The inequalities that are equivalent are 3x+6≤8+ 2x and 12-3x ≤18
What are inequalities?
Inequalities are simply defined as relations that makes a non-equal comparison between two mathematical expressions, equations or numbers.
It is mostly used to compare two numbers or expressions based on the magnitude on the number line.
Inequality signs in mathematic include;
< represents less than> represents greater than≤ represents less than or equal to≥ represents greater than or equal toGiven the inequalities;
3x + 6 ≤ 8 + 2x
collect like terms
3x - 2x≤ 8 - 6
subtract like terms
x ≤ 2
12-3x ≤18
collect like terms
3x≤ 18 - 12
3x ≤ 6
Divide both sides by 3
x ≤ 2
Hence, the inequalities are 3x+6≤8+ 2x and 12-3x ≤18
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Your friend secretly chooses a number. She says that when you divide the number by 4, add 6, and then multiply by -3, the result is -27. What number did your friend choose?
Answer: 12
Step-by-step explanation:
Say that your friends number is x
She says that when you divide the number by 4, add 6, and then multiply by -3, the result is -27, so:
(x/4 + 6) * -3 = -27
We can solve the equation by first dividing by -3 on both sides:
x/4 + 6 = 9
Multiply both sides by 4:
x + 24 = 36
Subtract 24 from both sides:
x = 12
Double checking...
(12/4 + 6) * -3
= (3+6) * -3
= 9 * -3
= -27
Correct :>
So your friend chose the number 12
Find the function rule
X. Y
-2, -3
1, 3
3, 7
5, 11
Answer:
The function rule for this set of ordered pairs is y = 2x + 1.
This can be determined by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
The slope (m) can be calculated by using the formula:
m = (change in y) / (change in x)
For the ordered pair (1, 3) and (3, 7), we can see that change in x = 3 - 1 = 2 and change in y = 7 - 3 = 4, so m = 4/2 = 2.
Then, using any of the point we can find the b which is y-intercept. let's take the point (-2, -3) and substitute the values in the function y = 2x + b
-3 = 2(-2) + b
-3 = -4 + b
b = 1
So, the function rule is y = 2x + 1
An electronic store sells an average of 60 entertainment systems per month at an average of $800 more than the cost price. For every $20 increase in the selling price, the store sells one fewer system. What amount over the cost price will maximize revenue?
Let x be the cost price of an entertainment system.
The selling price is x+800
The number of systems sold is 60-((x+800-x)/20) = 60-((800)/20) = 60-40 = 20 systems
The revenue is the product of the number of systems sold and the selling price.
R = 20(x+800) = 20x+16000
To maximize the revenue, we need to differentiate the above equation with respect to x and set it to 0 and solve for x.
dR/dx = 20 = 0
20x = 0
x = 0
Therefore, the cost price of an entertainment system is 0 and the store should sell the system at x+800 = 800
This means that the store should sell the system at $800 more than the cost price to maximize the revenue.
I need help on this question it’s on similar figures
Answer:
a) the triangles are similar triangles because they are the same shape. The angles in both triangles have the same value.
b) The similarity ratio between the two triangles is 0.5, because the lengths of the sides of the triangle on the right are double the value of the lengths of the sides of the triangle on the left.
c) angle U = angle G. angle V = angle H. angle T = angle F.
UV/GH = VT/HF = TU/FG = 0.5
How do I solve 8-4x>-12
The solution to the given inequality expression is; x < 5
How to solve Inequality expressions?We want to solve the inequality expression;
8 - 4x > -12
Add 4x + 12 to both sides using addition property of equality to get;
8 - 4x + 4x + 12 > -12 + 4x + 12
20 > 4x
Divide both sides by 4 using division property of equality to get;
20/4 > 4x/4
x < 5
That expression is what we will have as our final solution to the inequality expression .
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1
Select all quadrilaterals for which a diagonal is also a
line of symmetry.
(Select all that apply. )
trapezoid
isosceles trapezoid
parallelogram
rhombus
rectangle
square
Correct answer is parallelogram and rhombus.
A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees.
Rhombuses are a particular sort of quadrilateral in Euclidean geometry. It is a unique instance of a parallelogram in which the diagonals meet at a 90-degree angle and all sides are equal. This is a rhombus' fundamental characteristic. A rhombus has a diamond-shaped form. As a result, it is also known as a diamond.
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rectangle, rhombus
got it wrong on my test and was given the correct answers, so here they are.
When isabella young received her bank statement, she noticed that her present balance was the same as her previous balance. Her deposits were 1/2 her present balance, her withdrawals were 1/3 her present balance, and her auto payments were 1/4 her present balance. Her direct deposit was 1/10 her present balance. The account had a $9. 29 service charge but no interest. What is isabella present balance?
According to Isabella transactions, her present balance in bank statement is -$9.45
The term called transaction in math is defined as a finalized agreement between a seller and a buyer for transferring goods, services, or financial assets in exchange for money
Here let us consider that Isabella's present balance be X.
According to the problem statements regarding her deposits, there is withdrawals, auto-payments, direct deposit and service charge are also done on the account.
Then those transaction values are calculated as,
=> (1/2)x - (1/3)x -(1/4)x +(1/10x) -$9.29 = x
Here by finding the LCM of common terms, then we get
=> (1/60)x - $9.29 = x
When we solve it for x, then we get the equation like the following,
=> 59x = -$9.29 × 60
=> 59x = -$557.4
Therefore the value of x is -$9.45.
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Anita is an airline attendant. Last week, she worked on flights on 1 small jet and 2 large jets, which could seat a total of 253 passengers. The week before, she was assigned to flights on 5 small jets and 4 large jets, which could seat a total of 725 passengers. How many seats were on each type of flight?
Answer:
Small jet seat capacity: 73
Large jet seat capacity = 90
Step-by-step explanation:
Let x be the number of seats on the small jet
Let y be the number of seats on the large jet
From the word description for last week:
Last week, she worked on flights on 1 small jet and 2 large jets, which could seat a total of 253 passengers
we can formulate the equation
1x + 2y = 253 .............(1)
For the week before:
The week before, she was assigned to flights on 5 small jets and 4 large jets, which could seat a total of 725 passengers
5x + 4y = 725 ...............(2)
Equation (1) x 2 ==>
2x + 4y = 2(253)
2x + 4y = 506 ..............(3)
So our two equations are:
5x + 4y = 725 . .............(2)
2x + 4y = 506 ..............(3)
Equation (2) - Equation (3) will eliminate the y terms making it possible to solve for x
(5x + 4y) - (2x + 4y) = 725 - 506
5x + 4y - 2x - 4y = 219
5x -2x +4y - 4y = 219
3x = 219
x = 219/3
x = 73
Plugging this value back into equation (1): 1x + 2y = 253 we get
1(73) + 2y = 253
73 + 2y = 253
2y = 253 - 73
2y = 180
y = 180/2
y = 90
Answer
Small jet seat capacity: 73
Large jet seat capacity = 90
the isosceles triangle has two sides of equal length that are longer then the length of the base the perimeter of the triangle is 15.7 centimeters the equation 2a+b=15.7 models this information if one of the longer sides is 6.3 centimeters which equation can be used to find the length of the base
The length of the base is 3.1 cm when you subtract 12.6 from btohs ides b is15.7.
The definition of an isosceles triangle?There are two equal sides and two equal angles in an isosceles triangle. The word is a combination of the Greek words iso (same) and skelos (leg). Equilateral triangles are those in which all of the sides are equal, while scalene triangles are those in which none of the sides are equal.
Equilateral triangles are those in which all of the sides are equal, while scalene triangles are those in which none of the sides are equal.
The equal sides of an isosimple triangle are longer than the base's length.
We know that identical sides are greater, thus 6.3 is one of the identical sides in the perimiter=15.7 equation, which is 2a+b=15,7.
2a denotes the two identical sides: 2(6.3) + b = 15.7
The answer is base=3.1 cm when you subtract 12.6 from btohs ides b=15.7.
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Halla el FCM de 114, 138 y 234 usando el método de factorización prima
(escriba su respuesta)
The HCF of the numbers 114, 138 and 234 is 6.
The term HCF in math is also know as the greatest common factor or highest common factor of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder.
Here we have given the numbers 114, 138 and 234.
And we need to find the HCF of the numbers.
By using the prime factorization method, here we have identified the factors of the numbers, and it can be written as
The factors of 114 are: 1, 2, 3, 6, 19, 38, 57, 114
The factors of 138 are: 1, 2, 3, 6, 23, 46, 69, 138
The factors of 234 are: 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234
While we looking into the given number we have identified that the the greatest common factor is 6.
Complete Question:
Find the HCF of the numbers 114, 138, and 234 by using the prime factorization method.
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7.Maddie performed a calculation on her calculator and received a result of 8E3.
What are the standard form and scientific notation for this value?
Select two answers: one for standard form and one for scientific notation.
The scientific notation of the given result is 8 x 10³
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).
We are given that Maddie performed a calculation on her calculator and received a result of 8E3.
WE know that "E" means the power of ten
Therefore,
8E3 = 8 x 10³
This is the scientific notation.
For the standard form it should be 8,000.
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You toss two coins. In how many ways can they fall?
You toss three coins. In how many ways can they fall?
You throw two dice. In how many ways can they fall?
The ways they can fall are 4,8 and 36
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
Given;
Two coins, three coins and two dices are tossed
Probability of two coins;
=2x2=4
Probability of three coins;
=2x2x2=8
Probability of two dices;
=6x6=36
Therefore, the probability of coins and dice will be 4,8 and 36
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Complete the explanation of how you could use the work backward problem-solving strategy to solve the equation
x/5 − 3 = 2.
The equation says that a number was divided by 5 and that 3 was then subtracted from the quotient, giving the result 2. So, working backward, first add (blank)to 2, giving (blank). Then multiply that result by (blank), giving x = (blank)
The solution to the equation is described as follows:
The equation says that a number was divided by 5 and that 3 was then subtracted from the quotient, giving the result 2. So, working backward, first add 3 to 2, giving 5. Then multiply that result by 5, giving x = 25.
How to solve the equation?The equation for this problem is described as follows:
x/5 - 3 = 2.
We must isolate the variable x, hence the first step is adding 3 to 2, as follows:
x/5 = 2 + 3
x/5 = 5.
Then we apply cross multiplication, multiplying the result by 5, as follows:
x = 5(5)
x = 25.
Which is the solution to the equation.
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On a trip to the mall Ziva spent 25% of her budget on shoes. Her total budget was $250. How much did she spend on shoes?
Answer:
$62.50
Step-by-step explanation:
We multiply 0.25(25% as a decimal) by $250 to get $62.50.
90 is 0.6 of what number
Answer:
150
Step-by-step explanation:
90/0.6 = 150
Check:
150*0.6 = 90
Then:
90 is 0.6 of 150
Directions: Set up a proportion and then solve. Remember to label your answer. 1) Goodyear can make 100 Tires in 45 minutes at their factory in Akron, Ohio! b. How long will a. How many tires can they make in 135 minutes?
Answer:300 tires
Step-by-step explanation: I set it up like this 100:45
X : 135
Then I am trying to find x. I cross multiplied. (100 times 135) and (45 times x) which is 45x= 13500 then if you know simple algebra then you get x by itself so you divide 13500 and 45 which equals 300.
The table shows the results of a survey of 100 people selected at random Airport
at an airport. Find the experimental probability that a person selected at Destinations
random is going to City B.
Number of
Destination Responses
City
A
28
City B
40
City C
16
City D
14
City E
2
The experimental probability that a person selected at random is going to City Bis 1
(Simplify your answer. )
The experimental probability that a person selected at random is going to City C is 4/25.
Number of responses from destination A = 22
Number of responses from destination B = 40
Number of responses from destination C = 16
Number of responses from destination D = 14
Number of responses from destination E = 8
As we know, the formula of experimental probability is
Probability of an Event P(E) = Total Number of times an event occurs/Total number of trials.
Number of responses from destination C = 16
Total number of responses from all destinations = 100
∴ Probability of an Event P(C) = 16/100 = 4/25
--The given question is incorrect; the correct question is
"The table shows the results of a survey of 100 people selected at random at an airport. Find the experimental probability that a person selected at random is going to City C."--
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. eight times the quotient of 6 and 3
Answer: 16
Step-by-step explanation:
8 * (6/3)
= 8 * 2
= 16
Formulate a erie and how a proof by PMI to validate.
Give at leat one example each on the operation of function.
In at leat 50 word; What have you learned in GE4?
The student has learned that GE4 is an introduction to mathematical proof and problem solving, including basic algebra, functions, sets, and the different approaches to problem solving.
Example of operation of function:
1. f(x) = x^2 + 3x - 2
When x = 3, f(3) = 3^2 + 3(3) - 2 = 14
2. g(x) = x^3 + 3
When x = 4, g(4) = 4^3 + 3 = 67
I have learned that GE4 is an introduction to mathematical proof and problem solving. We have gone through a variety of topics such as basic algebra, functions, and sets. We have also learned about the different approaches to problem solving, such as working backwards, proof by cases, and proof by PMI. I have also been introduced to the basics of logic and proof writing.
This answer explains the proof by PMI for the erie that if n is an odd number, then n^2 is an odd number. Two examples of operations of functions are also given. The student has learned that GE4 is an introduction to mathematical proof and problem solving, including basic algebra, functions, sets, and the different approaches to problem solving.
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15. write this problem in slop intercept form.
nick is given $50 to spend on a vacation. he decides to spend $5 a day. the amount nick has left and the number of days are related.
Answer: 10 I'm not sure ok
Step-by-step explanation: divide 50 and 5 you get 10
For each expression, circle any like terms and list any variables.
The final resultant expressions are 3.9 - 0.8 x , 1.5 + t+0.66 x ,
77/5 k - 3m.
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given expressions,
-2.5x+3.9 + 1.7x
3.9 + 1.7x-2.5x
3.9 - 0.8 x
1 1/2 + t + 2/3 s
= (2+1) / 2 + t+ 2/3 s
= 3/2 + t + 2/3 s
= 1.5 + t+0.66 x
15k+2/5 k -3m
k(15+2/5 ) - 3m
k (75 + 2 / 5 ) - 3m
77/5 k - 3m
Hence, The final resultant expressions 3.9 - 0.8 x , 1.5 + t+0.66 x ,
77/5 k - 3m
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simplify [17-8] - [13-4]
Answer:
0
Step-by-step explanation:
First, you do 17 - 8, which is 9 and then you do 13 - 4, which is 9. Then, you subtract 9 from 9, which gives you 0.
i need sm help lol ahhhhhhhh
Answer:
????????????????????
Write an equation in slope intercept form passing through the point (-10,1) and parallel to the line 10x+5y=15
Answer: y=-2x-19
Step-by-step explanation:
First, you should arrange the equation in the form of y=mx+c (that is the standard form of this type of equation)
10x+5y=15
5y=-10x+15
[tex]\frac{5y}{5} =\frac{-10x}{5}+\frac{15}{5}[/tex]
y=-2x+3 (now you got the equation in the simple form)
now you should substitute the given point (-10,1) into the simplified equation
y= 1 & x=-10
1=-2(-10)+c (the y-intercept must be taken as c )
c= 1 - 20
c= -19
therefore the equation will be : y=-2x-19
it will be the same gradient as the other line for this line too as the lines are parallel, you should only find the y-intercept. The gradient of the other line will stay the same as long as they are parallel lines.
Help please!! (5k + 2m)(3p + 4s)
In each row decide whether the expression in column A is equivalent to the expression In column b. If they are not equivalent show how to change one expression to make them both equivalent. YAWL HELP URGENTLY IM GONNA CRY
I apologize for misunderstanding your question.
Regarding your new question, it depends on the specific expressions provided in column A and column B. Without knowing the exact expressions, I am unable to determine if they are equivalent or not. Additionally, if they are not equivalent, then to make them equivalent, you can use algebraic properties such as the commutative property, associative property, distributive property and simplification techniques to change one of the expressions so that it has the same value as the other expression for every input in their domain.
Please let me know the specific expressions you are working with and I will be happy to help you determine their equivalence and/or how to change one of the expressions to make them equivalent.
Answer:
SO bassically its is equivalent bc i seethat the dgene is really good
Step-by-step explanation:
1 + 1 =2w + 2x +2y = 3x and equiavelnt number
An angle is two collinear rays with a common endpoint. Find an example that contradicts this definition. How would you change the definition to make it more accurate? Part B: Give an example of an undefined term and how it pertains to angles
For the definition "An angle is 2 collinear rays with a common endpoint" , then
(a) the contradictory example is "When two rays are collinear having a common end point; then the rays do not form an angle instead they form a line."
(b) the changed definition is , "An angle is formed at the intersection of two non-collinear rays that have the same endpoint " ;
(c) the example is "the Plane" .
The Angles are formed when the two straight lines or rays meet at a common endpoint.
Part(a) ;
An example which contradicts this definition of angles is "When two rays are collinear with a common endpoint; the rays do not form an angle ,instead they form a line" because when all the points of two lines are collinear then all the points of the two lines will be overlapping .
Part(b) ;
The change that need to be made in the definition of angle is "An angle is formed at intersection of two non-collinear rays which have same endpoint ".
Part(c) ;
The Example of the undefined term is :
Undefined terms do not have a formal definition; an example of this is "the plane" . The plane pertains to the angles because the plane determines the parameter to be measured.
The given question is incomplete , the complete question is
An angle is two collinear rays with a common endpoint.
(a) Find an example that contradicts this definition.
(b) How would you change the definition to make it more accurate ?
(c) Give an example of an undefined term and how it pertains to angles .
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Write the slope-intercept form of the equation of the line through the given points.
through: (2, -4) and (2,-5)
Answer
undefined
Step-by-step explanation:
Answer:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
To find the equation of a line passing through two given points, we can use the slope-intercept form, and use the slope formula:
slope = (y2 - y1) / (x2 - x1)
Given the points (2, -4) and (2, -5), we can see that the x-coordinates are the same, which means that the line is a vertical line.
Since the line is vertical, the slope is undefined, and we can say the line can be represented by the equation x = 2
This is the equation of the line passing through the given points (2, -4) and (2, -5) in slope-intercept form.
a living room needs to be re-carpeted. it measures 18 feet long by 15 feet wide. how many square yards of carpet will need to be purchased?
Answer:
66?
Step-by-step explanation:
18+18= 36
15+15= 30
30+36= 66
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded. Number of Hours Total Number of Students 0 1 1 3 2 3 3 10 4 9 5 6 6 3 Determine the probability that a student studied for exactly 5 hours. Round to the nearest hundredth. 0.83 0.21 0.17 0.14
There is a 0.17 percent chance that a student spent 4 hours in class.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. Probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.
To determine the probability.
The number of students that has 5 hours is 6
The total number of students are 35.
P(5 hours) = 6/35
P(5 hours) = 0. 17
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