Answers
Answer:
Domain → x > 0
Solution → x = 100
Step-by-step explanation:
Given equation is,
[tex]x^{0.5\text{logx}}=0.01x^2[/tex]
Since, log of any number 'x' is defined when x > 0
Therefore, domain of the equation → x > 0
By taking log on both the sides of the equation,
[tex]\text{log}(x^{0.5\text{logx}})=\text{log}(0.01x^2)[/tex]
0.5(logx)(logx) = log(0.01) + log(x²)
0.5(logx)²= -2 + 2log(x)
Let log(x) = a
Then the equation becomes as,
0.5a² = -2 + 2a
0.5a² - 2a + 2 = 0
a² - 4a + 4 = 0
(a - 2)² = 0
a = 2
Since, a = log(x)
log(x) = 2
x = 10²
x = 100
Therefore, solution of the given equation is x = 100.
[tex]\boxed{\boxed{\pink{\tt \leadsto The \ domain \ of \ x \ is \ (0,\infty ). }}}[/tex]
Step-by-step explanation:A equation is given to us and need to find the domain of the equation . So , given equation is ,
[tex]\bf\implies x^{0.5\:log\ x } = 0.01x^2 [/tex]
Now , let's simplify this equation to find the domain of x .
[tex]\bf\implies x^{0.5\:log\ x } = 0.01x^2 \\\\\bf\implies x^{0.5\:log\ x } -0.01x^2 =0 \\\\\bf \implies x^{log \:x^{\frac{1}{2}}} - 0.01x^2=0 \\\\\bf\implies x^{log \ \sqrt{x}} - 0.01x^2=0 [/tex]
Now set the argument in log( √x) Greater than or equal to zero to see where the expression is defined. Since the value of log is non - negative.
[tex]\bf\implies \sqrt{x} > 0 \\\\\bf\implies (\sqrt{x})^2>0^2 \\\\\bf\implies x>0\\\\\bf\implies \boxed{\red{\bf x \in ( 0, \infty ) }}[/tex]
In set builder Notation we can write as ,
[tex]\boxed{\red{\bf \{ x | x > 0 \} }}[/tex]
Hence the domain of x is ( 0 , ∞ ) .Related Questions
SOMEONE PLEASE HELP EVEN IF ITS ON QUESTION ANSWERED OR TWO
Use 45-45-90 & 30-60-90 Special Right Triangles to Solve. find the missing sir length. Leave you answers as radicals in simplest form
Answers
Answer:1) y=20,x=20√2,2) a=12,b=6
Step-by-step explanation:
In a food processing plant, a machine fastens plastic lids on to glass jars. The chart shows the number of lids the machine has attached after certain lengths of time.Which is a correct interpretation of the average rate of change for this linear function?
The machine attaches 20 lids every 8 seconds.
The machine attaches 2 lids every 5 seconds.
The machine attaches 8 lids every 10 seconds.
The machine attaches 8 lids every second.
Answers
please helppp ;-; how do you determine the end behavior of a function?
Answers
Answer:
End Behavior of a Function. The end behavior of a polynomial function is the behavior of the graph of f( x ) as x approaches positive infinity or negative infinity. The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.
Step-by-step explanation:
PLEASE ANSWER QUICK I NEED TO FINISH IN 50 MINUTES FOR MY TEST
James and Willis are both painting a room. James could complete it in 6 hours by himself. Together they can complete the room in 2 hours. How long would it take Willis to paint the room by himself?
Answers
Answer: Willis will take 3 hours to paint the room by himself.
Step-by-step explanation:
Given: Time taken by James to complete job by himself = 6 hours
Let Time taken by Willis to complete job by himself = t hours
Together they take 2 hours.
[tex]\dfrac{1}{6}+\dfrac{1}{t}=\dfrac{1}{2}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{2}-\dfrac{1}{6}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{3-1}{6}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{2}{6}\\\\\Rightarrow\ t=\dfrac{6}{2}\\\\\Rightarrow\ t=3[/tex]
So, Willis will take 3 hours to paint the room by himself.
Lindsay earns $10 per hour plus $3 for each subscription she sells. What will Lindsay earn
for selling 12 subscriptions in an 8-hour day?
Answers
Your answer is 116
Janice puts a fence around her rectangular garden. The garden has a length that is 9 feet less than 3 times the width. Which system of equations represents is the dimensions of the rectangular garden if the perimeter is 63?
Answers
Step-by-step explanation:
Let the width of the garden be b and its length is 9 feet less than 3 times the width.
Length = 3b-9 ...(1)
The perimeter of the garden = 63
We need to find the system of equations that represents is the dimensions of the rectangular garden.
Perimeter = 2(l+b)
63 = 2(3b-9+b) [from equation (1)]
31.5 = (3b-9+b)
31.5 = (4b-9)
31.5+9 = 4b.....(2)
b = 10.12
Hence, the equations are showsn in equation (1) and (2).
for any positive integer n, the sum of the first n positive integers equals n(n 1)/2. what is the sum of all the even integers between 99 and 301 ?
Answers
The sum of all the even integers between 99 and 301 is 20200
To find the sum of even integers between 99 and 301, we will use the arithmetic progressions(AP). The even numbers can be considered as an AP with common difference 2.
In this case, the first even integer will be 100 and the last even integer will be 300.
nth term of the AP = first term + (n-1) x common difference
⇒ 300 = 100 + (n-1) x 2
Therefore, n = (200 + 2 )/2 = 101
That is, there are 101 even integers between 99 and 301.
Sum of the 'n' terms in an AP = n/2 ( first term + last term)
= 101/2 (300+100)
= 20200
Thus sum of all the even integers between 99 and 301 = 20200
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if 0<0<90, is sin 0 equal to cos (90-0) and for what reason
Answers
Answer:
When the angle becomes zero, then the base becomes 0, and the perpendicular and the hypotenuse becomes the same line. Since in cos 90, base is 0, therefore therefore cos 90 is zero
Step-by-step explanation:
Kia has 4 necklaces , 7 bracelets ,and 5 rings to bracelets
Answers
Answer:
What are you asking?
Step-by-step explanation:
Remember : anything can be graphed using an ______
Answers
find the value of x in the triangle shown below
Answers
Answer:
x = 3
4^2 + x^2 = 5^2
solve for x
16 + x^2 = 25
x^2 = 25-16
x^2 = 9
sqrt of x^2 = 3
---
Hope this helps! If so, please mark my answer as brainliest!
it would be nice if someone can help me
Answers
Answer:
Solution is 16r-14s
Step-by-step explanation:
2(7r-2s)+2(r-5s)
14r-4s+2r-10s
16r-14s
16r - 14s
Step-by-step explanation:The perimeter is a measure of a polygon that describes the distance around the boundaries of a shape.
Perimeter Formula
The perimeter of a rectangle is equal to [tex]l + l + w + w[/tex], where [tex]l[/tex] is the length and [tex]w[/tex] is the width. This can be simplified to [tex]2l+2w[/tex]. Now, we can plug in the expression we are given for width and length.
[tex]2(r-5s)+2(7r-2s)[/tex]Simplifying the Expression
The expression above does accurately depict the perimeter, but it should be simplified to make the expression easier to understand and use.
First, distribute the 2 inside the parentheses.
[tex]2r-10s+14r-4s[/tex]The next step is to combine like terms. Like terms are terms that have the same power and variable. For example, 2r and 14r are like terms.
16r - 14sThis is the simplified expression and the final answer.
there are 8 elements in a set a, there are 5 elements in a set b, and 3 elements of those are shared both a and b. how many elements are in union of a and b?
Answers
There are 10 elements in the union of A and B.
What is the union of A and B?
The union of A and B will contain all of the elements found in either A or B or both sets. The union of sets is represented by the set notation. To find the union of two sets A and B, use the union B formula. Simply putting all of A and B's elements in one set and removing duplicates yields the union.So, set A has 8 elements and set B has 5 elements.
Both have 3 elements in common. So, 3 + (8 - 3) + (5 - 3) = 3 + 5 + 2 = 10Therefore, there are 10 elements in the union of A and B.
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area of square increasing at 112 centimeters squared per second, rate of change when side is 7 centimeters
Answers
The area rate of change of side of square is 8 cm/s;
dA/dt = 112 cm²/s;
Area = (r)²; where r is the side of square;
dA/dt = (dA/dr)(dr/dt);
dA/dr = 2r and dA/dt = 112 cm²/s;
Therefore; dr/dt = 112/2r at r = 7;
dr/dt = 112/14 = 8 cm/s;
Rate of change of side of square is 8 cm/s;
area is the quantity that expresses the extent of a area on the plane or on a curved floor. The location of a aircraft region or plane place refers to the location of a shape or planar lamina, at the same time as surface place refers to the vicinity of an open floor or the boundary of a 3-dimensional object.
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Which of the following geometric objects could have its length measured?
A. Ray
B. Point
C. Line segment
D. Line
Answers
Pls help will give Brainlyist
Answers
Answer:
B
Step-by-step explanation:
Mandy buys 5.5 packs of organic milk from the neighborhood store. Each pack is priced at $3.96. How much does Mandy spend in all on his purchase?
Answers
Answer:
$21.78
Step-by-step explanation:
We know that each pack of milk costs $3.96, so if we buy 5.5 of these, we will have to pay $3.96 5.5 times. In other words, we must multiply 3.96 by 5.5:
3.96 * 5.5 = 21.78
Thus, Mandy spends $21.78 in all.
Need help with Radical Rational Exponents and with work plz.
Answers
Identify the range of the function y=-3x+6 when the domain is {-1,2,4}
A. {-6,0,9}
B. {-9}
C. {3,-12,-18}
D. {-3,12}
E. {-6,9}
Answers
When the domain is {-1,2,4} , the range of the function y =-3x+6 is {-6,0,9}
Given,
The function y= -3x+6
The domain of the function is the complete set of all possible input for the function.
The domain = {-1,2,4}
The range of the function is the complete set of all possible output for the function.
Substitute the values in the function
f(-1)= -3×-1+6
=3+6
= 9
f(2)= -3×2+6
=-6+6
= 0
f(4)= -3×4+6
=-12+6
=-6
So, -6,0 and 9 the possible output of the function y= -3x+6
The range of the function y= -3x+6 is {-6,0,9}
Hence, When the domain is {-1,2,4} , the range of the function y =-3x+6 is {-6,0,9}
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All boys grow up 3.75 inches per year. You measure a boy who is 9 years old
has a height of 4 feet 10 1/4 inch. What was the closest height of the boy
when he was six and a half years old?
I need help on this ASAP!!!
Answers
Answer:
UwU UwU UwU UwU
Step-by-step explanation:
I WILL GIVE BRAINLIEST IF YOU SOLVE THIS
Answers
Answer:
linear regression: S = 2.3n - 4.2
Step-by-step explanation:
Give harmful effects of carbon dioxide
Answers
Answer:
I hope this helps you
Step-by-step explanation:
Exposure to CO2 can produce a variety of health effects. These may include headaches, dizziness, restlessness, a tingling or pins or needles feeling, difficulty breathing, sweating, tiredness, increased heart rate, elevated blood pressure, coma, asphyxia, and convulsions.
Given g(x) = 1/2x+ 5, find the following.
g(4)
g(-10)
g(0)
Answers
Answer:
g4
Step-by-step explanation:
m
Solve for x
Here we go again with the same thing♀️
Answers
For the function f(x)•= x2 + 4, identify the values of f(0),
f(1/2), and f(-1).
Answers
Answer:
the question is wrong may be.
If there are no Domain Restrictions, what is the domain?
Answers
Answer:
If there are no restrictions, the domain is all real numbers.
- infinity < x < infinity
Answer:
Step-by-step explanation:
Functions are a correspondence between two sets, called the domain and the range. When defining a function, you usually state what kind of numbers the domain (x) and range (f(x)) values can be. But even if you say they are real numbers, that doesn’t mean that all real numbers can be used for x. It also doesn’t mean that all real numbers can be function values, f(x). There may be restrictions on the domain and range. The restrictions partly depend on the type of function.
In this topic, all functions will be restricted to real number values. That is, only real numbers can be used in the domain, and only real numbers can be in the range.
Each face of a pyramid is an isosceles triangle with a 84° vertex angle. What are the measures of the base angles?
Need asappp!
Answers
Step by step
The base angles are the 2 congruent angles in an isosceles triangle.
Sum of the interior angles =180 degrees.
The vertex is 84, so we know one angle.
180 - 84 = 96
Since the base angles will be equal, we divide 96 by 2 = 48.
The base angles will each be 48 degrees.
4.Triangle ABC is shown on the coordinate grid to the right. What are the coordinates of triangle A’B’C’ if the rule (x, y) → (–x – 3, y + 2) was applied to coordinates of triangle ABC?
Answers
Answer:
what grade is this
Step-by-step explanation:
I can check it and then I'll get back to you in 30 min
You can work a maximum of 20 hours a week. You need to
make $195 In order to cover your expenses. Your translation
Job pays $15 an hour and your tutoring job pays $8 an hour.
Write a system of inequalities to express this situation. What is
the least possible number of hours you can work at your
translation job and still meet the requirements?
hours
Answers
Answer:
for connexus Modeling With Systems of Inequalities Quick Check as of 1-7-21
Step-by-step explanation:
1)C
2)C
3)D
4)C
5)C
Answer:
x=5
Step-by-step explanation:
What is the missing side length, x, in this
right triangle?
X
A.
5 meters
B. 10 meters
26 m
24 m
4
C. 12 meters
D. 43 meters