In the activity, Heavy Flying, we looked at constraints for transporting packages from Careful Calculators and Charlie's
Chicken Feed
• Charlie's Chicken Feed containers weigh 40 pounds and are 2 cubic feet in volume.
• Careful Calculators containers weigh 50 pounds and are 3 cubic feet in volume.
On Monday, the pilot transferred containers that totaled 30,000 pounds and 1,600 cubic feet in volume.
1. Write a system of equations to model this situation.
2. Write a matrix equation to model this situation.
3. Solve. How many of each container was transported?
Show your work by uploading a picture or typing in the text box.
Answers
Answer: 500 chicken feed and 200 careful calculators
Step-by-step explanation:
2x+3y=1,600
40x+50y=30,000
those are your first two equations
your first matrix equation for A is 2, 3,40,50 and B is 1,600 and 30,000 when you enter those in your calculator and 500 and 200 should be your result.
a) The system of equations are 2x + 3y = 1600 and 40x + 50y = 30000
b) The matrix equations are solved
c) The solution to the system of equations is
The number of chicken feed = 500
The number of careful calculators = 200
What is multiplication of matrices?The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix
Given data ,
Let the number of chicken feed be represented as x
Let the number of careful calculators be y
Now , the equation will be
Charlie's Chicken Feed containers weigh 40 pounds and are 2 cubic feet in volume
And , Careful Calculators containers weigh 50 pounds and are 3 cubic feet in volume
Substituting the values in the matrices , we get
[tex]\left[\begin{array}{ccc}2 &3 \\ 40 &50 \\\end{array}\right] * \left[\begin{array}{ccc}x\\y\\\end{array}\right]= \left[\begin{array}{ccc}1600\\30000\\\end{array}\right][/tex]
On simplifying the matrix equation , we get
2x + 3y = 1600 be equation (1)
40x + 50y = 30000 be equation (2)
Now , multiply equation (1) by 20 , we get
40x + 60y = 32000 be equation (3)
Subtracting equation (2) from equation (3) , we get
10y = 2000
Divide by 10 on both sides of the equation , we get
y = 200 careful calculators
Substituting the value of y in equation (1) , we get
2x + 3 ( 200 ) = 1600
2x + 600 = 1600
Subtracting 600 on both sides of the equation , we get
2x = 1000
Divide by 2 on both sides of the equation , we get
x = 500 chicken feeds
Therefore , the value of x and y are 500 and 200 respectively
Hence , the system of matrix equations are solved
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Related Questions
a shipping crate is a perfect cube with volume of 2,197 cubic feet. the ceiling of the warehouse is 14 feet high. will the crate fit in the warehouse explain why
Answers
Answer:
As the height of warehouse is greater than the height of crate, the crate will fit in the warehouse.
Step-by-step explanation:
Given that
Volume of cube = V = 2197 cubic feet
Side of cube = a =?
Height of ware house = h = 14 feet
In order for the crate to fit in the warehouse the height of crate has to be less than the height of warehouse i.e. a<h
In order to check this we have to find the side/height of crate
So,
[tex]V = a^3\\2197 = a^3[/tex]
Taking cube root on both sides
[tex]\sqrt[3]{a^3} = \sqrt[3]{2197}\\\sqrt[3]{a^3} = \sqrt[3]{13^3}\\ a = 13\ feet[/tex]
So the height of cube is 13 feet.
Comparing the height of c and height of ware house we can conclude that
Height of Warehouse > Height of crate
h>a
14>13
As the height of warehouse is greater than the height of crate, the crate will fit in the warehouse.
Which inequality is represented by the number line?
PICTURE ATTACHED PLEASE HELP ME!!!
Answers
Answer:
A i think
Step-by-step explanation:
cause its gonna be more than 6- so yeah if it is right then b
A math book comprises of two sections: arithmetic and geometry in the ratio 5:3. How much of each type of content will be needed to make a book of 480 pages?
Answers
Answer:
Arithmetic content = 300 pages
Geometric content = 180 pages
Step-by-step explanation:
Arithmetic : Geometry = 5 : 3
Total pages of book = 480
How much of each type of content will be needed to make a book of 480 pages?
Total ratio = arithmetic + geometric
= 5 + 3
= 8
Arithmetic content = 5 / 8 × 480
= 0.625 × 480
= 300
Arithmetic content = 300 pages
Geometric content = 3 / 8 × 480
= 0.375 × 480
= 180
Geometric content = 180 pages
PLEASE HELP :(
Mario is spending the day at the county fair. The admission ticket costs $10.00. Each ride ticket costs $2.50.
Which equation can be used to find y, the total cost of Mario’s day at the fair, given x represents the number of ride tickets he purchases?
y = 2.50x + 10
y=2.50(x+10)
y = 10x + 2.50
y=2.50x−10
Answers
Answer:
y = 2.50x + 10
Step-by-step explanation:
y=mx+b
x=number of rides
y=cost
Answer:
a is the answer
Step-by-step explanation:
is 2/5 a rational number , irrational number, whole number , or integer?
Answers
Answer:
Rational number
Step-by-step explanation:
An irrational number is like pi, something that you can never write down completely.
2/5 is not a whole number, or an integer because it's a fraction of a number.
26=6k+8-6+2k
Need ASAP
Answers
Answer: k = 3
Step-by-step explanation:
Answer:
k=3
Step-by-step explanation:
26=6k+8-6+2k
combine all common integers from the same side, (8-6) and (6k+2k).
8-6=2
6k+2k=8
Which now translates the equation to 26=8k+2.
26=8k+2
continue by moving the (2) to the other side, do so by subtracting 26-2.
26-2=24
24=8k
Lastly, move the 8 to the other side of the equation by dividing 24/8.
24/8=3
Therefore, k=3
The graph shows the number of each kind of book in Hero's personal library. A book is
chosen randomly.
What is the probability that the book is a romance book?
Answers
Answer:
[tex]\displaystyle p=\frac{1}{15}[/tex]
Step-by-step explanation:
Probability
The simple probability of a random event can be calculated as the ratio between the possible favorable cases and the total possible cases.
The pie chart shows the number of books in Hero's library grouped by category.
The total number of books is 14 + 10 + 4 + 2 = 30
The number of romance books is 2
Thus, the probability of randomly choosing a romance book out of the total books is:
[tex]\displaystyle p=\frac{2}{30}[/tex]
Simplifying:
[tex]\mathbf{\displaystyle p=\frac{1}{15}}[/tex]
This corresponds to the first option
Answer:
1/15
or
[tex]\frac{1}{15}[/tex]
explanation:
If the equation y=2x-1 is translated down six units, the new equation would be...
Answers
Answer:
2x-6
Step-by-step explanation:
have a nice day!! :))
Michelle plans on raising $80 for her softball team. To raise the money, she is selling team shirts for $10 each.
So far she has raised $20. To calculate how many more shirts she needs to sell, Michelle subtracts 20 from 80
and then divides by 10.
Which of the equations below can be solved using the same steps?
A. 10.0 + 20 = 80
B. 200 + 10 = 80
C. 80.0 - 200 = 10
D. 102 + 20= 80
Answers
Answer:
what none of these make sense
A town population of 14000 and grows 3.5% every year. What will be the population after 14 years to the nearest whole number
Answers
Answer:
22662
Step-by-step explanation:
Since the growth is exponential, your equation will be y = a • b^x. a being the beginning amount, b the percentage it increases by, and x is the time taken.
y = 14000 • 1.035^14
= 22661.72
Round your answer since people can only be integers and your answer is a population of 22662
LaShawn solved the equation below to the determine the solution. 3 x minus 8 = negative x + 4 (x minus 2) How many solutions does LaShawn’s equation have? zero one two infinitely many
Answers
Answer: D
D-infinitely many
Step-by-step explanation:
Took the Analyzing Solutions quiz on Edge 2020
Answer: D
D-infinitely many
Step-by-step explanation:
Edge 2020
What is the length of BC?
O 11
O 23
O 40
O 60
Plz help
Answers
Answer:
BC = 40
Step-by-step explanation:
Answer:
X=23
BC = 40
Step-by-step explanation:
11) How many kilograms of How many kilograms of calcium are there
in 173 pounds of calcium? (1 lb = 454 g; 1
kg 1000 g)
A) 78.5 kg
B) 110 kg
C) 78500 kg D) 1.10 kg
Answers
Explanation. First, we must convert the lbs into grams, we can do this my multiplying 454 by 173 and get 78,500. Then convert it to kg, there are 1,000 g in a kg do divide 78,500 by 1,000 to get 78.5 kg. Let me know if it’s correct so others can use it. Brainliest would be appreciated.
Good luck :)
The kilogrammes of calcium found in 173 pounds of calcium is = 78.5 kg. That is option A.
First convert the 173 pounds of calcium to gramma
1 lb(pounds) = 454 g;
Therefore 173 pounds = 173 ×454
= 78,542g
But, 1000 g = 1kg
Therefore, 78542g = 78542 ÷1000
= 78.542
=78.5kg.
Therefore, the kilogrammes of calcium found in 173 pounds of calcium is = 78.5kg.
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Ixl help me please and thanks!!!!
Answers
Seeing that both triangles are side by side and share a side, we know that that side of both triangles is congruent.
Then when you look at the angles, you will see that one on each triangle has one curved line. This one curved line shows that these angles are congruent.
There is then the two curved lines you can find on both triangles as well. This shows that both those angles are congruent.
With this information, you should be able to tell that two angles of the triangles are congruent, and one side of both triangles are congruent, with the order that these are shown on the triangles being an angle, then a side, then another angle, the answer would be ASA, or angle, side angle.
Write the equation in y=Mx+B
Answers
Answer:
y=2x-2
Step-by-step explanation:
y intercept is (0,-2) so that is b value. slope is 2 so that is your m value
does 27 divided by 5 result in 5 and 6
Answers
Answer:
27 divided by 5 = 5.4
Step-by-step explanation:
The radius of a circle is 16.7 in. Find the circumference to the nearest tenth.
Answers
16.7 inches times 3.14 in or pie, equals 52.4 inches, and because you were given the radius and not the diameter, you multiply 52.4 inches by 2 to get 104.9 or 105 inches.
The circumference of the circle is 105 in to the nearest tenth.
What is the circumference of the circle?The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
The circumference of the circle = 2πr
We are given that the radius of a circle is 16.7 in.
We need to determine the circumference to the nearest tenth.
Radius r = 16.7
Then circumference of the circle = 2πr
= 2 x 3.14 x 16.7
= 104.87
Therefore, the circumference of the circle is 105.
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Ariana borrowed some money from her friend in order to help buy a new video game system. Ariana originally borrowed $150 and agreed to pay back her friend $15 per week
Answers
Answer:
if it how long it will it take to pay her friend back its 135 weeks
Step-by-step explanation:
Write the slope-intercept form for the equation of the line.
Answers
**To find the slope you find 2 points in the line and use the formula y2-y1 / x2-x1
(2,0) (0,-4) -4-0 / 0-2 = -4 / -2 = 2**
Y=mx+b —> y=2x-4
One number is 2 less than a second number.twice the second number is 37 more than 5 times the first. Find more the two number
Answers
Answer:
The numbers are -11 and -9.
Step-by-step explanation:
The two numbers are x and y.
x = y - 2
2y = 5x + 37
2y = 5(y - 2) + 37
2y = 5y - 10 + 37
3y = - 27
y = -9
x = - 11
What is 5+5 I will give brainliest
Answers
Answer:
5+5=10
tep-by-step explanation:
please help me there are more questions after this.
Answers
Find all solutions by factoring.
c? + 13c + 40 = 0
Answers
Answer: c = -5, -8
Step-by-step explanation:
c^2 +13c+40=0
(c+5)(c+8)=40
c = -5, -8
The ratio of fiction to non-fiction books at school library is 3 to 5. If there are 240 books in the library how many non-fiction books are in the library?
Answers
Answer:
150
Step-by-step explanation:
The ratio is 3:5, so you can make this equation:
[tex]3x+5x=240[/tex], because for any integer x, the ratio will stay the same.
solve that:
[tex]3x+5x=240\\8x=240\\x=30[/tex]
We're not down yet!
we need to find 5x, not x.
[tex]5*30=150[/tex]
There are 150 non-fiction books in the library.
check!
150+90=240
The are 150 non-fiction books are in the library.
What is ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
The ratio of fiction to non-fiction books at school library is 3 to 5.
Total books = 240
So, the number of non fiction books
= 240 x 5/8
= 30 x5
= 150
Hence, there are 150 non fiction book.
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Which event prevented Descartes from publishing The World after he was done writing the book? serving as a soldier during the Thirty Years’ War accepting an invitation to tutor the queen of Sweden awaking from sleep due to three vivid dreams learning of Galileo’s imprisonment
Answers
Answer:
Learning of Galileo’s imprisonment
Step-by-step explanation:
I just went over this last week and i am 100% sure that this is correct
Quadratic functions q and ware graphed on the same coordinate grid.
The vertex of the graph of g is 18 units below the vertex of the graph of w.
Which pair of functions could have been used to create the graphs of q and w?
Answers
Answer:q(x)=18x^2 and W(X) = x^2
Step-by-step explanation:
The pair of functions that used for developing the graph of g and w is [tex]q(x)=18x^2\ and\ W(X) = x^2[/tex]
What is the vertex of the parabola?The vertex of a parabola should be the point where the parabola crosses its axis of symmetry. In the case when the coefficient of the x2 term is positive, so the vertex will be the lowest point on the graph.
Since The vertex of the graph of g is 18 units below the vertex of the graph of w so the above functions should be considered.
Therefore, The pair of functions that used for developing the graph of g and w is [tex]q(x)=18x^2\ and\ W(X) = x^2[/tex]
Learn more about graph here: https://brainly.com/question/18536923
!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
x = 22°
3x + 2 = 64°
Step-by-step explanation:
All angles in a triangle must add up to 180°
90 + x + 3x + 2 = 180
Rearrange and collect like terms and place them on either side
4x = 88
x = 22°
3x + 2
3(22) + 2
= 64°
y= -1/2x-3 . Pease answer quickly, thank you <3
Answers
Answer:
Step-by-step explanation:
y = f(x) = - [tex]\frac{1}{2}[/tex] x - 3
f(- 4) = - [tex]\frac{1}{2}[/tex] (- 4) - 3 = - 1
f( - 2) = - [tex]\frac{1}{2}[/tex] (- 2) - 3 = - 2
x ║ - 4 ║ - 2 ║ 0 ║ 2 ║ 4 ║
y ║ - 1 ║ - 2 ║ - 3║- 4║- 5║
Question - Which image shows a 90 degree clockwise rotation about the origin?
Can somebody help me with this. Will mark brainliest!
Answers
Answer:
Choice 1!
Step-by-step explanation:
Thomas went to the store to buy video games for $13.50 each and controllers that cost $55 each and controllers. the total amount that Thomas spent can be represented by c=13.50+p, where c is the total cost, g is the number of games he bought, and p is the cost of the controllers. the controllers cost $55 and Thomas spent $136 total
Answers
Answer:6 games
Step-by-step explanation:
Thomas spent a total of 136 dollars so you subtract 55 from 136 and divide by 13.50 to get 6.