
Now, the average speed =[tex]\frac{\text{Total distance}}{\text{Total time}}[/tex]
[tex]=\frac{2+2}{0.2+\frac{2}{30}}\\=\frac{4}{\frac{6+2}{30}}\\=\frac{4\times30}{8}=\frac{120}{8}=15\ mph[/tex]
Answer:
the answer is 15
Completed by Jerome Maples Jr.
Step-by-step explanation:
A store buys items at a wholesale price of $45 each. If the store marks up the price, and no discounts are given, which could be possible retail prices?
hurry
Answer:49 65
Step-by-step explanation:
what are the properties of real numbers?
Final answer:
The properties of real numbers include closure, commutative, associative, identity, and inverse properties. These properties govern how real numbers behave in addition and multiplication operations.
Explanation:
The properties of real numbers refer to the characteristics and behavior of numbers that belong to the real number system. The real number system includes all rational and irrational numbers, such as whole numbers, integers, fractions, decimals, and square roots.
The properties of real numbers include:
Closure property: The sum or product of any two real numbers is also a real number. For example, the sum of 3.14 and 4 is 7.14, which is a real number.Commutative property: The order of addition or multiplication does not affect the result. For example, 2 + 3 is equal to 3 + 2, and 2 × 3 is equal to 3 × 2.Associative property: The grouping of real numbers in addition or multiplication does not affect the result. For example, (2 + 3) + 4 is equal to 2 + (3 + 4), and (2 × 3) × 4 is equal to 2 × (3 × 4).Identity property: The sum of a real number and zero is equal to the number itself. For example, 2 + 0 is equal to 2. The product of a real number and one is equal to the number itself. For example, 3 × 1 is equal to 3.Inverse property: Every real number has an additive inverse and a multiplicative inverse. The additive inverse of a real number is the number that, when added, gives zero as the result. For example, the additive inverse of 5 is -5, as 5 + (-5) = 0. The multiplicative inverse of a non-zero real number is the number that, when multiplied, gives one as the result. For example, the multiplicative inverse of 2 is 1/2, as 2 × (1/2) = 1.These properties of real numbers are fundamental in algebraic operations and calculations. They provide a basis for solving equations, simplifying expressions, and working with mathematical concepts.
Find the quotient.
2^3 ÷ 5^2
A circle has an area of 40 square meters. Which answer is closest to the measure of its diameter?
A.1.8 meters
B.4 meters
C.3.6 meters
D.7.1
Answer:
Option D. [tex]7.1\ m[/tex]
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
In this problem we have
[tex]A=40\ m^{2}[/tex]
substitute and solve for r
[tex]40=\pi r^{2}[/tex]
[tex]r^{2}=40/( \pi)[/tex]
[tex]r=3.57\ m[/tex]
Multiply the radius by [tex]2[/tex] to obtain the diameter
so
[tex]3.57*2=7.14\ m[/tex]
which geometric construction is shown below
According to apex, the answer is "Doubling the Square"
Pauline is building a fence around her vegetable garden, what length of fence will she need to build?
Given that (-8,-5) is on the graph of f(x), find the corresponding point for the function f(x-2)
Answer:
(3,-8)
Step-by-step explanation:
The perimeter of a rectangle is 54cm. The area of the same rectangle is 176 cm^2. What are the dimensions of the rectangle?
A. 11 cm by 16 cm
B. 8 cm by 22 cm
C. 5.5 cm by 32 cm
D. 4 cm by 44 cm
Given is rectangle with perimeter = 54 centimeters and area = 176 squared centimeters.
Let's consider the length of rectangle = L and width of rectangle = W.
We know the following formulas for rectangle :-
Perimeter = 2 x (L + W)
Area = L x W
So we have 2 x (L + W) = 54 and L x W = 176.
L + W = 27 and L x W = 176
We need to find two positive integers such that their sum is 27 and product is 176.
Using trial and error, we have two such positive integers such that 11 + 16 = 27 and 11 x 16 = 176.
So, the dimensions of rectangle would be 11cm x 16cm.
Hence, option A is correct i.e. 11 cm by 16 cm.
the formula, P=v^2/R, gives the relationship between resistance (R), voltage (V) and power P). solve the formula for resistance.
Answer: [tex]R=\frac{V^2}{P}[/tex]
Step-by-step explanation:
Given formula : [tex]P=\frac{V^2}{R}[/tex], gives the relationship between resistance (R), voltage (V) and power P).
When we multiply R to the both sides of the above equation, we get
[tex]PR=v^2[/tex]
Now, divide P on the sides, we get
[tex]R=\frac{V^2}{P}[/tex]
Hence, the formula for resistance will be
[tex]R=\frac{V^2}{P}[/tex], gives the relationship between resistance (R), voltage (V) and power (P).
What is eight more than twice the greatest negative integer?
Rodney models the factorization of a trinomial with algebra tiles as shown. Rodney forgot to place x-tiles in zero pairs in the model of the trinomial. How many zero pairs of x-tiles should he place in the model? pairs
Answer:
I believe the answer is 3. : )
please help thank you.
The tables below represent the profits earned by a merchandiser from four new consignments of t-shirts. Each consignment contained t-shirts of five different sizes. If we were to plot each of the t-shirt sizes and the profit earned on each new size, we would get a different graph for each consignment. Almost all the graphs showed some association between the two variables, except one consignment, which showed no association. Which of the following consignments shows no association?
In graph 2, the dots are scattered and also no association.
What is an association?
An association (relationship) between two numerical variables can be described by its form, direction, strength, and outliers. A scatter plot shows the association between two variables. A scatter plot matrix shows all pairwise scatter plots for many variables.
For the given situation,
There are four new consignments of t-shirts.
Each consignment contained t-shirts of five different sizes.
Graph is plotted as shown below between each of the t-shirt sizes and the profit earned on each new size.
If one variable increases as the other variable increases, there is said to be a positive association.
Two variables have a negative association when the values of one variable tend to decrease as the values of the other variable increase.
No association means that there is no line and all the dots are scattered.
From the graph shown, in graph 2 the dots are scattered. Thus no association.
Hence we can conclude that in graph 2, the dots are scattered and also no association.
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At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path. The bicyclist heading north is riding 5 km/hour faster than the bicyclist heading south. At 10:45, they are 47.25 km apart. Find the two bicyclists’ rates.
What is the solution to the equation 5x + 2y = -9
a.(2,-4)
b.(-1,2)
c.(-2,5)
d.(1,-3)
In order to find which one of the given points is a solution to the equation, we need to plug each point in the equation and check which one fits in .
The equation is :
5x+2y=-9
a.(2,-4)
5x+2y=-9
LHS: 5x+2y
Plugging (2,-4) in this,
5(2) +2(-4) = 10-8 =2
RHS : -9
LHS ≠RHS
So (2,-4) is not the solution.
b.(-1,2)
5x+2y=-9
LHS: 5x+2y
Plugging (-1,2) in this,
5(-1) +2(2) = -5+4 =-1
RHS : -9
LHS ≠RHS
So (-1,2) is not the solution.
c.(-2,5)
5x+2y=-9
LHS: 5x+2y
Plugging (-2,5) in this,
5(-2) +2(5) = -10+10 =0
RHS : -9
LHS ≠RHS
So (-2,5) is not the solution.
d.(1,-3)
5x+2y=-9
LHS: 5x+2y
Plugging (1,-3) in this,
5(1) +2(-3) = 5-6=-1
RHS : -9
LHS ≠RHS
So (1,-3) is not the solution.
None of the given options is a solution to the given equation.
What is the projection of (3,4) onto (3,1)?
the answer can also be written as 1.3(3,1)
WILL GIVE BRAINLIEST!
If ∠A, and ∠B, are complementary angles and if m∠A is 37°, what is m∠B?
A. 37°
B. 53°
C. 74°
D. 143°
Answer:
For this one the answer is b: 53 :)
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