Answer:
[tex]\left|2x-6\right|<4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:1<x<5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(1,\:5\right)\end{bmatrix}[/tex]
Therefore, the 3rd graph represents the solutions to inequality.
Please also check the graph below.
Step-by-step explanation:
Given the expression
[tex]|2x\:-\:6|\:<\:4[/tex]
[tex]\mathrm{Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a[/tex]
[tex]-4<2x-6<4[/tex]
[tex]2x-6>-4\quad \mathrm{and}\quad \:2x-6<4[/tex]
condition 1
[tex]2x-6>-4[/tex]
Add 6 to both sides
[tex]2x-6+6>-4+6[/tex]
[tex]2x>2[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}>\frac{2}{2}[/tex]
[tex]x>1[/tex]
condition 2
[tex]2x-6<4[/tex]
Add 6 to both sides
[tex]2x-6+6<4+6[/tex]
[tex]2x<10[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}<\frac{10}{2}[/tex]
[tex]x<5[/tex]
combine the intervals
[tex]x>1\quad \mathrm{and}\quad \:x<5[/tex]
Merging overlapping intervals
[tex]1<x<5[/tex]
Thus,
[tex]\left|2x-6\right|<4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:1<x<5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(1,\:5\right)\end{bmatrix}[/tex]
Therefore, the 3rd graph represents the solutions to inequality.
Please also check the graph below.
Ben walked 4 miles in a half-hour. Find out how many miles he can walk in an hour
Answer:
8
Step-by-step explanation:
4 miles= 30= half hour x 2 equals 60= hour so its basic math 4 x 2
Original Grade: 80
New Grade: 100
Find The Percent Of Increase
?%
I really need to know
Answer:
20%
Step-by-step explanation:
What is equivalent to (6xp)+3
Answer:
1(6xp+3)
Step-by-step explanation:
Multiply
PLEASE HELP FAST!
Determine the domain of the relation graph below.
A.) (-4,2]
B.) [-4,2)
C.) [-1,5)
D.) [1,5]
Answer: The answer is option A.
Step-by-step explanation: A white, non colored dot means always use a ( bracket. A solid, colored dot means use the [ bracket. Now it's farthest left at -4, and farthest right at 2. Thus, option A
pls answer fast!!! HURRY
Which term can be added to the list so that the greatest common factor of the three terms is 12h3?
36h3, 12h6, __________
6h3
12h2
30h4
48h5
Answer:
The term that can be added to the list so the GCF is 12h3 would be 48h5.
I hope this helped!! :)
Provide two examples that support the healthcare industry’s reliance on metrology for accuracy of instruments.
Answer:
because they need to measure the dosages for the patients.
And because they need to know how to accurately measure the patients height, and weight so they know what dosage to give them.
Step-by-step explanation:
plz mark brainliest
60 students in a school election 45% voted for aliyah. how many votes did aliyah get?
Answer:
27
Step-by-step explanation:
60 times .45 equals 27
find the domain of the following equations and solve them
Answer:
Domain → x > 0
Solution → x = 100
Step-by-step explanation:
Given equation is,
[tex]x^{0.5\text{logx}}=0.01x^2[/tex]
Since, log of any number 'x' is defined when x > 0
Therefore, domain of the equation → x > 0
By taking log on both the sides of the equation,
[tex]\text{log}(x^{0.5\text{logx}})=\text{log}(0.01x^2)[/tex]
0.5(logx)(logx) = log(0.01) + log(x²)
0.5(logx)²= -2 + 2log(x)
Let log(x) = a
Then the equation becomes as,
0.5a² = -2 + 2a
0.5a² - 2a + 2 = 0
a² - 4a + 4 = 0
(a - 2)² = 0
a = 2
Since, a = log(x)
log(x) = 2
x = 10²
x = 100
Therefore, solution of the given equation is x = 100.
[tex]\boxed{\boxed{\pink{\tt \leadsto The \ domain \ of \ x \ is \ (0,\infty ). }}}[/tex]
Step-by-step explanation:A equation is given to us and need to find the domain of the equation . So , given equation is ,
[tex]\bf\implies x^{0.5\:log\ x } = 0.01x^2 [/tex]
Now , let's simplify this equation to find the domain of x .
[tex]\bf\implies x^{0.5\:log\ x } = 0.01x^2 \\\\\bf\implies x^{0.5\:log\ x } -0.01x^2 =0 \\\\\bf \implies x^{log \:x^{\frac{1}{2}}} - 0.01x^2=0 \\\\\bf\implies x^{log \ \sqrt{x}} - 0.01x^2=0 [/tex]
Now set the argument in log( √x) Greater than or equal to zero to see where the expression is defined. Since the value of log is non - negative.
[tex]\bf\implies \sqrt{x} > 0 \\\\\bf\implies (\sqrt{x})^2>0^2 \\\\\bf\implies x>0\\\\\bf\implies \boxed{\red{\bf x \in ( 0, \infty ) }}[/tex]
In set builder Notation we can write as ,
[tex]\boxed{\red{\bf \{ x | x > 0 \} }}[/tex]
Hence the domain of x is ( 0 , ∞ ) .PLZ HELP I NEED TO PASS MATH LOL, What is the value of the expression (−10)(−7)? Enter your answer in the box.
70
Two negatives make a positive
Ben's car needs work. The mechanic charges $140 for parts plus $48 per hour for
labor. The mechanic said the bill will be at least $300. What is the possible number of
hours that the mechanic will work on Joe's car? Use an inequality to solve this problem.
the mechanic will work at least 6hours
What is the perimeter of the shape below?
Answer:
what are the units?
Step-by-step explanation:
depends on the side of 1 square
if it is 1 unit, perimeter is 22 units
show your solution
find the 6 and 7 term
Answer:
1/6 and 1/7
Step-by-step explanation:
1/6 and 1/7
As we can see the denominator keeps increasing by 1 but the numerator stays as 1 :
1/1 or 1 is the first term
1/2 is the 2nd term
1/3 is the 3rd term
So :
1/6 is the 6th term
and 1/7 is the 7th term
If FGH=QRS, find the measure of Q.
Answer: 28
Step-by-step explanation: i got the same test
Layton conducts an experiment throughout the school year to determine the most common answer
choice used by teachers at his school. The data he collected is shown in the table.
Which of the following is a valid conclusion based on the data he collected?
A. A student would be equally likely to select answer choice C as they would to select answer
choice A and D
B. A student would be equally likely to select answer choice A and B as they would to select
answer choice C
C. A student would be twice as likely to select answer choice C than answer choice A
D. A student would be less likely to select answer choice B than answer choice A
Answer:
pick a because the data is better for that chart
i need help can someone figure these out?
Answer:the 2nd one is 30000 divided by 2000 is 15
Step-by-step explanation: so 15 minutes til they crash the plane
Answer:
1) y= 25x+50
2) y= -2,000x+30,000
3) y= 1.5x+5
Step-by-step explanation:
In each equation, there is a set amount (50 dollars, 30,000 feet, and 5 centimeters) and an amount that is influenced by another variable such as time(25 dollars, 2,000 feet, 1.5 centimeters). Hope this helped :)
multiple choice, plz help
What is the new position of the drone relative to the top of the building?
Answer:
The new position of the drone relative to the top of the building would be:
[tex]-12\frac{5}{8}[/tex]Hence, option (B) is correct.
Step-by-step explanation:
Given that a drone flies up [tex]75\frac{3}{4}[/tex] ft above the top floor of a building.
As it flies away from the building and goes down [tex]117\frac{7}{8}[/tex].
Thus, the new position becomes
[tex]75\frac{3}{4}-117\frac{7}{8}[/tex]
[tex]=\frac{303}{4}-117\frac{7}{8}[/tex]
[tex]=\frac{303}{4}-\frac{943}{8}[/tex]
The LCM of 4,8: 8
Adjusting fractions based on LCM
[tex]=\frac{606}{8}-\frac{943}{8}[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]=\frac{606-943}{8}[/tex]
[tex]=-\frac{337}{8}[/tex]
Converting improper fractions to mixed numbers
[tex]=-42\frac{1}{8}[/tex]
THEN IT RISES ANOTHER [tex]29\frac{1}{2}\:\:[/tex] and HOVERS onwards:
As the drone rises again another [tex]29\frac{1}{2}\:\:[/tex] ft, the final position can be calculated by adding [tex]29\frac{1}{2}\:\:[/tex] ft in [tex]-42\frac{1}{8}[/tex] ft.
i.e
[tex]-42\frac{1}{8}+29\frac{1}{2}[/tex]
[tex]=-\frac{337}{8}+29\frac{1}{2}[/tex]
[tex]=-\frac{337}{8}+\frac{59}{2}[/tex]
The LCM of 8, 2: 8
Adjusting fractions based on LCM
[tex]=-\frac{337}{8}+\frac{236}{8}[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]=\frac{-337+236}{8}[/tex]
[tex]=-\frac{101}{8}[/tex]
Converting improper fractions to mixed numbers
[tex]=-12\frac{5}{8}[/tex]
Therefore, the new position of the drone relative to the top of the building would be:
[tex]-12\frac{5}{8}[/tex]Hence, option (B) is correct.
How many different axes of symmetry does this parallelogram have?
A. 0
B. 1
C. 2
D. 4
Answer:
B. 1
Step-by-step explanation:
Given parallelogram has only one axis of symmetry.
The distance between two towns is 120km. There are approximately 8 km in 5 miles. What is the approximate distance in miles between the two towns
1. 0.04
2. 0.15
Explanation:i just finished that assignment for properties of probability distributions.
i hope this is what you were looking for!
6. 0.3k - 4m (k=20 and m= -2)
The value of the expression 6 + 0.3k - 4m at k = 20 and m = -2 is 20.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, An expression 6 + 0.3k - 4m, The value of the expression can be obtained at k = 20 and m = - 2 if we simply replace this numerical values of k and m which is,
= 6 + (0.3)×20 - 4(-2).
= 6 + 6 + 8.
= 20.
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ2
January 30, 2019 was the coldest day in Minneapolis-St paul i’m over 20 years the lowest temperature recorded that day was -28f the warmest temperature was 15 higher
Answer:
Whats the question?????
Lilian is packing gifts for the needy. She has 240 toys and 180 books to pack
Answer: okay what’s the question?
Step-by-step explanation:
Answer:
she will have to pack 420 items
she could pack 12 items in 35 boxes
Step-by-step explanation:
if you could give the whole question i could help with that
Find the values of r and t.
Solve the following system by substitution:
y = -1x - 5
4x - 8y = 4
Answer:
x = - 3
y = - 2
Step-by-step explanation:
We have y = -1x - 5, so substitute that for y in the second equation:
4x - 8y = 4
4x - 8(-1x - 5) = 4
Now, solve for x:
4x + 8x + 40 = 4
12x + 40 = 4
12x = - 36
x = -3
Now, substitute - 3 in for x in the first equation:
y = -1x - 5 = -1(-3) - 5
y = 3 - 5
y = -2
You can check that these are right by substituting them into:
4x - 8y = 4
4(-3) - 8(-2) = 4
-12 + 16 = 4
4 = 4
So, you know that you solved correctly.
what is the slope of the line please help thank you (picture)
Answer: D
Step-by-step explanation: just think rise over run, everytime it hits a cross in the graph count how many tiles there were between crosses and put the y diffrence on top of the x difference
The area of the triangle is 20cm² and the width is 10cm.What is the height of the triangle? Can someone explain it To me step By step?
Answer:
4
Step-by-step explanation:
The formula of an area of a triangle is:
area = height × width ÷ 2
We can put in the values of the area and width first.
20 = height × 10 ÷ 2
20 = height × 5
Shift the (×5) to the left-hand side of the equation, making it (÷5).
20 ÷ 5 = height
height = 4
Answer:
A=1/2b×h
we have,
b=10 cm
A=20cm2
1/2b×h=20cm2
1/210×h=20
5h=20
h=4cm
What are the roots of the equation x2 – 10x + 21 = 0?
Answer:
Step-by-step explanation:
H
Which of the following equations has a slope of -3 and a y-intercept of 8?
y=−8−3x
y=8−3x
y=8x−3
y=−8x−3
PLEASE HELP IM GONNA FAIL SENIOR YEAR
Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B are mutually exclusive, then
P(A or B) = 0
P(A and B) = 0.16
P(A and B) = 0
P(A or B) = 0.16
both Option a and Option b are true.
By definition, events that are mutually exclusive can not occur together. This means that the probability of event A and event B occuring together is 0
Hello, I am struggling a bit with this question please help
Answer:
-7.4
-2/3
⅔-0.1
0
4/8
2.7
5 1/9
29/4
Step-by-step explanation:
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
Answer:
Step-by-step explanation:
first put everything in decimal
-0.1,2.7,0.25,7.25,0,-7.4,5.667
lowest to greatest
-0.1,-7.5,0,0.25,2.7,5.667,7.25
-0.1,-7.25,0,4/8,2.7,51/9,29/4