|| x²-2x|-|3x-20|| = |x²+x-20|.
Find the positive integral value of x
Answers
Answer:
x ∈ {2, 3, 4, 5, 6}
Step-by-step explanation:
You want the positive integer solutions of ||x²-2x|-|3x-20|| = |x²+x-20|.
DomainsEach of the absolute value functions has turning points where the argument is zero. Those turning points are ...
x²-2x ⇒ x(x-2) = 0 ⇒ turning points at x=0 and x=2
3x-20 ⇒ x -20/3 = 0 ⇒ turning point at x=20/3
x²+x-20 ⇒ (x+5)(x-4) = 0 ⇒ turning points at x=-5 and x=4
In numerical order, the turning points are ...
x ∈ {-5, 0, 2, 4, 20/3}
These divide the domain of the equation into 6 intervals. Since we are concerned only with positive integer solutions, we are only interested in the intervals ...
[0, 2), [2, 4), [4, 20/3), [20/3, ∞)
Domain [0, 2)In this domain, x²-2x < 0, 3x-20 < 0, and x²+x-20 < 0. This means the equation becomes ...
|-(x² -2x) +(3x -20)| = -(x² +x -20)
The difference in the absolute value bars is negative, so we get the equation ...
-(-x² +2x +3x -20) = -x² -x +20
2x² -4x = 0 . . . . . . . add x²+x+20
x = 0 . . . . . x = 2 is not in the domain
There are no positive integer solutions in this domain.
Domain [2, 4)In this domain, x²-2x > 0, 3x-20 < 0, and x²+x-20 < 0. This means the equation becomes ...
|(x² -2x) +(3x -20)| = -(x² +x -20)
The difference in the absolute value bars is negative, so we get the equation ...
-(x² -2x +3x -20) = -x² -x +20
0 = 0 . . . . . . . . . . . . add x² +x -20
2 ≤ x < 4 . . . . . . . . all x-values in the domain are solutions
The positive integer solutions are x = 2, x = 3.
Domain [4, 6 2/3)In this domain, x²-2x > 0, 3x-20 < 0, and x²+x-20 > 0. This means the equation becomes ...
|(x² -2x) +(3x -20)| = x² +x -20
The difference in the absolute value bars is positive, so we get the equation ...
(x² -2x +3x -20) = x² +x -20
0 = 0 . . . . . . . subtract x² +x -20
4 ≤ x < 6 2/3 . . . . . . . . . all values of x in the domain are solutions
The positive integer solutions are x = 4, x = 5, x = 6.
Domain [6 2/3, ∞)In this domain, x²-2x > 0, 3x-20 > 0, and x²+x-20 > 0. This means the equation becomes ...
|(x² -2x) -(3x -20)| = x² +x -20
The difference in the absolute value bars is positive, so we get the equation ...
x² -2x -3x +20 = x² +x -20
-6x +40 = 0 . . . . . . . subtract x² +x -20
x = 6 2/3 . . . . . . . add 6x, divide by 6
There are no positive integer solutions in this domain.
The positive integer values of x are {2, 3, 4, 5, 6}.
Related Questions
Joe is playing a game with a regular die. If the number that turns up is
even, he will gain 5 times the number that comes up. If it is odd, he will
lose 10 times the number that comes
up. He tosses a 3. Express the
results as an integer.
Answers
The required solution will be -30 which is expressed as an integer.
To represent this in a general context, we may utilize functions that are referred to in terms of the number tossed.
We know that if the number he gets is an even number, he will get 5 times the number.
As a result, the function for when the integer x is even is f(x) = 5x.
If the number is an odd number, he will lose 10 times the number.
As a result, the function for when the integer x is odd is f(x)=-10x.
Finally, Joe tosses a 3, which is an odd integer, hence the function we will represent is f(x) = - 10x.
⇒ f(3) = -10(3) = -30
Thus, the required solution will be -30 which is expressed as an integer.
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Please solve with explanation (High Points)
Answers
The equation of the transformed function is f(x)= -1/3[tex]\sqrt{2(x-6)}[/tex] -3.
Given that,
The f(x) = square root of X base function is transformed by a reflection in the x-axis, a vertical stretch by a factor of 3, a horizontal compression by a factor of 1/2, a vertical translation by a factor of 3, a vertical translation by a factor of 3 down, and then a horizontal translation by a factor of 6 right.
We have to verify the changed function's equation.
Take the function
f(x)=√x
The function reflection in the x-axis,
f(x)=-√x
The function is vertical stretch by a factor of 3.
f(x)= -1/3√x
The function is horizontal compression by a factor of 1/2.
f(x)= -1/3[tex]\sqrt{2x}[/tex]
The function is vertical translation by a factor of 3 down,
f(x)= -1/3[tex]\sqrt{2x}[/tex] -3
The function is horizontal translation by a factor of 6 right.
f(x)= -1/3[tex]\sqrt{2(x-6)}[/tex] -3
Therefore, The equation of the transformed function is f(x)= -1/3[tex]\sqrt{2(x-6)}[/tex] -3.
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Simplify -4 (x + 1) + 6x write urr answer in factored form
Answers
x = 1
Step-by-step explanation:
[tex]{ \orange{ \tt{ - 4(x + 1) + 6x}}}[/tex]
Multiply -4 with (x+1) then the Eqⁿ becomes
[tex]{ \orange{ \tt{ - 4x - 4 + 6x}}}[/tex]
Step (1):- [tex]{ \red{ \sf{combine \: like \: terms}}}[/tex]
You can see the like terms i.e. -4x and 6x. Now, add this like terms.
[tex]{ \orange{ \tt{ - 4x + 6x - 4}}}[/tex]
[tex]{ = \orange{ \tt {2x - 4}}}[/tex]
Step (2):- [tex]{ \red{ \sf{ common \: factor}}}[/tex]
Take 2 as common in 2x-4 then,
[tex]{ \orange{ \tt{2(x - 2)}}}[/tex]
[tex]{ \orange{ \tt{2x - 2 = 0}}}[/tex]
[tex]{ \orange{ \tt{2x = 2}}}[/tex]
[tex]{ \blue{ \boxed{ \purple{ \sf{x = 1}}}}}[/tex]
HELP!!
If the product of two numbers is positive, which of the following expressions must be true?
1. The factors had different signs.
2. One of the factors was negative.
3. One of the factors was positive.
4. The factors had the same sign.
Answers
Answer:
4: The factors had the same sign
Step-by-step explanation:
They are both positive (i think)
Yuson spends $584 on equipment to start his own landscaping company. He charges $26 per hour. Write a linear equation in slope-intercept form to represent his profits, y, after working x hours.
Answers
The equation for profit in slope-intercept form is written as y = 26x - 584
Linear EquationA linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation is given as y = mx + c
m = slopec = y-interceptIn this problem, the constant or fixed value is the amount he spent on the equipment and the slope is the amount he charges per hour.
The equation of profit can be represented as y = 26x - 584
Where x = number of hours he worked.
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The surface area for a rectangular prism with a square base is given by the expression. 2s2+4sh, where side s is the side length of the square base and h is the height of the prism. What is the surface area in square feet of a rectangular prism with a square base, where s=4 feet and h=6 ?
Answers
Answer:
128 square feet
Step-by-step explanation:
2(4)^2 + 4 * 4 * 6 =
= 2 * 16 + 16 * 6 =
= 32 + 96 =
= 128 square feet
Which of the following is equivalent to 17g - 2g?
Answers
The equivalent expression to 17g-2g will be (17-2)g.
According to the question,
We have the following expression:
17g-2g
Now, we can simplify this expression easily to find the equivalent expression.
So, our first step will be to take g as a common factor from both the terms. Now, we have the following expression:
(Note that the common factor means that the variable or the number taken as a common factor should be able to divide the terms given in the expression.)
(17-2)g
Now, this can be solved further because 2 can be subtracted from 17 because they both are integers without any variable.
Hence, the correct option is C.
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To rent a certain meeting room, a college charges a reservation fee of $37 and an additional fee of $6.40 per hour. The chemistry club wants to spend at most $88.20 on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room? Use t for the number of hours the meeting room is rented, and solve your inequality for t .
Answers
If the chemistry club wants to spend at most $88.20 on renting the meeting room. The possible amounts of time for which they could rent the meeting room is 8.
How to find the possible amounts of time?Let t represent the number of hours the meeting room is rented
Formulate an inequality and use the inequality to find the time
37 + 6.40t < 88.20
Combine like terms
6.40t < 88.20 - 37
6.40t < 51.20
Divide both side by 6.40t
t = 51.20 /6.40
t < 8
Therefore the time is 8.
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Line v has an equation of y = -2x + 5. Perpendicular to line v is line w, which passes through
the point (6, -5). What is the equation of line w?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Answers
Answer:
Line W's equation is y= 1/2x - 8
Step-by-step explanation:
17. Represent and Connect The expression
-120 + 13.4m represents a submarine that
began at a depth of 120 feet below sea level and
ascended at a rate of 13.4 feet per minute. What
was the depth of the submarine after 6 minutes?
Please help me
Answers
OA. 20
B.O
345WN-OX
O C. -10
D. 10
0 -1
-2
-5
-10
-17
-26
-37
1
What is the average rate of change for this quadratic function for the interval
from x = 4 to x = 6?
2
6
Answers
Answer:
C. -10
Step-by-step explanation:
Using the average rate of change formula,
[tex]\frac{-37-(-17)}{6-4}=-10[/tex]
use the arithmetic sequence 12,15,18,21...
what is the equation of the nth term of the sequence
Answers
Answer:
3n+9
Step-by-step explanation:
A population of beetles grows by 25% every month. If the beetle population starts with 1,600 beetles, which equation represents the population, P, after t months?
Answers
The equation which represents the population, P after t months is:
y = 1600(1+ 0.25)^t.
Given,
A population of beetles grows by 25% every month.
the beetle population starts with 1,600 beetles,
we are asked to determine the equation which represents the population, P after t months.
The equation for the population is:
Pf = Pi(1-r)^t
where pf = final value
pi = initial value
r = growth factor
t = time in years.
substitute the values in the equations.
let y represent the final population after t years.
r = 25%
convert percentage to decimal.
r = 0.25
y = 1600(1+ 0.25)^t
Hence we get the required answer.
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a delivery driver has an average daily gasoline expense of $55.00. the standard deviation is $10.00. the owner takes a sample of 54 bills. what is the probability the mean of his sample will be between $45.00 and $65.00? enter all answers to the nearest tenth.
Answers
The probability the mean of his sample will be between $45.00 and $65.00 is 0.6826.
Given:
A delivery driver has an average daily gasoline expense of $55.00. the standard deviation is $10.00. the owner takes a sample of 54 bills.
n = 54
standard error = 10/[tex]\sqrt{54}[/tex]
= 2.205
when x = 45,
z score = 45 - 55 / 10
= -10/10
= -1
probability at z = -1 is 0.3413
z score for x = 65
z = 65 - 55 / 10
= 10/10
= 1
probability at z = 1 is 0.3413
Total probability = 0.3413+0.3413
= 0.6826
Therefore the probability the mean of his sample will be between $45.00 and $65.00 is 0.6826.
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Write an equation for the table. Then find the value of y when x = 18
Distance
24
36
42
48
54
traveled, x
Time, y
1
7
10
13
16
Answers
Answer: maybe
12
Step-by-step explanation:
the answer is 12
During a one-month promotional campaign, Fran's Flix
gave either a free DVD rental or a
12-serving box of microwave popcorn to
new members. It cost the store $1 for each free
rental and $2 for each box of popcorn. In all, 59 new members were signed up and the
store's cost for the incentives was $103. How many of each incentive were given away?
Answers
If the store's cost for the incentives was $103.The amount of each incentive that were given away is: Free Rental 5, Box of popcorn 54.
How to find the incentive given?Let Free Rental = r
Let Box of popcorn = p
Total incentives:
r+p=59
r= 59-p Equation 1
r×1+p×2=103
r+2p=103 Equation 2
Put the value of r in (eq 2) from (eq 1)
r+2p=103 (eq 2)
59-p+2p=103
59+p=103
p=103-59
p=44
Put the value of p in (eq 1)
r=49-p...........(1)
r=49-44
r= 5
Free Rental = 5
Box of popcorn = 59 -5
Box of popcorn = 54
Therefore 5 and 54 incentive were given.
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T Mobile charges $20 for the 1st phone plan and $6 per line added. Jenny has at most $60 she can spend for family. Write an inequality to show how many lines she can have. a 20 + 6L ≤ 60 b 6 + 20L ‹ 60 c 20 + 6L > 60 d 6 + 20L ≥ 60
Answers
Answer:
A. 20 + 6L < 60
Step-by-step explanation:
It can't be B. or D. because 20L, not a thing in this problem. That leaves us with A. and C. being our only reasonable answers.
I chose A. because Jenny can't spend more than 60
Find the midpoint of the segment with the
following endpoints.
(8, 2) and (1, 10)
Answers
Answer:
(4.5 , 6)
Step-by-step explanation:
Finding the midpoints of segment when endpoints are given:
To find the midpoints, add the x-coordinates and divide by 2 and add the y-coordinates and divide by 2.
(8 , 2) ⇒ x₁ = 8 ; y₁ = 2
(1 , 10) ⇒ x₂ = 1 ; y₂ = 10
[tex]\sf Mipoint\left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)[/tex]
[tex]\sf = \left(\dfrac{8+1}{2},\dfrac{2+10}{2}\right)\\\\\\=\left(\dfrac{9}{2},\dfrac{12}{2}\right)\\\\\\=(4.5,6)[/tex]
What is m Please help!
Answers
72°
Explanation:
Vertical Angles are equal
Equation:
3x° + 54° = 7x° + 30°
4x° = 24°
x = 6°
Therefore, Angle M is 18° + 54° = 72°
I would appreciate it if you mark my answer as brainliest.
Answer:
Step-by-step explanation:
m just means measure. So the question is asking you what is the MEASURE of the ANGLE AEB.
Since angles AEB and CED are vertical angles, you can set the two expressions equal to each other and solve for X.
1) 3x + 54 = 7x - 30
2) 54 = 4x - 30
3) 84 = 4x
4) x = 21
Now that you know x, plug x into the expression for AEB, which is 3x + 54
3(21) + 54 = 117
m∠AEB = 117°
PLEASE HELP ME WILL GIVE BRAINLIEST!!!!!!!!!!!!!!
Solve this system of equations using the LINEAR COMBINATION method, then answer the questions below. 2x - y = - 46x + 5y = 4What did you get for the (x, y) solution to this system? (2.5 points)Explain what you did to create a pair of opposites so that you could combine the equations. (2.5 points)
Answers
Answer:x=5, y=-4
Step-by-step explanation:2x+9y = -26
-3x-7y = 13
Multiply the first equation by 3
3(2x+9y = -26)
6x +27y = -78
Multiply the second equation by 2
2(-3x-7y = 13)
-6x -14y = 26
Add these two equations together
6x +27y = -78
-6x -14y = 26
---------------------
13y = -52
Divide by 13
13y/13 = -52/13
y = -4
Now we need to find x
2x+9y = -26
2x+9(-4) = -26
2x-36=-26
Add 36 to each side
2x-36+36 = -26+36
2x=10
Divide by 2
2x/2 =10/2
x=5
the reflection of the point (8,0) across the x-axis is__
Answers
The reflection of the point (8,0) across the x-axis is (8, 0)
How to determine the image of the reflection?From the question, the point is given as:
Point = (8, 0)
Rewrite this point as
(x, y) = (8, 0)
The transformation is given as
Reflection across the x-axis
Mathematically, we have
(x, y) = (x, -y)
So,we have
Image = (8, 0)
Hence, the image of the reflection is (8, 0)
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Are these 4 problems SSS SAS ASA AAS HL
Answers
1. The first figure posses the SSS property.
2. The second figure posses the ASA property.
3. The third figure posses the hypotenuse length property.
4. The fourth figure posses the SAS property.
Given:
1. The first figure shows the SSS property.
Side-Side-Side criterion is referred to as the SSS criterion. According to this standard, two triangles are congruent if their respective triangles' three sides are equal to one another.
hence the two triangles are congruent.
2. The second figure posses the ASA property.
Angle-Side-Angle criterion is also known as ASA criterion. According to the ASA criterion, two triangles are congruent if any two of their included sides and related angles are equivalent in size to those of the other triangle.
hence the two triangles are congruent.
3. The third figure posses the hypotenuse length properety.
RHS criterion stands for right angle-hypotenuse-side congruence criterion. Under this criterion, two triangles are congruent, if the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle.
hence the two triangles are congruent.
4. The fourth figure posses the SAS property.
Side-Angle-Side criterion is referred to as the SAS criterion. According to this standard, two triangles are said to be congruent if their matching sides and included angles are the same on each side of each other.
hence the two triangles are congruent.
Hence we get the required answer.
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J.D. opened a savings account with $425. After
2 years, the total interest he earned was $10.20.
What was the annual interest rate?
Answers
The annual interest rate is 1.2%
The principal amount = $425
The total interest her earned = $10.20
The final amount = 425 + 10.20
= $435.2
Time period = 2 years
The simple interest
A = P(1 + rt)
Where A is the final amount
P is principal amount
r is the interest rate
t is the time period
Substitute the values in the equation
435.2 = 425(1 + r×2)
1 + 2r = 435.2 / 425
Divide the terms
1 + 2r = 1.024
2r = 1.024 - 1
2r = 0.024
r = 0.024/2
Divide the terms
r = 0.012
Then the percentage will be
r = 1.2%
Hence, the annual interest rate is 1.2%
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PLEASEEE ANSWER ASAP!
Question
Evaluate the expression.
2−[(2+10(−1)÷2)+1]
What is the value of the expression?
Enter your answer in the box.
Answers
The value of the expression will be;
⇒ 4
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 2 - [(2 + 10(−1) ÷ 2) + 1]
Now,
Solve the expression by using BODMAS rule as;
The expression is,
⇒ 2 - [(2 + 10(−1) ÷ 2) + 1]
⇒ 2 - [ (2 - 10 ÷ 2) + 1 ]
⇒ 2 - [(2 - 5) + 1 ]
⇒ 2 - [ - 3 + 1 ]
⇒ 2 - { - 2 ]
⇒ 2 + 2
⇒ 4
Thus, The value of the expression will be;
⇒ 4
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Use the diagram below
Answers
The measure of angle KJL from the given figure is 84°.
Given that, 3(m∠LJM)=2(m∠KJL) and m∠KJM=140°.
What is an angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
Here, m∠KJM=m∠LJM+m∠KJL
Now, (m∠LJM)=2/3 (m∠KJL)
140°= 2/3 (m∠KJL) + m∠KJL
⇒ [2(m∠KJL)+3(m∠KJL)]/3 = 140°
⇒ 5m∠KJL=420°
⇒ m∠KJL=420°/5
⇒ m∠KJL=84°
Hence, the measure of angle KJL from the given figure is 84°.
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lara writes the expression 1.5x 2.75y 3. maria writes the expression 3 1.5x 2.75y. which property can be used to prove the two expressions are equivalent?
Answers
The correct property is used to prove the two expressions are equivalent is;
''Commutative property''
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Lara writes the expression 1.5x + 2.75y + 3.
And, Maria writes the expression 3 + 1.5x + 2.75y.
Now,
Since, The commutative property states that;
a + b = b + a
So, Clearly, Here the commutative property used to prove the two expressions are equivalent, as;
⇒ 1.5x + 2.75y + 3 = 3 + 1.5x + 2.75y.
Thu, The correct property is used to prove the two expressions are equivalent is;
''Commutative property''
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someone help fast!! what is the slope of this graph!
Answers
Step-by-step explanation:
for every x change by +1, y changes by -3.
so, the slope is
-3/1 = -3
Answer:
-3
Step-by-step explanation:
I hope it helps :]
Draw a quadrilateral that has 2 separate pairs of equal length sides but is not a parallelogram.
Answers
A quadrilateral that has 2 separate pairs of equal length sides but is NOT a parallelogram is called a KITE.
What is a quadrilateral?
A quadrilateral is any polygon that has four sides and four vertices. They include;
Properties
Four sides (or edges)Four vertices (or corners), And internal angles that total 360 degrees make up a quadrilateral.What is a kite?
A quadrilateral is a polygon with four sides, commonly known as a kite. Four points on the plane must be "independent" in order for the kite to have four corners. As a result, none of the three are parallel to one another.
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A rectangle is 2 feet 11 inches wide and 1 yard 2 feet 1 inch long. What is the perimeter of the
rectangle in feet?
A 8 feet
B 24 feet
C 16 feet
D 18 feet
Answers
The perimeter of the rectangle is 16 feet.
The correct answer is an option (C)
In this question, the length of the rectangle is,
l = 1 yard 2 feet 1 inch
l = 3 feet + 2 feet + 0.0833 feet
l = 5.0833 feet
And the width of the rectangle is,
w = 2 feet 11 inches
w = 2 feet + 0.9167 feet
w = 2.9167 feet
So, the perimeter of the rectangle would be,
P = 2(l + w)
P = 2 * (5.0833 + 2.9167)
P = 16 feet
Therefore, the perimeter of the rectangle is 16 feet.
The correct answer is an option (C)
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find the slope (15,8),(-17,9)
Answers
Please give brainly if correct :)
Answer: -1/32
Step-by-step explanation:
Use the slope formula: y2-y1/x2-x1
Apply that:
9-8/-17-15 = 1/-32 = -1/32