Write this absolute value function as a piecewise function. y= 2|x|-3
Answers
A function can be written as piecewise function if it changes its behaviour ( increasing or decreasing ) about a point.
[tex]\begin{gathered} Thefunctionf\mleft(x\mright)=y=|x|changesitsbehaviourat|x|=0ie,x=0. \\ y=|x|=x,ifx<0=-x,ifx>0 \\ |x|=a\Rightarrow x=\pm a \end{gathered}[/tex]Here Here,
The given function is : y = 2|x| - 3
Here,
The function will change its behaviour when
| x | = 0
=> x = 0
Now,
If x < 0 , then ;
=> y = 2[–(x)] – 3
=> y = –2x – 3
=> y = – 2x – 3
If x ≥ 0 , then ;
=> y = 2(x) – 3
=> y = 2x – 3
=> y = 2x -3
Hence ,
y = – 2x – 3 , if x < 0
y = 2x - 3 , if x ≥ 0
[tex]f(x)=\begin{cases}-2x-3\text{ , if x < }0 \\ \\ 2x-3\text{ , if x }\ge0\end{cases}[/tex]
Related Questions
An initial investment of $200 is appreciated for 20 years in an account that earns 6% interest, compounded continuously. Find the amount of money in the account at the end of the period.
Answers
To calculate the final amount of money at the end of the period, considering that the interest is compounded continuously you have to use the following formula:
[tex]A=P\cdot e^{rt}[/tex]Where
A is the accrued amount at the end of the given time
P is the principal amount
r is the annual nomial interes expressed as a decimal value
t is the time period in years
For this investment, the initial value is P= $200
The interest rate is 6%, divide it by 6 to express it as a decimal value
[tex]\begin{gathered} r=\frac{6}{100} \\ r=0.06 \end{gathered}[/tex]The time is t= 20 years
[tex]\begin{gathered} A=200\cdot e^{0.06\cdot20} \\ A=200\cdot e^{\frac{6}{5}} \\ A=664.02 \end{gathered}[/tex]After 20 years, the amount of money in the account will be $664.02
help me with my work please
Answers
In the first one, the word increase means you will be add something
+42000
In the second one, the word withdrew means you will subtract something
-40
(a) Write the number 302.658 correct to 2 decimal places, (b) Write the number 302.658 correct to 2 significant figures.
Answers
The given number is,
302.658
to corrct to 2 decimal places,
302.66.
A word problem made out of the equation 1/4+3-7/8x<-2
Answers
The word problem of the expression is "Seven eighths of a number less three and a quarter is less than 2"
How to determine the word problem?The inequality expression is given as
1/4 + 3 - 7/8x < 2
From the above expression, we can see that:
The right-hand side of the inequality is 2 and the inequality symbol is less than
This means that the word problem must end in "less than 2"
Next, we analyse the left-hand side
1/4 + 3 - 7/8x
A statement that represents the above is
Seven eighths of a number less three and a quarter is less than 2
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A gardener makes a new circular flower bed. The bed is ten feet in diameter. Calculate the circumference and the area of the circular flower bed.
Answers
Answer:
C = 31.4159
A = 78.5398
Step-by-step explanation:
diameter = 10
radius = 5
plug into formula: C = 2π5
A = π * 5²
Find the equation for the line that passes through the point (−2,5), and that is perpendicular to the line with the equation x=−4.
Answers
The equation of the line perpendicular to x = -4 that passes through the point (-2,5) is y = 5 .
In the question ,
it is given that
the required line is perpendicular to x = -4
the slope of x = -4
x + 4 = 0
0.y = x + 4
slope = 1/0
so the slope of the perpendicular line [tex]=[/tex] 0 .
the equation of the perpendicular line passing through (-2,5) and slope as 0 is
(y - 5) [tex]=[/tex] 0*(x + 2)
y -5 = 0
y = 5
Therefore , The equation of the line perpendicular to x = -4 that passes through the point (-2,5) is y =5 .
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Is-7+9 = -9 + 7 true, false, or open?
Answers
-9+7=-2
so the answer is false
im having a little trouble understanding the commutative property and closure property, not a specific problem just would like a small explanation thanks!
Answers
Commutative property:
For addition and multiplication if you change the order of the addernds or factor is doesn't change the sum or multiplication.
Example:
Addition
[tex]\begin{gathered} a\pm b=b\pm a \\ \\ 5+3=3+5 \\ 8=8 \end{gathered}[/tex]Multiplication:
[tex]\begin{gathered} a\times b=b\times a \\ \\ 5\times3=3\times5 \\ 15=15 \end{gathered}[/tex]Closure property:
When you add or subtract any two intergers, the result will always be an interger.
Example:
[tex]\begin{gathered} a+b=c \\ \\ a,b,c\text{ are intergers} \\ \\ 8+13=21 \\ \end{gathered}[/tex]8, 13 and 21 are intergers
how do I find the first five terms of the geometric sequence?
Answers
To find the next term of a geometric sequence, the previous term is multiplied by the common ratio r.
[tex]\begin{gathered} r=\frac{1}{2} \\ a_{1=}20 \\ a_2=20\times\frac{1}{2}=10 \\ a_3=10\times\frac{1}{2}=5 \\ a_4=5\times\frac{1}{2}=\frac{5}{2} \\ a_5=\frac{5}{2}\times\frac{1}{2}=\frac{5}{4} \end{gathered}[/tex]The right arrow symbol used to show the transition from a point to its image after a transformation is not contained within the Equation Editor. If such a symbol is needed, type "RightArrow." For example: P(0, 0) RightArrow P′(1, 2).
Triangle ABC has coordinates
A
(
1
,
4
)
;
B
(
3
,
−
2
)
;
and
C
(
4
,
2
)
.
Find the coordinates of the image
A
'
B
'
C
'
after a reflection over the x-axis.
Answers
Answer:
Step-by-step explanation:
Given:
Vertices of triangle ABC are A (1,4), B(3,−2) and C(4,2).
Triangle ABC reflected over the x-axis to get the triangle A'B'C'.
To find:
The coordinates of the image A'B'C'.
Solution:
If a figure reflected over the x-axis, then rule of transformation is
Now, using this rule, we get
Therefore, the coordinates of the image A'B'C' after a reflection over the x-axis are A'(1,-4), B'(3,2) and C'(4,-2).
A visitor in a Las Vegas casino lost $200, won $100, and then lost $50. What was the change in the gambler's net worth (how much did the gambler win or lose overall)?
Answers
The gambler in a Las Vegas casino lost $150.
According to the question,
We have the following details:
The visitor lost $200 and $50 in a Las Vegas casino.
The visitor won $100.
So, in total, the visitor lost $250 overall.
Now, compare the amount the gambler lost and the gambler won in the casino. So, we notice that the gambler lost more amount.
Now, we will find the total amount lost:
Gambler's net worth = The amount lost - the amount won
Gambler's net worth = $(250-100)
Gambler's net worth = $150
Hence, the gambler lost $150 overall in the casino.
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how many irrational numbers are there between 1 and 6? is it infinite?
Answers
infinite numbers
Explanation
An Irrational Number is a real number that cannot be written as a simple fraction,for example Pi()
[tex]\pi=3.141592654[/tex]Step 1
between 0 an 6 we have 6 integers numbers :(1,2,3,4,5,6)
Step 2
Now check this
a number for example
[tex]\begin{gathered} 3.14 \\ is\text{ different to } \\ 3.145 \\ and\text{ it is diferrent to} \\ 3.1458 \end{gathered}[/tex]so, the answer is infinite numbers
Please help meeeeeeeeeeeeeeee
Answers
Answer:
-2 1/4 or 2.25
Step-by-step explanation:
i hope this helped and ita also self explanitory
Abigail and her friend Jaya are going to a carnival that has games and rides. Abigail played 7 games and went on 2 rides and spent a total of $24.75. Jaya played 3 games and went on 6 rides and spent a total of $33.75. Determine the cost of each game and the cost of each ride.
Answers
The cost of each game is $2.25.
The cost of each ride is $4.50.
What is the cost of each game and each ride?Here are the system of linear equations that can be derived from the question:
7g + 2r = 24.75 equation 1
3g + 6r = 33.75 equation 2
Where:
g = price of each game r = price of each rideIn order to determine the value of g, multiply equation 1 by 3:
21g + 6r = 74.25 equation 3
Subtract equation 2 from equation 3:
40.50 = 18g
g = 40.50 / 18
g = 2.25
In order to determine the value of r, substitute for g in equation 1 :
7(2.25) + 2r = 24.75
15.75 + 2r = 24.75
2r = 24.75 - 15.75
2r = 9
r = 9 /2
r = 4.50
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Find the volume of this cone. Use 3 for TT. V = 7 r26 3 8ft V [?]ft V 1 6ft Enter SRI nhte. Das
Answers
The diameter of the cone is d = 6 ft.
The height of cone is h = 8 ft.
Determine the radius of cone.
[tex]\begin{gathered} r=\frac{d}{2} \\ =\frac{6}{2} \\ =3 \end{gathered}[/tex]Determine the volume of cone.
[tex]\begin{gathered} V=\frac{\pi(3)^28}{3} \\ =\frac{\pi\cdot9\cdot8}{3} \\ =3\cdot3\cdot8 \\ =72 \end{gathered}[/tex]So volume of cone is 72 feet cube.
Answer: 72
Which of the following identities is used to expand the polynomial (3x - 4y)2?
Answers
Recall that to expand a binomial we can use the following formula:
[tex](a+b)^2=a^2+2ab+b^2.[/tex]The above is known as the square of the binomial.
Answer:
Square of binomial.
25 less than 4 times a number is 63. What is the number?
Answers
The number is 22
What is a number?
A number is a mathematical entity that may be used to count, measure, and name things. The natural numbers 1, 2, 3, 4, and so on are the original instances. Number words can be used to represent numbers in language. Individual numbers can be represented more generically by symbols known as numerals; for example, "5" is a numeral that represents the number five. Because only a small number of symbols can be memorized, fundamental numerals are often structured in a numeral system, which is a systematic method of representing any number. The most prevalent numeral system is the Hindu-Arabic numeral system, which allows any number to be represented using a combination of 10 fundamental numeric symbols known as digits.
4n - 25 = 63
or, 4n = 63 + 25
or, n = 88/4 = 22
Hence, the number is 22
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A sheriff patrols several neighborhoods in her patrol car it requires 3/15 of an hour to patrol an entire neighborhood how many neighborhoods can the sheriff patrol in 5/8 of an hour
Answers
Based on the time it takes to patrol one neighborhood, the number of neighborhoods that the sheriff can patrol in 5/8 of an hour is 3.125 neighborhoods
How to find the number of neighborhoods?The number of neighborhoods that the sheriff can patrol in 5/8 hours depends on the number of hours that it takes the sheriff to patrol one neighborhood.
The number of neighborhoods she can patrol can therefore be found by the formula:
= Number of hours sheriff has / Number of hours required to patrol one neighborhood
= 5/8 ÷ 3/15
= 5/8 x 15/ 3
= 75 / 24
= 3.125 neighborhoods
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A scale drawing for an apartment is shown below. In the drawing, 3cm represents 5m.
7,7,3,6
Answers
Actual area of the real back yard is 96 [tex]m^{2}[/tex]
[scale]=[drawing]/[real] —-> [real]=[drawing]/[scale]
scale=4 m/3 cm —> 0.75 cm/m
The backyard's measurements in the drawing are 9 x 6 cm.
Determine the backyard's actual dimensions
[Real]=[Drawing]/[Scale] for 9 cm
[real]=[9]/[0.75]——> 12 m
[Real]=[Drawing]/[Scale] for 6 cm
[real]=[6]/[0.75]——> 8 m
The backyard's actual measurements are 8 m × 12 m, and its actual size is 8 * 12 = 96 [tex]m^{2}[/tex].
Therefore the original area of the rectangle is 96 [tex]m^{2}[/tex].
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The complete question is as follows:
Below is a scale representation of a piece of land. In the illustration, 3 cm stands in for 4 m. Find the actual backyard space assuming the back is rectangular?
In the figure, CA and CE are opposite rays, CH bisects
Which of the following are linear pairs involving point F? Select all that apply.
last choices are
e)
f)
pls help im crying
Answers
The angles that form a linear pair involving point F are:
a. ∠DFC and ∠CFG
d. ∠HFD and ∠CFD
What is the Definition of a Linear Pair?A linear pair can be defined as the set of two angles that are adjacent to each other and share a common vertex and a common side, and also lie on a straight line.
Given the image in the question above, we see that:
Angle DFC and angle CFG share a common side FC and a common vertex point F, hence, they are adjacent angles that lie on a straight line, thus, they are a linear pair.
Angle HFD and angle CFD also share a common side FD and a common vertex point F. This makes them adjacent to each other. Also they are on a straight line. Therefore, angle HFD and angle CFD are a linear pair.
Thus, we can conclude that the angles that form a pair of angles that are classified as a linear pair are:
a. Angle DFC and angle CFG
d. Angle HFD and angle CFD
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Kevin measured how many times he arrived to work late if he took subway. the results are provided in the following table. Find the probability that Kevin will arrive on-time tomorrow if he plans to take subway. (round the answer to 2 decimal places)
Answers
ANSWER
86.67%
EXPLANATION
We want to find the probability that Kevin will arrive on time if he plans to take the subway.
To find this, we have to divide the number of times that Kevin was on-time by the total number of times that he took the measurement.
We have that out of 30 days that Kevin was on-time on 26 occasions.
Therefore, the probability that Kevin will arrive on-time the next day is:
[tex]\begin{gathered} P(on-\text{time) = }\frac{26}{30}\text{ = }\frac{13}{15} \\ P(on-\text{time) = 86.67\%} \end{gathered}[/tex]That is the answer.
A rectangle's base is 5 cm longer than its height. The rectangle's area is 50 cm². Find this rectangle's dimensions.
The rectangle's height is
The rectangle's base is
Answers
Answer:
The rectangle's height is 5 cm,The rectangle's base is 10 cm.Step-by-step explanation:
Let the dimensions be:
Base = b, Height = hGivenb = h + 5,A = 50 cm²The area of rectangle is:
A = bh h(h + 5) = 50h² + 5h = 50h² + 5h - 50 = 0h² - 5h + 10h - 50 = 0h(h - 5) + 10(h - 5) = 0(h - 5)(h + 10) = 0h - 5 = 0 and h + 10 = 0h = 5 and h = - 10The second value of h is negative and therefore discarded.
So we get:
h = 5 cm,b = 5 + 5 = 10 cmDomain and range of the quadratic function F(x)=-4(x+6)^2-9
Answers
Answer:
Domain: (-∞, ∞)
Range: (-∞, -9]
Step-by-step explanation:
What is Pythagoras Theorem? What is the formula for the same?
Answers
The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem can be expressed as, c2 = a2 + b2; where 'c' is the hypotenuse and 'a' and 'b' are the two legs of the triangle.
Answer:
Pythagoras theorem is a theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
The Pythagoras theorem equation is expressed as,
c²=a²+b²
where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two angles(opposite and adjacent)
Step-by-step explanation:
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Name: Date: Writing Linear Equations from Word Problems (Page 2) 5) You are planning a class pool party and have reserved the pool for $625. It will cost an additional $11 per person for food. Write a linear equation to represent the total cost of the pool party based on the number of people that will attend. a) If 26 people end up coming to the pool party how much will it cost you?
Answers
Consider that the reservation costs $625. Moreover, it is necessary to pay additional $11 per person for food. If x is the number of people, it means that it is necessary to pay 11x dollars for x people.
THen, the total cost is $625 plus 11x dollars. If y is the cost of the class pool party, you have the following algebraic equation which expresses the given situation:
y = 11x + 625
If there are 26 people in the party, that is, if x = 26, the cost is:
y = 11(26) + 625
y = 286 + 625
y = 911
Hence, the cost is $911
Harry HAS 1 1/2 KG whole-wheat flour. He uses 3/4 of the flour to bake bread. How much flour did he use?
Answers
Given the following parameter
Mass of flour wheat flour = 1 1/2 kg
If Harry used 3/4 of these flour to bake bread, the amount of flour used is expressed as:
[tex]A=\frac{3}{4}\text{ of 1}\frac{1}{2}[/tex]Convert the mixed fraction into an improper fraction to have:
[tex]\begin{gathered} A=\frac{3}{4}\times\frac{3}{2}kg \\ A=\frac{9}{8}kg \\ A=1\frac{1}{8}kg \end{gathered}[/tex]This shows that Harry used 1 1/8kg of the wheat flour to bake the bread
Neil and Barry each bought a new phone plan. Neil bought a plan that costs $80 for a new phone and $3per minute of talk, text, or data. Barry bought a plan that costs $230 for a new phone and $2 per minuteof talk, text, or data.7. Write an equation to represent eachfriend's phone plan.8. How much will each friend pay if they eachuse 100 minutes?10. How many minutes would it take for bothplans to cost the same amount?chorar the
Answers
7.-
Equation for Neil P = 80 + 3m
Equation for Barry P = 230 + 2m
8.-
Neil P = 80 + 3(100)
P = 80 + 300
P = $380
Barry P = 230 + 2(100)
P = 230 + 200
P = $430
10.-
P = 80 + 3m
P = 230 + 2m
80 + 3m = 230 + 2m
3m + 2m = 230 - 80
m = 150
Conrad has two willow trees in his backyard. The first tree is 4 feet taller than the second one. If the second one is 28 feet tall, what is the height, in feet, of the first tree?
Answers
The first tree is 28ft tall, and the second tree is 4 ft higher than the second one. Then we need to add 4ft to the height of the second tree:
[tex]28ft+4ft=32ft[/tex]The heigh of the first tree is 32ft
Trisha is using the recipe show to make a fruit salad. She wants to use 20 diced strawberries in her fruit salad. How many bananas, apples, and pears show Trisha use in her fruit salad? Fruit Salad Recipe 4 bananas 3 apples 6 pears 10 strawberries bananas apples pears
Answers
The original recipe has half of the number of strawberries She wants to use in her salad in this case we will need double the fruits of the recipe given
Bananas
4x2=8 bananas
Apples
3x2=6 apples
Pears
6x2=12 pears
please help me i need it asp
Answers
The solution of the system of equation is as follows:
x = 10 / 7y = - 5How to solve system of equation?The system of equation can be solved as follows:
6x + 4y = 10
-7x - 3y = 5
Hence, let's multiply equation(i) by 3 and multiply equation(ii) by 4
Therefore,
18x + 12y = 30
-28x - 12y = 20
add equation(ii) to equation(ii)
-10x = 50
y = 50 / -10
y = -5
Hence,
-7x - 3y = 5
-7x - 3(-5) = 5
-7x + 15 = 5
-7x = 5 - 15
-7x = - 10
x = 10 / 7
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