Explain why the solution set of the inequality |x|<5 is the intersection of two sets, while the solution set of the inequality |x|>5 is the union of two sets.The solution of |x|<5 is the set of numbers that makes either of two inequalities true. The solution set of |x|>5 is the set of numbers that makes both of two inequalities true. The solution of |x|<5 is the set of numbers between −5 and 5. The solution set of |x|>5 is the set of numbers greater than 5. The solution of |x|<5 is the set of numbers that makes both of two inequalities true. The solution of |x|>5 is the set of numbers that makes either of two inequalities true. The solution of |x|<5 is the set of numbers less than −5. The solution of |x|>5 is the set of numbers between −5 and 5.
Answers
Answer:
The region of the [tex]|x|<5[/tex] is the common area between -5 and 5.
But there is no common area for the solution of [tex]|x|>5[/tex].
Step-by-step explanation:
Given two modulus functions:
[tex]1.\ |x|<5\\2.\ |x|>5[/tex]
Let us have a look at the definition of modulus function first:
[tex]|x|=\left \{ {-{x}\ if\ x<0 \atop {x}\ if\ x>0} \right.[/tex]
Now, solving the above given modulus functions one by one using the definition of modulus function.
Solution 1 :
[tex]\pm x <5\\\Rightarrow x<5, -x<5\\OR\\\Rightarrow x<5, x>-5[/tex]
Kindly refer to the attached diagram for solution.
The area shaded in the green color shows the solution for this equation.
Solution 2 :
[tex]\pm x >5\\\Rightarrow x>5, -x>5\\OR\\\Rightarrow x>5, x<-5[/tex]
Kindly refer to the attached diagram for solution.
The area shaded in the blue color shows the solution for this equation.
We can clearly observe that the region of the first equation is the common area between -5 and 5.
But there is no common area for the solution of the second equation.
Therefore, solution of [tex]|x|<5[/tex] has intersection and
solution of [tex]|x|>5[/tex] has union.
Answer:
The solution of |x|<5 is the set of numbers that makes both of two inequalities true. The solution of |x|>5 is the set of numbers that makes either of two inequalities true.
Step-by-step explanation:
Related Questions
Please help me with number 10
Answers
Hope it helped
x+5/2=10 linear equations step by step explantion
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See attachment for math work and answer.
How do you illustrate
quadratic equation
in one variable?
Answers
Step-by-step explanation:
Quadratic Equation
Quadratic equation is in the form
ax2+bx+c=0
Where
a, b, & c = real-number constants
a & b = numerical coefficient or simply coefficients
a = coefficient of x2
b = coefficient of x
c = constant term or simply constant
a cannot be equal to zero while either b or c can be zero
Examples of Quadratic Equation
Some quadratic equation may not look like the one above. The general appearance of quadratic equation is a second degree curve so that the degree power of one variable is twice of another variable. Below are examples of equations that can be considered as quadratic.
1. 3x2+2x−8=0
2. x2−9=0
3. 2x2+5x=0
4. sin2θ−2sinθ−1=0
5. x−5x−−√+6=0
6. 10x1/3+x1/6−2=0
7. 2lnx−−−√−5lnx−−−√4−7=0
For us to see that the above examples can be treated as quadratic equation, we take example no. 6 above, 10x1/3 + x1/6 - 2 = 0. Let x1/6 = z, thus, x1/3 = z2. The equation can now be written in the form 10z2 + z - 2 = 0, which shows clearly to be quadratic equation.
Roots of a Quadratic Equation
The equation ax2 + bx + c = 0 can be factored into the form
(x−x1)(x−x2)=0
Where x1 and x2 are the roots of ax2 + bx + c = 0.
Quadratic Formula
For the quadratic equation ax2 + bx + c = 0,
x=−b±b2−4ac−−−−−−−√2a
See the derivation of quadratic formula here.
The quantity b2 - 4ac inside the radical is called discriminat.
• If b2 - 4ac = 0, the roots are real and equal.
• If b2 - 4ac > 0, the roots are real and unequal.
• If b2 - 4ac < 0, the roots are imaginary.
Sum and Product of Roots
If the roots of the quadratic equation ax2 + bx + c
= 0 are x1 and x2, then
Sum of roots
x1+x2=−ba
Product of roots
x1x2=ca
You may see the derivation of formulas for sum and product of roots here.
Find the distance between the two points in simplest radical form.
(-4,-3) and (5,9)
Anybody know anything bout Distance formula?and could maybe help with a couple questions please!
Answers
Step-by-step explanation:
Distance = √(5--4)^2 + (9--3)^2
= √ 9^2 + 12^2
√81 + 144 = √225=15
Answer:
15
Step-by-step explanation:
15
Plz Help :/ and Thank you...
Answers
banana good for you
(i made this in 3d paint btw)
Answer:
25c = t ??
Step-by-step explanation:
32 ounces of maple syrup for $3.99 OR 48 ounces of syrup for $4.99
Answers
solve for x 8(x+9)= -9x+21
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Answer:
x = -3
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
-3
Step-by-step explanation:
HELP ASAP!!
Solve the equation x² = 5. Round to the nearest tenth.
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Someone plz help me I’ll give branliest!!
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The vertex of the parabola shown is (4, -2)
In general, the vertex is (h,k)
So (h,k) = (4,-2) meaning h = 4 and k = -2
The equation of this parabola is y = (x-4)^2 - 2
Answer:
-2 is the correct option you're looking for.
Help please!!!!! put a answer and explanation WILL GIVE BRAINIEST
Answers
Answer:
1. false
2. true
3. false
4. true
Step-by-step explanation:
4. 1/9 rational + 2 irrational= 8 irrational
Which gives the correct domain and range for the following relation: (-3, 2) , (0, 4) ,
(-3, 0) , (1, 4)
A. Domain: {-3, 0, 4}, Range: {2, 4}
B.
Domain: {-3, 0, 1}, Range: {0, 2, 4}
C.
Domain: {-3, 0, 4}, Range: {0, 2, 4}
D.
Domain: {-3, 0, 1}, Range: {2, 4}
Answers
What is the difference between 5x +3 and 5(x+3)?
Answers
Step-by-step explanation:
for 5(x+3) you have to use the distributive property to find its standard form because it has parenthesis:
this would give you 5x+15 which is not the same as 5x+3.
What is the answer? Please explain how to answer it too.
Answers
Answer:
x=15
Step-by-step explanation:
8x=120
8x/8=120/8
x=15
The cost to rent a rug-cleaning machine from the supermarket is $23 per day. The supermarket charges a check-out fee of $45 for the rental. Tristanne spent $137 to rent the rug-cleaning machine. If d represents the number of days Tristanne rents the machine, which equation can be used to find the value of d?
23 d = 137
23 d + 45 = 137
45 d = 137
45 d + 23 = 137
Answers
Answer:
23d + 45 = 137
Explanation:
Since it is $23 per day, that dollar amount must be associated with a variable that multiples it per day that it is rented. Finally, you need to add the one time $45. This equation can then be used to find how many days it was rented for.
23d + 45 = 137
23d = 92 (Subtract 45 from both sides)
d = 4 (Divide by 23 on both sides)
The rug-cleaning machine was rented for 4 days. You found this using the equation: 23d + 45 = 137
Answer:
its b
Step-by-step explanation:
i got it correct edge2020
The measure of two angles are (5x + 24)° and (9x - 17)°. What is the value of x if these angles are congruent?
Answers
11 if x = 4
Answer:
the answer is 10.25
Step-by-step explanation:
The area of a parallelogram is 42 square inches. The base of the parallelogram is 6 inches. What is the height of the parallelogram? Explain how you can use the formula for the area of a parallelogram to solve the problem.
Answers
Answer:
7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
How many eighteens are there in 8/9?
Answers
Answer:
4/81
Step-by-step explanation:
8/9 divided by 18
what is the 385/6 as a proper fraction
Answers
Answer:
Step 1 - Find Whole Number
Calculate out how many times the denominator goes into the numerator. To do that, divide 385 by 6 and keep only what is to the left of the decimal point:
385 / 6 = 64.1667 = 64
Step 2 - Find New Numerator
Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.
385 - (6 x 64) = 1
Step 3 - Get Solution
Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer. 385/6 as a mixed number is:
64 1
___
6
Step-by-step explanation:
9a4 + 12a²b2 + 464
Which of the following is equivalent to the
expression shown above?
4
A) (3a2 +2623
B) (3a + 2b)*
C) (9a+4622
D) (9a + 4b)4
Answers
Answer:
c
Step-by-step explanation:
Which diagram suggests a correct construction of a line that is parallel to given line I and passes through given point Q?
Answers
option D is the correct answer
Consider the function represented by the equation y-6x-9=0. Which answer shows the equation written in
function notation with x as the independent variable?
YUX) = 6x+9
10 = x+
10 = 6 +9
Answers
Answer:
F ( x ) = ( 6 x +9 )
Step-by-step explanation:
Change to slope-intercept form y = mx + b:
y - 6x - 9 = 0
y = 6x + 9
As function notation where x is the independent variable: f(x) = 6x + 9
Five days a week, from Monday to Friday, Betsy takes the bus to school. Each day she has a probability of 90% of taking bus 1. If she does not take bus 1 then she will take bus 2.
What is the probability that she will take bus 1 on all five days?
Answers
Answer:
0.59
Step-by-step explanation:
Given that :
Probability of taking bus 1
P(b1) = 90% = 0.9
What is the probability that she will take bus 1 on all five days?
Five days from Monday to friday:
On Monday : p(b1) = 0.9
On Tuesday : p(b1) = 0.9
On Wednesday : p(b1) = 0.9
On Thursday : p(b1) = 0.9
On Friday : p(b1) = 0.9
Here we have an independent event:
Hence, probability of taking bus 1 on all five days :
(0.9 * 0.9 * 0.9 * 0.9 * 0.9)
= 0.59049
= 0.59
"7xy+2x-y+5y-xy combine all like terms and rewrite the expression above "
Answers
Answer:
6xy+2x+4y
Step-by-step explanation:
Hope this helped
What can you put between a 3 and a 4 so that the number is greater than 3, but less than 4?
Answers
10 to power 7 decimal
Answers
Answer:
10 mil
Step-by-step explanation: 10x10x10x10x10x10x10= 10,000,000
It costs twelve dollars to get in to the fair. Tickets for rides cost extra and are d dollars each
If Tyra buys 20 tickets, how much would it cost her for the fair?
20 d - $12
$12 d + 20
$12-20 d
$12 + 20 d
Answers
Answer:
$12 + 20d
Step-by-step explanation:
What is the product of 0.04 and 0.2?
A:0.008
B:0.81
C:0.08
D:0.8
Answers
Answer:
A. 0.008
I hope this helps!
Answer:
A. 0.008
Step-by-step explanation:
Product mean you multiply, so you multiply 0.04 and 0.2 and you get 0.008
0.04 x 0.2 = 0.008
Evaluate.
2⋅((42)−1)
Answers
Answer:
Hi there!
Your answer is:
Question was unclear! See below for answer possibilities!
Step-by-step explanation:
IF "-1" MEANS MULTIPLY BY NEGATIVE 1
2((42) -1 ))
2(-42)
-84IF "-1" MEANS SUBTRACT 1
2((42)-1)
2(41)
82Hope this helps
The width of a rectangle is 9 cm less than twice the length. the perimeter is 72 cm. What is the length and width
Answers
9 times 9=72
Step-by-step explanation:
if if the width is 9 then the length is 9 because 9 times 9 equals 72
Answer:
The length is 15
The width is 21
Step-by-step explanation:
Say the length of the rectangle is x.
Then, the width would be 2x-9.
You can use this to make the equation
x+x+2x-9+2x-9=72
6x-18=72
6x=90
x=15
2x-9=30-9=21
Therefore,
The length is 15
The width is 21
Find the value of p. p − 1 = 5 p + 3p − 8
Answers
Answer:
p = 1
Step-by-step explanation:
[add like terms]
p - 1 = 8 p - 8
[add 8 to both sides]
p + 7 = 8 p
[subtract p from both sides]
7 = 7 p
[divide each side by 7]
p = 1
Answer:
P=1
Step-by-step explanation:
collecting like terms we have
p - 5p - 3p = -8 + 1
-7p = -7
divide both sides by -7
p = 1