The number of order of each aircraft is an illustration of simultaneous equations.
You should order 7 Airbus A330-300s, 5 Boeing 767-300ERs and 9 Boeing Dreamliner 787-9s
To do this, we make use of the following representations:
A represents Airbus A330-300sB represents Boeing 767-300ERsC represents Boeing Dreamliner 787-9sFrom the question, we have the following equations
[tex]\mathbf{330A + 270B + 240C = 5850}[/tex] ----the number of passengers
[tex]\mathbf{B + C = 2A}[/tex] --- the relationship between the number of planes
[tex]\mathbf{250A + 200B + 240C =4950 }[/tex] --- the budget
Make A the subject in [tex]\mathbf{B + C = 2A}[/tex]
[tex]\mathbf{A=\frac{1}{2}(B + C)}[/tex]
Substitute [tex]\mathbf{A=\frac{1}{2}(B + C)}[/tex] in [tex]\mathbf{330A + 270B + 240C = 5850}[/tex]
[tex]\mathbf{330 \times \frac{1}{2}(B + C) + 270B + 240C = 5850}[/tex]
[tex]\mathbf{165B + 165C + 270B + 240C = 5850}[/tex]
[tex]\mathbf{435B + 405C = 5850}[/tex]
Divide through by 15
[tex]\mathbf{29B + 27C = 390}[/tex]
Make C the subject
[tex]\mathbf{C = \frac{390 - 29B}{27}}[/tex]
Substitute [tex]\mathbf{A=\frac{1}{2}(B + C)}[/tex] in [tex]\mathbf{250A + 200B + 240C =4950 }[/tex]
[tex]\mathbf{250 \times \frac{1}{2}(B + C) + 200B + 240C =4950 }[/tex]
[tex]\mathbf{125B + 125C + 200B + 240C =4950 }[/tex]
[tex]\mathbf{325B + 365C =4950 }[/tex]
Divide through by 5
[tex]\mathbf{65B + 73C =990}[/tex]
Substitute [tex]\mathbf{C = \frac{390 - 29B}{27}}[/tex]
[tex]\mathbf{65B + 73\times\frac{390 - 29B}{27} =990}[/tex]
Multiply through by 27
[tex]\mathbf{65B \times 27+ 73\times(390 - 29B) =990 \times 27}[/tex]
[tex]\mathbf{1755B+ 28470 - 2117B =26730}[/tex]
Collect like terms
[tex]\mathbf{1755B- 2117B =26730 - 28470}[/tex]
[tex]\mathbf{-362B =-1740}[/tex]
Solve for B
[tex]\mathbf{B =\frac{1740}{362}}[/tex]
[tex]\mathbf{B =5}[/tex] --- approximated
Substitute [tex]\mathbf{B =5}[/tex] in [tex]\mathbf{C = \frac{390 - 29B}{27}}[/tex]
[tex]\mathbf{C = \frac{390 - 29 \times 5}{27}}}[/tex]
[tex]\mathbf{C = \frac{245}{27}}}[/tex]
[tex]\mathbf{C = 9}[/tex] --- approximated
Recall that: [tex]\mathbf{A=\frac{1}{2}(B + C)}[/tex]
So, we have:
[tex]\mathbf{A = \frac{1}{2} \times (5 + 9)}[/tex]
[tex]\mathbf{A = \frac{1}{2} \times 14}[/tex]
[tex]\mathbf{A = 7}[/tex]
Hence, you should order 7 Airbus A330-300s, 5 Boeing 767-300ERs and 9 Boeing Dreamliner 787-9s
Read more about simultaneous equations at:
https://brainly.com/question/16763389
What is an equation of the line that passes through the point (−4,5) and is perpendicular to the line 4x+y=7
Answer:
[tex]y = \frac{1}{4} x + 6[/tex]
Step-by-step explanation:
rewrite the original equation
[tex]4x + y = 7 \\ y = - 4x + 7[/tex]
perpendicular line has a negative reciprocal slope. I will use this slope and substitute the points to find our y-intercept
[tex]5 = \frac{1}{4} ( - 4) + b \\ 5 = - 1 + b \\ b = 6[/tex]
the world population in 2016 was estimated to be 7.4 billion people and it is increasing by about 1.1% per year. assume that this percentage growth rate remains constant through 2030 explain why the population is an exponential function of time. what would you expect the world population to be in 2030
Answer:
1
Step-by-step explanation: i guessed
The ratio of the side length of square A to the length of Square B is 4:9 The side length of square A is 12 yards. What is the perimeter of Square B
Step-by-step explanation:
side A / side B = 4/9
side A = 12 yards
=>
12 / side B = 4/9
12 = side B × 4/9
9×12 = side B × 4
side B = 9×12/4 = 9×3 = 27 yards
perimeter of B is 4×side B = 4×27 = 108 yards
The tickets for a figure skating performance sold out in 4 hours. If there were 40,000 tickets sold, solve the equation 40,000−4x=0 to find the number of tickets sold per hour.
Answer: look it up
Step-by-step explanation:
Nia answered 18 of the 40 questions on the common assessment correctly. What percent of the questions did she answer correctly? What are you looking for? Circle one: Part whole percent
Answer:
Nia answerd 45% of the questions correctly.
pls help meeeee
pls....
Answer:
1→10
Step-by-step explanation:
12
27
45
105/4
49/2
2/15
2/9
22/45
7/12
1/3
Paloma decided to divide 1,292 by 31 using partial quotients. She uses 30 as her first partial quotient. Which are the partial quotients Paloma should show in her work
A 20, 10
B 30, 10,1
C 10,10,10,1
D 10,10,10,10,1
Mai spends 7 hours in school each day. Her lunch period is 30 minutes long, and she spends
a total of 42 minutes switching rooms between classes. The rest of her day is spent in 6 classes
that are all the same length. How long is each class?
Strategies Used:
A 11 hours
is
Box clue words,
numbers, & units
B 1 hours
Write the
expression or
с
hours
equation in
60
words
====
D
14 /
hours
Guess &
Check
so first of all we need to get rid of the time that isn't spent in class, because the question is asking about the time spent in class. so we would add 30+42 giving us 72 minutes, or 1 hour and 12 minutes. Now we can subtract 1 hour and 12 minutes from 7 hours to find the total time spent in class. Which would give us 5 hours and 48 minutes. (reminder; 60 minutes in 1 hour)
now that we have the total time spent in class, all that is left is division. The equation would be easier to solve when the hours are converted into minutes. 5 hours and 48 minutes equal, 348 minutes. Now we would divide 348 by 6 as there are 6 classes that take 348 minutes in all, and we wanna find how long 1 class takes. 348 divided by 6 would then give us 58. so each class takes 58 minutes.
(srry if the answer is wrong)
A baseball team played 75 games and lost 20% of them. How many games did the team lose?
O 15
O 20
O 55
O 60
Answer: 15
Step-by-step explanation: 20% → .20
.20 x 75 = 15
A train travels at 100 miles per hour. Write an equation that compares the time (t) with the distance (d).
t = 100d
d = 100t
d = t + 100
t = d + 100
Answer: d = 100t
Hope this helps!
Answer:
d = 100 * t
Step-by-step explanation:
d
------------
S l t
distance = d
time = t
speed = 100miles/h
d = 100 * t
Simplify the expression x+4+5/x-2÷x+6+15/x-2
Answer:
hope this helps
pls mark as brainliest
Simplify 72y^4/8y^7
72y^4
———
8y^7
Step-by-step explanation:
hi hi hi nice to meet you meet you
9р - Зр equivalent expression
Answer:
6p
Step-by-step explanation:
9p - 3p needs to have the like terms combined. 9 - 3 is 6, and since you have to keep the p, the answer is 6p.
Khali has a box with the dimensions shown. He plans to cover the box with glitter What is the total surface area to be covered with glitter? Show your work
Answer:
162
Step-by-step explanation:
4.5x9x4
solve the equation 3/4x-5=x
give your answers correct to 2 decimal places
Answer:
x = - 20
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] x - 5 = x ( multiply through by 4 to clear the fraction )
3x - 20 = 4x ( subtract 3x from both sides )
- 20 = x
What is the value of the expression 30-(-6)?
-180
-5
Ο Ο Ο Ο
5
24
Answer:30-(-6) is the same as 30+6. 36 is the value of the expression 30-(-6). If it were written:
30x(-6) = -180
30-6 = 24
But 30-(-6) = 36
Step-by-step explanation:
Need help with a math question
First: Find out their decimal form.
- 2 1/6 as a decimal is 2.16
7/3 as a decimal
To get 7/3 converted to decimal, you simply divide 7 by 3. Don't worry. You don't need to get the calculator out, because we did this for you.
7/3 as a decimal is:
2.333333333
I’m doing my math homework and I don’t understand it all. I did most of it in class but I don’t get it still so here’s the question
Question:
-4/3(3q -10)
Answer:
-4q+ 40/3
Step-by-step explanation:
If triangles ABC and XYZ are similar, what is the length of side b?
I don’t know what to do
Answer:
B
Step-by-step explanation:
What option best describes the relation shown in the mapping diagram below?
F(x)= 2x^3 + 5x^2 -x -6 is divided by x+1
What is the remainder and is it a fraction?
Remainder: 0 or -2
Is it a factor: yes or no
Step-by-step explanation:
substitute x= -1 into the equation to get the remainder
remainder= -2
the remainder is not a fraction
no, it is not a factor since its remainder is not zero
The graph of y = f (x) is given in the figure. Sketch = 1/2 ( + 2) − 2.
Answer:
y=1/2+2
Step-by-step explanation:
Carson has a smart phone data plan that costs $35 per month that includes 10 GB of data, but will charge an extra $15 per GB over the included amount. How much would Carson have to pay in a month where he used 3 GB over the limit? How much would Carson have to pay in a month where he used went over by x GB?
Answer:
3 GB over: $80 x GB over: $35+$15x
Step-by-step explanation:
3 GB over is 3 times 15 plus 35, which equals 80, x GB over is x times 15 plus 35. Boom, answer.
Your welcome!
Answer:
$80
Step-by-step explanation:
The equation y = 18x describes the amount of money Spongebob earns as a fry cook, where x is the
number of hours he works and y is the amount of money he earns. Show work. Complete sentence.
The table shows the amount of money Squidward earns as a cashier for different numbers of hours worked.
Squidward’s Earnings
Time (h) 3 5 8 10
Money earned
($) 48 80 128 160
(a) How much money does Spongebob earn per hour?
(b) How much money does Squidward earn per hour?
pls help and explain
Answer:
a. 18 dollars per hour
b. 16 dollars per hour
Step-by-step explanation:
for a, 18 is the slope of y=18x, meaning spongebob earns 18 dollars per hour
for b, since it seems like squidward earns 32 dollars every 2 hours, it can be guessed that he earns 16 dollars per hour, since 32/2 = 16
Pls answer the question in the photo
Answer:
correct answer to the problem is x= -9
Joe answered correctly.
Answer: nick
Step-by-step explanation: subtract 6 from both sides to get 0 on one side and then divide both sides by 2 to get x on its own
find the fractional form of sixty tow
seventh
sixty tow seven is not a number.
What is the inverse of the function?
f(x) = 3^x + 1
f^-1(x)= log3 (x) +1
f^-1(x)= log3(x)-1
f^-1(x)=log3(x+1)
f^-1(x)=log3(x-1)
Answer:
f^-1(x)=logs3(x+1)
Step-by-step explanation:
Let y=f(x)
[tex]\\ \rm\Rrightarrow y=3^x+1[/tex]
Interchange[tex]\\ \rm\Rrightarrow x=3^y+1[/tex]
[tex]\\ \rm\Rrightarrow lnx=ln(3^y+1)[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{ln(y-1)}{ln3}[/tex]
Again interchange
[tex]\\ \rm\Rrightarrow f^{-1}(x)=\dfrac{ln(x-1)}{ln3}[/tex]
A truck can be rented from Company A for $100 a day plus $0.50 per mile. Company B charges $40 a day plus $0.80 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same. At nothing miles, the rental costs are the same from either company.
Answer:
18 miles
Step-by-step explanation:
Let
The number of miles = x .According to Question ,
100 + 0.5(x) = 40 + 0.8(x) 100 + 0.5x = 40+ 0.8x 100 - 40 = 0.8x - 0.5x 60 = 0.3x x = 60/3 * 10 x = 184/8 x 4/5 = ? Help me please
hope it helps...................
[tex] \frac{4}{8} \times \frac{4}{5} [/tex]
Simplify:
[tex] \frac{4}{2} \times \frac{1}{5} [/tex]
[tex] \frac{4}{10} = \frac{2}{5} [/tex]
