Answer:
When solving a compound inequality, you can express the solution in two different ways: using a union or intersection.
Using a union:
A union represents the solutions that belong to either one inequality or the other, or both. You can express a union using the symbol "or," or by writing the solutions for each inequality separately and combining them using a "union" symbol (∪). For example, if you have the compound inequality "x > 2 or x < -3," you can express the solution as "x ∈ (-3, 2) ∪ (-∞, -3) ∪ (2, ∞)."
Using an intersection:
An intersection represents the solutions that belong to both inequalities. You can express an intersection using the symbol "and," or by writing the solutions for each inequality separately and combining them using an "intersection" symbol (∩). For example, if you have the compound inequality "x > 2 and x < -3," you can express the solution as "x ∈ (-3, 2) ∩ (-∞, -3) ∩ (2, ∞)."
Which method you use to express the solution will depend on the specific inequalities and the type of solutions you are looking for. It is important to carefully consider the inequality symbols (>, <, ≥, ≤) and the use of "and" or "or" in order to determine the correct solution.
When solving a compound inequality, the solution can be expressed in one of two ways: as an interval or as a union of intervals.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
An interval is a set of all real numbers between two given numbers, and is written in the form (a, b) or [a, b], where a and b are real numbers, and a < b. If a and b are included in the interval, then the interval is written as [a, b]; if a and b are not included in the interval, then the interval is written as (a, b).
A union of intervals is a combination of two or more intervals, and is written in the form (a, b) ∪ (c, d) or [a, b] ∪ [c, d], where a, b, c, and d are real numbers, and a < b and c < d.
When solving a compound inequality, it is important to first simplify the inequality by combining like terms, isolating the variable on one side of the inequality, and combining any separate inequalities into a single inequality. Then, the solution can be found by graphing the inequality on a number line, and shading the portion of the number line that represents the solution.
Once the solution is found the solution can be expressed either as an interval or as a union of intervals depending on the inequality. For example, if the inequality is x>1 and x<3, then the solution would be expressed as (1,3) and this is an example of an interval. If it's x>1 and x≥3 then the solution would be expressed as (1,3] U [3,∞) and this is an example of union of intervals.
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Solve 10ax + 9b = 8cx + d for x
Answer:
Step-by-step explanation:
Step 1: Subtract 8cx from both sides of the equation to get
10ax + 9b - 8cx = d
Step 2: Subtract 9b from both sides of the equation to get
10ax - 8cx = d - 9b
Step 3: Multiply both sides of the equation by (-1/10) to get
-8cx/10 = -(d - 9b)/10
Step 4: Add (d - 9b)/10 to both sides of the equation to get
-8cx/10 + (d - 9b)/10 = 0
Step 5: Simplify the left side of the equation to get
x = (9b - d)/80
Therefore, x = (9b - d)/80 is the solution to the equation 10ax + 9b = 8cx + d.
a sector of a circle of radius 10cm has an area of 25cm^2 find the angle at the centre of the circle ( take TT = 3.14) brainly
The angle at the center of the circle will be;
⇒ θ = 0.5 radian
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
A sector of a circle of radius 10 cm and has an area of 25 cm².
Now,
Since, We know that;
⇒ A = 1/2 r²θ
Where, A is area of circle , r is radius of circle and θ is the angle at the center of the circle.
Here, A sector of a circle of radius 10 cm and has an area of 25 cm².
Substitute all the given values, we get;
⇒ A = 1/2 r²θ
⇒ 25 = 1/2 × 10² × θ
⇒ 25 = 50 × θ
⇒ θ = 25 / 50
⇒ θ = 0.5 radian
Thus, The angle at the center of the circle = 0.5 radian
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Choose Yes or No to tell whether the expression represents a 20% discount off the price of an item that originally cost d dollars.
0.8d (yes or no)
d – 0.2 (yes or no)
d – 0.2d (yes or no)
1 – 0.2d (yes or no)
solve y=(1/2)x exponential graph
The value of the exponential graph y = ( 1/2 )ˣ is graphed
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
y = ( 1/2 )ˣ be equation (1)
On simplifying the equation , we get
y = 1 / (2ˣ)
Now , the graph of the function y = ( 1/2 )ˣ will be a slanting line which will not touch the x axis and passes through the point y = 1
The graph of the function y = ( 1/2 )ˣ is given below
Hence , the function is solved and the graph is plotted
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five less than four times a number is greater than or equal to 3. Is 2 a solution?
The statement five less than four times a number is greater than or equal
to 3 indeed has a solution results to 2.
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, A statement five less than four times a number is greater than or equal to 3.
Let, The unknown number be 'n'.
Therefore, The numerical form of the statement is,
4n - 5 ≥ 3.
4n ≥ 8.
n ≥ 2.
So, Yes 2 is a solution.
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9789 dived by 11 that’s it
Answer: 889.909090909
Step-by-step explanation:
divide
Identify two segments that are marked congruent to each other on the
diagram below. (Diagram is not to scale.)
LJ and LI are the figure's two congruent portions. Congruency means that the segments' sizes and shapes will be comparable.
What is congruency?Two triangles are said to be congruent to one another according to the Side-Angle-Side Congruence Theorem (SAS) if the included angle and corresponding two sides of one triangle match those of the other. Two sides that are being considered are determined to have an included angle. Therefore, using the SAS Congruence Theorem to prove that two triangles are congruent based on the fact that they have two pairs of corresponding sides and one pair of corresponding angles is insufficient.
given
The two segments LI and LJ that are marked in the illustration are congruent to one another.
Congruency means that the segments will have the same size and shape.
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A pizza shop sold 18 medium pizzas. The number of large pizzas sold was 3 times as many as the number of medium pizzas sold. How many pizzas did the pizza shop sell altogether?
Answer:
18 × 3 = 54
18 + 54 = 72
Therefore, the answer is 72.
Directions: Determine whether each relation is a function. Explain your answer.
X
12)
10)
#IN
13)
x
14)
15)
10
1
Therefore ,We can infer the following from the rule for when a relation represents a domain and range : 16) Is not a function. 18) Is not a function, while 17) Is one.
What is a domain?The domain of a function is the set of possible values that it can accept. The x-values of a function like f are represented by these numbers (x). A function's domain is the set of possible values on which it can be used. This set is the value that the function returns after the insertion of the x value. Y = f is the definition of a function with x as the independent variable and y as the dependent variable (x). A value of x is said to be in a function's domain if it can be successfully used to produce a single value of y by using the value of x.
Here,
we have that for this issue:
It is not a function in item 16 since input 5 is translated to outputs 2 and 4.
Item 17 is a function since each input is assigned to a single output.
It is not a function in item 18 since input -2 is mapped to outputs 13 and 15.
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Show how to use the unit rate to find the missing numbers on the double number line
Using the Double Number Line above, note that the unit that helps to find the missing numbers is given as:
3 and 915 and 518 and 624 and 827 and 9.What is a Unite Rate and How does it relate to a Double Number Line?Note that a unit rate is like a secret code to help you compare things. It helps you find missing numbers on a number line. For example, if 4 cookies cost $2, you can use the unit rate of $0.50/cookie to find out how much 8 cookies cost."
In the above case, we have several clues about the rate. The first relationship on the line is between 1 and 3.
But it only makes when we compare it to other iterations on the line such as 2 and 6.
Note that we can establish a relationship here which is that the greater number must be divided by three to get the lower number. That is:
3/3 = 1
6/3 = 2
Note well that the relationship between 0, 3, and 6 on the number line tell us that the upper units graduate in progressions of 3. that is:
0, 3, 6, 9, etc.
Thus, the missing numbers are:
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Lupe wrote two different fractions with the same denominator. both fractions were less than 1. can their sum equal? can their sum be greater than 1?
Answer: it depends on the number you took
Step-by-step explanation:
Bennet stated that the opposite of the opposite is always negative Kylie disagreed with bennet and stated that the opposite of the opposite of any number is always positive which erson is correct or are neither correct and explain how u know
Both Kylie and Bennet are correct.
Opposite of the opposite of a number is negative if the number is a positive number.
Opposite of the opposite of a number is positive if the number is a negative number.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number = x
The Opposite of x is -x.
Opposite of -x.
= -(-)
= x
Number = -x
The opposite of -x.
= -(-x)
= x
The opposite of x.
= -x
Thus,
Both the person is correct.
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16^x^2
= 8⁰
I’ll put a picture of it so you can better understand it. Also I’ll give you 30 points, so one of you better answer by 10:00 tomorrow.
Answer:
x=0
Step-by-step explanation:
[tex]16^{x^2}=8^0\\\\16^{x^2}=1\\\\x^2\ln(16)=0\\\\x^2=0\\\\x=0[/tex]
solve the equation a^2x^2 = abx + 2b^2 using completing the square method
The solution to the equation is
x = b/a ± √(b^2/a^2) / a.
What is the equation?Generally, To solve the equation using the completing the square method, we first move all the terms to one side of the equation by subtracting abx and 2b² from both sides, giving us:
a²x² = abx + 2b²
Which is
a²x² - abx - 2b² = 0
Next, we need to add and subtract a term so that the left side of the equation can be written as a perfect square.
We need to find the square of half of the coefficient of the x term, which is -ab/2a.
So we add and subtract (ab/2a)^2 = (b^2/a^2) on the left side of the equation:
a²x² - abx - 2b² + (b²/a²) - (b²/a²) = 0
This gives us the left side of the equation as
(ax - b/a)² = b²/a².
We can then take the square root of both sides:
ax - b/a = ±√(b²/a²)
Finally, we can add b/a to both sides to get the solution:
x = b/a ± √(b²/a²) / a
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The stranger decides to tell the captain his story. From the look on the stranger's face in Frankenstein, what kind of a story does the captain think he will hear?
A. A love story
B. A strange and harrowing story
C. A story that is funny and entertaining
D. A story that is boring and he really is not interested in hearing it
Answer: B strange and harrowing story.
Step-by-step explanation: Based on the description of the stranger's face in the novel, it is likely that the captain would expect the stranger to tell a strange and harrowing story. The stranger's face is described as "wild" and "ghastly," which suggests that the story he is about to tell may be disturbing or unsettling in some way. The captain may also expect the story to be emotionally intense, given the stranger's appearance and demeanor.
in a company, 60% of workers are women. if 800 people work on the company who aren't women, how many workers are there in all? use pencil and paper. show two different ways that you can solve this problem. how many workers in all?
Answer:
2000 workers
Step-by-step explanation:
All the workers: 100%
Women: 60%
Others: 40% = 800 workers
=> 1% of the workers: 800/40 = 20 workers
=> 100% = 20 x 100 = 2000 workers
(I can't think of another one)
At American Eagle a shirt is on sale from 25 to 15 what is the percent of change for the shirt
Answer:
Percent change = 15 - 25/25 × 100% = -10/25 × 100 = -40%
Step-by-step explanation:
Answer:
5 percent
Step-by-step explanation:
divide 25 by5 which gives you percent
PLEASE HURRY AND HELP!!!
Which of the following tables represents a linear relationship that is also proportional?
x y
0 3
3 6
6 9
x y
0 4
2 6
4 8
x y
0 0
6 3
12 6
x y
0 3
5 5
10 7
Table (x, y) equals (0, 0), (6, 3), and (12, 6) represents a linear relationship that is also proportional.
What are ratio and proportion?In its most basic form, a ratio is a comparison between two comparable quantities.
There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.
If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.
The first option is linear but not proportional as 3 ×2 = 6 and 6×2 = 12.
By observing the given options we conclude that the third option is linear and proportional as,
6 ÷ 2 = 3 and 12 ÷ 2 = 6.
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5+1r-2=9
Please explain step by step
Answer: 6
Step-by-step explanation:
Quintin raked his customer’s lawn for 1.2 hours. If Quintin charges $20 per hour, how much money did he make?
23.9 dollars I believe (I needa waste characters thi)
i dont understand this help
laucs ori nisiquiera estoy en universidad estoy en eseyo pe
alex, beverly and carl live on the same straight road. alex lives 12 miles from beverly and carl 4 mies from berve,y, how far does alex live from carl?
Helpp!!! Im stuck on this question!!!
for an inequality graph, if the line is dashed, that means that the border line is not part of the shaded region, so any points on it are not a solution of it, any points inside the shaded region or "true" region are solutions to it, only if the border line is solid then the border is part of the "true" region, Check the picture below.
What is equivalent to " two more than three times a number is seven
Answer:
if it’s asking for a numerical answer it would be 1.67
(Rounded to the nearest two)
Step-by-step explanation:
(Linear Relationships LC)
Which of the following tables represents a linear relationship that is also proportional?
x y
0 3
3 6
6 9
x y
0 4
2 6
4 8
x y
0 0
6 3
12 6
x y
0 3
5 5
10 7
PLEASE I NEED HELP ASAP
All the table show the linear relationship, but none of the table show the proportional relationship.
What is proportional relationship?A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Given:
A). x → y
0 → 3
3 → 6
6 → 9
To show the linear relationship:
We have to find the constant first difference.
That means,
6-3 = 3
And 9 - 6 = 3
The values of this table show the linear relationship.
To show the proportional relationship:
Let x/y = k (k is constant)
We have to find the k:
0/3 = 0,
3/6 = 1/2,
6/9 = 2/3.
The values of this table do not show the proportional relationship.
B). x → y
0 → 4
2 → 6
4 → 8
To show the linear relationship:
We have to find the constant first difference.
That means,
6-4 = 2
And 8 - 6 = 2
The values of this table show the linear relationship.
To show the proportional relationship:
Let x/y = k (k is constant)
We have to find the k:
0/4 = 4,
2/6 = 1/3,
4/8 = 1/2.
The values of this table do not show the proportional relationship.
C). x → y
0 → 0
6 → 3
12 → 6
To show the linear relationship:
We have to find the constant first difference.
That means,
3-0 = 3
And 6 - 3 = 3
The values of this table show the linear relationship.
To show the proportional relationship:
Let x/y = k (k is constant)
We have to find the k:
0/0 = undefined,
6/3 = 2,
12/6 = 2.
The values of this table do not show the proportional relationship.
D). x → y
0 → 3
5 → 5
10 → 7
To show the linear relationship:
We have to find the constant first difference.
That means,
5 - 3 = 2
And 7 - 5= 2
The values of this table show the linear relationship.
To show the proportional relationship:
Let x/y = k (k is constant)
We have to find the k:
0/3 = 0,
5/5 = 1,
10/7 = 10/7.
The values of this table do not show the proportional relationship.
Therefore, none of the table show the proportional relationship.
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PLSS I NEED THIS! Number 4
Answer:
(b) y < x-1; y ≤ -2x+2
Step-by-step explanation:
You want to know the inequalities represented on the graph showing a solid line with negative slope and a y-intercept of 2, and a dashed line with positive slope and a y-intercept of -1, where the shading is below both lines.
Line typeIf the line is included in the solution set (≤ or ≥ is used), the boundary line is graphed as a solid line. If the line is not included in the solution set (< or > is used), the boundary line is graphed as a dashed line.
Here, the line with positive slope is dashed, and the line with negative slope is solid.
y = x -1 . . . . is a line with positive slope
y = -2x +2 . . . . a line with negative slope
ShadingThe shading is below the line for y-values less than those on the line:
y < x -1 . . . . shading below a dashed line with positive slope
y ≤ -2x +2 . . . . shading below a solid line with negative slope
These are the inequalities of interest.
4/9 dividend by 2/3 =
Please help!!!will give brainlest
Answer:
2/3
Step-by-step explanation:
4/9 divided by 2/3 = 4/9 times 3/2
= 2/3
If a new video game costs the store $25 and they sell it for 37.50, what was the percent markup?
The percent markup of the supplied statement is equal to 50% after the problem is solved.
How much of a markup should I use?There isn't a predetermined "optimal" markup percentage, however most companies set their markup at 50%. A 50% markup, also referred to as "keystone," denotes a price that is 50% greater than the cost of the commodity or service.
Exactly how is markup determined?The gross profit of a unit is determined by subtracting its cost to produce or acquire for resale from its sales price to determine the markup percentage. The markup percentage is computed as (12 - 8) / 8 and equals 50% if an item is priced at $12 but costs the manufacturer $8 to produce.
According to the given information:Cost price of game=$25
Selling price of game=$37.50
Profit = selling price - cost price
Profit = 37.50 - 25
Profit / markup percentage = (profit /cost price ) * 100
= (12.50/25) * 100
= 50%
The percent markup of the supplied statement is equal to 50% after the problem is solved.
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5700 dollars is placed in an account with an annual interest rate of 6.5%. To the nearest year, how long will it take for the account value to reach 20900 dollars?
It will it take 56 years for the account value to reach $20,900.
What is Simple Interest?This amount is calculated based on the principal amount of a loan or the first deposit in a savings account. Simple interest does not compound, thus, a creditor will only pay interest on the principal amount and a borrower would never have to pay more interest on the previously accumulated interest.
formula for calculating Simple Interest, S.I:
S.I = P * R * T
100
Where,
S.I = Simple Interest
P =Pricipal
R = rate ( in percentage)
T= Time
To how long will it take for the account value to reach $20,900
S.I = $20,900
R = 6.5%
P =$ 5,700
T =?
S.I = P * R * T
100
$20,900 = $ 5,700 * 6.5 * T
100
Cross multiplying and Making Time, T subject of the formula we have:
$20,900 * 100 = $ 5,700 * 6.5 * T
T= $20,900 * 100
$ 5,700 * 6.5
T= 56.41
T ≈ 56 years
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Please help!!! I don’t know this answer ?
They will walk 6 laps and run 10 laps for a total of 16 miles considering each lap is of 1 mile.
What is mile?The mile is a customary unit of measurement in both the United States and the United Kingdom that is based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. It is also referred to as the international mile or statute mile to distinguish it from other miles.
In 1959, the statute mile was formally redefined with respect to SI units as exactly 1,609.344 metres, establishing a standard between the British Commonwealth and the United States.
With qualifications, mile is also used to describe or translate a wide range of units derived from or approximately comparable to the Roman mile, such as the nautical mile (now exactly 1.852 km), the Italian mile (roughly 1.852 km), and the Chinese mile (now 500 m exactly).
6 laps + 10 laps = 16 laps
1 mile each laps = 16 miles
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