1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Shtirlitz [24]
3 years ago
10

Your class is selling boxes of flower seeds as a fundraiser. The total profit p depends on the amount x that your class charges

for each box of seeds. The equation p equals negative 0.5 x squared plus 36 x minus 179 models the profit of the fundraiser.​ What's the smallest​ amount, in​ dollars, that you can charge and make a profit of at least ​$379​?
To make the desired​ profit, the smallest amount you can charge for each box is ​$
nothing.

Mathematics
2 answers:
Slav-nsk [51]3 years ago
8 0

Answer:

$ 22.6

Step-by-step explanation:

Given that

Price charged for each box of seeds = x

Profit gained from from selling boxes of seeds = p

The equation of profit is modeled as

P(x) = 0.5x² + 36x - 179

As per given information if the fundraisers make a profit of  $379 then find the minimum price charged for each box of seed.

Now our above equation becomes

379 = -0.5x² + 36x - 179

Simplifying

379+179 = -0.5x² + 36x

558 = -0.5x² + 36x

0.5x² - 36x + 558 =0

multipying both sides of equation by 2

2(0.5x² - 36x + 558) = 2x0

x² - 72x +1116 = 0

Using quadratic formula we get the following factors

x= 49.4 or x= 22.60

As we can the smalles value is 22.6

So, they can charge 22.6 dollar for each bag of seeds in order to get profit of 379 dollars.



Korolek [52]3 years ago
4 0

Answer:

<h2>We need to charge $22.58 to have $379 profit.</h2>

Step-by-step explanation:

The given equation is:

p=-0.5x^{2}+36x-179

Where <em>x </em>is the amount the class charges.

So, the problem is asking the smallest amount that can be charged if the profit is $379. Replacing this data, the expression would be:

-0.5x^{2}+36x-179\geq 379

"at least" means "equal or more than".

Now, we have to solve this quadratic inequality, which we can do by just graphing, because the solution of inequalities are intervals, which are specific regions.

As you can see in the image attached, the smallest amount is

x=-6\sqrt{5}+36=22.58

Therefore, we need to charge $22.58 to have $379 profit.

You might be interested in
A rancher with 420420 meters of fence intends to enclose a rectangular region along a river​ (which serves as a natural boundary
Kobotan [32]
Perimeter of Rectangle: 2W + 2L
One L is the river so we have 3 sides
420m/3 = 140m

Area of Rectangle is WL
140×140= 19,600 Sq meters

I'm assuming you may have another mathematical system the teacher wants you to use. Yet, I get Area is 19,600 Sq meters
4 0
3 years ago
Need help with this question
dybincka [34]
Download a math calculator or math awnsers
7 0
3 years ago
Read 2 more answers
Determine whether the given vectors are orthogonal, parallel or neither. (a) u=[-3,9,6], v=[4,-12,-8,], (b) u=[1,-1,2] v=[2,-1,1
nevsk [136]

Answer:

a) u v= (-3)*(4) + (9)*(-12)+ (6)*(-8)=-168

Since the dot product is not equal to zero then the two vectors are not orthogonal.

|u|= \sqrt{(-3)^2 +(9)^2 +(6)^2}=\sqrt{126}

|v| =\sqrt{(4)^2 +(-12)^2 +(-8)^2}=\sqrt{224}

cos \theta = \frac{uv}{|u| |v|}

\theta = cos^{-1} (\frac{uv}{|u| |v|})

If we replace we got:

\theta = cos^{-1} (\frac{-168}{\sqrt{126} \sqrt{224}})=cos^{-1} (-1) = \pi

Since the angle between the two vectors is 180 degrees we can conclude that are parallel

b) u v= (1)*(2) + (-1)*(-1)+ (2)*(1)=5

|u|= \sqrt{(1)^2 +(-1)^2 +(2)^2}=\sqrt{6}

|v| =\sqrt{(2)^2 +(-1)^2 +(1)^2}=\sqrt{6}

cos \theta = \frac{uv}{|u| |v|}

\theta = cos^{-1} (\frac{uv}{|u| |v|})

\theta = cos^{-1} (\frac{5}{\sqrt{6} \sqrt{6}})=cos^{-1} (\frac{5}{6}) = 33.557

Since the angle between the two vectors is not 0 or 180 degrees we can conclude that are either.

c) u v= (a)*(-b) + (b)*(a)+ (c)*(0)=-ab +ba +0 = -ab+ab =0

Since the dot product is equal to zero then the two vectors are orthogonal.

Step-by-step explanation:

For each case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.

Part a

u=[-3,9,6], v=[4,-12,-8,]

The dot product on this case is:

u v= (-3)*(4) + (9)*(-12)+ (6)*(-8)=-168

Since the dot product is not equal to zero then the two vectors are not orthogonal.

Now we can calculate the magnitude of each vector like this:

|u|= \sqrt{(-3)^2 +(9)^2 +(6)^2}=\sqrt{126}

|v| =\sqrt{(4)^2 +(-12)^2 +(-8)^2}=\sqrt{224}

And finally we can calculate the angle between the vectors like this:

cos \theta = \frac{uv}{|u| |v|}

And the angle is given by:

\theta = cos^{-1} (\frac{uv}{|u| |v|})

If we replace we got:

\theta = cos^{-1} (\frac{-168}{\sqrt{126} \sqrt{224}})=cos^{-1} (-1) = \pi

Since the angle between the two vectors is 180 degrees we can conclude that are parallel

Part b

u=[1,-1,2] v=[2,-1,1]

The dot product on this case is:

u v= (1)*(2) + (-1)*(-1)+ (2)*(1)=5

Since the dot product is not equal to zero then the two vectors are not orthogonal.

Now we can calculate the magnitude of each vector like this:

|u|= \sqrt{(1)^2 +(-1)^2 +(2)^2}=\sqrt{6}

|v| =\sqrt{(2)^2 +(-1)^2 +(1)^2}=\sqrt{6}

And finally we can calculate the angle between the vectors like this:

cos \theta = \frac{uv}{|u| |v|}

And the angle is given by:

\theta = cos^{-1} (\frac{uv}{|u| |v|})

If we replace we got:

\theta = cos^{-1} (\frac{5}{\sqrt{6} \sqrt{6}})=cos^{-1} (\frac{5}{6}) = 33.557

Since the angle between the two vectors is not 0 or 180 degrees we can conclude that are either.

Part c

u=[a,b,c] v=[-b,a,0]

The dot product on this case is:

u v= (a)*(-b) + (b)*(a)+ (c)*(0)=-ab +ba +0 = -ab+ab =0

Since the dot product is equal to zero then the two vectors are orthogonal.

5 0
3 years ago
Read 2 more answers
66.
Naddik [55]

Answer:  530.66 units²

<u>Step-by-step explanation:</u>

Area_{(circle)}=\pi r^2\qquad and\qquad r=\dfrac{diameter}{2}\\\\\\\implies Area_{(circle)}=\pi \bigg(\dfrac{diameter}{2}\bigg)^2\\\\\\\text{It is given that the diameter = 26:}\\A=\pi\bigg(\dfrac{26}{2}\bigg)^2\\\\\\.\quad =\pi \cdot 13^2\\\\\\.\quad =169\pi\\\\\\.\quad =\large\boxed{530.66}

3 0
3 years ago
I beg please help :(
Aloiza [94]

Answer:

(2.8, 0.8)

(0.8, -1.8)

Step-by-step explanation:

1. Home (Xa, Ya)= (8, 6)

San Antonio (Xb, Yb)=(-5, -7)

Xa-Xb=8-(-5)=13

Ya-Yb=6-(-7)=13

Emily  starts at 2/5 of the road, make it  (Xc, Yc)

Xc= Xa-(Xa-Xb)2/5=8-5.2=2.8

Yc=Ya-(Ya-Yb)2/5=6-5.2=0.8

=> Emily starts at (2.8, 0.8)

2.

Emily ends at 3/5 of the road, , make it  (Xd, Yd)

Xd= Xa-(Xa-Xb)3/5=8-7.8=0.8

Yd=Ya-(Ya-Yb)3/5=6-7.8=-1.8

=> Emily ends at (0.8, -1.8)

6 0
3 years ago
Other questions:
  • Pauline travels between two cities. first she drives for 45 minutes at an average speed of 85 km/hr then for 16 minutes at an av
    13·1 answer
  • which measure would you report to describe the diffrences between the most electricity used in 1 month and the least
    5·1 answer
  • ( please help this is the last question and i have 4 min left, thank you for the help!)
    15·1 answer
  • the rain caused the river to rise a total of 6 2/3 inches. the river was was rising a an average of 2/3 of an inch each hour. ho
    12·1 answer
  • Choose the correct simplification of the expression 3b/a-2
    9·2 answers
  • An acute angle θ is in a right triangle with sin θ = seven eighths. What is the value of cot θ?
    9·1 answer
  • Slope of -1,0 and 10,18
    15·2 answers
  • A small class has 10 students. Seven of the students are male and 3 are female. You write the name of each student on a small ca
    13·2 answers
  • Please answer this quick! Worth 23 POINTS!
    7·1 answer
  • Which of these is 3% equivalent to?<br> 0.003<br> 0.3<br> 0.03<br> 300
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!