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.
What is the greatest common factor of 14, 51 ,21
Answer:
The answer is 1
Step-by-step explanation:
14 = 2 × 7
51 = 3 × 17
21 = 3 × 7
I need this last one I would give all my pints bcz I don’t understand it
the one dot by itself is 6,-5 and the line that is pink with two black dots are the slope-intercept of the equation y=3/4x-2 and theirs the answer copy and paste my image and quote to answer the question.
find the area of the regular polygon
Answer:
433.4
Step-by-step explanation:
Height will be (14/2)/tan36 which is 9.63, then area for one triangle is 1/2*hb which is .5*9.63*7 is 43.34, times 10 you get 433.4
find the range value of x which satistfy inequality (x + 2)² > 2x + 7
Answer:
the range value of x which satisfy inequality [tex](x + 2)^2 > 2x + 7[/tex] is [tex]\mathbf{x>1 \ or \ x<-3}[/tex]
Step-by-step explanation:
We need to find the range value of x which satisfy inequality [tex](x + 2)^2 > 2x + 7[/tex]
Solving:
[tex](x + 2)^2 > 2x + 7[/tex]
Using formula: [tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex]x^2+4x+4>2x+7\\x^2+4x+4-2x-7>0\\x^2+4x-2x+4-7>0\\x^2+2x-3>0[/tex]
Now factoring the term: [tex]x^2+2x-3>0[/tex]
Breaking the middle term: 2x= 3x-x
[tex]x^2+2x-3>0\\x^2+3x-x-3>0\\x(x+3)-1(x+3)>0\\(x-1)(x+3)>0\\x-1>0 \ or \ x+3>0\\x>1 \ or \ x<-3[/tex]
So, the range value of x which satisfy inequality [tex](x + 2)^2 > 2x + 7[/tex] is [tex]\mathbf{x>1 \ or \ x<-3}[/tex]
A golf ball is hit with an initial velocity of 100 feet per second. The height of the golf ball can be represented by the equation h=100t−16t^2, where t is the time in seconds since the ball was hit and h is the height of the ball in feet. How long will it take for the ball to hit the ground?
Answer:
6.25 secondsStep-by-step explanation:
Using the the equation
h = 100t − 16t^2The ball hits the ground, when h = 0, solving below equation:
100t − 16t^2 = 04t(25 - 4t) = 0t = 0 seconds, this is the starting point when ball was hit25 - 4t = 0 ⇒ 4t = 25 ⇒ t= 25/4 = 6.25 seconds later the ball hits the groundAnswer:
6.30 seconds
Step-by-step explanation:
What is m / 5 - 2 = 8
Answer:
m=24
Step-by-step explanation:
First, we can combine like terms:
m/(5-2)=8
m/3=8
Now, we need to get m by itself. To do this, multiply by 3:
m/3*3=8*3
m=24
50
50 ÷ 5 = 10, 10-2 =8
kdjrjrjdjjfhrhy to truth thhrjrhejd
The question is in the image! Please help if u can its due really soon
Answer:
88°
Step-by-step explanation:
m∠AOB = m∠DOE = 88°
In the diagram shown, ZFEH is a right angle. If mZHEG = 41° then which statement below is true?
Answer:
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Step-by-step explanation:
If Lily got 18 questions right on a 20 questions
test, what percentage of the questions did she
get wrong?
Answer:
She got 10% of the questions wrong !
Step-by-step explanation:
To solve this problem I used cross multiplication
[tex]\frac{x}{100}= \frac{18}{20}[/tex]
18 x 100 =1800
1800 / 20 = 90
Since they are asking what she got wrong, not what she got right, you just need to subtract.
100% - 90% = 10%
hope this helped !
Answer:
10%
Step-by-step explanation:
18/20 Questions = 0.9 or 90% she got right
2/20 Questions = 0.1 or 10% she got wrong
On which number line do the points represent negative 4 and 1 over 2 and +3?
Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed between the 4th and 5th tick marks to the left of 0. A point labeled T is placed on the 3rd tick mark to the right of 0.
Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 3rd tick mark to the left of 0. A point labeled T is placed between the 4th and the 5th tick marks to the right of 0.
Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed is between the 4th and 5th tick marks to the left of 0. A point labeled T is placed between the 2nd and 1st tick marks to the left of 0.
Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed between the 2nd and the 3rd tick mark to the right of 0.
what is the answer PLZ help asap
Answer:
ITS A!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!=)
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Just put A :)
In 2020, a town was recorded as having a population of 10,000 and is predicted to grow at 5% every year. What will be the population in 2035, to the nearest whole number? *
Answer:
20789
Step-by-step explanation:
The equation of exponential growth is y=A(1+r)^t
A=10,000
r (rate)=0.05 (5% as a decimal)
t (time)=15 (2035-2020=15)
y=10,000(1+0.05)^15
y=20789.2817
you can't have part of a person, so y=20789
subtracting 1 from the product of 5 and x gives the same value as adding 10 to the product of 3 and x
Answer:
x = 11/2
Step-by-step explanation:
We would first put it in an equation
5x - 1 = 10 + 3x
We would first add 1 on both sides
5x = 11 + 3x
Then we subtract 3x on both sides
2x = 11
Divide both sides by 2
x = 11/2
The value of x from the given algebraic statement expression is;
x = 11/2
This is about simple Algebra.
The first expression is that; We are to subtract 1 from the product of 5 and x. This give; 5x - 1The second expression is that we are to add 10 to the product of 3 and x. This gives us; 3x + 10Finally, we are told that the first expression gives the same value as the second expression. This means that they are equal to each other and as such, we have;
5x - 1 = 3x + 10
Let's add 1 to both sides to get;
5x - 1 + 1 = 3x + 10 + 1
⇒ 5x = 3x + 11
Let's subtract 3x from both sides to get;
2x = 11
Divide both sides by 2 to get;
x = 11/2
Read more at; https://brainly.com/question/18358801
HELP ME!
CHOOSE CORRECT ANSWERS!
please help, i need to know this answer!!
Answer:
It is d
Step-by-step explanation:
n Huda evaluated the expression below. -3(8-5)--(-7) -3(3)- - (-7) -3(9)-(-7) 27-(-7) What was Huda's error? Huda evaluated (3) 2 incorrectly. 0 Huda found the product of -3 and 9 as positive. Huda subtracted -7 from 27 incorrectly. Huda did not follow the order of operations.
Answer:
B
Step-by-step explanation:
A chorus teacher is arranging students on bleachers for a performance. The 1st row of the bleachers has 10 students, the 2nd row has 14 students, the 3rd row has 18
students, and the 4th row has 22 students.
Assuming the trend continues, how many students will be on the 6th row of the bleachers?
Assuming the trend continues, there will be 30 students on the 6th row of the bleachers.
According to the question,
We have the following details:
Number of students in 1st row = 10
Number of students in 2nd row = 14
Number of students in 3rd row = 18
Number of students in 4th row = 22
Now, if we carefully observe the arrangement made by the chorus teacher, we will observe that the arrangement has a pattern.
It is to be noted that with each row 4 students are increasing.
For example, in 2nd row the number of students is 14 (4 more than the previous row), in 3rd row the number of students is 18 (4 more than the previous row), etc.
Now, we have to find the number of students in 6th row. So, first we need to find the number of students in 5th row.
Number of students in 5th row = number of students in 4th row + 4
Number of students in 5th row = 22+4
Number of students in 5th row = 26
Now,
Number of students in 6th row = number of students in 5th row + 4
Number of students in 6th row = 26+4
Number of students in 6th row = 30
Hence, there are 30 students on the 6th row of the bleachers.
To know more about row here
https://brainly.com/question/27917476
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Please help me out with those questions...
Answer:
D
Step-by-step explanation:
Three times a number increased by 8 is no more than the number decreased by 4. Find the number.
Answer:
(-oo, -6]Step-by-step explanation:
Let the number be x
3x + 8 ≤ x - 43x - x ≤ -4 - 82x ≤ -12x ≤ -6x = (-oo, -6]What is the area of a rectangle with a width of 6.5 feet and a length of 14 feet?
Answer:91 i think
Step-by-step explanation:
Answer:
91
Step-by-step explanation:
6.5 x 14 =91
what would the value of X be on this one?
Answer:
i think it's 51 because if you add 106 and 23 together it's 129 then 180-129= 51
Step-by-step explanation:
Which of the following is not a polynomial?
After eating dinner at a restaurant, Alex's bill before tax is $78.00. The sales tax rate is 8%. Alex decides to leave a 20% tip for the waiter based on the pre-tax am
Answer:
$99.84Step-by-step explanation:
Step one:
given data
we are told that before tax the bill is pretax= $78
the tax is 8%
and he left 20% of the pretax for the attendant.
Step two:
let us find the amount he paid for eating with tax
=8/100*78
=0.08*78
=$6.24
with tax the meal cost is
= 78+6.24
=$84.24
let us solve for the tip he left (note: it is 20% of the pretax)
=20/100*78
=0.2*100
=$15.6
the tip is $15.6
Step three:
the total amount he paid after eating plus tax and tip is
78+6.24+15.6
=$99.84
Answer:
99.84
Step-by-step explanation:
There are 14 boys and 13 girls in a class. Write the ratio of boys
to girls.
Answer
The answer is 14:13
Write each algebraic expression in words.
Then evaluate each expression for n = 6.
a) 4n:
b) n + 8:
c) n/2:
d) 7 + 3n:
e) 10n – 15:
f) 50 – 8n:
Please help :(((
Work out the value of the expression 2(a +5b) when a=4 and b=3
Answer:
38
Step-by-step explanation:
2(4+5(3))
2(4+15)
2(19)
38
Answer:
38
Step-by-step explanation:
2(4+5*3)
2(4+15)
2(19)
38
I'm analyzing a song for an assignment and I need a appropriate song to use, something popular. any suggestions? ( comment if full)
Answer:
id recommend any song by brent faiyaz or lost boy by ruth b because it has a little more meaning orrrr the bigger picture by lil baby (thats a good one :)) orrrr girl of my dreams by rod wave orrrr almost is never enough by ariana grande
Solve for X.
A. 10
B. 12
C. 15
D. 22
Answer:
B. 12Step-by-step explanation:
Since Z is midpoint of SR and Y is midpoint of QR, so as per triangle midpoint theorem ZY is parallel to SQ and measures half of its value:
SQ = 2ZY3x - 8 = 2(x + 2)3x - 8 = 2x + 43x - 2x = 4 + 8x = 12Correct answer choice is B
Answer:
the answer is B.12 ......
does anyone know the answer ? and if you do can you explain how to do it ?
Answer: I think its answer choice b
Step-by-step explanation:
You're dividing so you would be subtracting the exponents
Somone please help me on 9 and 10. I have done the rest but I am so confused on this. please
Answer:
C and A
Step-by-step explanation:
Remember what slope means: [tex]\frac{rise}{run}[/tex].
9. The first slope is 2, or [tex]\frac{2}{1}[/tex]. This means it is moving up 2 and over 1. The second option is the reciprocal, [tex]\frac{1}{2}[/tex]. The second slope moves up 1 and over 2. The first slope is going higher than the second at the same distance. But then we are given the third slope. I'm going to assume here that it does not matter whether the slope is negative or positive, you are only considering steepness. If our first slope moved up 2 and over 1, this slope moves down 4 and over 1, meaning it is covering more area over the same distance. So the steepest slope is option C.
10. Right off the bat we can get rid of option C. The slope is zero, meaning a flat line with no steepness. Next, we need to figure out if A or B is steeper.
First, we can turn them into mixed numbers in order to better be able to tell which is greater.
[tex]\frac{5}{3}=1\frac{2}{3}[/tex]
[tex]\frac{-3}{2}=-1\frac{1}{2}[/tex]
Because we don't care whether the line is ascending or descending, we will compare the absolute value of the slopes.
[tex]1\frac{2}{3} >1\frac{1}{2}[/tex]
So we can see that slope A, [tex]\frac{5}{3}[/tex] is steeper than slope B.
I hope this helps!
The vertices of a trapezoid are A(1,2), B(4,4), C(4,0). D(1.6).
Rotate the trapezoid 270 degrees counterclockwise about
the vertex a. What are the coordinates of the image?
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.