Domain: (-∞,∞) {x,x∈R }
Range: [0,∞)
Solution :
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation
Interval notation is a method to represent an interval on a number line. In other words, it is a way of writing subsets of the real number line. An interval comprises the numbers lying between two specific given numbers. For example, the set of numbers x satisfying 0 ≤ x ≤ 5 is an interval that contains 0, 5, and all numbers between 0 and 5.
Different Types Of Intervals
Intervals can be classified based on the numbers the set comprises. Some sets include the endpoints specified in the notation, while some might partially or not include the endpoints. In general, there are three types of intervals given as,
Open Interval
Closed Interval
Half-Open Interval
Let us understand the interval notation and different types of intervals in detail using solved examples.
Interval Notation:
y = |x4|
(−∞,∞)
Set-Builder Notation:
{x|x∈R}
The range is the set of all valid
y
values. Use the graph to find the range.
Interval Notation:
[0,∞)
Set-Builder Notation:
{y|y≥0}
Determine the domain and range.
Domain:
(−∞,∞),{x|x∈R}
Range:
[0,∞) , {y|y≥0}
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Suppose y varies directly as x. If y = 12 when x = 4:
Write the general variation equation
Find the constant of variation, k.
Write a variation equation relating x and y using the value of k found in b).
Find y when x = -5.
у
Answer:
y = -15
Step-by-step explanation:
Given that,
y varies directly as x i.e.
\(y\propto x\\\\y=kx\)
Where
k is the constant of variation.
Put y = 12 and x = 4 to find k.
\(k=\dfrac{y}{x}\\\\k=\dfrac{12}{4}\\\\k=3\)
Now put k = 3 and x = -5 and finding the value of y.
\(y=3\times -5\\\\y=-15\)
So, the value of y is equal to -15.
A 16 foot ladder is propped up against the roof of a house. The angle of elevation is 62 degrees. How tall is the house?
Answer is below.
Let's call the height of the house "h".
The ladder is propped up against the house, forming a right triangle with the wall of the house and the ground. The ladder is the hypotenuse of the triangle, and the height of the house is one of the legs.
We know that the length of the ladder is 16 feet, and the angle of elevation is 62 degrees. We can use trigonometry to find the height of the house.
The trigonometric function that relates the angle of elevation to the height and length of the ladder is the tangent function:
tan(62) = h/16
To solve for h, we can multiply both sides by 16:
16 tan(62) = h
Using a calculator, we can evaluate the tangent of 62 degrees to get:
16 tan(62) ≈ 28.6
So the height of the house is approximately 28.6 feet.
Find the value of x, 6,4, 3x, 4x+1
Answer:
If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.
6(3x) = 4(4x + 1)
18x = 16x + 4
2x = 4
x = 2
Pleaseeeeeee HELP!!!!!!
A piece of farm machinery clears 2/15 acre of land in 1/5 of an hour
Answer: D. 2/3
Step-by-step explanation:
If it is 1/5 of an hour, we times it by 5, to get full hour, right?
So, we also do ×5 for the acre of land, so we can get the amount of acres in a full 1 hour.
5 is the same as 5/1 as a fraction
1/5 × 5 = 5/5 ......1 hour
2/15 × 5/1 = 10/15
So we get, 10/15 acre of land cleared in 1 hour
We simplify 10/15,
Which becomes,
2/3.
In conclusion, this is the working out =
2/15 × 5 = 10/15 = 2/3
Mark my answer as the brainliest!what is the givien x-value that can used to make the prediction
Answer:
haha there is no question
Step-by-step explanation:
aww please check if there are more expect around to answer
what is the solution to the inequality below?
\( \sqrt{x} \leqslant 5\)
Answer:
\( x \leqslant \sqrt{5}\)
Step-by-step explanation:
Hope this helped!
What is the distance from home to library?
Check the picture below.
\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~5 - 2~~)^2 + (~~7 - 1~~)^2} \implies d=\sqrt{( 3 )^2 + ( 6 )^2} \\\\\\ d=\sqrt{ 9 + 36 } \implies d=\sqrt{ 45 }\implies d\approx 6.7\)
stuck on this question
Answer:
9:30am
Step-by-step explanation:
The gymnast spent time on
balance beam: 1 hr and 40 min => 60 + 40 = 100 minutes
vaulting: 1 hr => 60 minutes
the total time at camp is 100 + 60 = 160 minutes
so 12:10pm - 160 minutes = 09:30am
I don't need lengthy details I just want the answer
Answer:
Sue rode 1885 miles total
Step-by-step explanation:
There are 31 days in March, 30 in April, and 30 in May.
31 * 12 + 30 * 12 + 30 * 12 = 1092
There are 30 days in June and 31 in august.
30 * 13 + 31 * 13 = 793
Now we find the total:
1092 + 793 = 1885
The graph to the right is the uniform probability density function for a friend who is x minutes late. (a) Find the probability that the friend is between 10 and 30 minutes late. (b) It is 10 A.M. There is a 20% probability the friend will arrive within how many minutes? part a) what is the probability that the friend is between 10 and 30 minutes late_?
The probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.
Since the probability density function is uniform, the probability of the friend being between 10 and 30 minutes late is equal to the area of the rectangle that lies between x = 10 and x = 30, and below the curve of the probability density function.
The height of the rectangle is equal to the maximum value of the probability density function, which is 1/30 since the interval of possible values for x is [0, 30] minutes.
The width of the rectangle is equal to the difference between the upper and lower limits of the interval, which is 30 - 10 = 20 minutes.
Therefore, the probability of the friend being between 10 and 30 minutes late is:
P(10 < x < 30) = (height of rectangle) x (width of rectangle)
= (1/30) x 20
= 2/3
≈ 0.6667
So the probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.
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Please help, thank you!
we know angle RLP= 100⁰
also
angle RLP+ angle RLB=180⁰(Linear pair)
=>100⁰+angleRLB= 180⁰
=> angle RLB=80⁰
since BR and LR are equal, angle RBL and angle RLB are equal
therefore angle RBL is also equal to 80⁰
using angle sum property of triangles we know that the sum of all angles in a triangle is equal to 180⁰
=>angle BRL+angle RBL+angle RLB= 180⁰
=> angle BRL+80⁰+80⁰=180⁰
=>angle BRL = 180⁰-160⁰
=>angle BRL= 20⁰
I'm sorry it took me some time I'm a slow typer
Answer:
I think its c i'm not sure though i'm so sorry if i'm wrong I would recommend waiting for another answer if u don't trust me but good luck !
What is the quotient and the remainder of 7 divided by 5839
Answer: 834.142857143
Step-by-step explanation: I did it on paper this is like 3rd grade math.
A bag contains 8 red balls and 3 white balls. Two balls are drawn without replacement. (Enter your probabilities as fractions.) (a) What is the probability that the second ball is white, given that the first ball is red
Answer:
12/55
Step-by-step explanation:
Probability is the ratio of the number of possible outcomes to the number of total outcomes.
Given that the bag contains 8 red balls and 3 white balls, the probability of picking a red ball
p(r) = 8/(8+3) = 8/11
Probability of picking a white ball
= 3/11
when a red ball is picked first, the total number of balls reduces to 10 hence the probability that the second ball is white, given that the first ball is red
=8/11 * 3/10
= 24/110
= 12/55
complete solutions manual a first course in differential equations with modeling applications ninth edition differential equations with boundary-vary problems tenth edition
A first course in differential equations with modeling applications ninth edition is a textbook that covers the basics of differential equations and their applications in mathematical modeling.
It begins with an introduction to the concepts of differential equations, including the definition, solution methods, and the concept of modeling. It then covers topics such as first-order linear equations, higher-order linear equations, systems of linear differential equations, and nonlinear equations. It also has a chapter on boundary-value problems, which is a type of differential equation that involves a set of boundary conditions that must be satisfied for the solution to be valid.
In order to solve differential equations with boundary-value problems, we must first define the boundary conditions that must be satisfied for the solution to be valid. This involves setting up the boundary conditions in terms of the dependent and independent variables of the equation. We then solve the equation using the boundary conditions and the equation itself. The solution is then used to calculate values for the independent and dependent variables at the boundary points. Finally, we can verify the solution by substituting the calculated values into the equation and seeing if the solution is valid.
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g(x)
12 fy
10
88
8
6
4
4-3-2-12
-8
10
-1²1
f(x)
4 5 6 x
Which statement is true regarding the functions on the
graph?
Of(6) = g(3)
f(3) = g(3)
f(3) = g(6)
f(6) = g(6)
PLEASE HURRY IM TIMED!!!!
Answer: f(3) = g(6)
Step-by-step explanation: if you plug them in we see that f of 3 on the y axis intercept g of x so we then go up and see that g of 6 intercepts f of 3 so therefore that is the answer
Find the unit rate $ 6. 80 for 9 muffins
A package contains 20 golf balls. The total
weight of the golf balls is 32 ounces. Use the
model to show the number of ounces per
golf ball and the number of golf balls per
ounce. Write your answers in the blanks.
Answer: 1.6
Step-by-step explanation:
each golf is 1.6 ounces and you 20 golf balls in order to reach 32 ounces
Answer:
shown below
Step-by-step explanation:
golf balls per ounce = 5/8 or 0.625
ounces per gold ball = 8/5 or 1.6
The graph below shows triangle A and triangle B. The side lengths of triangle A are proportional to the side lengths of triangle B, and the corresponding angle measures of the two triangles are equal. image b63beb85ff8941fb976339f638c35c47 Which statement BEST describes the relationship between triangle A and triangle B? A The triangles are similar but not congruent. B The triangles are congruent but not similar. C The triangles are both similar and congruent. D The triangles are neither similar nor congruent.
Answer:A.The triangles are similar but not congruent
Step-by-step explanation:
In a congruent traingle:
the both triangles are same in shape and size
There are five theorems to see if the triangles are congruent
and neither particularly applies here
sss: the sides are not equal
as none of the sides are equal, then despite the angles, congruence is not possible
However it is evident that one of the triangles is proportionally bigger than the other but similar. Hence A is correct.
Step-by-step explanation:
A jumping spider hunts for its
food. When it gets close to its
prey, it jumps into the air and
pounces on it.
A jumping spider can jump
40 times its body length. One
jumping spider is 2 centimeters
long. How far can it jump?
Sixty men can build a wall in 40days but though they begin the work together, 55 men quit every ten days. The Time needed to build the wall is?
It would take 370 days to build the wall with the given conditions.
If 60 men can build a wall in 40 days, then the total man-days required to build the wall is:
60 men x 40 days = 2400 man-days
However, 55 men quit every ten days, which means that after 10 days, there are only 60 - 55 = 5 men left to work on the wall. After 20 days, there are only 5 - 55 = -50 men left, which means that the remaining 5 men cannot work any faster than they were already working. Therefore, we can assume that the remaining 5 men complete the wall on their own.
The number of man-days required for the first 10 days is:
60 men x 10 days = 600 man-days
The number of man-days required for the second 10 days is:
5 men x 10 days = 50 man-days
The total number of man-days required for the first 20 days is:
600 man-days + 50 man-days = 650 man-days
The remaining work can be completed by the 5 men in:
2400 man-days - 650 man-days = 1750 man-days
Therefore, the total time needed to build the wall is:
20 days + 1750 man-days / 5 men = 20 + 350 days = 370 days
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solve for the valuve of 3⁴ - 5 x 3
Answer:
66
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
3⁴ - 5 × 3
Step 2: Evaluate
Evaluate exponents: 81 - 5 × 3Multiply: 81 - 15Subtract: 66Anybody Know This Answer Well. ?
Answer:
no srry
Step-by-step explanation:
what is x
14= x over 3
Answer:
42
Step-by-step explanation:
14 = /3
3 ⋅ 14 = 3⋅ /3
x = 42
Express the product of 2x^2 +7x-10 and x+5 in Standard form.
Answer:
2x^3 + 17x^2 + 25x - 50
Step-by-step explanation:
I got half right, but I need help with the other half.
The distance between points (x₁, y₁) and (x₂, y₂), is given by the formula:
\(d_{12}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.\)We have the points:
• A = (0, 6),
,• B = (6, 6),
,• C = (6, 0),
,• D = (0, 0).
1) Using the formula above with:
• A = (x₁, y₁) = (0, 6),
,• B = (x₂, y₂) = (6, 6).
We get:
\(AB=6.\)2) Using the formula above with:
• B = (x₁, y₁) = (6, 6),
,• C = (x₂, y₂) = (6, 0).
We get:
\(BC=6.\)3) Using the formula above with:
• C = (x₁, y₁) = (6, 0),
,• D = (x₂, y₂) = (0, 0).
We get:
\(CD=6.\)4) Using the formula above with:
• D = (x₁, y₁) = (0, 0),
,• A = (x₂, y₂) = (0, 6).
We get:
\(DA=6.\)Answer• AB = 6
,• BC = 6
,• CD = 6
,• DA = 6
Since ABCD has four right angles and four straight sides, it is a square.
need help asap please
Answer:
\(\displaystyle yes\)
Step-by-step explanation:
If the angle of elevation is congruent in both triangles, then both smaller legs are congruent.
I am joyous to assist you at any time.
Write a system of equations to represent the scenario.
2) Clark and Bruce went to Taco Hut for lunch. Clark bought 4 burritos and 5 tacos, which cost him $6.71. Bru
bought 5 burritos and 3 tacos, which cost him $7.12.
Answer:
Step-by-step explanation:I need the same answer lol
Answer:
Step-by-step explanation:
Find x
14.2
18.5
find correct answer
From the circle the value of angle x is 90 degrees
We have to find the value of x
The radius of the circle is 18.5
As we observe the figure the angle x is opposite to the 90 degrees
The angle x and angle 90 degrees are vertical angles
We know that the vertical angles are equal or same
∠x = 90 degrees
Hence, the value of angle x is 90 degrees from the circle
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please help! i’ll mark brainliest
Answer:
B. 136
Step-by-step explanation:
∆ABC is similar to ∆EDC, therefore the ratio of their corresponding side lengths would be the same.
Thus:
AC/EC = AB/ED
(144 - x)/x = 51/3
(144 - x)/x = 17/1
Cross multiply
(144 - x)*1 = 17*x
144 - x = 17x
144 - x + x = 17x + x
144 = 18x
Divide both sides by 18
144/18 = 18x/18
8 = x
x = 8
✔️AC = 144 - x
Plug in the value of x
AC = 144 - 8
AC = 136
D.
Question 1
1 pts
Write the equation of a line through (3,1), parallel to y= 2+1
Oy=-=-1
Oy=-=-
Oy=-=-
Oy=-1
Answer:
last one
Step-by-step explanation: