Answer to this question is:
Domain of given function is (0,∞),{x|x>0}
Range of given function is (0,∞),{y|y>0}
Inverse of given function is 9/x²
The domain is all values of x that make the expression defined.The entire range of independent variable values is the domain of a function.
This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.
When choosing the domain, keep in mind that a fraction's denominator (bottom) cannot be 0.
Interval Notation:(0,∞)
Set-Builder Notation:{x|x>0}
The set of all valid y values constitutes the range.Graph may be used to find the values.
Interval Notation:(0,∞)
Set-Builder Notation:{y|y>0}
For calculation of inverse:
Interchange the variables x=3/√ySolve for yy=9/x²Replace y with f^-1(x)f^-1(x)=9/x²∴Domain of given function is (0,∞),{x|x>0}
Range of given function is (0,∞),{y|y>0}
Inverse of given function is 9/x²
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5x - 2x + 5 = 2x + 26
solving for x when d is on both sides
answer :
so this is the answer of the value of x
The solution of the linear equation is x = 21.
How to solve the linear equation for x?
Here we have the linear equation:
5x - 2x + 5 = 2x + 26
To solve this for x, move all the terms with x to the left side and all the others to the right side:
5x - 2x - 2x = 26 - 5
5x - 4x = 21
x = 21
The solution of the linear equation is x = 21.
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Linear equations
2e-12=7e+8
Answer: 1 = e
Step-by-step explanation:
Macario works part time at a clothing store in the mall. He is paid $9 per hour plus 12% commission on the items he sells in the store. Write an equation in slope-intercept form to represent Macario's hourly wage y.
The equation in the form of slope-intercept for Macario's hourly wage is y=9x+0.12s
What is a slope-intercept function?
A slope-intercept equation comprises the total amount paid as wages to Macario which includes the hourly rate of $9 multiplied by the number of hours spent working plus the 12% of total sales achieved by Macario, in essence, if we assume that the number of hours spent working is x and that total sale is s, the slope-intercept form that represents Macario's hourly wage y is shown thus:
y=9x+0.12s
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For each annual rate of change, find the corresponding growth or decay factor. -55 %
The decay factor for the annual rate of change of - 55 % is 0.45.
A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.
With the function displayed to the right, you may represent exponential growth or decay.
A(x) = a( 1 + r)ˣ
Where A is the amount after x time periods, a is the initial amount, x is the number of time periods, and r is the rate of change.
Now, we have the annual rate of change as:
r = - 55 % = - 55 / 100 = - 0.55
From the function A(x) = a( 1 + r)ˣ , the corresponding factor is 1 + r.
So, let B = 1 + r
B = 1 + r
B = 1 + (- 0.55)
B = 1 - 0.55
B = 0.45
Now, the value of B is less than 1 therefore, the corresponding decay factor is 0.45.
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The lines represented by y=-5x+10and5y=x+15 are
The lines represented by y = -5x + 10 and 5y = x + 15 are; Perpendicular
How to interpret slopes of lines?
We are given the equation of two lines as;
Line 1; y = -5x + 10
Line 2; 5y = x + 15
Now, the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, for the equation in line 1, we know that;
slope = -5 while the y-intercept is 10
For line 2, the equation can be rewritten as;
y = ¹/₅x + 3
Slope = 1/5
y-intercept = 3
Now, we know that when two lines are perpendicular, it means that their slopes are negative reciprocals of each other.
Slopes of lines 1 and 2 are negative reciprocals of each other and thus they are perpendicular.
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If the total price for two cars at a dealership is $ 108 , 000 $108,000, where one car’s price is $ 9000 $9000 less than twice the other, what is the price of the cheaper vehicle?
The price of the cheaper vehicle is $39,000
Calculating CostFrom the question, we are to determine the price of the cheaper vehicle
Let the cost of one of the cars b $x
and the cost of the other car be $y
From the given information,
The total price for two cars at a dealership is $108,000
That is
x + y = 108000 ----------- (1)
and
one car’s price is $9000 less than twice the other
x = 2y - 9000 ----------- (2)
Put equation (2) into equation (1)
x + y = 108000
2y - 9000 + y = 108000
2y + y - 9000 = 108000
2y + y = 108000 + 9000
3y = 117000
y = 117000/3
y = 39000
∴ The price of one of the vehicles is $39,000
Substitute this value into equation (2)
x = 2y - 9000
x = 2(39000) - 9000
x = 78000 - 9000
x = 69000
The price of the other vehicle is $69,000
Hence, the price of the cheaper vehicle is $39,000
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Write a description of a line. How are lines labeled?
1. A line can be described as a one-dimensional figure without thickness or width.
2. Lines are labeled with two points (A ↔ B). Lines can be marked using lowercase letters (for example, line k).
What is a line?
A line is a one-dimensional figure with a length only. A line does not have width or thickness.
A line can have line segments with two endpoints. A line cannot be measured, but its segments are measurable.
There are different types of lines, including:
Curved lineStraight lineVertical lineHorizontal lineParallel linesIntersecting lineTransversal linePerpendicular lineCurly and spiral lines.Thus, lines are one-dimensional with lengths and no widths or thicknesses.
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Write an equation in slope-intercept form of the line
The linear equation in the slope-intercept form is:
y = (-1/3)*x + 4
How to write the linear equation?Remember that if a line passes through two points (a, b) and (c, d), then the slope is given by:
slope = (d - b)/(c - a)
By looking at the graph, we can see that the points (0,4) and (3, 3), then the slope will be:
s = (3 - 4)/(3 - 0) = -1/3
And we can see that the y-intercept is y = 4 (because the line passes through the point (0,4))
Then the linear equation in the slope-intercept form is:
y = (-1/3)*x + 4
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What are the solutions for |3(x+4)|+8=23
a) x=1 and x= -9
b) x=1
c) x=9
d) x= -1 and x= 9
Question 4
Looking at your answer for the question above, we’re there any extraneous answers?
a) Yes
b) No
q3: -9, 1
q4: No
The reason there are multiple answers for this question is because of the absolute value sign. to solve this you can isolate the absolute value onto one side and solve for the positive and negative possibilities.
step 1: isolate the absolute value
|3(x+4)|+8=23 ----> |3(x+4)|=15
step 2: remove the absolute value sign the remember that now it has two answer possibilities where 15 can be both negative and positive and still be right. Then just solve just like you would a normal equation.
3(x+4)= +-15 ----> x+4= +-5
x = -9, 1
find the vertex y= -2x^2
The vertex of the function where the equation of the function is given as y = -2x^2 is (0, 0)
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the vertex of the function?The equation of the function is given as
y = -2x^2
A quadratic function is represented as
y = a(x - h)^2 + k
Where the vertex is
vertex = (h, k)
This means that the equation y = -2x^2 can be rewritten as
y = -2(x - 0)^2 + 0
When the equations are compared, we have
vertex = (h, k) = (0, 0)
Hence, the vertex of the function where the equation of the function is given as y = -2x^2 is (0, 0)
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Suppose you invest a dollars to earn an annual interest rate of r percent (as a decimal). After t years, the value of the investment with interest compounded yearly is A(t)=a(1+r) t . The value with interest compounded continuously is A(t)=a . e rt
b. Suppose you can earn interest at some rate between 0 \% and 5 \% . Use your. knowledge of the exponential function to explain why continuous compounding does not give you much of an investment advantage.
$1.051271 is the exponential function to explain why continuous compounding does not give you much of an investment advantage.
With an example, what is compound interest?
When you add the interest you have already earned back into your principal balance, you are earning compound interest, which increases your profits. Consider that you have $1,000 in a savings account earning 5% interest annually. If you made $50 in the first year, your new balance would be $1,050.Simple Interest: A = P(1+rt)
P: the principal, the amount invested
A: the new balance
t: the time
r: the rate, (in decimal form)
Ex 1 - If $1000 is invested now with simple interest of 8% per year. Find the new amount after two years.
P = $1000, t = 2 years, r = 0.08.
A = 1000(1+0.08(2)) = 1000(1.16) = 1160
B) Suppose you invest $1 at 5% compounded yearly.
Suppose you invest $1 at 5% compounded continuously.
The 1st case gives you $1*(1.05)1 = $1.05
The 2nd case gives you $1*e0.05 = $1.05127
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What value of x makes the equation -5x - (-6 - 4x) = -2(3x - 4) true?
Answer: [tex]x=\Large\boxed{\frac{2}{5} }[/tex]
Step-by-step explanation:
Given equation
[tex]-5x-(-6-4x)=-2(3x-4)[/tex]
Expand the parenthesis
[tex]-5x+6+4x=-2\times3x-2\times(-4)[/tex]
[tex]-5x+6+4x=-6x+8[/tex]
Combine like terms
[tex]-x+6=-6x+8[/tex]
Add 6x on both sides
[tex]-x+6+6x=-6x+8+6x[/tex]
[tex]5x+6=8[/tex]
Subtract 6 on both sides
[tex]5x+6-6=8-6[/tex]
[tex]5x=2[/tex]
Divide 5 on both sides
[tex]5x/5=2/5[/tex]
[tex]x=\Large\boxed{\frac{2}{5} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
3x +8x combining like terms
Hey there!
3x + 8x
= 3 + 8
= 11x
= 11
Therefore, your answer should be:
11x
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
a) how much £60 is worth in euros (€).
b) how much €98.60 is worth in pounds (£).
Exchange rate
£1 = €1.16
In the foreign exchange market, if a Pound is equal to 1.59 USD, one Euro is equal to 1.46 USD. So roughly speaking, one Pound is equal to 1.09 Euro.
given,
a ) £1 = €1.16
= £60 x 1.16 = 69.60
b) 0.87 pound = 1 euro
€98.60 ,
therefore , 98.60/0.87 = 113.33
Euro is the term used to specify the currency of European Union countries.Pound or British pound is the currency of Great Britain. There is one more term which refers to this currency. It is Pound Sterling. This is the financial term used to represent the currency Great Britain.The name “the euro” was chosen in 1995 by a European Council meeting in Madrid. The symbol € is based on the Greek letter epsilon (Є), with the first letter in the word “Europe” and with 2 parallel lines signifying stability. The ISO code for the euro is EUR.Convert Euro to British Pound
EUR GBP
1,000 EUR 876.24 GBP
5,000 EUR 4,381.2 GBP
10,000 EUR 8,762.4 GBP
50,000 EUR 43,812 GBP
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u=a+k solve for a please
Solving for the variable 'a' gives the equation a = u - k
What is subject of formula?A subject of formula can be defined as a variable written in terms of other variables in an equation or given expression.
It is also recognized as the variable that is being worked out in an equation or expression.
Given the equation:
u=a+k
To make the variable 'a' the subject of formula, we have to take all other variables to the other side of the equality sign, making the variable 'a' stand alone.
We then have;
u - k = a
This is also written as;
a = u - k
Thus, solving for the variable 'a' gives the equation a = u - k
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What is a rational number with a diameter of 7 that is between the square root of 7 and the square root of 8? Write your answer as an improper fraction.
The rational number between the square root of 7 and the square root of 8 is 27/10
What are rational expressions?Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.
This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals
How to determine the rational number?The features of the rational number are given as
Value = between the square root of 7 and the square root of 8
Rewrite the value properly
So, we have
Value = between √7 and √8
Evaluate the values of √7 and √8
So, we have
√7 = 2.65
√8 = 2.83
This means that the rational number is between 2.65 and 2.83
A number between 2.65 and 2.83 is 2.7
Express as fraction
value = 27/10
Hence, the rational number between the square root of 7 and the square root of 8 is 27/10
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Identify the percentage of growth or decay for the exponential function: y = 18(0.75) x
The percentage of decay for the exponential function: y = 18(0.75) x is 25%.
How to illustrate the information?This equation represents exponential decay. Whenever the base is less than 1, the function represents decay. When the base is greater than 1, the function represents growth. In this case, the base is 0.75 which is less than 1, representing decay.
The formula for exponential decay is y=a(1-r)x.
r is the decay rate, expressed as a decimal.
In this case, r = 1 - 0.75 = 0.25 which represents 25%.
Therefore, the percentage of decay for the exponential function: y = 18(0.75) x is 25%.
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math (find the area in square feet)
Answer: 50
Step-by-step explanation:
8x4 =32
6x3=18
32+18=50
Please help me please help me please help me please
Write each logarithmic expression as a single logarithm.
log 3+4 log x
The single logarithm of log 3 + 4 log x is = log (3x^4).
What is a logarithmic function?
A logarithmic function in mathematics is defined as the function which is the inverse of the exponential function. It is denoted by using the word log. For example log 10 = 1
Write the given logarithmic expression in a single logarithm. log 3 + 4 log x
Given logarithmic expression is log 3 + 4 log x
Applying given properties of logarithmic function;
log a + log b = log (ab)
2 log a = log a²
Now, log 3 + 4 log x = log 3 + log x^4
= log (3x^4)
Hence, the single logarithm of log 3 + 4 log x is = log (3x^4).
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X-2/5 + 1/2x-3=1 pls solve this
Answer:
44/15
Step-by-step explanation:
[tex]x-\frac{2}{5}+\frac{1}{2}x-3=1 \\ \\ \frac{3}{2}x-\frac{17}{5}=1 \\ \\ \frac{3}{2}x=\frac{22}{5} \\ \\ x=\frac{44}{15}[/tex]
A package of a 8 count AA batteries cost 6.40. A package of 20 count AA batteries cost 15.80. Which statement about the unit prices is true?
Part 2: What the answers to the worksheet
The rule is reflection in y=x (x, y)→(y, x) and reflection in y=-x (x, y)→(-y, -x).
Given that, a rotation and reflection composition is equivalent to other compositions.
What are rotation and reflection?Reflection is flipping an object across a line without changing its size or shape. Rotation is rotating an object about a fixed point without changing its size or shape.
Rotation rule:
Rotation of a point through 180°, about the origin when a point A (x, y) is rotated about the origin O through 180° in the anticlockwise or clockwise direction, it takes a new position A' (-x, -y).
Reflection rule:
A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis.
Therefore, the rule is reflection in y=x (x, y)→(y, x) and reflection in y=-x (x, y)→(-y, -x).
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The total cost (in cents) of x+2 markers is x³+5 x²+2 x-8
b. If you buy 7 markers, how much would each marker cost?
If you buy 7 markers , each marker would cost 9.42 ( cents ) .
Given : The total cost ( in cents ) of x + 2 markers is x³ + 5 x ² + 2 x - 8 .
To find : cost of 1 marker
Cost of 1 marker = ( x³ + 5 x ² + 2 x - 8 ) / ( x + 2 )
= [tex]x^{2}[/tex] + 3 x - 4
Substituting value of 7 in cost function
= [tex]x^{2}[/tex] + 3 x - 4 at x = 7
= 49 + 21 - 4
Cost of 7 markers = 66
Cost of 1 marker = 66 / 7
= 9.42
Therefore , if you buy 7 markers , each marker would cost 9.42 ( cents ) .
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Nick had $100 in a saving account over the next 6 months he worked at a seasonal store where each month he earn $400 and spent $250 he put the remaining amount in his savings account each month now that the job is over he plans to spend 200 per month for how many months can he make withdrawal from his savings account until his balance is zero dollars
If he plans to spend 200 per month, then the number of months he can make withdrawals from his savings account until his balance is zero dollars is equal to 5.
First, we calculate the money earned by Nick in 6 months
Money earned per month = $400
Money earned in 6 months = 400 × 6 = 2400
If he spends $250 out of the money earned per month, then the money spent in these 6 months can be calculated as follows;
Money spent per month = 250
Money spent in 6 months = 250 × 6 = 1500
Now we calculate the money put in the saving account in 6 months by subtraction;
Money added to the saving account = 2400 - 1500 = $900
As he already had $100 in the saving account,
Total amount of money in the saving account = 900 + 100 = 1000
If he plans to spend 200 per month, then the number of months he can make withdrawals can be calculated by division
Number of months = total money in the account ÷ money spent per month
Number of months = 1000 ÷ 200 = 5
Therefore, Nick can make withdrawals for 5 months from his savings account.
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Find each real root. ³√-27
The average temperature in the mountains is 61° in April. The average temperature in that same spot is −2° in December. Determine how much warmer this location is in April than in December, and determine which temperature is the farthest away from 0°.
61 + |−2| = 63°, −2° is the farthest from 0°
61 − |−2| = 59°, −2° is the farthest from 0°
61 + |−2| = 63°, 61° is the farthest from 0°
61 − |−2| = 59°, 61° is the farthest from 0°
The location is 63° warmer in April than in December. The correct option is the third option 61 + |−2| = 63°, 61° is the farthest from 0°
From the question, we are to determine how much warmer the location is in April than in December
From the given information,
Average temperature in April = 61°
and
Average temperature in December = -2°
To determine how much warmer the location is, we will add the absolute values of the temperatures
That is,
61 + |-2|
= 61 + 2
= 63°
61° the temperature that is farthest from 0
Hence, the location is 63° warmer in April than in December. The correct option is the third option 61 + |−2| = 63°, 61° is the farthest from 0°
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i need help asap please help me
Answer: yo wassup picture isn't straight cant see
Step-by-step explanation:
A mountain grows by 2 centimeters every year. At this rate in how many years will the mountain grow by 1.3 meters?
well, let's keep in mind that a meter has 100 centimeters, thus 1.3 meters will be 1.3 * 100 cm, namely 130 cm.
[tex]\begin{array}{ccll} cm&year\\ \cline{1-2} 2 & 1\\ 130& x \end{array} \implies \cfrac{2}{130}~~=~~\cfrac{1}{x}\implies \cfrac{1}{65}=\cfrac{1}{x}\implies x=65[/tex]
A scout leader is going to pair a new member with one of the fifteen troop members. five of the boys love to go camping ten like to fish three enjoy archery twelve like to go hiking and one boy enjoys carving.what is the probability the new boy will be paired with a boy who does not love camping
The probability of the new boy being paired up with a boy who does not love camping is 2/3 or 66.66%
Total no. of troop members = 15
No. of boys who love camping = 5
No. of boys who love fishing = 10
No. of boys who love archery = 3
No. of boys who love hiking = 12
The boy who enjoys carving = 1
Boys who do not like camping = 1 - 5/15 = 10/15 = 2/3*100 = 66.66%
So, the probability that the new boy will be paired up with a boy who does not love camping is 66.66% or 2/3.
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