The absolute value of x in the inequality I 2x+1 I +2 I >1 showing the step by step solution is x > 2
What is absolute value?The absolute value of a real number x can be defined as the non-negative value of x without regard or consideration to its sign.
It is also known as the modulus of a number.
It is sometimes described as the magnitude of a real number regardless of its sign.
It is important to note that the absolute value must take a positive sign
Given the expression;
I I 2x+1 I +2 I > 1
expand the modulus value
2x + 1 + 2 > 1
collect like terms
2x > 1 + 1 + 2
Add like terms
2x > 4
Make 'x' the subject
x > 4/ 2
x > 2
Thus, the absolute value of x is x > 2
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What is
-10x -1 > 39
Answer:
Step-by-step explanation:
x<−4
hope this helps
Solve by taking square roots (r+8)(4r-1)=0
Answer:
The answer is r={-8,1/4}
May someone help me out on this question?
Answer:
y = 2 for x < 0
x for 0 ≤ x < 3
3 for x ≥ 3
Step-by-step explanation:
From the graph attached,
Equation of line (1),
y = 2
Where x < 0
Let the equation of line (2) is,
y = mx + b
y-intercept 'b' = 0 [line (2) passes through origin]
Slope of the line 'm' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{3}{3}[/tex]
= 1
Therefore, equation of line (2) will be,
y = x
where 0 ≤ x < 3
Equation of line (3) will be,
y = 3
Where x ≥ 3
Therefore, piecewise linear function will be,
y = 2 for x < 0
x for 0 ≤ x < 3
3 for x ≥ 3
Use the information to answer the question.
The equation y = 30x represents the distance, y, in miles, a domestic cat can run after hours. The table shows the distance, y, in miles, a domestic dog can run after x
hours.
Time(in hours)
0.5
1
2
Distance(in miles)
17.5
35
70
Part A
Based on this information, which statement is true?
1.The cat and dog run the same distance every hour
2.The cat runs more miles per hour than the dog
3.The distances the dog and cat run every hour cannot be compared.
4.The dog runs more miles per hour than the cat
.
Answer:
An elk was clocked running 45 miles per hour. Which equation shows the relationship between the distance, y, and time, x, that the elk ran? ... 17 QuestionsShow answers. Question 1. SURVEY ... Which mapping diagram represents a relationship that is a function? ... The equation y = 30x + 50 gives the cost y after x months.
Step-by-step explanation:
Cal is packing his suitcase to go on a trip. He wants to pack 4 pairs of pants chosen from the 8 pairs of pants in his closet and 5 shirts chosen from the 9 shirts in his closet. In how many different ways can this be done?
Answer:
8820 ways
Step-by-step explanation:
Given that :
Selecting 4 pairs of pant from 8 available and selecting 5 shirts from 9 available
Using combination :
4 pants from 8 = 8C4
5 shirts from 9 = 9C5
Recall:
nCr = n! / (n-r)! r!
8C4 * 9C5 = [8! /(8-4)!4!] * [9! /(9-5)!5!]
8C4 * 9C5 = (8! /4!4!) * (9! /4!5!)
8C4 * 9C5 = 70 * 126
8C4 * 9C5 = 8820 ways
Madison bought a dress priced at $98.25. The dress was 20% off. If she purchases the dress, what would the discounted price be?
A. $15.89
B. $78.25
C. $19.65
D. $78.60
Answer:
C. $19.65
Step-by-step explanation:
You have to find 20% of $98.25
This is equal to,
20% * $98.25 Because of usually means multiplication
= .20 * 98.25 Because .20 = 20%
= 19.65!
Write an equation for the line in point slope form, that passes through the following points
(3,4) (6,10)
The equation pf a line in point slope form is as follows:
y - 4 = 2(x - 3)
How to find equation of a line in point slope form?The equation of a line in point slope form can represented as follows:
The line passes through (3, 4)(6, 10).
Therefore, the point slope form is as follows:
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are the coordinatesTherefore,
m = 10 - 4 / 6 - 3
m = 6 / 3
m = 2
Hence, the equation pf a line in point slope form is as follows:
y - 4 = 2(x - 3)
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Please help stick on this !!!!!
Answer:
a) The new ordered pairs are X' (-3, -7), Y' (-2, -10), Z' (-5, -2)
b) The new ordered pairs are X' (6, 9), Y' (7, 12), Z' (4, 4)
Step-by-step explanation:
If the point (x, y) reflected across the x-axis, then its image is (x, -y), which means to reflect a point across the x-axis, change the sign of its y-coordinateIf the point (x, y) translated h units to the right and k units up, then its image is (x + h, y + k), which means add its x-coordinate by h and add its y-coordinate by k∵ X = (-3, 7), Y = (-2, 10), and Z = (-5, 2)
∵ The points reflected in the x-axis
→ Change the signs of the y-coordinates of the 3 points
∴ X' = (-3, -7), Y' = (-2, -10), and Z' = (-5, -2)
a) The new ordered pairs are X' (-3, -7), Y' (-2, -10), Z' (-5, -2)
∵ X = (-3, 7), Y = (-2, 10), and Z = (-5, 2)
∵ The points translated to be (x + 9, y + 2)
→ That means add the x-coordinates by 9 and y-coordinates by2
∴ X' = (-3 + 9, 7 + 2), Y' = (-2 + 9, 10 + 2), and Z' = (-5 + 9, 2 + 2)
∴ X' = (6, 9), Y' = (7, 12), and Z' = (4, 4)
b) The new ordered pairs are X' (6, 9), Y' (7, 12), Z' (4, 4)
Gabriel was given a gift card for a coffee shop. Each morning, Gabriel uses the card to
buy one cup of coffee. Each cup of coffee costs $4 and the original amount of money
on the gift card was $20. Make a table of values and then write an equation for A, in
terms of x, representing the amount money remaining on the card after buying x
cups of coffee.
Number of Cups of Coffee Amount of Money Remaining on Card
Answer: A =
YOU GET 60 POINTS!! Ronald rents a car from Cheap Rent-a-Car for $25 plus $0.05 per mile. Dixon rents a car from Great Cars for $40 plus $0.03 per mile. How many miles must they both drive for their rental fees to be the same?
Answer:
750 miles
Step-by-step explanation:
25+0.05x=40+0.03x
0.02x=15
x=750
Question in image. :)
a. f(a) =5a+12
we have 1. a=6
Therefore, where ever we find a we'll substitute in 6
f(6) =5(6) +12
6f=30+12
6f=42
so therefore 1. a=6 will match c on the right
2. a=2
f(2) =5(2) +12
2f = 10+12
2f = 22
therefore 2. a=2 will match a on the right
3. a=4
f(4) =5(4) +12
4f=20+12
4f=32
therefore 3. a=4 will match d on the right
4. a=5
f(5) =5(5) +12
5f=25+12
5f=37
therefore 4. a=5 will match b on the right
Determine the solution for the system of equations: y = -2x + 1 3x - 2y = 5 A. (1, -1) B. (-1, 1) C. (-1, 0) D. No Solution
Answer:
Step-by-step explanation: d
the smaller of two numbers is 2 less than 1/3 the larger. the sum of the two numberrs is 50 what is the value of the numbers
The smaller number is 14 and the larger number is 36.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let the smaller number would be x
And the larger number would be y
Given that the smaller of two numbers is 2 less than 1/3 the larger
So x - 2 = (1/3)y ⇒ 3x - 6 = y
The sum of the two numbers is 50
So x + y = 50
Substitute the value of equation 3x - 6 = y in the above equation,
⇒ x + 3x - 6 = 50
⇒ 4x = 50 + 6
⇒ x = 56/4
⇒ x = 14
Substitute the value of equation x = 14 in the equation x + y = 50,
⇒ 14 + y = 50
⇒ y = 36
Hence, the smaller number is 14 and the larger number is 36.
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Sarah is buying roses and carnations to make center pieces for prom, Roses, x, cos
$3 each and carnations, y, cost $1 each. She can spend no more than $75 on the
Flowers. Which graph represents the solution to the problem?
Answer: Third option.
Step-by-step explanation:
We have the variables:
x = number of roses that Sarah buys
y = number of carnations that Sarah buys.
Each rose costs $3, then the price for x roses is: x*$3.
Each carnation costs $1, then the price for y carnations is: y*$1.
The total price will be:
$3*x + $1*y
And she can spend no more than $75, then we have the inequality:
$3*x + $1*y ≤ $75
Writing this as a line, we have:
y ≤ 75 - 3*x
Then the graph of this will be:
A solid line with a negative slope and the shaded part will be below that line.
The value of y goes between 0 and 75.
The value x goes between 0 and the value of x such y = 0, this is:
y = 0 ≤ 75 - 3*x
3*x ≤ 75
x ≤ 75/3 = 25
Then the value of x goes between 0 and 25.
The correct option will be the third one.
The correct graph is option 3.
Given,
Sarah buys x no. of roses and y no. of carnations.
The cost of each roses be $3, so cost of x roses be 3 x .
And the cost of each carnations be $1, so cost of y carnations be y.
The total cost will be [tex]3x + y.[/tex]
But as given in question she can spend no more than $75, so we have the inequality [tex]3x + y \leq 75[/tex].
Writing the above equation as a line we have [tex]y\leq 75-3x[/tex].
So graph of above line will be a solid line with a negative slope and the shaded part will be below that line so the value of y goes in between 0 and 75.
Now, value of x when y is o will be calculated from [tex]y\leq 75-3x[/tex].
[tex]0\leq 75-3x[/tex]
[tex]3x\leq 75[/tex]
[tex]x\leq \frac{75}{3}[/tex]
[tex]x\leq 25[/tex]
Now we have values of x in between 0 and 25.
here we have y in between 0 and 75 with a negative slope and x in between 0 and 25. so the shaded part will be below that line goes in between 0 and 75 on y axis . option 3 has shaded part in between 0 and 75 on y axis so the correct option is 3.
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Which statistic (mean, median, or mode) is most appropriate in each of the following situations?
Tables in the dining hall are numbered 1 through 12 for students who eat there. The principal calls
out a number for the table that will go through the buffet line first. The other tables followin
order of the table numbers. One student is sure the principal calls certain tables more often. She
keeps track of which numbers are called over a 21-day period.
• Mean
• Median
• Mode
The statistic which is most appropriate in the given situation is Mode.
Mode is defined as the statistical method which gives the value of an entity that occurs the greatest number of times in a set of values of data. For example, if the marks of 5 students scored in a test are given as 35, 45, 35, 35, 50 then the mode of the given set of data is 35 as it occurs the maximum number of times. Here, the student is sure that the principal will call out the name of a certain number of tables very often. She keeps track of the tables over 21 days and as the table number was called out for the maximum number of times within 21 days the value of the table number will be given by the Mode of the data.
Thus, the most suitable method is Mode.
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how do you do this ??? pls helpppp
Answer: m<2 = 83 degrees
Step-by-step explanation:
The sum of angles on a straight line= 180 degrees
97 + <2 = 180
<2= 180 -97
= 83 degrees
Question in image :)
Answer:
A
x=> -6 is the inequality that represents the answer best.
Please help due in 10 minutes
+20 points if it’s right
Wrong answers will be blocked
Answer:
Step-by-step explanation: for the first picture
a, d,
second picture
1.DA = ZW
2. CB=YX
3. XY = BC
4. 8
sorry not sure about 5 and 6 though
what is the equation of the line that passes through the point 4,8 and has a slope of 3/2
Answer:
[tex]y = \frac{3}{2} x + 2[/tex]
Step-by-step explanation:
It gives us the slope in the question (3/2), so we can write an equation that looks like this:
[tex]y = \frac{3}{2} x + b[/tex]
To find the y-intercept we can plug the point (4,8) in the equation. Remember that 4 is x and 8 is y.
[tex]8 = \frac{3}{2} (4)+ b[/tex]
Now solve for b
[tex]8 = \frac{12}{2} + b\\8 = 6 + b\\2 = b[/tex]
Next, write the full equation using the slope and y-intercept:
[tex]y = \frac{3}{2} x + 2[/tex]
I hope this helps!!
- Kay :)
Answer:
[tex]y=\frac{3}{2}x+2[/tex]
Step-by-step explanation:
The image below shows proof that the equation [tex]y=\frac{3}{2}x+2[/tex] is the line that passes through point (4, 8) and has a slope of [tex]\frac{3}{2}[/tex].
Hope this helps! :)
A train is traveling at 60 km down the tracks, it continues traveling for 6
hours, how far did the train travel? *
A. 10 km
B. 120 km
C. 360 km
D. 12 km
please help with this!!
Answer:
the answer is a
Step-by-step explanation:
because 60/6= 10
A brand new TV bought on Black Friday was $599. The value of the TV
depreciates by 22% each year. When will the value of the TV be less than
$240?
A store has 7 red shirts, 15 black shirts, 13 white shirts, and 5 green shirts. Select the portion of the shirts that are black. Mark all that apply. *
Answer:
8/5 portion of black shirt is there
.6203 rounded to the nearest tenths
Answer:
.6200
Step-by-step explanation:
3 rounds down to 0.
Answer: 0.62
Step-by-step explanation: 0.62
what would -3/4 look like as a slope?
How can I obtain the graph of f(x) = -1/2(x + 2)^2 - 5 from the graph of g(x) = x^2? please show work
Answer:
read the full answer
Step-by-step explanation:
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Horizontal Shift: Right 2 Units
Vertical Shift: Up 5 Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: Stretched
TO VIEW GRAPH TRY M-A-T-H-W-A-Y
Kelly is knitting a scarf for her brother. It took her 1/3 hour to knit 3/8 foot of the scarf. What is Kelly’s knitting speed, in feet per hour?
1. 1 1/8 per hour
2. 3 feet per hour
3. 2 1/2 feet per hour
4. 4 1/2 feet per hour
it's 1 1/8 per hour.
Step-by-step explanation:
if it takes 1/3 hour to get 3/8, then if you add 6/8 which is the other 2/3 hour. you get 1 1/8
Where should you plot the ordered pair (3,4) in relation to the origin?
Answer:
3 goes on the x acsis 4 goes on the y axsis
Okay so I'm working on this assignment and I see this question and I'm very confused, aren't the first 2 answers the same and the next 2 are? I am very confused...
Answer:
actually no.
Step-by-step explanation:
I assume you know the 4 inequalites:
The 4 Inequalities
Symbol Words Example
> greater than x+3 > 2
< less than 7x < 28
≥ greater than or equal to 5 ≥ x−1
≤ less than or equal to 2y+1 ≤ 7
The "open circle" represents less than or greater than, and the "closed circle" represents greater than or equal to or less than or equal to.
Hope it helps! Have a great day! :) let me know if it helped
Answer:
No
Step-by-step explanation:
The first and 2nd answer are different because in the first one the circle is open and in the 2nd one the circle is closed. When the circle is open it means that the number that the circle is on is not a part of the asnwer. This is represented by < or > signs. When the circle is closed it means the number is included in the answer. This is represented by the [tex]\leq or \geq[/tex] symbol.
Tabby read 254 pages in 8 days. What is her unit rate in pages per day?
Answer:
31.75 round it off to 32 pages per day
Step-by-step explanation:
254/8=31.75 but you cant but a decimal so its 32
statistical models predict that the price (in dollars) of a 500 gb hard drive will change according to the function p(t)
The required expression that gives the number of months t in terms of the price p is, t(p) =√1/2 (600-p).
The given function is p(t) = 600 − 2t².
We need to find the expression that gives the number of months t (passed since January 1) in terms of the price p.
What is the function?Functions are the fundamental part of calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h.
Here, the expression that gives p in terms of t is, p(t) = 600 − 2t²----(1)
Where p represents the price and t represents the number of months t (passed since January 1).
From equation (1),
p= 600 − 2t²
⇒2t²=600-p
⇒t²=1/2 (600-p)
⇒t=±√1/2 (600-p)
But, the number of months can not be negative, t=√1/2 (600-p).
Since in this expression t is in the term of p.
Hence, the required expression that gives the number of months t in terms of the price p is, t(p) =√1/2 (600-p).
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Your question is incomplete, probably the complete question/missing part is:
Statistical models predict that the price (in dollars) of a 500 GB hard drive will change according to the function p(t) = 600 − 2t², where t is the month. Which expression gives the number of months t (passed since January 1) in terms of the price p?