Topic: Reduced row echelon form
Thanks for the help in advance
Let f, s, and t denote the hours needed by the first, second, and third sellers, respectively, to sell a given plant.
"In one hour, the first grower sells 3 fly traps … The second grower sells 1 fly trap … The third grower sells 3 fly traps …" - this means that for each hour f, the first grower sells a total of 3f fly traps. Similarly, the second grower sells 1s fly traps, and the third grower sells 3t fly traps. Together, they want to sell 39 fly traps, so that
3f + s + 3t = 39
You set up two more equations for the sundews and bladderworts:
f + 2s + 2t = 30
2f + s + 2t = 28
Now write the system of equations in augmented matrix form and row reduce it:
[tex]\left[\begin{array}{ccc|c}3&1&3&39\\1&2&2&30\\2&1&2&28\end{array}\right][/tex]
Add row 1 to -3 (row 2); this is to say, treating each row as a list, multiply through the second row by -3, then add the first row to that result. For example,
(3, 1, 3, 39) + -3 (1, 2, 2, 30) = (3, 1, 3, 39) + (-3, -6, -6, -90)
… = (3 - 3, 1 - 6, 3 - 6, 39 - 90)
… = (0, -5, -3, -51)
Also, add 2 (row 1) to -3 (row 3) :
[tex]\left[\begin{array}{ccc|c}3&1&3&39\\0&-5&-3&-51\\0&-1&0&-6\end{array}\right][/tex]
Multiply through the last two rows by -1 to make everything positive, and swap them around:
[tex]\left[\begin{array}{ccc|c}3&1&3&39\\0&1&0&6\\0&5&3&51\end{array}\right][/tex]
Next, add -5 (row 2) to row 3 :
[tex]\left[\begin{array}{ccc|c}3&1&3&39\\0&1&0&6\\0&0&3&21\end{array}\right][/tex]
Multiply through row 3 by 1/3 :
[tex]\left[\begin{array}{ccc|c}3&1&3&39\\0&1&0&6\\0&0&1&7\end{array}\right][/tex]
Add -1 (row 2) and -3 (row 3) to row 1 :
[tex]\left[\begin{array}{ccc|c}3&0&0&12\\0&1&0&6\\0&0&1&7\end{array}\right][/tex]
Multiply through row 1 by 1/3 :
[tex]\left[\begin{array}{ccc|c}1&0&0&4\\0&1&0&6\\0&0&1&7\end{array}\right][/tex]
This row-reduced matrix tells you that f = 4, s = 6, and t = 7. In other words, in order for the three growers to collectively sell the required number of plants, the first seller needs to work for 4 hours, the second seller needs to work for 6 hours, and the third seller needs to work for 7 hours.
Work out m and c for the line:y=3x-2
Howard deposited some money in the bank. How long will Howard have to leave $5000 in the bank to earn $250 in simple interest at 2%.
Answer:
t = 2.5 years
Step-by-step explanation:
Given that,
Principal = $5000
Interest = $250
Rate of interest = 2%
We need to find the time. We know that,
[tex]I=\dfrac{PRT}{100}[/tex]
Put all values to find T.
[tex]T=\dfrac{100I}{PR}\\\\T=\dfrac{100\times 250}{5000\times 2}\\\\T=2.5\ yrs[/tex]
So, it will take 2.5 years.
Given the median QR and trapezoid MOPN, what is the value of x?
5x - 7
P
27
Q
R
6x + 6
N
O A. 6
O B. 18
O C. 2
O D. 5
O E. 7
o
F. Cannot be determined
Answer:
D. 5
Step-by-step explanation:
Based on the midsegment theorem of a trapezoid, thus:
QR = ½(OP + MN)
Substitute
27 = ½((5x - 7) + (6x + 6))
27 = ½(5x - 7 + 6x + 6)
Add like terms
27 = ½(11x - 1)
Multiply both sides by 2
2*27 = 11x - 1
54 = 11x - 1
54 + 1 = 11x
55 = 11x
55/11 = x
5 = x
x = 5
please help with question 2
Answer:
K=3
Step-by-step explanation:
Substitute the X with 7.
-6x7+18=k(7-15)
Distribute and combine
-42+18= = -8k
Combine like terms
-8k= -24
K= 3
Answer:
The answer is k=3
Kyle ordered 7 large pepperoni pizzas from Wild Bill's Pizza, and he used the coupon shown above. If the total bill, after kyle used the coupon, was $82.50, what was the regular price of 1 pizza?
Answer:
Regular price of 1 pizza = $15 {Assuming discount coupon = $22.5}
Step-by-step explanation:
Let regular non discounted price of 7 pizzas be x
x - 22.5 = 82.5
x = 82.5 + 22.5
x = 105 (Regular Non discounted price of 7 pizzas)
Regular Price of 7 pizzas = 105
Regular price of 1 pizza = 105 / 7 = 15
You are scuba diving at -8 feet. You dive 5 feet deeper. What is your position in the water?
Answer:
-13 feet
Step-by-step explanation:
Answer:
-13 feet
Step-by-step explanation:
We Start With -8 and we go 5 feet deeper so -8-5 is -13
Plz help me I’m confused
Answer:
-10 minor -7 minor -1 minor +3
Step-by-step explanation:
first one: (14+6)/(-4+2)= -10
second one: (8+4)/(-9-3)=-1
third one: (3+4)/(3-4)= -7
last one: =+3
Find the sum of the first 59 terms of the arithmetic sequence.
49, 56, 63, 70, ...
What is the sum of the first 59 terms?
Answer:
its 56
Step-by-step explanation:
2 (3)^3 + 5
And explain how you got it
Answer:
59
Step-by-step explanation:
3^3=27
2x27=54
27+54+5=59
Answer:
2 times 3 i 6 o 3 plus 5 equal 8
Step-by-step explanation:
beca you supoed to multiply ad divide
20 apples cost R12.What will 16 of the apples cost?
Answer:
192
Step-by-step explanation:
you take 12 and multiple it by 16:
R12×16=R192
In the figure, the measure of angle 6 6 is 141° 141 ° . What is the measure of angle 5 5 ?
Answer:
131° 131°=5 5 is the measure for 5 5
Answer: 181
Step-by-step explanation: i got it right on imagine math and the person above me is correct
ur pretty and perfect! Have a great day!
Sarah and Mike have 59 ounces of almonds. They want to share these almonds equally with each other and 6 more friends. The number of ounces of almonds each person will get is between which two whole numbers?
3 and 4
6 and 7
7 and 8
8 and 9
please show work
the answer is between 7 and 8
hey im asking this question so u can get points lol
what color is the sky??
Step-by-step explanation:
it appears blue to the human eye.
What is (3 x 10^3) / (12 x 10^6)
Answer:
(3 x 10^3) / (12 x 10^6) = 0.00025
What group of americans were helped by andrew jackson
The figure below consists of a square and a right triangle. Find the missing length x.
Answer:
15 cm
Step-by-step explanation:
Since the square's side length is 8 cm, and one of its sides is the short leg of the triangle, the short leg of the triangle is 8 cm
Using the pythagorean theorem, solve for b (the missing side length x)
a² + b² = c²
8² + b² = 17²
64 + b² = 289
b² = 225
b = 15
So, the missing side length is 15 cm
Pretzels are given away for free at a local store. The tray is constantly replenished as people take the pretzels.The number of pretzels in the tray is given by the function P(t) = 20 + t^2 − 8cosπt , where t is measured in minutes. When t = 1 minute, find the average rate of change of pretzels in the tray over the next 30 seconds.
Answer:
The answer is "[tex]-13.5 \ / minute \\\\[/tex]"
Step-by-step explanation:
The average rate to the changes of pretzels form [tex]t= 1 \ minutes[/tex] to [tex]t=1.5 \ minutes[/tex] will be:
[tex]=\frac{P(1.5)-p(1)}{1.5-1}\\\\=\frac{(20+(1.5)^2- 8 \cos \pi (1.5))-(20+1^2 -8 \cos \pi)}{0.5}\\\\=\frac{22.25-29}{0.5}\\\\=\frac{-675}{50}\\\\=-13.5 \ / minute \\\\[/tex]
PLEASE HELP!!
Find the length of the diagonal of the rectangle. Round your answer to the nearest tenth.
Answer:
d = 15.8 m
Step-by-step explanation:
Apply the Pythagorean Theorem to find the length of the diagonal. The correct equation for this particular rectangle is
d = √(9² + 13²) = √250 = √25·√10 = 5√10
To the nearest tenth, this comes to d = 15.8 m
Answer: 15.8
Step-by-step explanation:
Is 1,4,9,16 an arthmetic sequence
Answer: No
Step-by-step explanation:
The sequence is not geometric or arithmetic because there is no common difference or common ratio between each term
Solomon rolls a six–sided die twice. What is the probability that he will get a 3 on one roll and 6 on the other roll?
Answer:
A
Step-by-step explanation:
Since each number is only shown once and there are six numbers, the probability of getting them is 6. Multiply the first times the second, and there's your answer.
Answer:
A) /36
Step-by-step explanation:
P(3) = 1/6
P(6) = 1/6
P(3 AND 6) = 1/6 x 1/6 = 1/36
YALL HAVE BEEN GETTING THESE WRONG LATELY SO PLZ HELP HELP
Answer: use the brainly app on your phone the take a picture of it
Step-by-step explanation:
Answer:
m=-4/3
Step-by-step explanation:
The equation for slope is y2-y1/x2-x1
m=(y2-y1)/(x2-x1)
m=(12--4)/(1-13)
m=16/-12
m=-4/3
Which set of side lengths create a right triangle ?
A(10,28,and 29)
B(6, 8,and 13)
C(7, 12 and 14)
D( 8 , 15 and 17)
Answer:
(8, 15 and 17)
Step-by-step explanation:
[tex]\sqrt{10^{2} +28^{2} } \neq 29[/tex]
[tex]\sqrt{6^{2} +8^{2} } \neq 13[/tex]
[tex]\sqrt{7^{2} +12^{2} } \neq 14[/tex]
[tex]\sqrt{8^{2} +15^{2} } =17[/tex]
Find the tangents of the acute angles in the right triangle
angle E to F=7
D to F 25
D toE=24
write as a fraction
f=50
d=40
Hope this helps
11. The rates for the following math tutoring services are listed below.
Tutoring Service Cost
Time
А
$50
45 minutes
B
$65
1 hour
C
$99
90 minutes
D
$90
2 hours
Which Tutoring Service charges the most per hour?
Answer: A
Step-by-step explanation:
A) 50/ 45 = 1.111....
B) 65/60 = 1.08333...
C) 99/90 = 1.1
D) 90/120 = .75
Answer:
A
Step-by-step explanation:
Divide each amount by the number of minutes to find the rate per minute. Then multiply by 60 to find the hourly rate. Then compare the hourly rates.
A
$50 / 45 min * 60 = $66.66/hour
B
$65 / 1 hour = $65/hour
C
$99 / 90 min * 60 = $66/hour
D
$90 / 2 hours = $45/hour
Answer: A
d) –4 + 3 ( 2 – x) = –8
Daje naj
Answer:
x = 3 and 1/3, or 3.333333...
Step-by-step explanation:
I'm assuming again that you want to find x
–4 + 3 ( 2 – x) = –8
Multiply
-4 + 6 - 3x = -8
Add 4 to both sides
6 - 3x = -4
Subtract 6 from both sides
-3x = -10
Multiply by -1
3x = 10
Divide by 3
x = 10/3
What is the slope of the line that passes through the points (-5,2) and (-7,6)
Answer:
-2
Step-by-step explanation:
compare these integers
-10_____ 1
A.<
B.=
C.>
Answer:
-10<1
which means that -10 is less than 1
Answer:
A
Step-by-step explanation:
-10 is smaller than 1 because all the negative numbers are less than 0 and all other positive numbers
Is a circle a function?
Step-by-step explanation:
a function that describes a set of points in Cartesian space by mapping each x-coordinate to a y-coordinate, then a circle cannot be described by a function because it fails what is known in High School as the vertical line test. A function, by definition, has a unique output for every input.
Tammys fish tank 18 liters of water in it. She plans to add 5 liters per minute until the tank has at least 63 liters. What are the possible numbers of minutes Tammy could add water?
Step-by-step explanation:
Hi,
63 = 5x + 18 represents this situation.
63 = 5x + 18
45 = 5x
9 = x
So, the possible number of mins are 1, 2, 3, 4, 5, 6, 7, 8, and 9.
You can also write this as x ≤ 9
I hope this helps :)