Write each of the following functions in a piecewise format and sketch its graph. For each function, find the value(s) of x where one piece ends and another begins (There's 3 problems/ screenshots) (20 pts)
Answers
Using the definition of the absolute value function, we have that, for item b, the function and breaking points are given as follows:
y = -3x - 1, x < -0.5.y = x + 1, x ≥ -0.5.The function breaks at x = -0.5.
For item c, we have that:
y = -2x - 2, x < -3.y = 4, -3 ≤ x ≤ 0.5.y = 4x + 2, x > 0.5.The function breaks x = -3 and x = 0.5.
For item d, we have that: (problem 59)
y = -2x - 2, x < -1.y = 2x + 2, x ≥ -1.The function breaks at x = -1.
The graphs are given at the end of the answer.
What is the absolute value function?The absolute value function is defined by the following piecewise rule, depending on the input of the function:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.
In general terms, we have that:
|f(x)| = f(x), f(x) ≥ 0.|f(x)| = -f(x), f(x) < 0.Then, for item b, we have that:
|2x + 1| = 2x + 1, x ≥ -0.5.|2x + 1| = -2x - 1, x < -0.5.Then:
y = -3x - 1, x < -0.5.y = x - 1, x ≥ -0.5.The function breaks at x = -0.5.
For item c, we have that:
|2x - 1| = 2x - 1, x ≥ 0.5.|2x - 1| = -2x + 1, x < 0.5.|x + 3| = x + 3, x ≥ -3.|x + 3| = -x - 3, x < -3.Then:
y = -2x - 2, x < -3.y = 4, -3 ≤ x ≤ 0.5.y = 4x + 2, x > 0.5.The function breaks x = -3 and x = 0.5.
For item d, we have that:
|x + 1| = x + 1, x ≥ -1.|x + 1| = -x - 1, x < -1.Hence:
y = -2x - 2, x < -1.y = 2x + 2, x ≥ -1.The function breaks at x = -1.
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Related Questions
Tell whether the difference of two positive integers is always, sometimes, or never positive.
Answers
The difference of two positive integers is sometimes positive.
How to illustrate the information?For example the difference of 3 and 5 will give a value of -2. This is negative.
On the other hand, the difference of 10 and 6 is 4. Therefore, this is positive.
Therefore, the difference of two positive integers is sometimes positive. It can also be negative.
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If w = 22, what is the value of 4w − 12?
Answers
Answer:76
Step-by-step explanation:
you replace W with 22
4(22)-12
=88-12
=72
hope this helps! :)
Answer:
76
Step-by-step explanation:
4w-12
4(22)= 88-12
88-12
76
Hope It Helps
Sorry If I'm Wrong
Consider the following vector field. f(x, y, z) = 5xyez i yzex k (a) find the curl of the vector field.
Answers
The curl of the vector field is:
[tex]=z e^x \hat{\imath}-\left(y z e^x-7 x y e^z\right) \hat{\jmath}-7 x e^z \hat{k}[/tex]
What do we mean by multivariable calculus?Multivariable calculus (also known as multivariate calculus) is the extension of one-variable calculus to multivariable calculus: the differentiation and integration of functions involving multiple variables rather than just one.Multivariable calculus is a fundamental component of advanced calculus. Calculus on Euclidean space is an advanced calculus topic.So,
To find the curve:
[Vector Field] Set up [curl F]:
[tex]Curl F=\left|\begin{array}{ccc}\hat{1} & \hat{\jmath} & \hat{k} \\\frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\7 x y e^z & 0 & y z e^x\end{array}\right|[/tex]
Simplify [3x3 Matrix Determinant] with [curl F]:
[tex]Curl F=\left|\begin{array}{cc}\frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\0 & y z e^x\end{array}\right| \hat{i}-\left|\begin{array}{cc}\frac{\partial}{\partial x} & \frac{\partial}{\partial z} \\7 x y e^z & y z e^x\end{array}\right| \hat{j}+\left|\begin{array}{cc}\frac{\partial}{\partial x} & \frac{\partial}{\partial y} \\7 x y e^z & 0\end{array}\right| \hat{k}[/tex]
Simplify [2x2 Matrix Determinant] with [curl F]:
[tex]Curl F=\left[\frac{\partial}{\partial y} y z e^x-\frac{\partial}{\partial z} 0\right] \hat{\mathrm{i}}-\left[\frac{\partial}{\partial x} y z e^x-\frac{\partial}{\partial z} 7 x y e^z\right] \hat{\mathrm{\jmath}}+\left[\frac{\partial}{\partial x} 0-\frac{\partial}{\partial y} 7 x y e^z\right] \hat{\mathrm{k}}[/tex]
The partial derivatives can be differentiated using the basic differentiation techniques listed above under "Calculus":
[tex]\begin{aligned}&\frac{\partial}{\partial y} y z e^x=z e^x \\&\frac{\partial}{\partial z} 0=0 \\&\frac{\partial}{\partial x} y z e^x=y z e^x \\&\frac{\partial}{\partial z} 7 x y e^z=7 x y e^z \\&\frac{\partial}{\partial x} 0=0 \\&\frac{\partial}{\partial y} 7 x y e^z=7 x e^z\end{aligned}[/tex]
When we substitute our partial derivative values, we get:
[tex]\begin{aligned}Curl F&=\left(z e^x-0\right) \hat{1}-\left(y z e^x-7 x y e^z\right) \hat{\jmath}+\left(0-7 x e^z\right) \hat{k} \\&=z e^x \hat{\imath}-\left(y z e^x-7 x y e^z\right) \hat{\jmath}-7 x e^z \hat{k}\end{aligned}[/tex]
So, we've discovered the curl of the given vector field.
Therefore, the curl of the vector field is:
[tex]=z e^x \hat{\imath}-\left(y z e^x-7 x y e^z\right) \hat{\jmath}-7 x e^z \hat{k}[/tex]
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The correct question is given below:
Consider the following vector field. f(x, y, z) = 7xyezi + yzexk (a) find the curl of the vector field.
Solve using zero-factor product property. (x + 7)(2x + 4)(3x - 6) = 0
Answers
Answer:
¯＼_(ツ)_/¯
Step-by-step explanation:
x(2x+4)+7(2x+4)[3x-6]=0
(2x^2 + 4x + 14x + 28)(3x-6)=0
(2x^2 + 18x + 28)(3x-6)=0
3x(2x^2 + 18x + 28) -6(2x^2 +18x + 28)=0
6x^2 + 54x^2 + 84x - 12x^2 - 108x - 168 =0
6x^2 + 54x^2 - 12x^2 + 84x - 108x - 168 =0
48x^2 - 24x - 168 =0 {quadratic equation}
Can you list all the real numbers frim 1 through 5? Explain
Answers
There is a infinite number of real numbers from 1 through 5
How to determine the count of real numbers from 1 through 5?The range is given as
1 to 5
The set of numbers is given as
Real numbers
Real numbers are any number that are not complex or imaginary numbers
This type of number covers all types of number that are not complex or imaginary numbers and it has an infinite count
Since the numbers cannot be counted, we can conclude that there is a infinite number of real numbers from 1 through 5
Hence, there is a infinite number of real numbers from 1 through 5
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A=5,5-(+2)+(-11,5)-(-6)
Answers
The value of the expression A will be negative 2.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The expression is given below.
A = 5.5 - 2 + (-11.5) - (-6)
Simplify the expression, then the value of the expression A will be
A = 5.5 - 2 - 11.5 + 6
A = 11.5 - 13.5
A = - 2
The value of the expression A will be negative 2.
Your question was incomplete, the question probably was ...
Find the sum of the expression A=5,5-(+2)+(-11,5)-(-6).
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Complete the square. x² +8 x+ ____
Answers
The full quadratic expression is expressed as follows:
x² + 8x + 16
What are equations?An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.
Equations can be graphed, just like a function.
To solve this problem we must complete square in the expression, it is necessary to note that perfect square trinomial has the form of:
(a + b)² = a² + 2ab + b²
x² + 8x + ?
x² = a²8x = 2abb = ?8x = 2xb
2b =8
b = 4
Let's complete the square
x² + 8x + (4)²
x² + 8x + 16
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Find the geometric mean between each pair of numbers.
45 and 5
Answers
For numbers 5 and 45 the value of the geometric mean of these numbers is
Gm (5, 45) = 15
What is the geometric mean?
The geometric mean is defined as a type of measure that is calculated as the root of a product between a set of numbers, it can be expressed as follows:
Gm (a, b) = √ab
Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b
a = 5
b = 45
We substitute and solve for the square root
Gm (5, 45) = √5×45
Gm (5, 45) = √225 ; In this case the square root is direct-
Gm (5, 45) = 15
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nine square root of two minus three square root of seven plus square root of eight minus square root of twenty eight
Answers
[tex]9\sqrt{2} - 3\sqrt{7} + \sqrt{8} - \sqrt{28}[/tex] =[tex]= 11\sqrt{2} - 5\sqrt{7}\\[/tex]
Given an Simplification :
[tex]9\sqrt{2} - 3\sqrt{7} + \sqrt{8} - \sqrt{28}Now, \sqrt{8} = \sqrt{2 \times 2 \times 2} = 2\sqrt{2}\sqrt{28} = \sqrt{2 \times 2 \times 7} = 2\sqrt{7}∴ 9\sqrt{2} - 3\sqrt{7} + \sqrt{8} - \sqrt{28}= 9\sqrt{2} - 3\sqrt{7} + 2\sqrt{2} - 2\sqrt{7}= 9\sqrt{2} + 2\sqrt{2} - 3\sqrt{7} - 2\sqrt{7}= 11\sqrt{2} - 5\sqrt{7}[/tex]
Simplifying rational expressions entails lowering the value of a rational expression to its simplest form. A rational expression is simplified in the same way that fractions are simplified. When the numerator and denominator of a rational number have no common factor other than 1, we consider it to be its simplified version in fractions. The same method may be used to simplify rational expressions; the only difference is that polynomials are included in the fraction.
The procedure for conducting operations on rational expressions is same to that for fractions.
Simplifying rational expressions means reducing their value to their most basic form. Rational expressions are simplified in the same manner that fractions are.
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Solve each equation. 5(s-12)-24 = 3(s+2)
Answers
The solution of the given linear equation in one variable 5(s -12) - 24 = 3(s + 2) is at s = 45.
According to the given question.
We have an equation.
5(s -12) - 24 = 3(s + 2)
Since, we have to solve the above linear equation in one variable.
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, the solution of the linear equation in one variable 5(s -12) - 24 = 3(s + 2) is given by
5(s - 12) -24 = 3(s + 2)
⇒ 5s - 60 - 24 = 3s + 6 ( by distributive rule)
⇒ 5s - 84 = 3s + 6
⇒ 5s - 3s = 84 + 6
⇒ 2s = 90
⇒ s = 90/2
⇒ s = 45
Hence, the solution of the given linear equation in one variable 5(s - 12) -24 = 3(s + 2) is at s = 45.
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Simplify the expression:
2(5 + 6q) =
Answers
Answer: Evaluate
2(5+6q)
Apply the distributive property
2×5+2×6q
Multiply the terms
10+2×6q
Solution
10+12q
Step-by-step explanation:
hope this helps
Name a pair of vertical angles.
Answers
Answer:
TWO PAIR OF VERTICAL ANGLES ARE
D,C
A,R
log6⁸+2log6³+log6¹²-log6²⁴
Answers
The solution of expression is 8log6.
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
According to the problem, we will use some of the basic logarithmic properties,
We have been given that expression as
⇒ log6⁸ + 2log6³ + log6¹² - log6²⁴
[used property : logₐ(xⁿ) = nlogₐx]
⇒ 8log6 + 6×2log6³ + 12log6 - 24log6
⇒ 8log6 + 12log6³ + 12log6 - 24log6
⇒ 8log6
Hence, the solution is 8log6.
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Which of the following has NO SOLUTION?
A x +5=5+x
B 2(x+5) = 2x + 10
с 3x - 5 =-3x - 5
D
x+7>x+10
OA
Answers
Answer:
D, since 7 is less than 10.
Write an equation of a parabola with its vertex at the origin and the given characteristics. directrix x=7
Answers
Answer:
ggr44tt55ttffghhtft hyy
Please help with problem 21 Algebra 1, it's in the attachment.
Answers
Explanation:
You want to identify the step that is occurring on each line of the solution to the equation 2(8u+2) = 3(2u-7).
1. 2(8u+2) = 3(2u-7) . . . . Original Equation
2. 16u +4 = 6u -21 . . . . Apply the distributive property
3. 16u +4 -6u = 6u -21 -6u . . . . subtract 6u from both sides
4. 10u +4 = -21 . . . . collect terms
5. 10u -4 = -21 -4 . . . . subtract 4 from both sides
6. 10u = -25 . . . . collect terms
7. 10u/10 = -25/10 . . . . divide both sides by 10
8. u = -2.5 . . . . simplify
Evaluate each function for the given value of x , and write the input x and output f(x) as an ordered pair.
f(x) = -12x/5 for x=-1
Answers
f (-1) = 12/5 the output for the given input .
How can you tell whether a function is linear or not?
Looking at a function's graph will reveal if it is linear or not with the greatest ease.When a linear function is plotted on a graph, a straight line is formed. A nonlinear function is curved in some way; it does not form a straight line.f(x) = -12x/5
Put x = -1 ⇒ - 12 * -1 /5
⇒ 12/5
Therefore f (-1) = 12/5
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3x+4y=10 , 2x +3y = 7
Answers
Answer: x=2, y=1
Step-by-step explanation:
The medical examiner is called in to determine how long a person has been deceased. The rate of decay is -0.026 and the temperature outside is 55 degrees. When the medical examiner arrives the temperature of the body was 82 degrees. Assuming the person had a normal body temperature of 98.6 degrees when they passed, how long had the person been deceased? Round answer to the nearest hour.
Answers
The person had been deceased for 12 hours
According to given data,
Temperature of normal person had 98.6 degrees,
and the temperature of the person was 82 degrees
outside temperature is 55 and
rate of decay is -0.026
The temperature of body drops :
98.6 - 82 = 16.6 degrees
[tex]\frac{16.6}{55}[/tex] ≈ 0.3
[tex]\frac{0.3}{0.026}[/tex] ≈ 12 hours
therefore, 12 hours had the person been deceased
The rules for exponential decay is f(x) = a b x, where b denotes the decay factor. In the rule of exponential decay function, the decay rate as a decimal. The decay rate represent as a percentage. We change it into a decimal by simply reducing the percent and dividing it by 100.
The amount reduces by a predetermined percentage at regular periods. The exponential decay formula is used to find decrease in growth.
f(x) = a (1 – r)x is form of generic
Where,
a = The initial value
r = decay rate
x = time period
Advantage of the exponential growth and decay graph
The domain is all Real numbers.
The range is all positive real numbers (exclude zero).
Graph has a y-intercept at (0,1). we know that zero power of any number is 1.
we get When b > 1, the graph increases. and 0 < b < 1, the graph decreases.
Has an asymptote (a line that the graph is very close, but never crosses). For graph the asymptote is the x-axis (y = 0).
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An art museum is putting together an exhibit using
paintings in its collection. The table shows the surface
areas of the paintings being considered. The museum
wants the displayed paintings to be of a similar size, so
it decides to display each painting with the mean surface
area with an absolute deviation of 1500 in.2. How many
paintings are displayed?
Painting Surface Areas
2200 in.²
1500 in.²
2000 in.²
850 in.²
4400 in.²
500 in.²
7800 in.²
2400 in ²
150 in.²
1200 in.²
3100 in.²
900 in.²
Answers
Answer:
17 paintings are displayed
Step-by-step explanation:
The flywheel on a steam engine rotates 60 revolutions every 15 seconds.
What is the flywheel’s rate of revolutions per second?
Identify the unit rate.
Answers
Answer:
Step-by-step explanation:
4 revolutions per second
i can figure out the answer to this question
Answers
The sum of the series of three numbers, which includes the counting number, n, the number before n, and the number after n is 3•n
What is a series?A series of a sequence of numbers is the sum of the numbers up to a specified term.
The given parameters;
n = A counting number
Counting numbers are the natural numbers which is the set of all positive integers.
Given that n is a counting number, we have that n is a positive whole number.
Which gives;
The whole number before n = n - 1
The whole number after n = n + 1
Which gives;
The sum of n, the whole number before n, and the whole number after n is part of a series and can be written mathematically as follows;
The sum = n + n - 1 + n + 1 = 3•n -1 + 1 = 3•n
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Riley has been keeping an eye on an emerald ring she likes. Its original price was $4,510, but it is now on clearance, marked down by 60%. What is the price of the ring now?
$
Answers
Answer:
Step-by-step explanation:
9989898989
At Sweet Stuff Fresh Produce the price of a bag of grapes depends on the total number of bags purchased at 1 time, as shown in the table below. In 2 trips to Sweet Stuff this week, Janelle purchased 3 bags of grapes on Monday and 4 bags of grapes on Wednesday. How much money would Janelle have saved if she had instead purchased 7 bags of grapes in 1 trip on Monday?
Answers
The amount that would be saved if 7 bags of grapes were bought on Monday is $2 (option J).
How much would be saved?The total cost of items bought on Monday and Wednesday would be added together. This amount would be subtracted from the total cost if the items were all bought on Monday.
The first step is to determine the total cost of the grapes bought on Monday and Wednesday.
Total cost of grapes = cost of grapes bought on Monday + cost of grapes bought on Wednesday
Cost of grapes bought on Monday = number of bags bought x price per bag
3 x $3 = $9
Cost of grapes bought on Wednesday = number of bags bought x price per bag
4 X $2.80 = $11.20
Total cost = $9 + $11.20 = $20.20
Cost or the 7 bags of grapes purchased in 1 trip = number of bags bought x price per bag
7 x $2.60 = 18.20
Amount saved = $20.20 - $18.20 = $2
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Find the measures of the labeled angles (x+81)° 4x°
(x+81)°=
Answers
By applying the vertical angles theorem to the two (2) angles, the measures of the labeled angles are equal to 108°.
What is the vertical angles theorem?The vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are generally formed whenever two (2) lines intersect each other are always congruent i.e equal to each other.
By applying the vertical angles theorem to the two (2) angles, we have:
(x + 81)° = 4x°
x + 81° = 4x°
4x° - x = 81°
3x° = 81°
x° = 81°/3
x° = 27°
Now, we can determine the measures of the labeled angles:
x + 81° = 27° + 81°
x + 81° = 108°
4x° = 4(27)
4x° = 108°
In conclusion, the measures of the labeled angles are equal to 108°.
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Please help me please help me please
Answers
Answer:
the answe r is I because it does not mirror the other side
X=3/5 Y=1/3 Y=2 4/5
work out the value of Z+XxY
Answers
Step-by-step explanation:
Given,
X = 3/5, Y = 1/3, Z = 2×4/5
the given question is to find out the value of Z+X×Y so the value is stated as
14/5+3/5×1/3
Here, 14/5 will be remains same and you should multiply 3/5×1/3.
Let 14/5 be equation number (1)
The L.C.M for 3/5×1/3 is 15. then,
3/5×15+1/3×15
___________
15
3×3+1×5
= -------------
15
9+5/15 = 14/15.
Let 14/15 be equation number (2)
Combine equation number (1) and (2) then
14/5+14/15
L.C.M.of 14/5 and 14/15 is 15.
14/5×15+14/15×15
-------------------------
15
[tex] = \frac{42 + 14}{15} [/tex]
[tex] \frac{56}{15} [/tex]
Under her cell phone plan, Ava pays a flat cost of $58 per month and $4 per gigabyte.
She wants to keep her bill at $62.40 per month. How many gigabytes of data can she
use while staying within her budget?
Answers
62.4=4x+58
Step 1) add like variables by subtracting 58 from both sides
62.4-58=4x+58-58
4.4=4x
Step 2) divide both sides by 4 to get x
x= 1.1
Answer is 1.1 gigabytes
Joshua purchased a game card for the arcade for a total of $18. He played two basketball hoop games for $3.25 each and four rounds of air hockey for $1.75 each. How much did he have left on the game card?
$4.50
$6.50
$13.00
$13.50
Answers
The amount left when Joshua played two basketball hoop games for $3.25 each and four rounds of air hockey for $1.75 each is A. $4.50.
How to calculate the value?From the information, Joshua purchased a game card for the arcade for a total of $18 and played two basketball hoop games for $3.25 each and four rounds of air hockey for $1.75 each.
Therefore, the amount left will be:
= Total amount with him - Amount spent
= $18 - (2 × $3.25) - (4 × $1.75)
= $18 - $6.50 - $7
= $4.50
The amount left is $4.50
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Answer:
4.50
Step-by-step explanation:
When striping the practice football field, Mr. Hawkins first painted the sidelines. Next he marked off 10-yard increments on one sideline. He then constructed lines perpendicular to the sidelines at each 10-yard mark. Why does this guarantee that the 10 -yard lines will be parallel?
Answers
This ensures that the lines will be parallel since two lines that are perpendicular to one another must also be parallel.
What is a perpendicular line?Two lines that meet or cross at right angles (90°) are known as perpendicular lines in geometry. The word "perpendicular" comes from the Latin "perpendicularis," which denotes a plumb line.
We can write two lines, AB and CD, as AB ⟂ CD if they are perpendicular to one another. The lines are denoted as being perpendicular by the ⟂ symbol.
The following list includes the two main characteristics of perpendicular lines.
These lines will always cross at right angles.Two lines will always be parallel to one another if they are perpendicular to the same line.Learn more about perpendicular
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