Express f(x) = |x| as a piecewise function.
Answers
The function f(x) = |x| uses the operator called "module" (the vertical bars), and what this operator does is the result will always be a positive number.
So, for example, the module of 3 is equal 3, and the module of -5 is equal 5.
The result is just the same number, but always positive.
So as we have a variable inside the bars, we have the module of x.
This means that if x is a positive number (x >= 0), the result will be x.
But if x is a negative number (x < 0), the result will be -x (because -x will be a positive number).
Then, expressing this as a piecewise function, we have:
\(\begin{gathered} f(x)=|x| \\ f(x)=\left\{ \begin{aligned}x,\text{ if }x\ge0 \\ -x,\text{ if }x<0\end{aligned}\right. \end{gathered}\)Related Questions
Morganton Company makes one product and it provided the following information to help prepare the master budget:
The budgeted selling price per unit is $60. Budgeted unit sales for June, July, August, and September are 8,600, 17,000, 19,000, and 20,000 units, respectively. All sales are on credit.
Thirty percent of credit sales are collected in the month of the sale and 70% in the following month.
The ending finished goods inventory equals 25% of the following month’s unit sales.
The ending raw materials inventory equals 10% of the following month’s raw materials production needs. Each unit of finished goods requires 5 pounds of raw materials. The raw materials cost $2.40 per pound.
Thirty five percent of raw materials purchases are paid for in the month of purchase and 65% in the following month.
The direct labor wage rate is $14 per hour. Each unit of finished goods requires two direct labor-hours.
The variable selling and administrative expense per unit sold is $1.80. The fixed selling and administrative expense per month is $67,000.
5. If 96,250 pounds of raw materials are needed to meet production in August, how many pounds of raw materials should be purchased in July?
Answers
Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July
X pounds - 0.35 * X pounds = 9,500 pounds
Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.
To determine the number of pounds of raw materials that should be purchased in July, we need to calculate the raw materials production needs for August and then consider the inventory policies given in the information provided.
Each unit of finished goods requires 5 pounds of raw materials. The budgeted unit sales for August are 19,000 units. Therefore, the raw materials production needs for August would be 19,000 units multiplied by 5 pounds per unit, which equals 95,000 pounds.
The ending raw materials inventory equals 10% of the following month’s raw materials production needs. Therefore, the desired ending raw materials inventory for July would be 10% of 95,000 pounds, which is 9,500 pounds.
To calculate the raw materials purchases for July, we need to consider the payment terms provided. Thirty-five percent of raw materials purchases are paid for in the month of purchase and 65% in the following month.
Let's assume the raw materials purchases for July are X pounds. Then the payment for 35% of X pounds will be made in July, and the payment for 65% of X pounds will be made in August.
The payment for raw materials purchases in July (35% of X pounds) will be:
0.35 * X pounds
The payment for raw materials purchases in August (65% of X pounds) will be:
0.65 * X pounds
Since the raw materials purchases for July should cover the desired ending raw materials inventory for July (9,500 pounds), we can set up the following equation:
Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July
X pounds - 0.35 * X pounds = 9,500 pounds
Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.
for such more question on equation
#SPJ8
The diagram shows a circle drawn inside a square.
The circle touches the edges of the square.
12 cm
Calculate the shaded area.
Take pie to be 3.142 and write down all the digits given by your calculator.
Answers
Answer:
144 - 36×3.142 = 30.888
30.888 ÷4 = 7.722
If a scientific team uses special equipment to measures the pressure under water and finds it to be 282 pounds per square foot, at what depth is the team making their measurements?
Answers
p=282 pounds per square foot =1 376.8 kg/m2
d- density of water
d≈997 kg/m³
p=d*h
h=p/d
h=1 376.8/997
h=1.38 m (about 4530 feet 105⁄64 inches)
Madelyn wants to buy a charm bracelet. Oxford Fine Jewelry charges $12 per charm, plus $40 for the bracelet. Espinoza Jewelers, in contrast, charges $14 per charm and $30 for the bracelet. If Madelyn wants to add a certain number of charms to her bracelet, the cost will be the same at either jewelry shop. How many charms would that be?
Answers
Using a system of equations, for Madelyn to add a certain number of charms to her bracelet, where the cost will be the same at either jewelry shop, the number of chams would be 5.
What is a system of equations?When two or more equations are solved concurrently, they are described as a system of equations.
Another description of a system of equations is simultaneous equations.
Oxford Fine Espinoza
Unit cost per charm $12 $14
The cost of the bracelet $40 $30
Let the number of charms = c
Equations:Equation 1: (Costs at Oxford Fine) 12c + 40
Equation 2: (Costs at Espinoza) 14c + 30
For the cost to be the same at either jewelry shop, Equation 1 must equal Equation 2:
12c + 40 = 14c + 30
-2c = -10
c = 5
Check:
12c + 40
12(5) + 40 = $100
14c + 30
14(5) + 30 = $100
Learn more about simultaneous equations at https://brainly.com/question/16863577
#SPJ1
all you need is in the photo and it's homework please don't do step by step
Answers
x-intercpets: value of x when f(x)=0. Use the quadratic formula:
\(\begin{gathered} x^2-4x-12=0 \\ \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \\ x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1)(-12)}}{2(1)} \\ \\ x=\frac{4\pm\sqrt[]{64}}{2} \\ \\ x=\frac{4\pm8}{2} \\ \\ x_1=\frac{4+8}{2}=6 \\ \\ x_2=\frac{4-8}{2}=-2 \end{gathered}\)X-intercept: (6,0) and (-2,0)y-intercept: value of f(x) when x=0:
\(\begin{gathered} f(0)=0^2-4(0)-12 \\ f(0)=-12 \end{gathered}\)Y-intercept: (0, -12)Vertex: use the next foruma to find the x value in vertex:
\(\begin{gathered} x=-\frac{b}{2a} \\ \\ x=-\frac{(-4)}{2(1)} \\ \\ x=\frac{4}{2}=2 \end{gathered}\)Use that value of x to find the coordinate in y for the vertex:
\(\begin{gathered} f(2)=2^2-4(2)-12 \\ f(2)=4-8-12 \\ f(2)=-16 \end{gathered}\)Vertex: (2, -16)Axis of symmetry: value of x in the vertex.
Axis of simmetry: x=2Maximim or minimum: if in the quadratic equation, the coefficient of the square x is possitive the parabola opens up and has a minimun value. If the coefficient of the square x is negative the parabola opens down and and has a maximum value.
Minimum
The minimum value is in the vertex (2 ,-16) is the value of the function f(x) in the vertex (the value of coordinate y):
Min value: -16Graph:
" alt="A number line going from 0 to 6.5 in increments of 0.5. An arrow goes from 0 to 2.5 and from 2.5 to 5."/>
Answers
The image you described features a number line that goes from 0 to 6.5 in increments of 0.5.
On this number line, there is an arrow that starts at 0 and extends to 2.5, and then continues from 2.5 to 5.
This image can be visualized as follows:
0 1 2 3 4 5 6 6.5
|--------|--------|--------|--------|--------|--------|--------|
|------------------------|------------------------|
0 to 2.5 2.5 to 5
The vertical lines represent the increments of 0.5 on the number line, and the arrow indicates the segments from 0 to 2.5 and from 2.5 to 5.
For such more questions on increments
https://brainly.com/question/28345851
#SPJ8
A grant writer had a taxable income of $49,550 last year. If he paid 10% of his
income between $0 and $8350, 15% of his income between $8350 and
$33,950, and 25% of his income between $33,950 and $49,550 in federal
income tax, how much did the grant writer pay in federal income tax last year?
A. $835
B. $3840
C. $3900
D. $8575
►
Answers
The writer paid $8575 in federal income tax last year.
How much federal income tax did he pay?To get federal income tax paid by the grant writer, we have to get amount of income taxed at each tax rate and then sum up the respective amounts.
Income taxed at 10%:
= $8350 - $0
= $8350
Tax paid at 10% rate: 10% of $8350 = $835
Income taxed at 15%:
= $33,950 - $8350
= $25,600
Tax paid at 15% rate: 15% of $25,600 = $3840
Income taxed at 25%:
= $49,550 - $33,950
= $15,600
Tax paid at 25% rate: 25% of $15,600 = $3900
The total federal income tax paid is:
= $835 + $3840 + $3900
= $8575.
Read more about income tax
brainly.com/question/30157668
#SPJ1
HELPPPPP GUYS I NEED IT AND IM NOT GOOD AT MATH!!
Answers
Answer:
-21
Step-by-step explanation:
Answer:
Option b-21
As coefficient is the number before variables
and here the number before is -21
Which value below is included in the solution set for the inequality statement? -3(x-4) > 6(x-1) 0-1 02 07 0 3 NEXT QUESTION ASK FOR HELP
Answers
The solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.
To determine which value is included in the solution set for the inequality statement -3(x-4) > 6(x-1), we need to solve the inequality for x.
Starting with the given inequality:
-3(x - 4) > 6(x - 1)
First, distribute -3 and 6 to the terms inside the parentheses:
-3x + 12 > 6x - 6
Next, combine like terms by subtracting 6x from both sides and adding 6 to both sides:
-3x - 6x > -6 - 12
-9x > -18
To isolate x, divide both sides of the inequality by -9. Remember that when dividing by a negative number, we need to reverse the inequality sign:
x < (-18) / (-9)
x < 2
Therefore, the solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.
for such more question on inequality
https://brainly.com/question/17448505
#SPJ8
students were asked to choose a city if 4/7 of them chose new york and 1/7 chose los angeles what fraction chose either new york or los angles
Answers
Answer: 5/7 of the kids chose New York or L.A.
Step-by-step explanation:
All you need to do in this problem is add the fraction of people that chose New York and the fraction of people that chose L.A:
4/7 + 1/7 = 5/7
Question in the pic, please explain your answer
Answers
The statement translated to an algebra equation will give the value of the unknown number w = 11/5
What is algebra?Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical expressions using letters to represent unknown values.
Let us represent the unknown number with the letter w so that the statement can be written as the equation:
5w - 8 = 3
add 8 to both sides
5w - 8 + 8 = 3 + 8
5w = 11
divide through by 5
5w/5 = 11/5
w = 11/5
Therefore, the statement translated to an algebra equation will give the value of the unknown number w = 11/5
Read more about algebra here: https://brainly.com/question/4344214
#SPJ1
Zero(s) of multiplicity one:
Zero(s) of multiplicity two:
Zero(s) of multiplicity three:
Please look at photo for the full question. Thank you.
Answers
The zeros and the multiplicities are
Zero(s) of multiplicity one: x = 6Zero(s) of multiplicity two: x = 11Zero(s) of multiplicity three: x = -6 and x = -5How to determine the zeros and the multiplicitiesfrom the question, we have the following parameters that can be used in our computation:
f(x) = (x + 6)³(x - 11)²(x - 6)(x + 5)³
The power of each factor are the multiplicities
So, we have
Zero(s) of multiplicity one:
x - 6 = 0
Zero(s) of multiplicity two:
x - 11 = 0
Zero(s) of multiplicity three:
x + 6 = 0 and x + 5 = 0
When evaluated, we have
Zero(s) of multiplicity one:
x = 6
Zero(s) of multiplicity two:
x = 11
Zero(s) of multiplicity three:
x = -6 and x = -5
Read more about polynomial at
https://brainly.com/question/30833611
#SPJ1
Guys please help! i will mark brainliest to the right answers
Note: in order for me to mark a brainliest 2 people need to answer
Answers
Answer:
y=-2x-2
Step-by-step explanation:
I'm guessing that the question is asking for the equation for slope-intercept for y=mx+b
Why? Well, the the slope formula is rise/run. As you can see, if you look the y-coordinate is consistently going down (negative) by two, and the x-coordinate it is going right by 1 every time and makes a triangle shape. You can actually draw it if you want to. And the -2 would be the y-intercept. (Exactly what it means, where the line means the y-axis)
Hope this helps! I explained this kinda weird but hopefully this is somewhat helpful.
help! I barely understand.
1 liter=1,000 millimeters
Answers
Answer:
500 milliliters
Step-by-step explanation:
2 liters= 2000 milliliters, so 2000/4 = 500
Which function has the same range as \(f(x)= - 2\sqrt{x} =-3 + 8\\\)
Answers
Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].
To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).
The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.
In other words, the range of f(x) is (-∞, 5].
So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.
Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.
For such more questions on range
https://brainly.com/question/30389189
#SPJ8
Help ASAP
2(x + 3) + (3x + 1)
Answers
Answer:
5x+7
Step-by-step explanation:
2x + 6 + ( 3x + 1 )
2x + 6 + 3x + 1
5x +7
What is the area of trapezoid DEFG with coordinates D (2, 3), E (4, 3), F (6, 1), and G (2, 1)? 12 square units 8 square units 6 square units 3 square units
Answers
The area of trapezoid DEFG having coordinates D (2, 3), E (4, 3), F (6, 1), and G (2, 1) is found to be 12 square units.
Explain about the trapezoid?An open, flat object with four straight sides or one pair of parallel sides is referred to as a trapezoid or trapezium.A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium could also be parallel.The diagram is attached for the question.
Area of trapezoid DEFG = 1/2(sum of parallel sides)*height
Area of trapezoid DEFG = 1/2*(2 + 4)*4
Area of trapezoid DEFG = 12 square units
Thus, the area of trapezoid DEFG having coordinates D (2, 3), E (4, 3), F (6, 1), and G (2, 1) is found to be 12 square units.
To know more about the trapezoid, here
https://brainly.com/question/1410008
#SPJ1
85% of the dogs at a park weighed over 50 pounds. If there were 400 dogs at the park, how many dogs at the park weighed over 50 pounds?
Answers
Answer:
425
Step-by-step explanation:
The number of dogs at the park that weighed over 50 pounds will be 332 dogs.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
85% of the dogs at a park weighed over 50 pounds. If there were 400 dogs at the park. Then the number of dogs at the park that weighed over 50 pounds will be given as,
⇒ 85% of 400
⇒ 0.85 x 400
⇒ 332 dogs
The number of dogs at the park that weighed over 50 pounds will be 332 dogs.
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ6
Help! I got 3 but it says its wrong. Anyone else have any answers that they solved for w/ proof?
Answers
Answer:
Your answer is indeed correct. f(-8) = 3
Step-by-step explanation:
\(f(x) = -x^{2} - 4x + 35\\f(-8) = -( -8)^{2} - 4(-8) + 35\\f(-8) = -64 + 32+ 35\\f(-8) = 3\)
CHECK
n =
Solve the equation.
−4(n − 6)= 12
Answers
\( - 4(n - 6) = 12 \\ (n - 6) = \frac{12}{ - 4} \\ n - 6 = - 3 \\ n = - 3 + 6 \\ n = 3\)
I NEED HELP REALLY REALLY FAST
Answers
Answer:
360
Step-by-step explanation:
360 because you multiply the height times the width and you get your answer hopefully this helps you
Which graph represents the compound inequality?
-3
54 -3 -2 -1 0 1 2 3 4 5
++
-5-4-3-2-1 0 1 2 3 4 5
-5-4-3-2-1 0 1 2 3 4 5
-5-4-3-2-1 0 1 2 3 4 5
Answers
The graph that represents the compound inequality –3 < n < 1 is option C.
The given inequality is -3<n<1.
We need to determine the graph of the given inequality.
What is inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
The graph that represents the compound inequality –3 < n < 1 is the straight line from -3 to 1 in which there is a hollow circle in the -3 point and in the 1 point. This is because < means that the possible values of n are only greater than -3 excluding -3 and less than -1 excluding -1.
Therefore, the graph that represents the compound inequality –3 < n < 1 is option C.
To learn more about inequalities visit:
https://brainly.com/question/20383699.
#SPJ1
HELP ME OUTT PLSS BXJXID
Answers
Answer:
d
Step-by-step explanation:
Answer: D
Step-by-step explanation:
The probability of picking a brown pencil greater than the probability as NOT picking a brown pencil because there more brown pencils than purple so there is a higher chance you will get a brown than NOT get a brown.
Which is more, 1 pound or 22 ounces?
Answers
Answer:
22 ounces is more
Step-by-step explanation:
1 pound is equal to 16 ounces
Answer:
1 pound
Step-by-step explanation:
1pound=16oz 22oz= 1.375pound
The numbers of customers that visited a store each hour for several hours after the store opened at 8 am are shown in the table. Hours after 8 am 1 3 4 6 9 Number of Customers 2 15 18 13 0 Which statement best describes the data?
Answers
The statement which best describes the data given is C) The data can be modeled by a quadratic function.
Given a data,
The numbers of customers that visited a store each hour for several hours after the store opened at 8 am are shown in the table.
It is clear that the number of customers increases to 18 for the first 4 hours and then decreases to 0 after 9 hours.
So this data cannot be modeled by a linear function or an exponential function.
Also since the number of customers arriving is not constant, this cannot be expressed as constant function.
So it is quadratic function.
Hence the correct option is c.
Learn more about Quadratic Functions here :
https://brainly.com/question/18958913
#SPJ1
How much would you have to deposit today to accumulate the SAME AMOUNT OF MONEY that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn?
Answers
Answer:
7606.62
Step-by-step explanation:
Start by finding how much you will have through the annuity. The question isn't that clear, so i will just assume it's an annuity due.
\(p(\frac{(1+i)^n-1}{i})*(1+i)\\i=.035/12= .0029166667\\n=10*12=120\\p=75 (given)\\75\frac{(1+.0029166667)^{120}-1}{.0029166667}*(1+.0029166667)= 10788.814149\\\)
Now just equate this to a time 0 payment at the same rate
\(10788.814149=(1+.0029166667)^{120}*x\\x= 7606.6228603=7606.62\)
As a quick note, if you were supposed to assume that your annuity was an annuity immediate the answer would be 7584.50.
Find the value of x.5x50dA. 40B. 8ОО OC. 10D. 26
Answers
Given:
The sum of two angles 5x and 50 degrees equals 90 degrees.
To find: The value of x
Explanation:
Since the sum of two given angles equals 90 degrees.
So, we can write it as,
\(5x+50=90\)Solving for x we get,
\(\begin{gathered} 5x=90-50 \\ 5x=40 \\ x=\frac{40}{5} \\ x=8 \end{gathered}\)Thus, the value of x is 8.
Final answer: The value of x is 8.
Please help geometry and triangles!!!
Answers
Answer:
For 6, iT would be 26
Step-by-step explanation:
The three points (2, −1), (8, ) and (11, 2) are collinear. Find the value of b.
Answers
I need help please.
Answers
Answer:
17/42
Step-by-step explanation:
you have to add all the jobs/assistan/worlerst and then make it as your denominator and then add how many profferser and instructor there are and make that your numerator