The vertices of the feasible region of the constraints is (0,2.5)
How to determine the vertices?The constraints are given as:
x + 3y ≤ 6
4x + 6y ≥ 9
x ≥ 0, y ≥ 0
Express the inequalities as equations
x + 3y = 6
4x + 6y = 9
Make x the subject in x + 3y = 6
x = 6 - 3y
Substitute x = 6 - 3y in 4x + 6y = 9
4(6 - 3y) + 6y = 9
Expand
24 - 12y + 6y = 9
Evaluate the like terms
-6y = -15
Divide by 6
y = 2.5
Substitute y = 2.5 in x = 6 - 3y
x = 6 - 3 * 2.5
Evaluate
x = -1.5
So, we have:
(x,y) = (-1.5, 2.5)
Recall that: x ≥ 0, y ≥ 0
This means that the feasible region must have positive coordinates or zero
So, we set x = 0
(x,y) = (0, 2.5)
Hence, the vertices of the feasible region of the constraints is (0,2.5)
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If the sum of six consecutive even integers is 438, what is the smallest of the six integers?
Can someone help me with these 2 geometry questions?? Will mark brainiest :)
Answer:
Thats to hard Do it your self
Hi guys can u guys help me add 322 + 12
Answer:
334 is the answer
Step-by-step explanation:
you add them together
Answer:
334 is the right answer
Step-by-step explanation:
please mark me brainliest
Solve the equation square root of x-2+5 = 7 for the variable. Show each step of your solution process
Answer:
x=4
Step-by-step explanation:
x+3=7
subtract 3 from both sides
simplify
If 6 pounds of apples cost $4.80 what is the cost per 9 pounds
Answer:
Cost of 1 pound apple:4.80/6=2.4
cost of 9 pounds apple:2.4 ×9=21.6
order the expression from least to greatest
Answer:
So it would be 4, 11, 20
Step-by-step explanation:
[tex]11^1 = 11[/tex]
[tex]2^2 * 5 = 20[/tex]
[tex]8^2-60 =4[/tex]
There are two types of packages that are available for hotel stay
- you can use the hotel unlimited for $500 a month
- Or you can spend $50 a day per visit.
Enter an equation that can be used to find the number of visits per month needed for the two packages to cost the same amount
Answer:
for one month 500$
for daily visit 50$
500$=50$*x days
x days=500$/50$
x days = 10 days
10 days of daily visits costs 500$ equal to one month
The radius of the circle shown below is 8 centimeters. What is the
approximate length of XY?
115
A. 50.3 cm
B. 16.1 cm
C. 8.0 cm
D. 64.2 cm
what is x- 2 1/2 = 6 3/4
Answer:
3 2/2
Step-by-step explanation:
How can you solve multistep equations that represent real world
scenarios?
Houa is driving to a concert and needs to pay for parking. There is an
automatic fee of $8 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $2 for every hour she had her car in the lot. How much total money would Houa have to pay for
parking if she left her car in the lot for 3 hours? How much total money would Houa have to pay if she left her car in the lot for 3 hours? How much would Houa have to pay if she left her car in the lot for t hours?
Cost of parking for 3 hours:
I
Cost of parking for t hours:
Step-by-step explanation:
let's create the corresponding equation.
it is linear, because the cost per hour is constant, no matter how many hours the car parks.
t is the variable indicating the amount of hours parking.
every hour costs $2.
and $8 is the starting value (we have to pay that, even if we have 0 hours parking time).
cost(t) = 2t + 8
so, the cost after 3 hours is
cost(3) = 2×3 + 8 = 6 + 8 = $14
simplify [tex]y^{-3}[/tex]
A CD is on sale for $10.00. The sales tax rate is 6%. How much will the total cost be for the CD
Answer:
$10.06
Step-by-step explanation:
Tax rate = 6% , convert into 0.06
10 × 0.06 = 0.6
10 + 0.6 = 10.06
Please help me!! I don't understand
No linksssss
Answer:
thanks haahhahahaha
Step-by-step explanation:
Emily reads a story book. o the first day, she reads 1/9 of the whole book, and on the second day, she reads 24 pages. The ratio of the number of pages read to the remaining pages in the two days is 1:4. How many pages are there in this book
Answer:
Step-by-step explanation:
Let P be the number of pages
First day reads P/9 pages
Second day reads 24 pages
two days reading is P/5 (1 page read for every 4 pages left)
P/9 + 24 = P/5
P + 24(9) = 9P/5
5P + 24(9)(5) = 9P
1080 = 4P
P = 270 pages
There are 270 pages in this book.
Given that,
Emily reads a storybook the first day,
She reads 1/9 of the whole book, and on the second day, she reads 24 pages.
The ratio of the number of pages read to the remaining pages in the two days is 1:4.
We have to find
How many pages are there in this book?
According to the question,
Let, P is the number of pages,
The first day Emily reads p/9 pages of the whole book,
And the second day she read 24 pages.
The ratio of the number of pages read to the remaining pages in the two days = 1;4 = p/5.
Therefore,
The number of pages reads first day + the number of pages read the second day = The ratio of the number of pages read to the remaining pages in the two days
[tex]\rm \dfrac{p}{9} + 24 = \dfrac{p}{5}\\\\ \dfrac{p}{5} - \dfrac{p}{9} = 24\\\\\dfrac{p \times 9 - p\times 5}{45} = 24\\\\ \dfrac{9p-5p}{45} = 24\\\\\dfrac{4p}{45} = 24\\\\4p = 24\times 45\\\\4p = 1080\\\\p = \dfrac{1080}{4}\\\\p = 270 \ pages[/tex]
Hence, there are 270 pages in this book.
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on tuesday a local a hamburger shop sold a combined total of 448 hamburgers and cheeseburgers , the number of cheeseburgers sold was three times the number of hamburgers sold how many hamburgers were sold on tuesday ?
Which equation represents this line in point-slope form?
A.
`(y + 4) = (4)/(3) (x + 3)`
B.
`(y −4) = -(4)/(3) (x +3)`
C.
`y= -(3)/(4)x`
D.
`4y− 3x = 0`
Answer:
The Answer is Option A or Option B
Step-by-step explanation:
First let's review what point slope form is.
[tex]y - y 1 = m(x - x1)[/tex]
To take a line and put it into point slope form you need to identify one of the points. In this case the point is either (-3, -4) or (-3, 4) but without a graph attached I cannot personally say which one it is.
You will also need to identify the slope of the line (m) based on the graph, so identify if the graph is ascending or descending. This alone can determine your answer
Again, there is no graph provided so it is up to you to determine if it is Option A or B.
I really hope this helps and you have a great rest of your day!
Note: I am not a professional educator so take my opinion carefully.
=)
(fog) f(x) = 1/x g(x) square root x+3
Answer:
see the step below, but I'm not sure if this you want
Step-by-step explanation:
[tex](fog) = \frac{1}{ \sqrt{x + 3} } [/tex]
[tex](fog) = \frac{ \sqrt{ x + 3} }{x + 3} [/tex]
what is the value of x that makes the equation 8 x -4 equal 96 true
Answer:
x= 12.5 or 25/2
Step-by-step explanation:
8x - 4 (+4) = 96 (+4)
8x (/8) = 100 (/8)
x= 12.5 or 25/2
George is building a rabbit run in his backyard he makes the length 2/7km and the width 1/5km draw a sketch of his rabbit run and then find the area
Here !
I hope this helps you a little ,
please need help with this Calculus question
I need help fast I forgot how to do this
Answer:
ABC & E are true statements about the graph
One hundred voters were asked whether they supported a bill that had
The question is cut off.
Solve this plz question plz
We have: [tex](-\frac{15}{18})[/tex] ÷ [tex](-\frac{20}{24})[/tex] = [tex]\frac{-15}{18} .\frac{-24}{20} = \frac{(-3)(5).(-4)(6)}{(3)(6).(4)(5)} = 1[/tex]
ANSWER: 1
ok done. Thank to me :>
Answer:
1
Step-by-step explanation:
[tex]( - \frac{15}{18} ) \div ( - \frac{20}{24} ) \\ now \: you \: have \: fraction \: divided \: by \: fraction \: then \: do \: reciprocal \: \\ ( - \frac{15}{18} ) \times ( - \frac{24}{20} ) \\ = 1[/tex]
Find the exact value of tan π/12.
[tex]\textit{Half-Angle Identities}\qquad tan\left(\cfrac{\theta}{2}\right)= \begin{cases} \pm \sqrt{\cfrac{1-cos(\theta)}{1+cos(\theta)}} \\\\ \cfrac{sin(\theta)}{1+cos(\theta)}~~\leftarrow \textit{let's use this one} \\\\ \cfrac{1-cos(\theta)}{sin(\theta)} \end{cases} \\\\\\ 2\cdot \cfrac{\pi }{12}\implies \cfrac{\pi }{6}~\hspace{10em} \cfrac{~~ \frac{\pi }{6}~~}{2}\implies \cfrac{\pi }{6}\cdot \cfrac{1}{2}\implies \cfrac{\pi }{12}[/tex]
so let's use the double of the angle in the half-angle identities, check the picture below for the cosine, sine pairs
[tex]tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{sin\left( \frac{\pi }{6} \right)}{1+cos\left( \frac{\pi }{6} \right)}\implies tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{~~ \frac{1}{2}~~}{1+\frac{\sqrt{3}}{2}}[/tex]
[tex]tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{~~ \frac{1}{2}~~}{~~\frac{2+\sqrt{3}}{2}~~}\implies tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{1}{2}\cdot \cfrac{2}{2+\sqrt{3}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{1}{2+\sqrt{3}}~\hfill[/tex]
What is the length of LN in the right triangle below?
Answer:
D 280
Step-by-step explanation:
Pythagoras theorem
Answer:
a
Step-by-step explanation:
LN=√19＾2 - 9＾2
=√361 - 81
=√280
A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below.
81 71 202 113 269 248 242
Find the median number of newspapers sold.
CE
O A. 242 newspapers
OB 175 newspapers
OC. 113 newspapers
OD. 202 newspapers
OD Step-by-step explanation:
The median of the of the number of newspapers sold by shopkeeper is 202 .
Given,
A store manager kept track of the number of newspapers sold each week over a seven-week period.
81 71 202 113 269 248 242.
Now,
The median of the dataset is the middle value of the dataset, which means that 50 % of the values are below the mean and 50% of the values are above the mean.
Rearrange the dataset in ascending order as
71, 81, 113, 202, 242, 248, 269.
Thus the median will be the 4th value.
Hence the median will be 202.
Thus the correct option will be 202 Newspapers.
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Given ω=[tex]\frac{3-2i}{5-6i}[/tex] , find ω in the a+bi form.
Answer:
Solution is given in the photo
Oceanside Bike Rental Shop charges 13 dollars plus 8 dollars an hour for renting a bike. Tim paid 45 dollars to rent a bike. How many hours did he pay to have the bike checked out?
Step-by-step explanation:
Shop charges =13
Many left for renting bike = 45-13 =$32
If renting for 1hr cost $8
then renting for X Hrs will cost $32
1/X =8/32 cross multiplying
8X= 32
X= 32÷8= 4hrs
need this soon please
Answer: pretty sure -7
Step-by-step explanation:
Answer:
-7
Step-by-step explanation:
(-80) - (-10) is -79
-70 / (+10) = -7