The solution to an inequality is given in set-builder notation as {x l x > two-thirds}.
option c. (two-thirds, [infinity]) is the correct option
What exactly is set builder notation?The set-builder notation can also be used to express sets using an interval or an equation. It is common practise for sets with an unlimited number of elements to write and represent their elements in this way. This makes use of a variable (or several) that fit under the group of typical numerical kinds, such as integers, real numbers, and natural numbers.
What is roster notation?The roster notation is a convenient way to express sets mathematically. Within the curly braces of the roster form, the elements (or members) of a set are listed in a row. In a roster notation, a comma is used to indicate the separation of every two elements when the set contains more than one element.
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Solve the system below by the method of your choice. Show all work.
−4x+4y=−8
4x−6y=16
Isolate one of the two variables in one of the equations.
How to solve the system?Substitute the expression that is equal to the isolated variable from Step 1 into the other equation.Determine which variable will be eliminated. ...Combine the equations using addition. ...Solve the new equation for the remaining variable.Substitute the value for that variable into one of the original equations and solve.Solve the linear equation for the remaining variable.The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.(- 2, - 4 )
- 4x + 4y = - 8 → (1)
4x - 6y = 16 → (2)
adding (1) and (2) term by term will eliminate x
0 - 2y = 8
- 2y = 8 ( divide both sides by - 2 )
y = - 4
substitute y = - 4 into either of the 2 equations and solve for x
substituting into (2)
4x - 6(- 4) = 16
4x + 24 = 16 ( subtract 24 from both sides )
4x = - 8 ( divide both sides by 4 )
x = - 2
solution is (- 2, - 4 )
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5. What are the real and complex solutions of the polynomial equation? (1 point)
x-8=0
01+i3, and 1-i√√3
O2,-1+13, and-1-i√√3
O2, 1+2i √√3, and 1-2i √√3
02, 2+2i √√3, and 2-2i
The real and complex solutions of the polynomial equation [tex]x^{3} - 8[/tex] = 0 is 2, -1 + [tex]\sqrt{3}[/tex]i and -1 - [tex]\sqrt{3}[/tex]i. option 2 is correct.
Polynomial equation: what is it?Polynomial equations are those created using exponents, coefficients, and variables. The greater of its possible exponents is referred to as the equation's degree. By factoring polynomials according to their degree and the variables in the equation, we may find their solutions.
Our equation is [tex]x^{3} - 8[/tex]
and we know that: [tex]x^{3} = 8[/tex]
then we can write our equation as: [tex]x^{3} - 2^{3}[/tex]
And using the identity: [tex]a^{3} - b^{3} = (a-b) *(a^{2} +ab+b^{2} )[/tex]
where a = x and b = 2, then our equation is:
them, if x = 2 the first part is zero, so x = 2 is a solution, and now we need to see the second part in order to find the complex solutions.
[tex]x^{2} + 2x +2^{2}[/tex] = 0
Here we need to use.
a[tex]x^{2}[/tex] + bx + c = 0 if for a, b and c constants, then:
x = [tex]-b +-\sqrt{b^{2} - 4ac } /2a[/tex]
in our problem we have:
x = -2 +-[tex]\sqrt{4 - 16}[/tex] /2
x = -1 +-[tex]\sqrt{-3}[/tex]
x = -1 +-[tex]\sqrt{3}[/tex] i
So here we have two complex solutions: -1 + [tex]\sqrt{3}[/tex]i and -1 - [tex]\sqrt{3}[/tex]i
So the value of x are 2, -1 + [tex]\sqrt{3}[/tex]i and -1 - [tex]\sqrt{3}[/tex]i
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I think you mean
What are the real and complex solutions of the polynomial equation? (1 point)
[tex]x^{3} - 8[/tex] = 0
( the equation is [tex]x^{3} - 8[/tex] = 0 and not x-8 =0)
Rule: Start at ? Subtract 6 then multiply by 2 each time
? 22- 32- 52
Step-by-step explanation:
let the number be x
So,
(x - 6) × 2 = 22
2x - 12 = 22
2x = 34
x = 17
Thus, the answer is 17
Consider the line y = 9x - 3.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Zero is the slope of a line parallel to this line.
-1/9 is the slope of a line perpendicular to this line.
What is slope?According to linguists, the Middle English adverb aslope, which meaning "at an angle," is where the term slope is said to have originated. A steep hill or the ramp in a parking garage are examples of things that are at an angle or on a slope and may be described using the word's noun form.
The ratio of the vertical change between two places is referred to as the slope. A line's slope is another indicator of how steep it is. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
The line becomes: y = 9x - 3
line is in the Slope-Intercept form : y = mx + c
Now comparing this two and we get slope, (m) = 9
So, The line perpendicular will have slope (m') = -1/m
or, m' = -1/9
The line parallel to this line will have slope (m'') = 0
because here the two lines are parallel, so they have no slope.
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What is meant by the trend component of a time series? How is a linear trend different from a nonlinear trend? CO What is meant by the trend component of a time series? ary OA. The trend component represents changes in time-series data that are unpredictable and cannot be associated with a seasonal, cyclical, or random component. OB. The trend component is the long-term increase or decrease in a variable being measured over time. OC. The trend component is a wavelike pattern that is repeated throughout a time series and has a recurrence period of at most one year. D. The trend component is a wavelike pattern within the time series that repeats itself throughout the time series and has a recurrence period of more than one year.
Answer: A trend line is a line on a scatter plot, drawn near points, that approximates the association between the data sets.
Step-by-step explanation:
2. The linear trend in precipitation is the dominant trend type. The nonlinear trends occur much less frequently and more widely scattered over the globe. However, the nonlinear trends are credible patterns of change in precipitation.
3. The trend is the component of a time series that represents variations of low frequency in a time series, the high and medium frequency fluctuations having been filtered out. This component can be viewed as those variations with a period longer than a chosen threshold
4. The trend component represents changes in time-series data that are unpredictable and cannot be associated with a seasonal, cyclical, or random component. OB. The trend component is the long-term increase or decrease in a variable being measured over time.
5. The trend is the component of a time series that represents variations of low frequency in a time series, the high and medium frequency fluctuations having been filtered out.
6. The trend component is the long-term increase or decrease in a variable being measured over time.
At a college, the cost of tuition increased by 10%. Let b represent the former cost of tuition. Use the expression b+0.10b for the new cost of tuition.
a. Write an equivalent expression by combining like terms.
b. If the cost increases by 10%, you can multiply the former cost by %.
The equivalent expression by combining like terms is 1.10b and
If the cost increases by 10%, you can multiply the former cost by 110%
How to determine the equivalent expression by combining like terms.From the question, we have the following parameters that can be used in our computation:
Expression of 10% raise = b + 0.10b
Evaluate the like terms in the above expression
So, we have the following representation
Expression of 10% raise = 1.10b
Hence, the expression is 1.10b
How to complete the blankRecall that we have the mathematical statement to be
If the cost increases by 10%, you can multiply the former cost by %.
In this case, the factor is calculated as
factor = 1 + 10%
So, we have
Factor = 110%
So, the missing expression in the statement 110%
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What value for a in the system of equations below would yield no solutions for the system? Explain how you obtained your answer.
ax+12y=−6
2x−6y=4
a=
After solving the provided question, The value for a in the system of equations below would yield no solutions for the system is [tex]= > a = 18 - 20\frac{y}{x}[/tex]
A system of equations is what?several equations at once, multiple equations In algebra, you must work together to solve two or more equations (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, there must be an equal number of equations and unknowns.
When there are two variables and you are given two pieces of information about how those variables are related, a system of equations is used. To address a number of typical problems, a system of equations can be employed.
[tex]3x-5y=15\\multiply with 6\\18x -30y = 90\\compare the equation with \\ax-10y=90\\then \\18x -30y = ax-10y\\ax = 18x + 10y -30y\\ax = 18x-20y\\a= (18x -20 y) / x\\[/tex]
[tex]= > a = 18 - 20\frac{y}{x}[/tex]
x≠o
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What is the next term in the sequence −10,−17,−24,−31,
Answer:
-38
Step-by-step explanation:
The sequence is decreasing by 7 everytime
-10 to -17 decrease of 7
-17 to -24 decrease of 7
-24 to -31 decrease of 7
Jack broke apart 5x216 a 5x200 5x16 to multiply mentally what trategy did Jack ue?
In the given situation where Jack writes 5 * 216 as (5*200) + (5*16), he uses the distributive property.
What is distributive property?The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.
For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication.
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.
So, in this instance, the multiplication is as follows:
5 * 216
This multiplication can be rewritten as follows:
5*(200+16)
We then put the distributive property to use. So, we have:
(5*200) + (5*16)
Therefore, in the given situation where Jack writes 5 * 216 as (5*200) + (5*16), he uses the distributive property.
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Correct question:
Jack broke apart 5x216 as (5x200)+(5x16) to multiply mentally. What strategy did Jack use?
A pinball machine which normally sells for $1999 is on sale for $1750. Find the discount and the rate of discount.
HELP ME THIS IS DUE TODAY!!
Answer: 12.5%
Step-by-step explanation:
Take 1750 divided by 1999, then time 100% = 87.5%
100% - 87.5% = 12.5%
The rate of discount is 12.5%
a)Find the value of 8^1/3
b)Find the value of 8^2/3
c)FInd the value of 16^3/4
a) The value of 8^1/3 is 2
b) The value of 8^2/3 is 4
c) The value of 16^3/4 is 8
How to determine the values of a, b, and cInformation given in the problem
a) the value of 8^1/3
b) the value of 8^2/3
c) the value of 16^3/4
This equation represents exponents in fraction form and the basics for the calculation is from
a^(b/c) =
[tex]\sqrt[c]{a}^{b}[/tex]
Rewriting the expression is done as below
8^1/3
=∛8
= 2
8^2/3
= ∛8²
= 2²
= 4
16^3/4
[tex]\sqrt[4]{16}^{3}[/tex]
= 2³
= 8
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our school's girls volleyball team has $14$ players, including a set of $3$ triplets: alicia, amanda, and anna. in how many ways can we choose $6$ starters with no restrictions? (the triplets are treated as distinguishable.)
There are 990 ways to select 6 starters from a possible 14 using precisely two of the three triplets.
= C(3,2) = 3! / ( 2! x 1! ) = 3
To select the final 4 starters out of the 11 players ,
= C(11,4) = 11! / (4!7!)
= 330
There are a total of 6 ways to select starters.
= 3*330 = 990
Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method.
The number of combinations can be counted in simpler situations. Combination is the taking together of n items, k at a time, without repetition.
The terms k-selection or k-combination with repetition are frequently used to describe combinations where repetition is permitted.
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Hi pls help me and explain
The linear model representing the information is y = 600x + 1500.
To produce 12 solar heaters it cost $8,700.
The domain of the linear model is [1, 80].
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
10 solar heaters = $7500
20 solar heaters = $13,500
The linear model can be in the form of y = mx + c
m = (13,500 - 7500)/(20 - 10)
m = 6000/10
m = 600
Now,
(10, 7500) = (x, y)
7500 = 600 x 10 + c
c = 7500 - 6000
c = 1500
Now,
The linear model is y = 600x + 1500.
Where y is the cost of x solar heaters.
Now,
x = 12,
y = 600 x 12 + 1500
y = 7200 + 1500
y = 8700
Now,
y ≤ 50,000
We see that,
x = 81
y = 600 x 81 + 1500 = 48600 + 1500 = 50,100
x = 80
y = 600 x 80 + 1500 = 48000 + 1500 = 49,500
The domain is from x = 1 to x = 80.
Thus,
The linear model is y = 600x + 1500.
$8,700 is the cost to produce 12 solar heaters.
The domain is [1, 80].
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Find the slope of the line that passes through (2, 14) and (10, 5).
Answer:
m=-12/5
Step-by-step explanation:
yes
Ann Dyslecki is buying a sports car. She financed $ 5590 at her
bank and agreed to repay it in four years. Her monthly payment
was $ 149,60. Find the total amount to be repaid and the finance
charge.
Answer:
5590-149,60
Step-by-step explanation:
sum completed
A population of 50 foxes in a wildlife preserve doubles in size every 14 years. The function y = 50.2*, where x is the number of 14-year periods, models the population
growth. How many foxes will there be after 42 years?
After 42 years there will be foxes. (Type a whole number.)
Answer:
400
Step-by-step explanation:
You want to know the number of foxes predicted after 42 years by y = 50·2^x, where x is measured in 14-year periods.
Periods42 years is 42/14 = 3 14-year periods. Using x=3 in the equation, we predict ...
y = 50·2^3 = 50·8 = 400
foxes.
After 42 years, there will be 400 foxes.
__
Additional comment
It is often convenient to use time measured in 1-year periods. In that case, the equation could be written ...
y = 50·2^(t/14)
Then t/14 is the number of 14-year periods when t is in years.
Daniela notices
a pattern in her scrapbook. The leaves on the first page
are green. The second page has yellow leaves. The third
page has green leaves. The next page has yellow
leaves. Is this a repeating or growing pattern
Answer:
I think it's repeating pattern
Judi Imhoff's previous balance was $717.52. She received $4.36 in interest and had $125.00 and $276.95 in deposits and $90.00 in withdrawals. What is her new balance?
After checking Judi Imhoff's account statement her new balance is $1003.83
What is an account statement?
A statement of accounts is a document that lists all the transactions you have with a certain client during a specific time period. In order to inform their clients of the amount they owe for purchases made during that time period on credit, company owners typically issue statements of accounts to their clients. The manual explains the statement of accounts' contents and demonstrates how to file it for clients.
Your bank may send you a monthly or annual statement if you have a savings account.
account statement for the quarter. All deposits are reflected on the account statement,
withdrawals, as well as interest that is added to your account.
The new balance = Previous Balance + Interest + Deposits - Withdrawals
The new balance = $717.52 + $4.36 + ($125.00 + $276.95) - $90.00
So, the new balance of Judi Imhoff is $1003.83
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Scott has a bag containing plain chocolate pieces and another bag containing peanut chocolate pieces. The bag with plain chocolate pieces contains 6 blue, 1 yellow, 3 green, and 2 red candies. The bag with peanut chocolate pieces contains 3 blue, 1 yellow, and 4 green candies. Scott will randomly select 1 candy from each bag. What is the probability that Scott will select a green candy from each bag?
Answer: 35%
Step-by-step explanation:
The total amount of candy is 20, and there is 7 green candy, so we got 7/20. Then we multiplied 20 and 7 by 5, so we got 100 and 35, so we got 35/100, which is 35%
Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
3,12,48,...
This is __ sequence and the ____ is equal to.
| |
Arthmatic, geomatric commom ratio, commom difference
Answer:
3
12
12
48
48
192
192
768
768
I hope I helped you
An arithmetic sequence has a 2nd term of -2 and a 7th term of 18.
1. What is the 10th term in the sequence? 2. Write an explicit formula for the sequence.
3. Write a recursive formula for the sequence.
4. What is the sum of the first 10 terms?
The arithmetic sequence has a 2nd term of -2 and a 7th term of 18 has the following answers.
What is arithmetic progression?
An progression or arithmetic sequence may be a sequence of numbers specified the difference between the consecutive terms is constant.
Main body:
General formula for arithmetic sequence
a + (n-1)d = aₙ
arithmetic sequence has a 2nd term of -2 , which means
a+d = -2
a = -(d+2) ---------(1)
7th term of 18 , which means
a+ 6d = 18
substituting value from equation 1,
-(d+2) +6d = 18
-d -2 +6d = 18
5d = 20
d = 5
using d= 5 in equation 1,
a = -(5+2)
a =-7
A) 10th term
=a +9d
= -7+9*5
= 38
B) recursive formula for the sequence = aₙ+1=aₙ+d .
Hence for the given sequence , it is
a₃ = a₂ +d
a₃ = -2+5
a₃ = 3
C) sum of first 10 terms
Sₙ = n/2{2a+ (n-1)d}
S₁₀ = 5 {2*-7 + 9*5}
S₁₀ = 5[ -14 +45]
S₁₀ = 5*31
= 105
Hence the sum of the first 10 terms is 105.\
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6 = a/4 + 2
Solve For Unknown variable
Answer:
a = 16
Step-by-step explanation:
6 = [tex]\frac{a}{4}[/tex] + 2 ( subtract 2 from both sides )
4 = [tex]\frac{a}{4}[/tex] ( multiply both sides by 4 to clear the fraction )
4 × 4 = a , that is
a = 16
what does side b equal?
Answer: 8.6
same side s C and B
Answer: 7.2
Step-by-step explanation:
Since this is a right triangle we can use the Pythagorean theorem to solve for side b.
Pythagorean theorem: a²+b²=c²
Since the side length opposite the right angle is the hypotenuse we plug 11.2 in for C
(8.6)² + b²=(11.2)²
73.96 + b² = 125.44
b²=51.48
b = 7.17495644586
b=7.2
please help me i need it before tomorrow if possible. i need all 4 answered
The answer to this Question based on Thales Theorem is x = 8
What is Thales Theorem?
It says that when we join the mid points of two sides of a triangle the line is parallel to third side of triangle then the length of this joined line is half of length of third side
Here in Question given figure is like trapezium but we can extend it to make a triangle then by thales theorem we need to apply on other two sides hence joined line is parallel to third lines hence will be half of it
Solution:
1/2(x) = 2x - 12
x = 2(2x-12)
x = 4x - 24
24 = 3x
x = 8
Hence required value of x is 8
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What is an equation of the line that passes through the point (-5,-3) and is parallel to the line 3x+5y=15
Answer: [tex]y+3=-\frac{3}{5}(x+5)[/tex]
Step-by-step explanation:
The equation of the given line can be rearranged as follows:
[tex]3x+5y=15\\\\5y=-3x+15\\\\y=-\frac{3}{5}x+3[/tex]
Parallel lines have the same slope, so the slope of the line we need to find is -3/5.
Substituting into point-slope form, the equation of the line is [tex]y+3=-\frac{3}{5}(x+5)[/tex].
Determine the domain of (g ∘ f)(x) if f (x) = x2 + 2x − 4 and g of x is equal to 1 over the quantity x plus 1 end quantity period
{x ∈ ℝ}
{x ∈ ℝ| x ≠ −1}
{x ∈ ℝ| x ≠ −3, 1}
{x ∈ ℝ| x ≠ −3, −1, 1}
The domain of the function (g·f)(x) is {x∈ℝ|x ≠ -1}. Therefore, option B is the correct answer.
Given that, f(x)=x²+2x-4 and g(x) =[tex]\frac{1}{(x+1)}[/tex].
What is the function?Functions are the fundamental part of the 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.
Here, (g·f)(x) can be determined as follows
(g·f)(x)=g(x)×f(x)
= [tex]\frac{1}{(x+1)} \times x^2+2x-4[/tex]
Find the domain by finding where the expression is defined.
Interval Notation:
(-∞,-1)∪(-1,∞)
Set-Builder Notation:
{x∈ℝ|x ≠ -1}
The domain of the function (g·f)(x) is {x∈ℝ|x ≠ -1}. Therefore, option B is the correct answer.
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In four middle schools, the teacher to student ratio is equivalent. How many teachers and students are at each school? Enter the correct answers in the boxes in the table.
As the teacher-to-student ratio is equivalent in all schools, the number of students in school B is 506, the number of teachers in school C is 25 and the number of students in school D is 792 respectively.
What are ratio and proportion?
An equation known as proportion shows that the two ratios presented are equal to one another. A ratio is the comparative or condensed form of two quantities of the same type. The majority of the explanations for ratios and proportions use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers.
Given, the teacher-to-student ratio is equivalent for all schools.
For school A, ratio of teacher-to-student = 15/330 = 1:22
Then, for school B, the number of students = 23*22 = 506
For school C, the number of teachers = 550/22 = 25
For school D, the number of students = 36*22 = 792
Hence, these are the required number of students and teachers for the respective schools.
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For the function f(x) = -2x² + 12, determine f(4).
A) -20
B) 48
C) 76
D) -52
Answer: A.-20
Step-by-step explanation:
f(4)=-2(4)^2+12
f(4)=-2(16)+12
f(4)=-32+12
f(4)=-20
im not sure I'm very very bad at math
Answer:
Step-by-step explanation:
for the first car 374/17 = 22 m per second
for bus 414/23 = 18 m per second
so the car is moving faster
car is moving faster than (22-18)=4 m per second from the bus
Answer: Car: 22 meters per second, Bus: 18 meters per second. The bus travels faster at 4 meters per second.
Step-by-step explanation: First, you should write a proportional relationship for meters per second so the car would be 374/17 and the bus would be written as 414/23. This is so you can know that you divide 374 by 17 to get 18, and 374 by 17 to get 22. So, you had it backward, the bus is faster by 4 meters per second, I hope this helped, for me (a 7th grader) this was review math, so I hoped this helped you.
You are considering taking some courses at your local community college on a part-time basis for the upcoming school year. For a student who carries fewer than twelve credits (the full-time minimum), the tuition is $155 for each credit hour taken. All students, part-time or full-time, must pay a $20 parking fee for the semester. This fixed fee is added directly to your tuition and is included in your total bill. Write an equation to determine the total bill , t, for a student carrying fewer than twelve credit hours. Use n to represent the number of hours taken for the semester. Then, determine the total bill if you take nine credit hours. A. T + 20 = 155 n; $1395 b. T = 155 n + 20; $1395 c. T = 155 n + 20; $1415 d. T + 20 = 155 n; $1415.
The total bill if the student takes nine credit hours at the community college is T = $1415.
What are linear equations?One or more variables can be present in a linear equation, but their maximal possible power is only one. The graph of a linear equation will thus always be a straight line. Y = mx + b, where m denotes the line's slope and b its y-intercept, or point of intersection with the y-axis, is how linear equations are expressed. Many real-world situations, such as the connection between two variables or the distance travelled at a constant pace, may be modelled using linear equations. In order to obtain the value of the variable(s) necessary to make the equation true, one must use algebraic methods.
How to solve?
The total bill, t, for a student carrying fewer than twelve credit hours is given by,
T = 155 n + 20, where n represents the hours taken for semester.
The total bill if the student takes nine credit hours is T = 155(9) + 20 = $1415.
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