x = 4, y = 3 for the given equation 2x - 3 y = -1 , y = x - 1 .
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The meanings of the word equation and its cognates in various languages can vary slightly. For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfil the equality are known as the equation's solutions.Given data :
2x - 3 y = -1
y = x - 1
In a system of equations, there are multiple equations present. We actually look for the point at which these equations are identical when we attempt to solve a system of equations problem. In order to solve such an issue, we typically employ the substitution method, which involves inserting the values of one variable into the initial expression in order to determine the value of the second variable.
3y=2x+1
y= (2/3)x + 1/3 = x-1
x/3 =4/3
x = 4, y=3
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Solve the quadratic equation 3x2 + x - 5 = 0
The quadratic equation 3x² + 2x - 5 = 0 is solved to give x = 1 and -5/3
How to solve the quadratic equationFrom the information given, we have the quadratic equation as;
3x² + 2x - 5 = 0
Using the factorization method of solving quadratic equation, we have to take the following steps
Multiply the coefficient of x² by the constant -5
Find the pair factors of the product of their multiplication that sums up to 2
The pair factors are +5 and -3
Substitute the values
3x² + 5x - 3x - 5 = 0
Add parentheses
(3x² + 5x) - (3x - 5) =0
factorize the values
x(3x +5) - 1(3x + 5) = 0
The values of x are;
x= 1 and x = -5/3
Thus, the values are 1 and -5/3
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The complete question:
Solve the quadratic equation 3x2 + 2x - 5 = 0 using factorization method
tickets number one 1 to 20 are mixed up and then a ticket is drawn at random what's the probability that the ticket drawn at random has a multiple of four or five
The probability that the ticket drawn at random has a multiple of four or five is 2/5.
We have to determine the probability that the ticket drawn at random has a multiple of four or five.
Tickets number 1 to 20 are mixed up and then a ticket is drawn at random.
Total number of tickets = 20
The possible numbers of tickets that are multiple of four or five = 4, 5, 8, 10, 12, 15, 16, 20
So total number of outcome that are multiple of four or five = 8
So, the probability that the ticket drawn at random has a multiple of four or five = Total number of outcome that are multiple of four or five/Total number of tickets
The probability that the ticket drawn at random has a multiple of four or five = 8/20
The probability that the ticket drawn at random has a multiple of four or five = 2/5
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Please help me find the value and what kind of angle is this?
Answer: consecutive interior angles and x=66°
Step-by-step explanation:
The angles are consecutive interior angles. The property is consecutive interior angles are supplementary.
2x+24+24=180 [combine like terms]
2x+48=180 [subtract both sides by 48]
2x=132 [divide both sides by 2]
x=66
Therefore, the angle is consecutive interior angles and x=66°.
Dylan invested $6,100 in an account paying an interest rate of 2 % compounded
daily. Violet invested $6,100 in an account paying an interest rate of 2 %
compounded continuously. To the nearest hundredth of a year, how much longer
would it take for Violet's money to triple than for Dylan's money to triple?
Violet's money tripled Dylan's money to triple= 23,249.95.
Dylan invested $6,100 in an account paying an interest rate of 2% compound.
Violet invested $6,100 in an account paying an interest rate of 2%
compound.
The formula for compound amounts is A = P(1 + r/n)^(nt),
where n is the number of compounding periods per year, t is the number of years, P is the initial amount invested and r is the annual interest rate as a decimal fraction.
Here,
A = ($6100)(1 + 0.02/4)^(12*4)
Evaluating this we get:
A = ($6100)(1.005)^48, or
A = ($6100)(`1.2704)
A = $7,749.98
Violet's money to triple than for Dylan's money to triple
=3(A)=3*7749.98=23249.95.
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According to the 2010 U. S. Census, 11. 7% of the people in the state of Oregon were Hispanic or Latino. A political party wants to know how much impact the Hispanic and Latino vote will have, so they wonder if the percentage has changed since then. They take a random sample of 853 adults in Oregon and ask, among other things, their race. 110 of the people surveyed were Hispanic or Latino. Can the party conclude that the Hispanic or Latino proportion of the population has changed since 2010
The test hypothesis for the 2010 U. S. Census is H0 = Oregon < Latino.
In math the term called hypothesis is defined as an idea that is suggested as the possible explanation for something but has not yet been found to be true or correct.
Here we know that in 2010 U. S. Census, 11. 7% of the people in the state of Oregon were Hispanic or Latino.
And here we have also know that random sample of 853 adults in Oregon and 110 of the people surveyed were Hispanic or Latino.
Then the sample proportion is calculated as,
=> sample proportion=113/853=0.1325
And the value of Test statistic is,
=> z = (0.1325-0.117)/√(0.117*(1-0.117)/853)
=> z = 1.41
So, the hypothesis is written as,
=> H0 = Oregon < Latino.
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what is the vaulue of |6| - | -6| - (-6)
Answer:
I think it is just 6
Step-by-step explanation:
I hope it helped!
What is the model function of this situation? A population of 16 salmon triples every year.
f(x)=ab^x
Step-by-step explanation:
a = 16
b = 3
because only the factor 3 gets repeatedly added every year (x).
the rest (the starting value that gets tripled and then tripled and then tripled ... every year) is constant.
f(x) = 16×3^x
as you know, exponents have the higher priority to multiplications.
if you want to be save you can use brackets like
f(x) = 16×(3^x)
Solve each trigonometric function IN THE INTERVAL [0, 360)
sin 2x − √3 / 2 = 0
The solution of the trigonometric function sin 2x − √3/2 = 0 will be 30°, 60°, 210°, and 240°.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The trigonometric equation is given below.
sin 2x − √3/2 = 0
Simplify the equation, then we have
sin 2x − √3/2 = 0
sin 2x = √3/2
sin 2x = sin 60°, sin 120°
2x = 60°, 120°, 420°, 480°
x = 30°, 60°, 210°, 240°
The solution of the trigonometric function sin 2x − √3/2 = 0 will be 30°, 60°, 210°, and 240°.
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graph the relation. find the domain and range.
The domain of the relation is 0 ≤ x ≤ 4 and the range of the relation is all real numbers (-∞, ∞)
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
We know that Domain : the set of possible x-values (the "input" values)
And also, we know that Range : the set of y-values (the "output" values)
In the given graph we have attached below, the domain of the relation is 0 ≤ x ≤ 4
The range = all real numbers (-∞, ∞)
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Mr. Snow keeps a list of vocabulary terms that he wants his students to memorize from the textbook.
He began the year with 15 terms on the list. Of the 35 new terms in each chapter, Mr. Snow puts the definitions of 10 terms on the wall and adds the remaining terms to the vocabulary list to be memorized.
.Write an equation in slope-intercept form to represent the situation. Use x for the independent variable and y for the dependent variable. Identify what both variables represent.
The linear function in slope-intercept form that represents the equation is given as follows:
y = 15 + 25x.
The variables are given as follows:
Variable x: number of chapters read.Variable y: number of terms on the list.How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which:
The slope m represents the number of words added to the list for each chapter.The intercept b represents the initial number of words in the list.He began the year with 15 terms on the list, hence the parameter b is given as follows:
b = 15.
Of the 35 new terms in each chapter, Mr. Snow puts the definitions of 10 terms on the wall and adds the remaining terms to the vocabulary list to be memorized, hence the slope m is obtained as follows:
m = 35 - 10
m = 25.
Then the function is:
y = 25x + 15.
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Question B is where I am confused
Dan should leave his house at least on 08.33 am.
What is Addition?Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.
The process of doing addition is also called as finding the sum.
We have,
Dan has to get to work at 10.30 am.
There is a 20 minute walk from the bus stop in Coventry to work.
Dan should arrive at the bus stop in Coventry at 10.10 am.
The latest time of the bus that reaches Coventry closest to the time that Dan should reach at the bus stop in Coventry is 10.06.
The bus which reaches at Coventry at 10.06 depart from Birmingham at 08.38.
There is a 5 minutes to walk from his house to Birmingham bus stop.
Dan should leave the house at 08.33 am.
The latest time that Dan should leave the house is 08.33 am.
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a particular professor is known for his arbitrary grading policies. each paper receives a grade from the set {a, a-, b . b, b-, c }, with equal probability, independent of other papers. how many papers do you expect to hand in before you receive each possible grade at least once?
Papers do you expect to hand in before you receive each possible grade at least once is 14.7.
given,
Total number of grades= 6
Imagine Y to be number of papers till we get all grades once. Hence
Yi= Number of papers till we get i th newer grades
Expected value of Y₆= ?
The difference between getting a new grade maybe represented as
Xi= Yi+1 - Yi
Using above equation for Y₆, we get
[Y₆]= ∑⁵i=o Xi
which means, we need to get 5 different grades from the first grade.
Number of tries to see second new grade maybe represented as
X₁= {(6-1)/6}, which, for generalization is written as Xi=geo{(6-i)/6}
Xi represents the success probability of seeing further new grade.
Expected value of Xi is inverse of parameter of geometric distribution, which is,
[Xi] = 6/(6-i) = 6.{1/(6-i)}
Expected value of Y₆= [∑⁵ i=0 Xi] = ∑⁵ i=0 [Xi]
Substituting value of [Xi] in the above expression
6.∑⁵i=0 {1/(6-i)} = 6. ∑⁶i=1 (1/i)
Now solving for 6 grades
Y₆ = 6[(1/6) + (2/6) + (3/6) + (4/6) + (5/6) + (6/6)]
Y₆ = 6 x 2.45 = 14.7
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In a recent student government election, the ratio of students who voted for the winner to all the students who voted was 0.85. The number of students who voted was 60. How many votes did the winner get?
In a recent student government election, the number of vote of the winner is 51
How to determine the ratioAn ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.
In a proportion, two ratios are specified to be equal to one another in an equation.
The number of votes of the winner is calculated by writing the ratio
= number of the students who voted / total number of students
let x be the number of students that voted the winner
85 / 100 = x / 60
100x = 60 * 85
x = 5100 / 100
x = 51
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Twenty percent of US adults have some type of mental illness. You randomly select six US adults. Find the
probability that the number of US adults who have some type of mental illness is (a) exactly two, (b) at
least one, and (c) less than three.
This is a Binomial
distribution
a.
b.
C.
a. The probability of exactly two US adults having a mental illness in a sample of six is 0.235904
B. The probability of at least one US adult having a mental illness is >=21
C. The probability of less than three US adults having a mental illness is <=3
How do we find the values of the probabilities?a. The probability of exactly two US adults having a mental illness in a sample of six is given by the binomial probability formula:
P(X = 2) = (6 choose 2) * (0.2)^2 * (0.8)^4 = 0.235904
b. To find the probability of at least one US adult having a mental illness, we need to find the probability of zero or one or two or three or four or five or six US adults having a mental illness.
This can be found by summing the probabilities of each event:
P(X >= 1) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)
c. To find the probability of less than three US adults having a mental illness, we need to find the probability of zero or one or two US adults having a mental illness.
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
Note that the binomial probability formula can be used to find the individual probabilities as well.
Therefore, the correct answer is as given above
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Amal can run 1/8 mile in 1/12 minutes. If Amal can maintain that pace, how long will it take him to run 1 mile?
It will take 2/3 minutes to run 1 mile.
What is division?
The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Amal can run 1/8 mile in 1/12 minutes.
If Amal can maintain that pace,
it will take him to run 1 mile,
= 1/12 ÷ 1/8
= 1/12 x 8/1
= 8/12
= 2/3 minutes.
Therefore, the required time is 2/3 minutes.
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2/8 4. 5 Homework (Math)
Hi Kennedy, when you submit this form, the owner will be able to see your name and email address.
* Required
1. Some friends go to the store to buy school supplies. Nick spends $4. 89. Riley spends 3 times as
much as Nick. Clay spends $12. 73 more than Riley. How much did Clay spend? *
(1 Point)
Enter your answer
If Nick spends $4.89 and Riley spends 3 times as much as Nick and Clay spends $12.73 more than Riley , then the total amount spent by Clay is $27.4 .
The amount Nick spends to buy School Supplies is = $4.89 ,
the amount spent by Riley is 3 times of amount spent by Nick ,
that means , Riley spent = 3 × 4.89 = $14.67 ,
the amount spent by Clay is $12.73 more than the amount spent by Riley , which means ;
Clay spent is = $14.67 + $12.73 = $27.4 .
Therefore , Clay spent $27.4 to buy school supplies .
The given question is incomplete , the complete question is
Some friends go to the store to buy school supplies. Nick spends $4.89 Riley spends 3 times as much as Nick. Clay spends $12.73 more than Riley. How much did Clay spend ?
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Find the cp
Tea set : sp = 1546, profit % = 9%
HELPP PLEASE ITS URGENT!!!!!!!! ¡!! ¡!!!!!!!!!!!!!!!!!!! ¡!!!!!!
Answer: CP = 1418.34
Step-by-step explanation: We've to calculate the cost price (CP)
Selling price (SP) = 1546, Profit% = 9%
According to the formula,
Profit%= [tex]\frac{SP-CP}{CP} * 100[/tex]
9 = [tex]\frac{1546-CP}{CP} *100[/tex]
9*CP = (1546-CP)*100
109CP = 154600
CP = 154600/109
CP= 1418.34
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you have a coin which comes heads with probability 1/5 and you toss is 700 times if there are multiple coins in a row we call them a streak what is the expected number of streaks
If there are multiple coins in a row we call them a streak , the expected number of streaks here are 224
Attempt: I interpreted the number of streaks as the number of switch between either H to T or T to H in the sequence + 1.
The problem has a markov chain structure and so we can obtain the following equations, given S(n)
A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.
number of strike in sequence with n coins:
S(n|H) = 0.2s(n-1) + 0.8 (1+s(n-1))
S(n|T) = 0.8s(n-1) + 0.2(1+s(n-1))
This implies S(n) = S(n|T)p(T) + S(n|H)p(H)
= S(n-1) + 8/25
Therefore, E[S(700)] = 224.
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3/4 x +3-2x = -1/4 +1/2x+5
step by step pleasz lets me know what to add sub etc...
The value of x from the expression 3/4 x +3-2x = -1/4 +1/2x+5 can be simplified as 45/29.
What is simplification?The concept that will be used is simplification. To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
3/4x +3-2x = -1/4 +1/2x+5
We can simplify by collecting the like terms,
3/4x - 1/2x - 2x = -1/4 + 5 -3
Then we can simplify further as:
-29x/20 = - 9/4
29x = (20*9)/4
29x= 45
x= 45/29
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What is a asymptote?
Answer:
It is a line that continually approaches a given curve but does not meet it at any finite distance.
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
An asymptote is a line that continually approaches a given curve but does not meet it at any finite distance.
For example, for the rational function [tex]f(x)=\frac{1}{x}[/tex], there's a horizontal asymptote at y=0 because as x approaches infinity, y gets increasingly closer to 0.
Same goes for the vertical asymptote of x=0 where as y approaches infinity, x gets increasingly closer to 0.
a spherical snowball is melting in such a manner that its radius is changing at a constant rate, decreasing from 34 cm to 18 cm in 30 minutes. at what rate, in cubic cm per minute, is the volume of the snowball changing at the instant the radius is 6 cm?
The rate at which the volume of the snowball is changing at the instant the radius is 6 cm is -241.27 cm³/min.
The volume of a sphere is given by the formula V = 4/3πr³, where r is the radius of the sphere. To find the rate at which the volume is changing, we need to take the derivative of this equation with respect to time, using the chain rule.
dV/dt = 4/3π(3r²) dr/dt
We know that the radius of the snowball is decreasing at a constant rate, so we can find the value of dr/dt by using the information given in the problem. The radius is decreasing from 34 cm to 18 cm in 30 minutes, which means that:
dr/dt = (34 - 18) cm / 30 minutes = -0.5333 cm/min
Now that we know the rate at which the radius is changing, we can substitute it into the equation for dV/dt and find the rate at which the volume is changing.
We know that the radius is 6 cm at the instant the volume is changing, so we can substitute that into the equation:
dV/dt = 4/3π(3r²) dr/dt = 4/3(π)(3)(6 cm)²(-0.5333 cm/min) = -241.27 cm³/min
So, the rate at which the volume of the snowball is changing at the instant the radius is 6 cm is -241.27 cm³/min.
Note that the negative sign indicates that the volume is decreasing.
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Determine the perimeter of the right triangle shown. Round your answer to the nearest whole number, if necessary.
O 7 Units
O 14 Units
O 25 Units
O 26 Units
Answer: 26 units
Step-by-step explanation:
Let's label the left side as side a, the bottom as side b, and the hypotenuse (the diagonal side) as side c.
As you can see, side a is 8 units, and side b is 7 units. To calculate side c, you need to plug both a and b in to the Pythagoras' theorem, which states that a² + b² = c².
> 8² + 7² = c²
> 64 + 49 = c²
> 113 = c²
> c = 10.63 which would round up to 11.
Now adding up all the sides together, a + b + c = 7 + 8 + 11 = 26 units
Solve log x = 4. (5 points) 10,000 1,000 40 4
log(x) = 4 can be restated as an exponential statement: 10^4 = x
x = 10000
The height of a vase is 45. 7 centimeters when rounded to the nearest tenth of a centimeter. What is the shortest possible height of the vase? Give your answer to 3 decimal places
The shortest possible height of the vase rounded to the nearest tenth of a centimetres is 45.650.
The concept of rounding the numbers will be used here to find the answer. Concerning this, we must know, that a number will be rounded to next digit, if the subsequent number if 5 or more than 5.
We know 6 preceedes 7 and the number is rounded to nearest tenth. So, the just possible number will be 45.69. However, as mentioned, it will be rounded to 45.7. The same will happen for till 45.65. Proceeding before this, we get 45.64 which will not be rounded to 45.7. Thus, the smallest possible number is 45.65 centimetres.
Similarly, the 1 at hundredths place will be the smallest number. This is because, rounding off 5 will eventually lead to rounding off to 45.7.
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What is the percent of increase from 45 to 72?
The percent of increase from 45 to 72 is 60%.
How to find the percent of increase?Using this formula to find the percent of increase
Percent of increase= End value - Start value /Start value
Where:
End value = 72
Start value = 45
Let plug the formula
Percent of increase =(72 - 45) /45
Percent of increase =27 /45 × 100
Percent of increase = 60%
Therefore we can conclude that the percent of increase is 60%.
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a fire station is to be located along a road of length a, where a is a fixed positive real number. if fires will occur at points uniformly chosen on (0, a), where should the station be located so as to minimize the expected distance from the fire?
If fires occur at points uniformly chosen on (0, A), then [tex]a = \frac{A}{2}[/tex] is the second derivative where should the station be located so as to minimize the expected distance from the fire.
From the question, a fire station is to be located along a road of length A, A < ∞.
If fires occur at points uniformly chosen on (0, A), then we have to find where should the station be located so as to minimize the expected distance from the fire.
E∣X−a∣ = [tex]\int^{A}_{0}|x-a| \frac{1}{A} dx[/tex]
E∣X−a∣ = [tex]\int^{a}_{0}|a-x| \frac{1}{A} dx+\int^{A}_{a}|x-a| \frac{1}{A} dx[/tex]
Now integrating.
E∣X−a∣ = [tex]\frac{1}{A}\left(\frac{a^2}{2}+\frac{A^2}{2}-aA-\left(\frac{a^2}{2}-a^2\right)\right)[/tex]
E∣X−a∣ = [tex]\frac{a^2}{A}-a+\frac{A}{2}[/tex]
If we set the derivative to zero, we get [tex]\frac{2a}{A}-1=0[/tex], where [tex]a = \frac{A}{2}[/tex] is the derivative. One can look at the second derivative, which is always positive, to see if this is the minimizer.
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The complete question is:
A fire station is to be located along a road of length A, A < ∞. If fires occur at points uniformly chosen on (0, A), where should the station be located so as to minimize the expected distance from the fire? That is, choose a so as to minimize E[∣X−a∣] when X is uniformly distributed over (0, A).
an automobile manufacturer claims that their jeep has a 55 miles/gallon (mpg) rating. an independent testing firm has been contracted to test the mpg for this jeep. after testing 751 jeeps they found a mean mpg of 54.6 with a standard deviation of 2.7 mpg. is there sufficient evidence at the 0.05 level that the jeeps have an incorrect manufacturer's mpg rating? state the null and alternative hypotheses for the above scenario.
Null hypothesis: H₀ : μ = 55
Alternative hypothesis: H₁: μ [tex]\neq[/tex] 55
Given,
Rating = 55 mpg
For a two-tailed alternative hypothesis, it involves the "not equal to symbol,≠ ". This can never be in the null hypothesis. In order to reject the null hypothesis, the test statistic must be smaller than the critical value on the left tail or greater than the critical value on the right tail.
the claim is the jeep has a 55 mpg rating and we want to test whether the rating is correct or incorrect. So, it is a two-tailed hypothesis because the rating can be less than or more than 55 mpg.
Therefore, H₀ : μ = 55
H₁: μ [tex]\neq[/tex] 55
These are the required null and alternative hypotheses.
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Solve for x:
1/4 |x + 1| ≥ 4
Please show how its done
Answer:
x ≤ - 17 or x ≥ 15
Step-by-step explanation:
[tex]\frac{1}{4}[/tex] | x + 1 | ≥ 4 ( multiply both sides by 4 to clear the fraction )
| x + 1 | ≥ 16
Inequalities of the type | ax + b | ≥ c , have solutions of the form
ax + b ≤ - c or ax + b ≥ c , then
x + 1 ≤ - 16 ( subtract 1 from both sides )
x ≤ - 17
or
x + 1 ≥ 16 ( subtract 1 from both sides )
x ≥ 15
solution is x ≤ - 17 or x ≥ 16
See screenshot below.
By polar form properties, the product of complex numbers (5 · cos 225° + i 5 · sin 225°) and (2 · cos 135° + i r₂ · sin 135°).
How to multiply complex numbers
In this question we find the case of the product of two complex numbers in rectangular form but including features of polar form (magnitude, direction). Then, we have the following situation:
(r₁ · cos θ₁ + i r₁ · sin θ₁) · (r₂ · cos θ₂ + i r₂ · sin θ₂)
Result can be found easily by transforming the expression into polar form:
(r₁, θ₁) · (r₂, θ₂) = (r₁ · r₂, θ₁ + θ₂)
[r₁ · r₂ · cos (θ₁ + θ₂) + i r₁ · r₂ · sin (θ₁ + θ₂)]
If we know that r₁ = 5, r₂ = 2, θ₁ = 225° and θ₂ = 135°, then the product of the complex number is:
10 · [cos 360° + i sin 360°]
10 · (1 + i 0)
10
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Convert. Simplify your answer and write it as a proper fraction or as a whole or mixed
number.
? Teaspoons = 7 1/3 tablespoons
Based on the conversion of tablespoon to teaspoon, 7 1/3 tablespoons is equal to 22 teaspoons.
What is a conversion factor?In Science, a conversion factor is a number that is used to convert a number in one set of units to another, either by dividing or multiplying.
Generally speaking, there are three (3) teaspoons in one (1) tablespoon. This ultimately implies that, a proportion or ratio for the conversion of tablespoon to teaspoon would be written as follows;
Conversion:
3 teaspoons (tsp) = 1 tablespoon (tbsp)
X teaspoons (tsp) = 7 1/3 tablespoons (tbsp)
Cross-multiplying, we have:
X teaspoons (tsp) = 7 1/3 × 3
X teaspoons (tsp) = 22/3 × 3
X teaspoons (tsp) = 22 teaspoons.
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