Answers
Answer:
1 a)8 miles per hour 1 b) 1 hour and 90 minutes 2 a) 24 hours and 6minutes 2 b) 3hours 3 a) 260 hours and 45 minutes 3 b) 40 minutes
Step-by-step explanation:
I don't know for sure if this is all correct but at least you'll have something to write down
Answer:
1a. 8 miles per hour
1b. 32 km per hour
2a. 28 miles
2b. 3 hours
3a. 2925
3b. 1/4 hour or 15 minutes
Step-by-step explanation:
For number 1a, think of 2 1/2 hours equals 20 miles as 2 1/2x=20. The x being hours, and the 20 being 20 miles. You want the equation to become x=?. So you divide 2 1/2x=20 by 2 1/2 to make the equation start with x=. You end up with x=8. Or you could just think of it as divide 20 miles by 2 1/2 hours. Either way, you end up with 8 miles per hour. For number 1b, you do the same thing as before, but you have to make 4 hours and 45 minutes a fraction. So, the are 60 minutes in an hour, so the fraction would be 45/60. Then you simplify that down to 3/4. So, 152 km divided by 4 3/4 is 32 km per hour.
For number 2a, set aside 30 minutes for now. She can go 24 miles in 3 hours. Because 8 miles times 3 hours equals 24 miles. It’s like instrad of 8 miles per hour, it’s 24 miles per 3 hours. Then, because 30 minutes is half of an hour, 8 divided by 2 would make it 4 miles per half an hour. So 24 plus 4 is 28 miles. For number 2b, you want to know how many hours it took to travel 1980 miles. Since you already knowmthat is takes one hour to go 660 miles, pretend that each 660 miles is one hour. So you divide 1980 by 660 so see how many one hours fit. You get 3. So, an airplane can fly 1980 miles in 3 hours.
For number 3a, like 2a, you basically multiply the constant speed by the full hours then the fraction, and add them together. You could also just multiply the constant speed by the number 3 3/4. That way you get the miles per 3 3/4 hours. 3 3/4 times 780 is 2925. So the plane can fly 2925. For number 3b, to get the 2 miles per ? hours, you have to divde 8 by 4 to get to 2. So you divide 1 hour by 4 to get the answer. So it’s 1/4, (one fourth of an hour) or 15 minutes 1/4 of 60 (the amount of minutes in an hour) for Mary to go 2 miles.
Related Questions
1. The sum of 4th and 6th progression is 42. The sum of 3rd and 9th term of the progression is 52. Find a). First term b.) the common difference. c). the sum of the first 10 terms of the progression.
Answers
Answer:
a) The first term of the progression is 4.5.
b) The common difference of the progression is 4.
c) The sum of the first 10 terms of the progression is 225.
Step-by-step explanation:
To solve this problem, you can use the formula for the sum of an arithmetic series. An arithmetic series is a sequence of numbers in which each term is obtained by adding a fixed number, called the common difference, to the preceding term.
The sum of an arithmetic series with n terms and a common difference d is given by:
Sum = n/2 * (2a + (n-1)d)
Where a is the first term of the series and d is the common difference.
In this problem, you are given that the sum of the 4th and 6th terms is 42 and the sum of the 3rd and 9th terms is 52. You can use these two equations to solve for a and d.
First, let's find the sum of the 4th and 6th terms:
Sum = 4/2 * (2a + 3d) = 42
This simplifies to:
2a + 3d = 21
Next, let's find the sum of the 3rd and 9th terms:
Sum = 6/2 * (2a + 5d) = 52
This simplifies to:
2a + 5d = 26
Now that we have two equations, we can solve for a and d by using substitution or elimination.
To use substitution, we can solve the second equation for d:
d = (26 - 2a)/5
Then, we can substitute this expression for d into the first equation:
2a + 3((26 - 2a)/5) = 21
This simplifies to:
2a + 3(26 - 2a)/5 = 21
Which simplifies to:
2a + 3(26)/5 - 3(2a)/5 = 21
This simplifies to:
2a + 3(26)/5 - 6a/5 = 21
This simplifies to:
-4a + 3(26)/5 = 21
This simplifies to:
-4a + 39 = 21
This simplifies to:
-4a = -18
This simplifies to:
a = 4.5
Now that we know the value of a, we can substitute it back into one of the original equations to find the value of d:
2(4.5) + 3d = 21
This simplifies to:
9 + 3d = 21
This simplifies to:
3d = 12
This simplifies to:
d = 4
Now that we have found the values of a and d, we can use the formula for the sum of an arithmetic series to find the sum of the first 10 terms of the progression:
Sum = 10/2 * (2(4.5) + (10-1)(4))
= 10/2 * (9 + 36)
= 10/2 * 45
= 225
Therefore, the sum of the first 10 terms of the progression is 225.
Answer:
Hence,
Common difference is
First term is
Sum of first 10 terms is 47
Step-by-step explanation:
a4 + a6 =42 eq1
a3 + a9 =52 eq
a1=?
d=?
S10=?
From eq 1,
a4 + a6=42
a1+3d + a1+5d =42
2a1 + 8d= 42 eq 3
From eq 2,
a3 + a9 =52
a1+2d + a1+8d = 52
2a1 + 10d = 52 eq 4
Subtract eq 3 from eq
2a1 + 10d =52
-2a1 -8d = -42
==============
2d = 10
d=5....
≈=======================
Putting value of d in eq
2a1 +10 d=52
2a1+ 50 =52
a1 =1
================
Now we find sum of first 10 terms,
S10 = 2a1 + 9d
S10 = 2+45
S10 = 47
===========
which of the following pearson correlations shows the greatest strength or consistency of relationship? 0.85 0.95 -0.35 -0.70
Answers
0.95 is Pearson correlation shows the greatest strength or consistency of relationship
Pearson correlation is a statistic measuring the linear interdependence between two variables or two sets of data.
The value of correlation coefficient must be between -1.00 and +1.00 that measures the strength and direction of the relationship between two variables.
When one variable changes, the other variable changes in the same direction.
The closer to either indicates a stronger relationship or the greatest strength or the consistency of the relationship.
The strongest must be 0.95. It is a strong positive correlation.
The correct answer is = 0.95
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Fill in the P = X x values to give a legitimate probability distribution for the discrete random variable X , whose possible values are − 2 , 1 , 2 , 3 , and 6 .
Answers
Answer:
2
Step-by-step explanation:
whose possible values are − 2 , 1 , 2 , 3 , and 6 .
James was eating a bag of candies that came in eight different colors. He noticed that there appeared to be far fewer green candies than any of the other colors and wondered if the true proportion of green candies was lower than the 12.5% that would be expected if all of the candies came in even amounts. For the sake of statistics, he decided that he would need to buy more candy to test his hypothesis. James randomly selected several bags and candies and recorded the color of each piece of candy. He found that out of the first 400 candies that he chose, 39 of them were green. James conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of green candies was lower than 12.5%.
Answers
uuuuuuuuuuuuuuuurrrrrrrrrrrrrrrr mom
3(x-7)+12=1/4(12x-8)-7
Answers
Answer:
What's the question? Ill try to answer in comments
Step-by-step explanation:
DEF is shown on the coordinate plane below.
D(-9,8)
E(9,5)
F(-5,-9)
What is the perimeter of DEF? If necessary, round your answer to the nearest tenth.
Answers
Answer:
55.5
Step-by-step explanation:
[tex]DE=\sqrt{(-9-9)^2+(8-5)^2}=\sqrt{333} \\ \\ DF=\sqrt{(-9-(-5))^2+(-9-8)^2}=\sqrt{305} \\ \\ EF=\sqrt{(-5-9)^2+(-9-5)^2}=\sqrt{392}[/tex]
The perimeter is thus [tex]\sqrt{333}+\sqrt{305}+\sqrt{392} \approx 55.5[/tex].
What is the value of c?
c= ? °
Answers
Answer:
c = 50°
Step-by-step explanation:
Since Triangle QRP is an isosceles triangle, the base angles of the triangle are equal.
Angle RQP = 180 - 115
= 65° (sum of angles on straight line)
Angle RPQ = Angle RQP = 65°
c = 180 - 65 - 65
= 50° (sum of angles in a triangle)
A box exerts a force of 10,000 N over an area of 1 m2. What pressure is the box exerting on the floor?
Answers
Answer:
The area is in contact with the ground if A box exerts 10,000 Pa of pressure on the ground. If the box weighs 1000 N is 10 m².
( which is D/10 m²).
Step-by-step explanation:
so what is pressure?
In the physical sciences, pressure is defined as the stress at a point within a confined fluid or the perpendicular force per unit area. A 42-pound box with a bottom area of 84 square inches will impose pressure on a surface equal to the force divided by the area it is applied to, or half a pound per square inch.
Answer: 10,000 pa
Step-by-step explanation:
Pressure = Force / Area
Force = 10,000
Area = 1 m^2
Pressure = 10,000 / 1
Pressure = 10,000 pa.
Let the set be defined as follows. A= 5, 8, 34, 59, 73, 79,89. Find the total number of proper subsets of A. Find the total number of subsets of A.
Answers
Answer:
Step-by-step explanation: As we know the number of elements in set A are 7 and the formula to calculate the number of proper subsets is 2^n – 1
Therefore substituting the values in formula . n is number of elements of set A. Here n=7
so 2^7-1= 128-1=127
Ans:127
Which example illustrates the associative property for addition?
(3 x 7) + 8 = 3+ (7 x 8) = (3x 8) + 7
(3+7) x 8 = 3 x (7 + 8) = (3 + 8) x 7
(3+ 7) + 8 = 3x (7 x 8) = (3 + 8) + 7
(3 + 7) + 8 = 3 + (7 + 8) = (3 + 8) + 7
Answers
Answer:
The answer is that the third example illustrates the associative property for addition. The associative property states that the order in which numbers are added does not affect the result. In other words, (a + b) + c = a + (b + c) for all numbers a, b, and c.
The third example follows this pattern:
(3 + 7) + 8 = 3 + (7 + 8) = (3 + 8) + 7
The other examples do not follow this pattern, so they do not illustrate the associative property for addition.
Step-by-step explanation:
The third example illustrates the associative property for addition. The associative property states that the order in which numbers are added does not affect the result. In other words, (a + b) + c = a + (b + c) for all numbers a, b, and c.
The third example follows this pattern:
(3 + 7) + 8 = 3 + (7 + 8) = (3 + 8) + 7
The other examples do not follow this pattern, so they do not illustrate the associative property for addition.
The first example illustrates the associative property for multiplication, which states that the order in which numbers are multiplied does not affect the result. In other words, (a x b) x c = a x (b x c) for all numbers a, b, and c.
The second example is not a valid mathematical expression, as it attempts to add a number and a product.
Answer:
(3 + 7) + 8 = 3 + (7 + 8) = (3 + 8) + 7
Step-by-step explanation:
The equations for associative property for addition are:
(a + b) + c = a + (b + c)
So, (3 + 7) + 8 = 3 + (7 + 8) = (3 + 8) + 7 is the answer!
125x ^ 3 - 27 = 0
Solve this by factoring
Answers
Answer:
x = 3/5
Step-by-step explanation:
[tex]125x^{3} -27=0[/tex]
[tex]125x^{3} =27[/tex]
[tex]\sqrt[3]{125x^{3} } =\sqrt[3]{27}[/tex]
[tex]5x=3[/tex]
[tex]x=\frac{3}{5}[/tex]
Hope this helps
5 triangles are shown. Triangles 1 and 4 are identical. Triangle 2 has identical side lengths and angle measures but is rotated. Triangle 3 has a smaller base than triangles 1, 2, and 4. Triangle 5 is double the size of triangles 1, 2, and 4.
Which statement best describes one of these transformations?
Triangle 1 is rotated to result in triangle 2.
Triangle 1 is dilated to result in triangle 3.
Triangle 1 is reflected to result in triangle 4.
Triangle 1 is stretched to result in triangle 5.
Answers
A statement which best describes one of these transformations is that: A. triangle 1 is rotated to result in triangle 2.
What are the types of transformation?In Mathematics, there are four (4) main types of transformation and these include the following:
RotationReflectionDilationTranslationWhat is a rotation?In Mathematics, a rotation simply refers to a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
Since triangle 2 has identical (similar) side lengths and angle measures, but is rotated and triangles 1 and 4 are identical, we can logically deduce that triangle 1 underwent a rotation to produce triangle 2.
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Nathan and some friends are going to the movies. At the theater, they sell a bag of popcorn for $4.50 and a drink for $4.25. How much would it cost if they bought p bags of popcorn and d drinks?
Answers
If they purchased 7 bags of popcorn and 3 drinks, the price would be $44.25; p bags of popcorn and d beverages would cost 4.50p+4.25d.
What is a formula?
Equation is the name given to two or more expressions with the equal sign.
Due to that
$4.50 worth of popcorn
beverage for $4.25.
There are 3 drinks and 7 bags of popcorn.
So let's calculate the overall cost.
7(4.50)+3(4.25)
31.5+12.75
44.25
So if they purchased 7 bags of popcorn and 3 beverages, the price would be $44.25
The price for p bags of popcorn and d drinks must now be determined.
4.50p+4.25d
Therefore, the price would be $44.25 if they purchased 7 bags of popcorn and 3 drinks, and the cost would be 4.50p+4.25d for p bags of popcorn and d beverages.
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What is the degree form for 4pi/9?
Answers
Answer:
80 degrees
Step-by-step explanation:
π=180 degrees
4π/9 =
4*180/9 = ==> substitute 180 for π
720/9 = ==> simplify
80 degrees
80 degree
Step-by-step explanation:
4*20
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A principal P, invested 9.5% compounded continuously, increases to an amount K times the original principal after t years, where t = ln(K)/0.095.
a. Complete the table. (Round your answers to one decimal place)
K t
1
2
3
4
6
8
10
12
b. Sketch the graph of the function.
Answers
Answer:
[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12} K & t\\\cline{1-2} \vphantom{\dfrac12} 1 & 0\\\vphantom{\dfrac12} 2 & 7.3\\\vphantom{\dfrac12} 3&11.6 \\\vphantom{\dfrac12} 4& 14.6\\\vphantom{\dfrac12} 6&18.9 \\\vphantom{\dfrac12} 8& 21.9\\\vphantom{\dfrac12} 10& 24.2\\\vphantom{\dfrac12} 12&26.2\\ \cline{1-2}\end{array}[/tex]
See attachment for the graph.
Step-by-step explanation:
Part (a)Given equation for t:
[tex]t=\dfrac{\ln (K)}{0.095}[/tex]
Substitute the given values of K into the equation for t and round the answers to one decimal place:
[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12} K & t\\\cline{1-2} \vphantom{\dfrac12} 1 & 0\\\vphantom{\dfrac12} 2 & 7.3\\\vphantom{\dfrac12} 3&11.6 \\\vphantom{\dfrac12} 4& 14.6\\\vphantom{\dfrac12} 6&18.9 \\\vphantom{\dfrac12} 8& 21.9\\\vphantom{\dfrac12} 10& 24.2\\\vphantom{\dfrac12} 12&26.2\\ \cline{1-2}\end{array}[/tex]
Part (b)To sketch the graph of the given function (see attachment):
Plot the values of K along the x-axis.Plot the values of t along the y-axis.Plot the points from the table from part (a).Draw a curve through the plotted points.Catherine Hart works 37 hours per week.
Her hourly rate of pay is $15.50 per hour. A
student calculated Catherine's weekly
paycheck as $570.00, and her annual
income as $13,764.00. These calculations
are wrong. Explain why these calculations
are wrong.
Answers
Weekly paycheck of Catherine is $573.5 and her annual income is $29,904.01.
What is Unit Rate?Unit rate is defined as the number of one quantity needed for a single other quantity.
In other words, if we know the unit rate, we can calculate any amount of one quantity corresponding to any amount of the other quantity by multiplying the unit rate with the number of other quantity.
Here unit rate of Catherine's pay = $15.50 per hour
Given that Catherine works 37 hours per week.
Weekly paycheck of Catherine = unit rate × number of hours per week
= 15.50 × 37
= $573.5
Annual Income of Catherine = Unit rate × number of hours per year
There are 52.143 weeks in a year.
Catherine works 37 hours per week.
Number of hours Catherine working in an year = 52.143 × 37 = 1929.291
Annual Income of Catherine = 15.50 × 1929.291
= $29,904.01
Hence, calculation of student is wrong since the weekly paycheck is $573.5 and her annual income is $29,904.01.
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Suppose that the duration of a particular type of criminal trial is known to have a mean of 21 days and a standard deviation of seven days. We randomly sample nine trials.a. Find the probability that the total length of the nine trials is at least 225 days. Round to at least three decimal places.b. Ninety percent of the total of nine of these types of trials will last at least how long? Round to the nearest integer.
Answers
a)There is a 4% probability that all nine trials will last at least 225 days.
b)Approximately at least 163 days, 90% of the total of 9 of these trials will last.
Given, A typical criminal trial lasts 21 days on average, with a 7-day
standard variation. There are nine trials chosen at random.
Let's look at the mean, which is 21, and the standard deviation, which is 7, respectively. Sample size is 9 people.
Assume that X is the sum of the nine trails' days and X represents the total number of days.
It is understood that X may have any distribution if it is a random variable with an unknown or known distribution. If n is increased, the probability that the random variable X, which is made up of sums, has a normal distribution increases.
a)There is a 4% probability that all nine trials will last at least 225 days.
b)Approximately at least 163 days, 90% of the total of 9 of these trials will last.
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There is a 4% probability that all nine trials will last at least 225 days.
Approximately at least 163 days, 90% of the total of 9 of these trials will last.
Given an ABCD inscribed quadrilateral, where the AB side is the diagonal of the circum- circle of the quadrilateral. BC = 3cm, CD = 5 cm and BCDZ = 120°. Give the length of the BD diagonal, AB and AD sides and the other angles.
Answers
Answer:
Step-by-step explanation:
Given an ABCD inscribed quadrilateral, where the AB side is the diagonal of the circum-circle of the quadrilateral, we can calculate various properties by using basic trigonometry. Firstly, let us determine the length of BD. Since BCDZ = 120° and BC = 3cm ,we can use Sine rule to find out BD which will be equal to 4 cm. Secondly, we need to find AB and AD sides lengths as well as other angles in order for our calculations to be complete. To do this we will use Cosine rule since all three sides are known: BC=3cm; CD=5cm;BD=4 cm . This gives us a value for angle CBD which is approximately 39° and consequently angle BAD is also 39° since they add up together (BAD+CBD)to 180 degrees due their being opposite each other on a straight line..Finally ,using cosine again with these new values gives us both AB(6)and AD(2).
To summarise : Lengths -AB: 6 cm ; BD : 4 cm ;AD 2CM Angles - BCDZ :120 ° ; CBD & BAD :39 °
In conclusion , given an ABCD inscribed quadrilateral whose one side was already identified as its circumference diameter it was possible through simple trigonometric equations such s Sines Rule or Cosines Rule determine its remaining lengths ans angles accurately .
3 miles is the same as how many kilometers?
Hint: 1 mi≈ 1.6 km
Round your answer to the nearest tenth.
Answers
Answer: 4.8
Step-by-step explanation:
What is the value of p?
p=?°
Answers
Answer:
p = 82°
Step-by-step explanation:
Since Triangle HIJ is an isosceles triangle, the base angles of the triangle are equal.
Angle IHJ = 180 - 131
= 49° (sum of angles on a straight line)
Angle IJH = Angle IHJ = 49°
p = 180 - 49 - 49
= 82° (sum of angles in a triangle)
13. a) (6 pts total) The same series of books you've been wanting cost $44 at Barnes and Noble and are on sale for $35
at Target. If you have a 25% off coupon for Barnes and Noble and a 5% RedCard discount at Target, find what the
price before tax would be at each of the two retailers.
Answers
Answer:
The price before tax at Barnes and Noble is $33, and the price before tax at Target is $33.25.
Step-by-step explanation:
Is (1, 4) a solution to this system of equations?
y = x + 9
y = 10x + 7
yes
Submit
no
Answers
Answer:
no
Step-by-step explanation
y=x+9
4=1+9
1+9=10
10 is not equal to 4
y=10x+7
=40+7
47 does not equal 4
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Simplify the factorial expression.
(n-5)!/(n-3)!
Answers
Answer:
[tex]\cfrac{1}{(n-4)(n-3)}[/tex]----------------------------------------
Simplify considering that (n - 3) > (n - 5) and their difference is 2:
[tex]\cfrac{(n-5)!}{(n-3)!}=\cfrac{(n-5)!}{(n-5)!(n-4)(n-3)} =\cfrac{1}{(n-4)(n-3)}[/tex]let's find.
[tex] \frac{3}{4} - \frac{1}{6} [/tex]
Answers
So, we need to find the LCM of 4 and 6, so we’ll list the multiples of both numbers to find a common factor.
LCM of 4 and 6:
4: 4, 8, 12, 16
4•1=4, 4•2=8, 4•3=12, and 4•4=15
6: 6, 12, 18
6•1=6, 6•2=12, 6•3=18
The LCM is the product of two factors of different numbers. Looking at the list, the least common multiple is 12 because 12 is a product of two factors of 4 and 6. Therefore, the goal is to get both denominators equal to 12 through multiplication.
3/4 - 1/6
To do this, we need to multiply each fraction by a factor that produces 12. We know that 4•3=12 and 6•2=12, meaning to get 12 as both denominators, we must multiply 3/4 by 3 and 1/6 by 2. Remember, to preserver the fraction’s proportionality, we need to multiply the entire fraction by these factors, meaning the numerator and denominator.
3•3/4•3 - 2•1/2•6
Because 4•3=12 and 6•2=12, the denominators will both be twelve, but the numerators of both fractions also must be multiplied.
9/12 - 2/12
Now that we have common denominators, we can subtract the fractions. The rule for subtracting and adding fractions is to add the denominators and keep the denominators untouched.
9/12 - 2/12 = 9-2/12
Answer: 7/12
TEXT ANSWER
Markita is reading a book. She decides to read the same amount of
pages every day. The line y = -45x + 750 represents how many pages
are left in her book 'x' days after she has begun reading it.
a. How many pages does the book have?
b. How many pages does she read per day?
Answers
Answer:
a. 750 pages
b. 45 pages
Step-by-step explanation:
If you're decreasing 45 of something each day from 750, it makes sense that the 'something' is pages; instead of decreasing, it's reading.
So
a. 750 pages
b. 45 pages
The sum of three numbers is 24. The third is 11 less than 3 times the second. 8 times the first is 4 less than 10 times the second. Find the numbers
Answers
Answer:
F + S + T = 24 F= 1st number, S = 2nd, T = 3rd
Step-by-step explanation:
T = 2S - 11
9F = 7 + 2S
divide by 9
F + (7+2S)/9
substitute for F and T
(7+2S)/9 + S + 2S -11 = 24
7+2S + 9S + 18S - 99 = 216
29S = 216 + 99 - 7 = 308
S = 308/29 = the 2nd number
T = 2S -11 = 616/29 -11 = 616/29 - 319/29 = 297/29 = 3rd number
F = (7+2S)/9 = (7 +616/29)/9 = 819/261 = 1st number
the 3 numbers are 819/261, 308/29 and 297/29
they sum to 819/261 + 308/29 + 297/29 = about 3.14 + 10.62 +10.24 = 24
F =( 7+2(10.62))/9 = (7+ 21.24)/9 = 28.24/9 = 314
S = 308/29 = 10.62
T = 2S-11 = 2(10.62) - 11 = 21.24-11 = 10.24
although odds are the problem may have been mis-copied or has a slight typo, with more integer type solutions in the corrected version. If the problem had an 8 instead of 9, (8F = 7+ 2S) then F=3.5, S=10.5, T = 10 as exact answers, not rounded off. 3.5+10.5+ 10 = 24
First number: [tex]\frac{167}{21}[/tex];
Second number: [tex]\frac{142}{21}[/tex];
Third number: [tex]\frac{130}{14}[/tex].
Step-by-step explanation:1. Assign variables to each number.First number: "x";
Second number: "y";
Third number: "z".
2. Form equations based on the problem's statement.Equation 1. "The sum of three numbers is 24", hence:
[tex](1)x+y+z=24[/tex]
Equation 2. "The third is 11 less than 3 times the second.", hence:
[tex](2)z=3y-11\\ \\(2)-3y+z=-11[/tex]
Equation 3. "8 times the first is 4 less than 10 times the second.", hence:
[tex](3)8x=10y-4\\\\(3)8x-10y=-4[/tex]
3. Group the 3 equations.[tex](1)x+y+z=24\\\\(2)-3y+z=-11\\\\(3)8x-10y=-4[/tex]
4. Expand the equations.As you may see, the 3 variables don't always appear on all 3 equations. Therefore, we'll have to introduce them even though they don't appear. For this, we write the variable with a coefficient of 0 next to it
[tex](1)x+y+z=24\\\\(2)0x-3y+z=-11\\\\(3)8x-10y+0z=-4[/tex]
5. Rewrite the equations as a 3x4 matrix.Using the coefficient of each variable in each equation, rewrite the system of equation into a matrix like this:
[tex]\left[\begin{array}{cccc}1&1&1&24\\0&-3&1&-11\\8&-10&0&-4\end{array}\right][/tex]
6. Convert this matrix into the row-echelon form.Check the attached image to see the steps to making this convertion.
a) Getting the 1 on column 1.
Since there's already a 1 there, we skip this step.
b) Getting the 0 on column 1.
Since there's already a 0 there, we skip this step.
c) Getting the 0 on column 1.
Multiply row 1 values by "-8" and add them to row 3. The result of these operations should be:
[tex]\left[\begin{array}{cccc}1&1&1&24\\0&-3&1&-11\\0&-18&-8&-196\end{array}\right][/tex]
d) Getting the 1 on column 2.
Since we are working with column 2 and row 2, you may use the pivot value "-3" (the one that corresponds to the intersection of column 2 and row 2) and divide row 2 by itself to obtain a 1. Result is the following:
[tex]\left[\begin{array}{cccc}1&1&1&24\\0&1&-\frac{1}{3} &\frac{-11}{-3} \\0&-18&-8&-196\end{array}\right][/tex]
e) Getting the 0 on column 2.
Multiply row 2 by "18" and add it to row 3. Resulting table is:
[tex]\left[\begin{array}{cccc}1&1&1&24\\0&1&-\frac{1}{3} &\frac{-11}{-3} \\0&0&-14&-130\end{array}\right][/tex]
f) Getting the 1 on column 3.
We are working with column 3 and row 3, the intersection value is "-14" and we may use it as a pivot value. Hence, we may divide row 3 by "-14" in order to obtain the number 1 in column 3. Final table is:
[tex]\left[\begin{array}{cccc}1&1&1&24\\0&1&-\frac{1}{3} &\frac{-11}{-3} \\0&0&1&\frac{-130}{-14}\end{array}\right][/tex]
7. Calculate the values.Starting from the bottom up, take the expression of the resulting matrix and calculate the values of each variable.
a) From row 3 we have:
[tex]0x+0y+z=\frac{-130}{-14} \\ \\z=\frac{130}{14}\\ \\[/tex]
b) From row 2 we have:
[tex]0x+y-\frac{1}{3} z=\frac{-11}{-3} \\ \\y-\frac{1}{3} z=\frac{11}{3}\\ \\y-\frac{1}{3} (\frac{130}{14} )=\frac{11}{3}\\ \\y-\frac{130}{42} =\frac{11}{3} \\ \\y=\frac{11}{3}+\frac{130}{42}\\\\y=\frac{11*14}{3*14}+\frac{130}{42}\\ \\y=\frac{154}{42}+\frac{130}{42}\\ \\y=\frac{284}{42} \\\\y=\frac{142}{21}[/tex]
c) From row 1 we have:
[tex]x+y+z=24\\ \\x+\frac{142}{21}+\frac{130}{14} =24\\ \\x=24-\frac{142}{21}-\frac{130}{14}\\ \\x=\frac{1008}{42} -\frac{284}{42} -\frac{390}{42} \\ \\x=\frac{167}{21}[/tex]
8. Verify that the numbers work correctly in each of the equations.Equation 1: [tex]\frac{167}{21} +\frac{142}{21} +\frac{130}{14} =24[/tex] Correct.
Equation 2: [tex]-3(\frac{142}{21} )+\frac{130}{14} =-11[/tex] Correct.
Equation 3: [tex]8(\frac{167}{21} )-10(\frac{142}{21} )=-4[/tex] Correct.
9. Conclude.First number: [tex]\frac{167}{21}[/tex];
Second number: [tex]\frac{142}{21}[/tex];
Third number: [tex]\frac{130}{14}[/tex].
Important: Check the attached Excel sheet to see the changes made in the matrix.
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7. When the height of the sand in a particular rectangular sandbox is
leveled out then the height of the sand, in inches (in.), is proportional to
the volume of sand, in cubic inches (in.3), in the sandbox. When the
height of the sand is 1.25 in. the volume of the sand is 280 in.3. A
playground has 3 of these sandboxes.
What is the total volume of the sand, in cubic inches (in.3), that is
needed for the playground when the height of the sand in each sandbox
is 4.5 in.?
Show your work in the provided space.
Answers
The Total volume of sand in cubic inches needed for the playground when the height of the sand in each sandbox is 4.5 in is; 2700 in³
How to solve mathematical proportions?
We are told that the height of the sand, in inches (in.), is proportional to
the volume of sand.
Let the volume be denoted as V
Let the height be denoted as h
Thus;
V ∝ h
Then to equate this, we will have a constant of proportionality;
V = kh
where k is constant of proportionality
When the height of the sand is 1.25 in., the volume of the sand is 280 in³ and this gives;
280 = 1.25k
k = 250/1.25
k = 200
Now, ware told that the height of sand in a box is now 4.5 inches and so;
V = 200 * 4.5
V = 900 in³
Since the playground has 3 of such boxes, then we can say that;
Total volume of sand on the playground = 900 * 3 = 2700 in³
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What is the y/x rationp
Answers
Answer:
3/2
Step-by-step explanation:
9/6
(9:3)/(6:3) = 3/2
6/4
(6:2)/(4:2) = 3/2
3/2
If a₁ = 6 and an
an-1 + 3 then find the value of a4.
Answers
Answer:
a₄ = 15
Step-by-step explanation:
using the recursive relation [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 3 and a₁ = 6 , then
a₂ = a₁ + 3 = 6 + 3 = 9
a₃ = a₂ + 13= 9 + 3 = 12
a₄ = a₃ + 3 = 12 + 3 = 15
-3x-4y=-1, 3x-y=-4 solve by elimination
Answers
Hope it’s correct
y = 1, and x = -1
if you need to show your work:
if you combine the two equations together (eliminating x), it goes like this
-3x - 4y = -1
3x - y = -4
-5y = -5
y = 1
this means:
-3x - 4 = -1
-3x = 3
x= -1
and
3x - 1 = -4
3x = -3
x = -1