The general solution of the system x' (t) is[tex]X(t)=c_1\left(\left[\begin{array}{c}-5 \\2\end{array}\right] \cos 3 t-\left[\begin{array}{l}1 \\0\end{array}\right] \sin 3 t\right)[/tex][tex]+c_2\left(\left[\begin{array}{c}1 \\0\end{array}\right] \cos 3 t+\left[\begin{array}{c}-5 \\2\end{array}\right] \sin 3 t\right)\end{gathered}[/tex]
The given system of equation is X'A=X
where
[tex]$$A=\left[\begin{array}{cc}-15 & -39 \\6 & 15\end{array}\right]$$[/tex]
Eigenvector of a square matrix is defined as a non-vector in which when a given matrix is multiplied, it is equal to a scalar multiple of that vector. Let us suppose that A is an n x n square matrix, and if v be a non-zero vector, then the product of matrix A, and vector v is defined as the product of a scalar quantity λ and the given vector, such that:
Av =λvWhere
v = Eigenvector and λ be the scalar quantity that is termed as eigenvalue associated with given matrix A
The values of A are given by
[tex]$|A-\lambda I|=0 \\\left|\begin{array}{cc}-15-\lambda & -39 \\6 & 15-\lambda\end{array}\right|=0 \\[/tex]
[tex](-15-\lambda)(15-\lambda)-(6)(-39)=0 \\[/tex]
[tex]\Rightarrow-(15+\lambda)(15-\lambda)+(6)(39)=0 \\[/tex]
[tex]\\\Rightarrow(15+\lambda)(15-\lambda)-(6)(39)=0 \\\\\Rightarrow 225-\lambda^2-234=0 \\[/tex]
[tex]\Rightarrow-\lambda^2-9=0 \\[/tex]
[tex]\Rightarrow \lambda^2=-9 \\[/tex]
[tex]\Rightarrow \lambda=\pm 3 i[/tex]
Now, eigen vector u corresponding to [tex]$\lambda=3 i$[/tex] is given by
[tex]$$\begin{gathered}{[A-3 i I] u=O} \\{\left[\begin{array}{cc}-15-3 i & -39 \\6 & 15-3 i\end{array}\right]\left[\begin{array}{l}u_1 \\u_2\end{array}\right]=\left[\begin{array}{l}0 \\0\end{array}\right]} \\\\\end{gathered}$$[/tex]
Applying [tex]R_2 \rightarrow R_2-6 R_1[/tex]
[tex]& {\left[\begin{array}{cc}1 & \frac{-39}{-15-3 i} \\0 & 0\end{array}\right]\left[\begin{array}{l}u_1 \\u_2\end{array}\right]=\left[\begin{array}{l}0 \\0\end{array}\right]} \\[/tex]
[tex]& \Rightarrow u_1+\frac{39}{15+3 i} u_2=0 \\[/tex]
[tex]& \Rightarrow u_1=-\frac{13}{5+i} u_2=-\frac{13}{5+i} * \frac{5-i}{5-i} u_2=-\frac{13(5-i)}{26} u_2=-\frac{5-i}{2} u_2 \\[/tex]
Thus, by choosing [tex]$u_2[/tex]=1 eigenvector corresponding to [tex]$\lambda=3 i$[/tex] is [tex]$$u=\left[\begin{array}{c}-\frac{5-i}{2} \\1\end{array}\right]$$[/tex]
[tex]R_1 \rightarrow \frac{1}{-15+3 i} R_1 \\[/tex]
[tex]{\left[\begin{array}{cc}1 & \frac{-39}{-15+3 i} \\6 & 15+3 i\end{array}\right]\left[\begin{array}{l}v_1 \\v_2\end{array}\right]=\left[\begin{array}{l}0 \\0\end{array}\right]} \\[/tex]
Applying [tex]R_2 \rightarrow R_2-6 R_1 \\[/tex]
[tex]{\left[\begin{array}{cc}1 & \frac{-39}{-15+3 i} \\0 & 0\end{array}\right]\left[\begin{array}{l}v_1 \\v_2\end{array}\right]=\left[\begin{array}{l}0 \\0\end{array}\right]} \\[/tex]
[tex]\Rightarrow v_1+\frac{39}{15-3 i} v_2=0 \\\Rightarrow v_1=-\frac{39}{15-3 i}[/tex]
[tex]\begin{gathered}\Rightarrow v_1+\frac{39}{15-3 i} v_2=0 \\\v_2=-\frac{13(5+i)}{26} \\\Rightarrow v_1==-\frac{5+i}{2}\end{gathered}$$[/tex]
Thus, by choosing [tex]$v_2=1$[/tex] eigenvector corresponding to [tex]$\lambda=-3 i$[/tex] is
[tex]$$v=\left[\begin{array}{c}-\frac{5+i}{2} \\1\end{array}\right]$$[/tex]
Hence, the general solution is given by
[tex]X(t)=c_1 e^{3 i t} u+c_2 e^{-3 i t} v \text { [using } e^{i t}=\cos t+i \sin t \\[/tex]
[tex]X(t)=c_1\left[\begin{array}{c}-\frac{5-i}{2}(\cos 3 t+i \sin 3 t) \\(\cos 3 t+i \sin 3 t)\end{array}\right]+c_2\left[\begin{array}{c}-\frac{5+i}{2}(\cos 3 t-i \sin 3 t) \\(\cos 3 t-i \sin 3 t)\end{array}\right] \\[/tex]
[tex]X(t)=c_1\left[\begin{array}{c}-\frac{5}{2}(\cos 3 t+i \sin 3 t)+\frac{i}{2}(\cos 3 t+i \sin 3 t) \\(\cos 3 t+i \sin 3 t)\end{array}\right][/tex][tex]+c_2\left[\begin{array}{c}-\frac{5}{2}(\cos 3 t-i \sin 3 t)-\frac{i}{2}(\cos 3 t-i \sin 3 t) \\(\cos 3 t-i \sin 3 t)\end{array}\right] \\[/tex]
[tex]X(t)=c_1\left[\begin{array}{c}-\frac{5}{2} \cos 3 t-\frac{5 i}{2} \sin 3 t+\frac{i}{2} \cos 3 t-\frac{1}{2} \sin 3 t \\\cos 3 t+i \sin 3 t\end{array}\right][/tex][tex]+c_2\left[\begin{array}{c}-\frac{5}{2} \cos 3 t+\frac{5}{2} i \sin 3 t-\frac{i}{2} \cos 3 t-\frac{1}{2} \sin 3 t \\\cos 3 t-i \sin 3 t\end{array}\right ][/tex]
[tex]X(t)=c_1\left(\left[\begin{array}{c}-5 \\2\end{array}\right] \cos 3 t-\left[\begin{array}{l}1 \\0\end{array}\right] \sin 3 t\right)[/tex][tex]+c_2\left(\left[\begin{array}{c}1 \\0\end{array}\right] \cos 3 t+\left[\begin{array}{c}-5 \\2\end{array}\right] \sin 3 t\right)\end{gathered}[/tex]
Therefore, the general solution of the system X(t) is [tex]X(t)=c_1\left(\left[\begin{array}{c}-5 \\2\end{array}\right] \cos 3 t-\left[\begin{array}{l}1 \\0\end{array}\right] \sin 3 t\right)[/tex][tex]+c_2\left(\left[\begin{array}{c}1 \\0\end{array}\right] \cos 3 t+\left[\begin{array}{c}-5 \\2\end{array}\right] \sin 3 t\right)\end{gathered}[/tex].
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3
10
3
Kathy has of a yard of fabric. She needs
of a yard to make a
4
headband. How many WHOLE headbands can she make?
Kathy can make 10 headbands from 3/4 of a yard of fabrics.
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The unit rate is the ratio of two different units. The unit rate must always have a denominator equal to 1.
Kathy has 3/4 of a yard of fabric. She needs 3/10 of a yard to make a 4 headband.
Hence:
3/10 yards = 4 head band
For 3/4 yard:
number of headbands = 3/4 yard * 4 headband per 3/10 yard = 3/4 * 4 / (3/10) = 3/4 * 4 * 10/3 = 10
Kathy can make 10 headbands
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what's the probability tgat a junior bio major who has taken statistics has also taken a computer course
The probability that a junior bio major who has taken statistics has also taken a computer course is 13.46%.
We are trying to find the probability that a junior bio major who has taken a statistics course has also taken a computer course. This is referred to as the conditional probability, denoted as P(computer | statistics).
To calculate this, we can use the formula:
P(computer | statistics) = P(computer and statistics) / P(statistics)
This formula states that the probability of a junior bio major taking a computer course given that they have taken a statistics course is equal to the probability of them taking both a computer and statistics course divided by the probability of them taking only a statistics course.
The information given in the problem is as follows:
P(statistics) = 52%
P(computer) = 23%
P(computer and statistics) = 7%
So we can plug these values into the formula to calculate the conditional probability:
P(computer | statistics) = P(computer and statistics) / P(statistics) = 7% / 52% = 0.1346153846153846 or 13.46%
Therefore, the probability that a junior bio major who has taken statistics has also taken a computer course is 13.46%.
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The complete Question is:
A university requires its biology majors to take a course called BioRe search. The prerequisite for this course is that students must have taken either a Statistics course or a computer course. By the time they are juniors, 52% of the Biology majors have taken Statistics, 23% have had a computer course , and 7% have done both. What's the probability that a junior bio major who has taken statistics has also taken a computer course?
make x the subject: y=4x+3
Answer:
y equals to 4x + 3
subtract 3 on both side
4 - 3 equals to 4x + 3 - 3
divide the equation by 4 on both sides
y-3/4 = 4x/4
X = y-3/4
the last page of a book is numbered 764. the book is 3.00 cm thick. what is the average thickness of a sheet of paper in the book, in centimeters?
The average thickness of a page in the book= is 0.00393cm
determining the thickness of a page
One page has a thickness of 0.12 mm. Therefore, it's easy; all you have to do is add up the pages and divide that number by two. Then double that result by a page's thickness.
A book has 764 pages in total, including the final page.
3.0 cm is how thick the book is.
Divide across 764 to find the thickness of a page from the book: 3.0/764 = 0.003926701
which is roughly equal to 0.00393 cm
Consequently, 0.00393 cm is the average thickness of a book page.
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525 corn plants, which are all arranged in rows. the number of plants in each row is 4 less than the number of rows. how many rows of corn plants are on the farm?
The required number corn plants are on the farm are 21.
How to find the number of plants in the row of garden?metre stick counting techniques. Count the seedlings for each metre of the row using a metre stick. To calculate plants per square metre, multiply that amount by 100, then divide it by the seed spacing in centimeters.
According to data:Let the number of rows be x.
the number of corn plants = x - 4
So,
x(x - 4) = 525
x^2 - 4x - 525 = 0
On solving the above quadratic equation, we get
x = 25, x = -21
Thus, number of corn plants in the row are 52 - 4 = 21
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The NFL decided to change the number of regular season games from 16 to 17 games. What is the percent increase? Answer to the hundredth place.
Answer:
6.25%
Step-by-step explanation:
17 - 16/16 x 100% = 6.25%
Suppose a student named Marcus wants to learn about the sleeping habits of students in his class. Marcus wants to collect data from his classmates to learn how many hours of sleep his classmates get. He then wants to process this data with a computer and visualize it in a Histogram. Which of the following would be the best technique for Marcus to collect this data
From the above given options by using app is more accurate and reliable so option b is correct
The question is incomplete the options are not given the options are:
a. Marcus should ask each of his classmates to write down on a piece of paper how many hours of sleep they get per night and hand the paper to him.
b. Marcus should have them download an app that tracks their phone geolocation and activity so he can see when their phones are in their rooms and not being used. From this data he can figure out how long each student sleeps.
given that
Marcus wants to learn about the sleeping habits of students in his class.
Marcus wants to collect data from his classmates to learn how many hours of sleep his classmates get.
He then wants to process this data with a computer and visualize it in a Histogram
survey can be done in different ways:
1. by asking question
2. survey
3. observation
From the above given options by using app is more accurate and reliable so option b is correct
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pick a two digit number greater than 49 but less than 65 rewrite your two digit number is a difference of two numbers, show how to use the identity (x - y)² = x² - 2xy + y² to square your number.
The exterior sides of two adjacent angles make a right angle. The first angle has a measure that is 6 more than half of the second . What are the measures of both angles ?
Answer:
Angle 1 = 34°
Angle 2 = 56°
Step-by-step explanation:
To solve, recall that a right angle equals 90°, then write an equation using the given information equalling 90°. For this problem, let the second angle equal x. So,
[tex]x+(\frac{1}{2}x+6)=90\\\frac{3}{2}x+6=90\\\frac{3}{2}x=84\\3x=168\\x=56[/tex]
The angle measure of the second angle is 56°. To find the angle measure of the first angle, subtract 56° from the given 90°. The first angle measure is 34°. To check:
[tex]34=(\frac{1}{2})(56)+6\\34=28+6\\34=34[/tex]
The derived angle measures are correct.
The formula for the area of a triangle is A = bh/2.
If the base increases by 10%, and the height increases by 10%,
then the area A increases by X%. Find the exact value of X.
The formula for the area of a triangle is A = bh/2.
If the base increases by 10% from b to b(1+10/100) = b(1.1) and the height increases by 10% from h to h(1+10/100) = h(1.1)
then the new area A' = (b(1.1))(h(1.1))/2
To find the percentage increase in area we can use the formula:
X% = (A'-A)/A * 100%
Plugging in the values we have
X% = (b(1.1)h(1.1))/2 - bh/2 / bh/2 * 100%
Simplifying we get
X% = (bh(1.1)^2 - bh)/(bh/2) * 100% = (1.1)^2 * 100% - 100% = 21%
Therefore, the area A increases by 21%.
I hope this helps :)
define a positive integer n to be a factorial tail if there is some positive integer m such that the decimal representation of m! ends with exactly n zeroes. how many positive integers less than 1992 are not factorial tails?
On solving the provided question, we can say that there are 7975/5 - 1595 distinct positive number f(m) less than 1992, 1991-1595 = 396 positive integer.
What is integer?Zero, a positive integer, or a negative integer denoted by a minus sign are all examples of integers. A negative number is the additive reciprocal of a positive number that it corresponds to. A bold Z or a bold "mathbb Z" is frequently used in mathematical notation to denote a group of integers. A positive, negative, or zero integer—not a fraction—is referred to as an integer (pronounced IN-tuh-jer). The numbers -5, 1, 5, 8, 97, and 3,043 are examples of integers. 1.43, 1 3/4, 3.14, and other numbers are non-integer examples. Integers are a collection of integers and their antipodes. Decimals and fractions are not part of the set of integers.
suppose number of zeroes m! be f(m)
f(m) = m/5 + m/25 + m/125 + m/625 + ...
f(m) = f(m+1) = f(m+2) = f(m+3) = f(m+4)
since, f(m)< m/5 + m/25 + m/125 + m/625 + ... = m/4
f(7975) = 1991
there are 7975/5 - 1595 distinct positive number f(m) less than 1992, 1991-1595 = 396 positive integer
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A donut shop make 150 donuts in 10 hours how much donuts will they make in 18 hours???
Answer:
270 donuts
Step-by-step explanation:
We need to find the number of donuts they make per hour. To find that, take the known number of donuts divided by the known number of hours.
150/10=15, so 15 donuts per hour.
Now, we multiply 18x15 and find they will have made 270 donuts.
How do you write an interval notation on quadratic inequality?
Solve for x values that satisfy a quadratic inequality to write interval notation. This usually involves factoring the quadratic and putting it equal to zero, then utilizing the inequality sign to select viable solutions. After finding the answers, write (a,b) to indicate the interval of x-values that make the inequality true. The interval notation for -3 and 5 is (-3,5).
What is interval notation?Generally, Before you can create an interval notation for a quadratic inequality, you must first solve for the values of x that are compatible with the inequality being satisfied. In most cases, this will require factoring the quadratic expression and fixing it so that it equals zero.
After that, the sign of inequality will be used to decide which solutions are appropriate. After you have determined the solutions, you may indicate the range of x-values that cause the inequality to hold using the notation (a,b), where a and b stand for the solutions, respectively.
As an illustration, the interval notation would look like this if the answers were -3 and 5. (-3,5).
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evaluate [tex]5\sqrt{75} - 3\sqrt{48} +2\sqrt{27\\}[/tex]
Answer:
[tex]19\sqrt{3}[/tex]
Step-by-step explanation:
Simple math. You could extrapolate the square roots and simplify the coefficients to easily subtract numbers with the same roots.
Geoffrey draws a triangle, one of the angles measure 75 and one of the angles measure 40 what is the measure of the third angle?
As per the measures of given triangle, the measure of the third side is 65°
The term triangle in math is defined as a three-sided polygon, which has three vertices.
Here we have know that the three sides are connected with each other end to end at a point, which forms the angles of the triangle.
Here we have given that Geoffrey draws a triangle, one of the angles measure 75 and one of the angles measure 40
As we all know that the sum of all three angles of the triangle is equal to 180 degrees.
Then let us consider that the third side is x.
Then it can be calculated as,
=> 75 + 40 + x = 180
=> 115 + x = 180
=> x = 180 - 115
=> x = 65°
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what can multiply to equal 30 but adds to equal 9
Answer:1, 2, 3, 5, 6, 10, 15 and 30.
Step-by-step explanation:
Determine the equation of the circle with center (0, -5) containing the point
(-√60,-6).
Answer:
x² + (y + 5)² = 61
Step-by-step explanation:
the equation of a circle in standard form is
(x - a)² + (y - b)² = r²
where (a, b ) are the coordinates of the centre and r is the radius
here (a, b ) = (0, - 5 ) and r has to be found
(x - 0)² + (y - (- 5) )² = r² , that is
x² + (y + 5)² = r²
the radius is the distance from the centre to a point on the circle.
using the distance formula to find r
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (0, - 5 ) and (x₂, y₂ ) = (- [tex]\sqrt{60}[/tex] , - 6 )
r = [tex]\sqrt{(-\sqrt{60}-0)^2+(-6-(-5))^2 }[/tex]
= [tex]\sqrt{(-\sqrt{60})^2+(-1)^2 }[/tex]
= [tex]\sqrt{60+1}[/tex]
= [tex]\sqrt{61}[/tex]
then r² = ( [tex]\sqrt{61}[/tex] )² = 61
the equation of the circle is then
x² + (y + 5)² = 61
how do sociologists know if the sample they are using is representative? a. if the sample has an even number, decided by the researcher, of people from several different categories or backgrounds
If the sample has the same mix of people, in the same proportions, as the population being studied then sociologists know if the sample they are using is representative. So the option c is correct.
No subject is off-limits when sociologists use the sociological lens and start asking questions. Every facet of human behaviour has the potential to be studied. Sociologists cast doubt on the society that people have built and inhabit. They observe behavioral patterns as individuals navigate that world.
Sociologists have uncovered workplace patterns that have revolutionized industries, family patterns that have educated parents, and educational patterns that have supported structural changes in classrooms by using sociological methodologies, methodical research, and a scholarly interpretive approach.
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The complete question is;
How do sociologists know if the sample they are using is representative?
a. If the people in the sample freely volunteered to serve as representatives
b. If the sample has an even number, decided by the researcher, of people from several different categories or backgrounds
c. If the sample has the same mix of people, in the same proportions, as the population being studied
d. If the participants have been interviewed to reveal possible bias.
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.75, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Equally likely and unlikely
Likely
Unlikely
This value is not possible to represent probability of a chance event.
It is likely to randomly select a chocolate chip cookie from the batch.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
here,
The probability of selecting the chocolate chip is given as 0.75.
Which is more than 50%
So, it is likely to randomly select a chocolate chip cookie from the batch.
Thus, It is likely to randomly select a chocolate chip cookie from the batch.
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Answer: B: Likely
Step-by-step explanation:
which grade it now scoring option averages some but not necessarily all of your attempts? keep the highest averaging do no harm imagine that your instructor chose to use the do no harm scoring method in grade it now mode. here are your scores: first attempt: 2/10 second attempt: 10/10 third attempt: 3/10 what would be your final score? 5 6 10
keep the highest averaging do no harm imagine that your instructor chose to use the do no harm scoring method in grade it now mode. so My final score is 5/10
What is Mode?
In statistics, the value that consistently appears in a particular set is referred to as the mode. The mode or modal value in a data set is sometimes referred to as the value or number that occurs most frequently in the data set. In addition to mean and median, it is one of the three measures of central tendency.
For a limited number of observations, the mode is simple to find. There could be one mode, several modes, or none at all for a given collection of values.
When we use highest scoring method in Mode, we keep the Highest will give the highest score if the scores are different.
So that the final score is 5/10
because average of 2/10+3/10+10/10 /3= 5/10
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which of the following is false the intermediate value theorem mean value theorem extreme value theorem
Which of the following is untrue: the extreme value theorem, mean value theorem, or intermediate value theorem? All three of the calculus-related theorems—Intermediate Value Theorem, Mean Value Theorem, and Extreme Value Theorem—are valid.
Write about the theorem.According to the intermediate value theorem, a continuous function must take on the value "c" at some point in the interval if it is defined on a closed interval and the value "c" is between the function's minimum and maximum values.
According to the Mean Value Theorem, if a function can be differentiated on an open interval, then at least one point in the interval has a derivative equal to the function's average slope.
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Complete Question is: Which of the following is false according to calculus: the extreme value theorem, mean value theorem, or intermediate value theorem?
addition subtraction of radicals
Step-by-step explanation:
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A local ice-cream shop sells ice-cream cones for $2.00, and customers can choose from the following options.Ice-cream flavorType of cone: sugar or waffleChocolate dipped for an additional $0.50Sprinkles for an additional $0.50Which of the following is a quantitative variable?answer choicesIce-cream flavorType of coneChocolate dipped or notSprinkles or notThe total cost of the cone
4, 5 and 6 are quantitative variable
given that
Quantitative variablesWhen you collect quantitative data, the numbers you record represent real amounts that can be added, subtracted, divided, etc. There are two types of quantitative variables: discrete and continuous.
When you graph or plot statistical data, make sure you have quantitative data of known units. If you don’t have known units, then you won’t be able to graph it.
Variables whose values result from counting or measuring something.
Examples: height, weight, time in the 100 yard dash, number of items sold to a shopper
answer choices
1. Type of cone
2.Chocolate dipped: yes / no
3.Sprinkles: yes / no
4.Cost of chocolate dip
5.Cost of sprinkles
6.Cost of one cone
4, 5 and 6 are quantitative variable
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A grocery store sells a bag of 6 oranges for $5.22. What is the cost of oranges, in dollars per orange?
jason is driving from his home to his office, which is $20$ miles away. he normally drives at a constant speed of $50$ miles per hour for the whole trip. however today, twelve minutes into his drive, his car breaks down. he calls a taxi, and it arrives fifteen minutes later. the taxi driver then takes him to his office driving at a constant speed of $40$ miles per hour. how much longer was this trip today than his usual drive to work, in minutes?
Jason's trip was 9 minutes longer than his usual drive to work.
Given that,
Distance from Jason's home to office = 20 miles
Speed of driving from home to office = 50 miles/hour
Total time taken to reach from home to office = distance ÷ speed = 20/50 = 0.4 hours = 24 minutes
Thus, on a normal day, Jason takes 0.4 hours to reach his office from home.
Now, Jason drove for 12 minutes when his car broke down,
The taxi arrived 15 minutes later and drove at 40 miles/hour,
Total time spent to reach office from taxi= distance ÷ speed = 20/40 = 0.5 hours= 30 minutes
Although he already spent 12 minutes driving before the taxi arrived so,
30 - 12 = 18 minutes.
But, he waited for the taxi to arrive for 15 minutes so,
18+15 = 33 minutes.
Thus, today Jason took 33 minutes to reach the office from his home.
Therefore, Jason took (33- 24)minutes which is equal to 9 minutes longer than his usual drive to work.
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From 8.30, bell A rings every 8 minutes and Bell B rings every 32 minutes. after how many minutes will the ring again at the same time for the second time.
Answer:
9:02
Step-by-step explanation:
The least common multiple (LCM) of 8 and 32 is 32.
Therefore, both bells will ring at the same time after 32 minutes, at 9:02.
plese hurrrrrrrrrrrrrrrry
A right triangle and two of its side lengths are shown in the diagram.
Which measurement is closest to the value of x in centimeters? Round to the nearest tenth.
100 points
Answer: 14.4
Step-by-step explanation:
Pythagorean theorem states that a² + b² = c²
Using this,
8² + 12² = c²
64 + 144 = c²
208 = c²
c = 14.4 when rounded to the nearest tenth
i really need help
please and thank you
The equation 70 + 9.5x = 184 represents the situation and the number of visits is 12 if Marques has a points card for a movie theater.
We define a linear equation.Any model that meets the algebraic equation y=mx+b is said to be linear. B is the slope, and m is the y-intercept. Since both y and x are distinct factors, the preceding sentence is commonly referred as a "mathematical model with two variables." Two-variable linear equations are referred to as bivariate equations. There are several applications for linear equations, all of which end in zero.
Here,
It is given that:
Marques has a points card for a movie theater. • He receives 70 rewards points just for signing up
Let x be the number of visits.
The linear equation can be framed as follows:
70 + 9.5x = 184
9.5x = 184 - 70
After solving the above linear equation in one variable:
9.5x = 114
x = 12
Thus, the equation 70 + 9.5x = 184 represents the situation and the number of visits is 12 if Marques has a points card for a movie theater.
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Eleri books a climbing activity.
There are 138 people in total on the activity.
The people are put into teams.
There are 12 people in each team.
Any people left over are in a small group.
How many teams are there?
Show how many people are in the small group.
Show your working and your and your answer here
Answer:
Step-by-step explanation:
Divide 138 by 12.
The answer would be 11.5.
Lets leave the 0.5 right now.
So, there would be 11 teams left and the other people left will be in the small group.
Now, multiply 12 by 11. You get 132. Subtract that from 138 and you get the remainder which is 6.
Hence, the number of people in the small group would be 6.
Thanks
Answer:
11 teams & 6 people in the small group
Step-by-step explanation:
138 = 11.5
12
So we can take it as 11 teams
12 × 11 = 132
138 -132 = 6
Therefore remaining people are added to small group
store a sells four times as many products as store b and one fifth as many as store c. if store c sells 122,420 products, how many products does store b sell?
If store c sells 122,420 products, then store b sells 6121 products.
Let x = number of products store a sells
If store a sells one fifth as many as store c, then we can write this expression as:
x = 1/5(122,420)
Evaluating, we have:
x = 24,484
If store a sells four times as many products as store b, then we can write the expression for the number of products store b sells as:
x = 4(number of products store b sells)
Plug in the value of x, we have:
24,484 = 4(number of products store b sells)
number of products store b sells = 6121
Therefore, store b sells 6121 products.
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