express the function f(x)=1+|2x-5| in piecewise form without using absolute values
Answers
The function f(x)=1+|2x-5| in piecewise form without using absolute values will be f₁ = 4, f₂ = 2 and a = 5/2.
Given that,
f(x) = 1 + |2x - 5|
And,
f(x) = {f₁ x < a
{f₂ x ≥ a
Now,
We have,
f(x) = 1 + |2x - 5|
And,
By definition of absolute value,
|x| = {x x ≥ 0
{-x x < 0
And,
Given the absolute value,
|2x - 5|
Solve for x,
i.e.
2x - 5 = 0
We get,
x = 5/2 = 2.5
i.e.
a = 5/2
i.e.
For all values greater than x = 5/2, 2x - 5 is positive,
And,
For all values less than x = 5/2, 2x - 5 is negative.
So,
|x| = {x x ≥ 5/2
{-x x < 5/2
i.e.
|2x - 5| = {2x - 5 x ≥ 5/2
{-(2x - 5) x < 5/2
Now,
f(1) = 1 + |2(1) - 5|
We get,
f₁ = 4
And,
f(2) = 1 + |2(2) - 5|
We get,
f₂ = 2
Hence we can say that the function f(x)=1+|2x-5| in piecewise form without using absolute values will be f₁ = 4, f₂ = 2 and a = 5/2.
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Related Questions
Things are usually pretty uneventful during the day in the reptile building as the snakes prefer their beauty sleep, but the critters are stirring as they sense freedom. The python is the first one to leave her cage, and she begins to slowly slither towards the exit at a pace of 1 mile per hour. The anaconda decides to snooze for another 30 minutes before beginning the long trek ahead. He leaves his cage after the python has already traveled half a mile, and he slithers at a pace of 5 miles per hour. Write an equation to represent this scenario letting x represent the number of hours it would take.
Answers
The linear functions that model the positions of the Python and of the Anaconda are given as follows:
P(x) = 0.5 + x.A(x) = 5x.What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For the functions in this problem, we have that:
The initial position is the intercept.The velocity is the slope.Considering their velocities, and that when the Anaconda leaves the Python has already traveled half a mile, the functions are given as follows:
P(x) = 0.5 + x.A(x) = 5x.More can be learned about linear functions at https://brainly.com/question/24808124
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Suppose Emma is hosting a party and knows at least 3 are
coming. The party is capped at 12 guests. Let g(x) model
the number of tables Emma needs to set up if x guests
attend. What is the domain of the function? Use set
notation.
Guests
3-6
7 - 10
11 - 12
Tables Needed
1
2
3
Answers
Step-by-step explanation:
the first answer is -3 the second answer is -2/3 outside -1
um can u guys pls help
Answers
Answer:
if I can't explain in one line, then I will include the steps in the explanation.
2x - 7 2x - 7 = x + 97Step-by-step explanation(Q3):
[tex]3^2-\left(5-3\right)^3+6\\5-3=2\\3^2-2^3+6\\3^2=9\\9-2^3+6\\2^3=8\\9-8+6\\9-8=1\\1+6\\1+6=7\\=7[/tex]
Hope it helps!
PLEASE HELP! NEED THIS ASAP! PLS HELP!!
Nick mowed about 3/7 of the school lawn yesterday. he mowed another 1/4 of the lawn this morning. how much is left to mow?
Answers
Answer:
9/28 of the lawn is left
Step-by-step explanation:
Make 3/7 and 1/4 have the same denominator
3/7 becomes 12/28 and 1/4 becomes 7/28
added together is 19/28
9/28 of the lawn is left
Find the area
(Simplify your answer)
Answers
Answer:
why isnt there a backround base? it wouldnt be area if isnt so
Step-by-step explanation:
The area is 960 m
because 48*15=720
and 10*24=240
720+240= 960
Write equations for the horizontal and vertical lines passing through the point (1,8)
Answers
Answer:
Vertical: x = 1
Horiz: y = 8
Step-by-step explanation:
The equation of a
vertical line is always:
x = anumber
The equation of a horizontal line is in the form:
y = anumber
In the question a point is given, the point (1,8) is in the form (x,y) So x is 1 and y is 8.
We can fill in this given information to complete the equations.
Vertical: x = 1
Horizontal: y = 8
Your phone is losing charge at a rate of 2%every 7 minutes. You check and see that you have 44% left. Write the function of total charge left where x is in minutes. Find the y-intercept, x-intercept and slope.
Answers
The y-intercept, x-intercept and slope are 100, 350 and 2 / 7, respectively.
How to describe the linear equation describing the discharge of a phone
In accordance with the statement, the phone charge decreases linearly in time based on the following linear model:
c(x) = 100 - (Δy / Δx) · x
Where:
c(t) - Current charge of the cell phone, in percentage.Δc - Current charge change, in percentage.Δx - Time change, in minutes.x - Time, in minutes.If we know that Δy = 2, Δx = 7, then the linear equation is:
c(x) = 100 - (2 / 7) · x
Then, the y-intercept, x-intercept and slope are, respectively:
y-intercept
b = 100
x-intercept
0 = 100 - (2 / 7) · x
(2 / 7) · x = 100
2 · x = 700
x = 350
Slope
m = 2 / 7
The y-intercept, x-intercept and slope are 100, 350 and 2 / 7, respectively.
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Caroline rewrote a quadratic equation in vertex form by completing the square, but her work has errors.
f(x)
-2x² + 12x15
-2(x² - 6x) — 15
-2(x² - 6x + 9) - 9 - 15
-2(x - 3)²9 - 15
-2(x - 3)² - 24
Identify the first error in her work.
Answers
The required error in Caroline's quadratic equation in vertex form by completing the square is -2(x² - 6x + 9) - 9 - 15 is should be -18 in place of -9.
Given that,
To figure out the error made by Caroline in the calculation of a quadratic equation in vertex form by completing the square.
His calculation,
= -2x² + 12x - 15
= -2(x² - 6x) — 15
= -2(x² - 6x + 9) - 9 - 15-2(x - 3)²9 - 15
= -2(x - 3)² - 24
Correct calculation,
= -2x² + 12x - 15
= -2(x² - 6x) - 15
= -2(x² - 6x + 9) - 18 - 15
= -2(x - 3)² - 18 - 15
= -2(x - 3)² - 33
Thus, the required error in Caroline's quadratic equation in vertex form by completing the square is -2(x² - 6x + 9) - 9 - 15 is should be -18 in place of -9.
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Given g(x)=-2x^(2)+1, find the indicated values. g(0)
Answers
Answer:
[tex]g(x) = 2 {x}^{2} + 1 \\ g(0) = 2 ({0})^{2} + 1 \\ = 2(0) + 1 \\ = 1[/tex]
m ebd = 29 bc bisects abd and be bisects cbd find m abc
Answers
We can conclude that in the question, angle m∠ABC = 58°.
What are angles?When two straight lines or rays intersect at a common endpoint, an angle is formed. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner." Angles in geometry are classified according to their measurement. Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle, and full rotation are the names of basic angles.So,
∠EBD is 29° and line EB bisects ∠CBD.
Then, ∠CBD = ∠CBE + ∠EBD∠CBD = 29 + 29 = 58°Similarly, ∠CBD = 58° and line CB bisects ∠ABD
Then, ∠ABD = ∠ABC + ∠CBD ∠ABD = 58 + 58 = 116°Hence, ∠ABC = 58° as ∠CBD is also 58° because common line BC bisects the angle ∠ABD.
Therefore, angle m ∠ABD = 58°.
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David is going out for a pizza. The Pizza costs $10.50 plus $1.50 for each extra topping ,x. Write an equation to represent the total cost of the pizza, t.
Dependent variable:________
Independent variable:____
Equation:____ (Use your equation to determine the total cost of the pizza with 3 extra toppings).
Answers
10.50+1.50x=total cost
since they wanted 3 topings it would be x=3
10.50+(1.50*3)
simplify
10.50+4.50=15
I hope this helps
Natalie works as a playground supervisor for 8 weeks during the summer at a rate of
$15.27/h. She works a 40-hour week but averages 3 hours of overtime each week,
paid at time and a half. How much will she earn each week, and for the whole
summer?
Answers
Natalie will be paid $656.61 for a week and for summer $10505.76.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that Natalie earns $15.27 per hour while working as a playground supervisor for 8 weeks throughout the summer. Although she works a 40-hour week, she typically puts in 3 hours of overtime.
For a week = ( 40 + 3 ) x 15.27 = $656.61
For a summer = 4 x 4 = 16 weeks
For a summer = 16 x $656.61 = $10505.76
Therefore, Natalie will be paid $656.61 for a week and for summer $10505.76.
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Y=-3x+6 and y=1/3x-8 determine if the equation are parallel, perpendicular, or neither
Answers
Answer:8
Step-by-step explanation:
1
please help
please good graph
Answers
You can see the graphs in the attached image. The order is the same as on page. Note that 7. and 8. give us an infinite number of solutions, and no solutions, respectively.
Workoutthe size of angle x [parrallel lines in a triangle]
Answers
The size of angle is X=13
y + 98 =180(LP)
Y =180-98
Y=82
<AOB + <OAB + <OBA=180(Sum of all angles of triangles)
85 + X + 82 =180
167 + X =180
X = 180-167
X=13
In Euclidean geometry, any three points that are not collinear produce a singular triangle angle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle angle is contained in a plane, and there is only one plane that contains that triangle. All triangles angle are enclosed in a single plane if all of the geometry is the Euclidean plane, however, this is no longer true in higher-dimensional Euclidean spaces.
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If the cost, C(x), for manufacturing x units of a certain product is given by
C(x) = x² - 19x+60
find the number of units manufactured at a cost of $8900.
Answers
The number of units manufactured at a cost of $8900 will be 104 units.
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
If the cost, C(x), for manufacturing x units of a certain product is given by
C(x) = x² - 19x + 60
The number of units manufactured at a cost of $8900 will be given by factorization.
x² - 19x + 60 = 8900
x² - 19x - 8840 = 0
x² - 104x + 85x - 8840 = 0
x(x - 104) + 85(x - 104) = 0
(x - 104)(x + 85) = 0
x = 104, -85
The number of units manufactured at a cost of $8900 will be 104 units.
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Find two numbers whose sum is 52 and whose product is as large as possible? [Hint: Let x and 52-x be the two positive numbers. Their product can be
described by the function f(x)=x(52-x).]?
Answers
The two numbers whose sum is 52 and the product is maximum are 26 and 26.
How to find the sum of algebraic fractions?Finding the least common multiples of the denominator expressions can help. Then using the similar method as we use in the sum of fractions would give the sum of algebraic fractions.
We need to find the two numbers whose sum is 52 and the product is maximum.
So, the multiples of 52 are
2, 26, 4, 13,
So, here we can see that the sum of 26 to itself would be equal to 52.
26 + 26 = 52
The product is also maximum compared to others.
26 x 26 = 676
Therefore, the two numbers are 26 and 26.
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x - (-3) = 8
what does x equal?
Answers
Answer:
x = 5
Step-by-step explanation:
Change "minus a negative" to "plus a positive"
x - (-3) = 8
x + 3 = 8
Next, subtract 3 from both sides.
x + 3 - 3 = 8 - 3
x = 5
Check it!
x - (-3) = 8
5 - (-3) = 8
5 + 3 = 8
8 = 8 Check!
A surveyor needs to find the distance from point A to point B across a canyon. She places a stake at A, and a coworker places a stake at B on the other side of the canyon. The surveyor then locates C on the same side of the canyon as A such that CA ⊥ AB. A fourth stake is placed at E, the midpoint of CA. Finally, a stake is placed at D such that CD ⊥ CA and D,E, and B are sited as lying along the same line.
b. If A C=1300 meters, D C=550 meters, and D E=851.5 meters, what is AB? Explain your reasoning.
Answers
The value of line AB is 550 meters.
What do we presume by the congruency of a triangle?Two triangles are said to be congruent if all three corresponding sides and angles are equal in size.To appear identical, these triangles can be moved, rotated, flipped, and turned.They will coincide if they are moved.Congruence exists when two triangles satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
First, we'll prove that △BEA ≅ △DEC.
∠A = ∠C = (BA and CD is ⊥ AC)AE = CE = (E is the midpoint of AC)∠AEB = ∠DEC = (Inversely opposite angles)So, △BEA ≅ △DEC is under ASA condition.
Then, DC is identical to AB.Therefore, the value of AB is 550 meters.
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Help Please
A woman has a total of $9,000to invest. She invests part of the money in an account that pays 7%per year and the rest in an account that pays 9%per year. If the interest earned in the first year is $710, how much did she invest in each account? She invested $ ____at 7%and $_____at 9%.
Answers
Answer:
5000.00 gives us 350
4000.00 gives us 360
Pls pls pls pls pls pls pls pls
Answers
the correct statement is the first one.
The inverse of 6^2 is 6^(1/2), then 6^(1/2) is the square root of 6.
Which statement explains why 6^(1/2) is equal to √6?Well, this is just a notation thing.
We know the following property for exponents:
(a^n)^m = a^(n*m)
And we know that the square rooth is the inverse of the square power (exponent equal to 2) such that:
√x^2 = 2
Then if we define the square root as an exponent, let's say that is an exponent "a" we will have:
√x = x^a
Rewritting the above relation again, we can write:
√(x^2) = (x^2)^a = x^(2*a)
And we know that it must be equal to x, so we get:
x^(2*a) = x
This means that 2*a = 1
then a = 1/2
√x = x(1/2)
Then the correct statement is the first one.
The inverse of 6^2 is 6^(1/2), then 6^(1/2) is the square root of 6.
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determine whether the following graph represents a function
1. one to one function
2. Not a function
3. Function, but not one to one
Answers
Answer:
3. function, but not one to one
Step-by-step explanation:
If you do a vertical line test anywhere you draw a vertical line will only hit in one spot
If you do a horizontal line test to check If the line is one to one it hits in multiple spots therefore the line that is graphed is a function but not one to one
In Exercises 1-16, solve the inequality. Graph the solution
1. 3y ≤ -9
Answers
By solving the inequality we get [tex]y\leq -3[/tex]
What is graphing the inequality?
The act of illustrating which area of the number line contains values that will "satisfy" the specified inequality is known as graphing the inequality. Take a look at the first inequality, "x > -5." The numbers that can be used to substitute x in our inequality to produce a true statement can be shown on a graph of our inequality.
[tex]3y\leq -9[/tex]
Dividing above equation by 3 we get,
[tex]\frac{3y}{3}\leq \frac{-9}{3}\\y\leq -3[/tex]
Graph of [tex]y\leq -3[/tex] is
Therefore by solving the inequality we get [tex]y\leq -3[/tex]
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A rectangular painting measures 13 inches by 20 inches and contains a frame of uniform width around the four edges. The perimeter of the rectangle formed by the painting and its frame is 98 inches. Determine the width of the frame.
Answers
The width of the frame is 8 inches.
We are given that:
The measures of the rectangular painting are:
Length = 13 inches
width = 20 inches
Now, the frame is of uniform with around the corner.
Let it be x inches.
So the new dimensions will be:
Length = 13 + x inches
Width = 20 + x inches.
Also, we are given that:
Perimeter = 98 inches
So, we get that:
P = 2(l + b)
Substituting the values, we get that:
98 = 2 (13 + x + 20 + x)
98 = 2( 33 + 2 x)
98 = 66 + 4 x
4 x = 98 - 66
4 x = 32
x = 32 / 4
x = 8 inches.
Therefore, the width of the frame is 8 inches.
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Find the slope of the line passing through the
points (-3, 3) and (5, 9)
Answers
Answer: 3/4
Step-by-step explanation:
The slope of the line passing through the points (-3,3) and (5,9) is 3/4
The formula for calculating the slope of a line is expressed as:
Given the coordinate (-3,3) and (5,9), substitute the coordinates into the formula as shown below;
Hence the slope of the line passing through the points (-3,3) and (5,9) is 3/4
Mrs. Rushdan buys 4 bananas and 6 apples. What is the ratios for
bananas to apples?
Answers
Answer:
2;3, that is the ratio =)
Step-by-step explanation:
Answer:The answer would be 4 to 6 or 4:6
Points P, Q, R, and S are collinear Point Q is between P and R, R is between Q and S, and PQ congruent RS. If PS=23 and PR= 18, what is the value of QR?
Answers
The value of QR when points P, Q, R and S are collinear is .13
We are given that:
Points P, Q, R and S are collinear points.
Also,
PS = 23
PR = 18
We need to find the value for QR.
Now, we have that PQ is congruent to RS.
So, This means that PQ = RS
This can also be written as:
PR - QR = RS
18 - QR = RS
Also,
PR + RS = PS
Substituting the values, we get that:
18 + ( 18 - QR ) = 23
18 - QR = 23 - 18
18 - QR = 5
QR = 18 - 5
QR = 13
Therefore, we get that, the value of QR when points P, Q, R and S are collinear is .13
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State whether each sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
An equilateral triangle is always equiangular.
Answers
The given sentence about equilateral triangle is true.
A statement is given in the question.
We have to tell whether the statement is true or false.
What is an equilateral triangle ?
An equilateral triangle is a triangle in which all sides and all angles are equal.
As per the question ;
The statement given is , "An equilateral triangle is always equiangular."
Let's check whether it is true or false ;
We know that ,
Equiangular meant equal angles and we know that all the angles of equilateral triangle are equal.
Also ;
An equilateral triangle can also said as an isosceles triangle, that meant any two sides that are equal have equal opposite angles.
So ;
All three sides of an equilateral triangle are equal, all three angles are equal, too. We can conclude that every equilateral triangle is also equiangular.
Thus , the given statement about equilateral triangle is true.
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Simplify the expression. Write your answers using integers or improper fractions.
− 3/2(1/2 n+2n−3)+4n
Answers
The expression is simplified to n - 16/ 4
What are algebraic expressions?
Algebraic expressions are expressions comprising of terms, variables, factors, constants and coefficients.
They are also made up of mathematical operations such as addition, subtraction, multiplication, division, bracket, etc.
Given the expression;
− 3/2(1/2 n+2n−3)+4n
Solve the variables in the bracket, we have;
- 3/ 2 { n + 4n - 6 / 2} + 4n
-3/2 { 5n - 6/ 2 } + 4n
expand the bracket
- 15n - 18/ 4 + 4n
Fin the LCM
-15n - 16 + 16n /4
n - 16/ 4
Thus, the expression is simplified to n - 16/ 4
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PLSSS HURRY I REALLY NEED THIS
Answers
Answer: 1/10
Step-by-step explanation: -2/5+1/2=0.1
If we convert 0.1 into a fraction, it becomes 1/10.
Answer:
1/10 is the answer
Step-by-step explanation:if correct mark as BRAINLIEST