How would you solve absolute value equations with "or" and "and"? Sometimes even with coefficients.
9514 1404 393
Explanation:
In general, a system of equations has a solution that satisfies all of the equations. That is, the solution set is the intersection (and) of the solution sets of the individual equations in the system. Equations involving the absolute value function are no different.
That being said, you need to consider the meaning of an equation involving the absolute value function.
The function itself is piecewise defined:
[tex]\displaystyle |x|=\left\{ {x, x\ge0} \atop {-x, x<0}} \right.[/tex]
So, any equation involving the absolute value function automatically resolves to two equations, each with its own condition on the function value.
__
Example 1:
|x+1| > 3
is equivalent to the two disjoint conditional equations ...
(x +1) > 3 and (x +1) ≥ 0 . . . . OR
-(x +1) > 3 and (x +1) < 0
the first of these has the solution x > 2; the second of these has the solution x < -4. The solution set of this equation is the OR of the two solution sets:
x < -4 or x > 2
__
Example 2:
|x +1| < 3
is equivalent to the two disjoint conditional equations ...
(x +1) < 3 and (x +1) ≥ 0 . . . . OR
-(x +1) < 3 and (x +1) < 0
The first of these has the solution -1 ≤ x < 2, and the second of these has the solution -4 < x < -1. Again, the solution set of this equation is the OR of the two solution sets. However, we find we can write that union as a single compound inequality:
-4 < x < 2
__
When an absolute value equation involves more than one absolute value function, then the equation will probably resolve into multiple equations, each defined on its own domain. Sometimes keeping those domains straight can be tedious.
Above, we have considered inequalities. If you have an equation, you need to consider that it will likely resolve to two equations. The solution set will be the OR of the solutions to those two equations.
Example 3:
|x +1| = 3
is equivalent to the two conditional equations ...
(x +1) = 3 and (x +1) ≥ 0 . . . . OR
-(x +1) = 3 and (x +1) < 0
The first of these has the solution x = 2; the second has the solution x = -4. The solution set is the OR of these two solutions:
x = -4 or x = 2
__
The "and" condition restricts the domain of each of the individual pieces of the equation. The "or" condition applies to the collection of solutions that may exist in each of those restricted domains.
Anyone can help me please
Answer:
(3x)(x-2)(x-1)
Step-by-step explanation:
First we can factor out the 3x from each and are then left with x^2-3x+2. Now we can go ahead and factor. Looking for two variables that multiply to become positive 2 and add to become negative 3, we get negative 2 and negative 1. We now know that both (x-1) and (x-2) are factors. We now have all three factors and we can multiply to check if we get the right answer, and we do.
PLEASE HELP!!!
In a music competition, a participant has to score a total of at least 40 points in the first four rounds combined to move on to the fifth and final round. Glenn scored 4 points in the first round. He then went on to score additional points in the second, third, and fourth rounds. In each of those rounds, his score was identical. Which inequality best shows the number of points, p, that Glenn scored in each of the second, third, and fourth rounds if he earned a place in the finals?
4 + 3p ≤ 40
4 + 3p ≥ 40
4p + 3 ≥ 40
4p + 3 ≤ 40
Answer:
its c bro
Step-by-step explanation:
help!!!!!!!!!!!!!!!!!!!!!
Answer:
proportional
Step-by-step explanation:
because none of the number repeat :) hope that helped
Which multiplicative property is being illustrated below?
(Type commutative, associative, or identity)
5 × 2 × 4 = 2 × 5 × 4
PLEASE HELP!!!
Tank chu. :3
jean is x years old and jonathan is y years old how many years older is jean then jonathan
Answer:
x-y
Step-by-step explanation:
Graph y=15x+3.
Question 2
Identify the x-intercept.
x-intercept:
Answer:
y=19
Step-by-step explanation:
| m^2 + n^2 |
When m = -5 and n = 3, the value of the expression is *blank*
Answer:
the value of the expression is -16
Step-by-step explanation:
[tex]-5^{2} + 3^{2}[/tex]
3. Find the measure of the missing angle.
Help me plzzzz i need help ASAP!!!
A jump rope is 2 2/5 ft long. if 15 jump ropes are laid end to end, how long do they reach?
Question 27 please help I think it’s $11.12 but idk
Ajay reads aloud from a sports magazine. He comes across the measurement 0.63 kilometer. How should he read this measurement aloud? Explain how you know.
Answer:
"sixty-three hundredths of a Kilometer"
Step-by-step explanation:
Decimal measurements are read based on the place of their digits. In this case, Ajay would read this measurement as "sixty-three hundredths of a Kilometer". This is because the final digit of the decimal form measurement is in the "hundredths" position. One more to the right and it would be in the "thousandths" while one more to the left would be the "tenths"
PLEASE HELP THANKS!!
Answer: a) x = 5 b) x = 12
Step-by-step explanation: For each one you just do the inverse to get it on the other side of the equal sign. For example x + 3 = 8 would be like this :
1. x + 3 = 8
2. x + 3 - 3 = 8 -3
( + 3 - 3 cancels out)
3. x = 5
a. x + 3 = 8
x = 8 - 3
x = 5
b. x - 5 = 7
x = 7 + 5
x = 12
46% of the students that were surveyed like to eat at McDonalds. If 351 students do not like to eat at McDonalds, how many people were surveyed?
Answer:
Answer:650 people were surveyed
Which is a correct statement about the description “two less than the quotient of a number cubed and sixteen, increased by eight” when n = 4?
The correct expression is StartFraction n cubed Over 16 EndFraction minus 2 + 8.
The correct expression is 2 minus StartFraction n cubed Over 16 EndFraction + 8.
One of the steps to determining the value when n = 4 is 1 minus 2 + 8.
One of the steps to determining the value when n = 4 is 2 minus 1 + 8.
The value when n = 4 is 6.
The value when n = 4 is 7.
The value when n = 4 is 9.
The value when n = 4 is 10.
Answer:
A and H are correct
Step-by-step explanation:
I took the quiz
The expression for the given statement is n³/16-2+8. Therefore, the options A and H are correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given statement is “two less than the quotient of a number cubed and sixteen, increased by eight”
"Two less than x" describes "x- 2"
"Quotient of x and y" describes x/y
"x increased by y" describes x+y
n³/16 is the quotient and 2 is subtracted and 8 is increased which means 8 is added.
So, the expression is n³/16-2+8
= n³/16 +6
When n=4, we get
4³/16 +6
= 4+6
= 10
Therefore, the options A and H are correct answer.
To learn more about an expression visit;
https://brainly.com/question/28170201.
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Question 3: Quadrilateral A'B'C'E' is the image of quadrilateral ABCE after a dilation centered
at point F. What is the scale factor of this dilation? Explain your work in at least 2 sentences.
C
6
B
C'
B 3
3
1.5
2.5 5
A
E
А
E
==========================================================
Explanation:
We have AB = 3 and A'B' = 1.5; the ratio between the two segment lengths is (A'B')/(AB) = (1.5)/(3) = 1/2 = 0.5
Similarly,
(B'C')/(BC) = (3)/(6) = 1/2 = 0.5(C'E')/(CE) = (2.5)/(5) = 1/2 = 0.5You only need to pick one of these statements to be able to find the scale factor. The scale factor of 1/2 or 0.5 indicates that the image is half as small compared to the preimage. More specifically, each segment of the image is half as small compared to the corresponding segment on the preimage.
A'B' is half as small as ABB'C' is half as small as BCC'E' is half as small as CEA'E' is half as small as AEWe don't have numbers for AE and A'E', but the last statement above must be true because the dilation applies to all segment lengths.
The scale factor of this dilation in the given quadrilateral will be equal to 0.5 times.
What is a Polygon?A polygon is described in geometry as a compact, two-dimensional shape having three or more straight lines. Poly, which means "many," and gon, which means "angle," make up the Greek word "Polygon." Polygons of several kinds can be seen all around us.
As per the given information in the question,
AB = 3 and A'B' = 1.5;
Then, a ratio of the two segment lengths exists.,
(A'B')/(AB) = (1.5)/(3) = 1/2
(A'B')/(AB) = 0.5
In the similar way,
(B'C')/(BC) = (3)/(6) = 1/2
(B'C')/(BC) = 0.5
(C'E')/(CE) = (2.5)/(5) = 1/2
(C'E')/(CE) = 0.5
A'B' is half as small as AB, B'C' is half as small as BC, C'E' is half as small as CE, A'E' is half as small as AE.
To know more about Polygon:
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What is an equation in slope intercept form for the line perpendicular to y = - 2x + 5
that contains (-8, 1)?
1
A.O
y - 8 = 2 (x + 1)
B. O y=-2x - 1
C.O. 1
=
0:0 x = žy + 14
Answer:
[tex]\displaystyle y =\frac{1}{2}x+5[/tex]
Step-by-step explanation:
Equation of the line
The slope-intercept form of a line is given by:
[tex]y=mx+b[/tex]
Being:
m = the slope of the line
b = the y-intercept
We can also use the point-slope form of the line:
[tex]y - k=m(x-h)[/tex]
Being:
(h,k) = A point that belongs to the line
Two lines of slopes m1 and m2 are perpendicular if:
[tex]m_1.m_2=-1[/tex]
We are given the line:
[tex]y=-2x+5[/tex]
Whose slope is m1=-2
Thus, the perpendicular line has a slope of:
[tex]\displaystyle m_2=-\frac{1}{m_1}[/tex]
[tex]\displaystyle m_2=-\frac{1}{-2}[/tex]
[tex]\displaystyle m_2=\frac{1}{2}[/tex]
The required line contains the point (-8,1), thus the equation is:
[tex]\displaystyle y - 1=\frac{1}{2}(x+8)[/tex]
Removing the parentheses:
[tex]\displaystyle y - 1=\frac{1}{2}x+\frac{1}{2}\cdot 8[/tex]
Adding 1:
[tex]\displaystyle y =\frac{1}{2}x+\frac{1}{2}\cdot 8+1[/tex]
Operating:
[tex]\displaystyle y =\frac{1}{2}x+4+1[/tex]
[tex]\mathbf{\displaystyle y =\frac{1}{2}x+5}[/tex]
[tex]\sqrt[4]{x-8}[/tex]
(6x + 3y + 4) - (8x +9y)
liner expressions...
Answer:
−2⋅(x+3y−2)
Step-by-step explanation:
Step-by-step explanation:
(6x + 3y + 4) - (8x +9y)
6x + 3y + 4 - 8x - 9y)
-2x -6y + 4 (.°. Take 2 as common)
2(-x -3y + 2)
-x -3y + 2 = 0
or
x + 3y - 2 = 0
The price of a pair of Jordan’s increases from 52 to $64 what is the percent increase to the nearest
Answer:23%
Step-by-step explanation:
1
We are given the data:
2
The definition of percent increase is:
3
We determine the percent of increase:
PLEASE HELPPPP Which point is in the graphed solution set of this system of inequalities?
{5x−3y>113x+3y<21
A) (−1, 2)
B) (4, 6)
C) (4, 0)
D) (10, −2)
Answer:
(4,0)
Step-by-step explanation:
i took the test and i got the wrong answer :/
Answer:
Its C 4,0 I took the test and got 100%
Step-by-step explanation:
10 out of 40 pencils in Ms. K's class
are missing erasers. What percent
of the pencils are missing erasers in
Ms. K's class?
Answer:
25%
Step-by-step explanation:
plz mark brainliest
if the point (12,4) lies on a graph of direct variation, what is the constant of variation.
Answer:
it is 3:1
Step-by-step explanation:
Mr. Potter's class will take a test for 1 hours. They need to finish by half past 11 to get to lunch on time.
What is the latest time the class can start the test to get to lunch on time?
Answer:
hope this helps
Step-by-step explanation:
he need to get it done within the hour
PLEASE HELP ASAP
What is the value of B for the following triangular prism?
48 in2
60 in2
65 in2
30 in2
Answer:
the answer is 30 in2
Step-by-step explanation:
Baxter has a recipe for salad dressing that calls for 2/3 cup olive oil, 1/4 cup vinigar, and 4/3 cup puréed avocado. How much vinegar does baxter need to make 6 cups of dressing?
Answer:
1 1/2 cups of vinegar
Step-by-step explanation:
Baxter has a recipe for salad dressing that calls for 2/3 cup olive oil, 1/4 cup vinegar, and 4/3 cup puréed avocado. How much vinegar does baxter need to make 6 cups of dressing?
1 cup of dressing = 1/4 cup vinegar
6 cups of dressing = x
Cross Multiply
1 × x = 6 × 1/4
x = 6/4
x = 1 1/2 cups of vinegar
A student designs a container to prevent an egg from breaking when dropped from a height of 30 feet. Write a function that gives the height h (in feet) of the container after t seconds.
Answer:
As i understand, you put an egg inside a container, and then you drop it from 30ft above the ground.
Now, when the container is in the air, the only force acting on it will be the gravitational force (we can discard things like the air resistance, as we do not know the shape or volume of the container).
The gravitational acceleration is g = 32.2ft/s^2
Then the acceleration of the container will be:
A(t) = -32.2ft/s^2
For the velocity, we need to integrate over time to get:
V(t) = (-32.2ft/s^2)*t + v0
where v0 is the initial velocity, as the container is "dropped", the initial velocity is zero, then:
V(t) = (-32.2ft/s^2)*t
For the position, or height in this case, we integrate again over time, and get:
P(t) = (1/2)*(-32.2ft/s^2)*t^2 + p0
Where p0 is the initial height, 30 ft in this case.
Then the equation for the height, as a function of time, is:
P(t) = (-16.1ft/s^2)*t^2 + 30ft.
Where the fact that the container is made in such a way that an egg inside of it does not break (For example, made of a really dense and elastic material that can absorb all the energy of the impact), does not change anything in this equation, as the kinematics do not depend on that kind of properties.
A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every black marble. How many red marbles are in the bag? (Consider using a double number line, tape diagram, or ratio table)
Answer:
there are 101 black marbles
Step-by-step explanation:
Please help me with this math question
Answer:
what are you trying to find?
ANY MATH EXPERTS PLS HELP RN I GOT 5 MIN LEFT I'LL PUT BRAINLIEST TO WHOEVER ANSWERS CORRECTLY FIRST