if the supply and demand functions for a commodity are given by p-q=10 and q(2p-10)=2100, what is the equilibrium price and what is the corresponding number of units supplies and demanded
Answers
Answer:
If p - q = 10, then p = 10 + q. Replace the other p with this:
q(2(10 + q) - 10) = 3600
q(20 + 2q - 10) = 3600
q(10 + 2q) = 360
The equilibrium point of a demand and supply function is the point where both functions are equal.
The equilibrium price is 40, and the corresponding demand is 30 supplies
Given
[tex]p- q = 10[/tex] --- the supply function
[tex]q(2p - 10) = 2100[/tex] --- the demand function
Make q the subject in [tex]p- q = 10[/tex]
[tex]q = p - 10[/tex]
Substitute [tex]q = p - 10[/tex] in [tex]q(2p - 10) = 2100[/tex]
[tex](p - 10)(2p - 10) = 2100[/tex]
Factor out 2
[tex]2(p - 10)(p - 5) = 2100[/tex]
Divide both sides by 2
[tex](p - 10)(p - 5) = 1050[/tex]
Open brackets
[tex]p^2 -10p - 5p + 50 = 1050[/tex]
[tex]p^2 -10p - 5p + 50 - 1050 =0[/tex]
[tex]p^2 -15p - 1000 =0[/tex]
Expand
[tex]p^2 -40p + 25p- 1000 =0[/tex]
Factorize
[tex]p(p -40) + 25(p- 40) =0[/tex]
Factor out p - 40
[tex](p+ 25) (p- 40) =0[/tex]
Solve for p
[tex]p = -25[/tex] or [tex]p = 40[/tex]
The price cannot be negative.
So: [tex]p =40[/tex]
Recall that:
[tex]q = p - 10[/tex]
[tex]q = 40 - 10[/tex]
[tex]q = 30[/tex]
Hence, the equilibrium price is 40, and the corresponding number of supplies is 30
See attachment for the graphs of both functions
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Related Questions
This exact same question has been asked a few times, but I’m finding several different answers. Could someone please clarify.
Thank you in advance.
Answers
Answer:
The last one (D)
Step-by-step explanation:
Jonathan would have to check how much he's paid off after each of the months which means he would need to subtract that from total amount of money that he's pay for the new computer
Find the area of the trapezoidal shown
Answers
Answer:
may you show us the pic so we can help?
Step-by-step explanation:
ANSWER THE QUESTION PLEASE & THANK YOU ! Show that the equation y +2 = 2(3x + 1) is linear and that it represents a proportional relationship
between x and y.
Part 1 out of 4
y +2=2(3x + 1)
y +2=
JX +
✓ Check
Next
Answers
Answer:
y+2=6x+2
Step-by-step explanation:
[tex]y+2=2(3x+1)\\y+2=6x+2\\y=6x+2-2\\y=6x[/tex]
Since the exponent/degree of x and y both the variables are 1 the equation is linear and y=6x represents a proportional relationship between x and y
HELPPP ME!!! ASAP
PLZZZZZZZZZZ
Answers
ANSWER:i think its C
Step-by-step explanation:
The total amount y (in dollars) in your savings account after buying x video games is represented by y= 90-10x. You have $40 in your account after buying video games. How many video games did you buy?
Answers
5 video games bought.
Explanation:
Step one) identify all variables.
> y = money in bank acc AFTER buying (x) video games.
Step two) y = $40
Step three) substitute
> 40 = 90 - 10x.
Step Four) solve for x
> subtract 90 both sides.
-50 = -10x
DIVIDE by -10 on both sides ( to isolated x)
This equals 5 = x
x is number of video games bought meaning >> 5 video games bought
*sings body by Megan Thee Stallion*
Find the ratio a:b if it is given that ... a+3b/5=a-2b/2. HELP RIGHT NOW PLS
Answers
By simplifying the given equation, we can see that the ratio a:b is:
8:1
How to find the ratio a:b?
We start with the equation:
(a + 3b)/5 = (a - 2b)/2
The first thing we need to isolate each variable in one side of the equation.
(a + 3b)/5 = (a - 2b)/2
2*(a + 3b) = 5*(a - 2b)
2a + 6b = 5a - 10b
6b + 10b = 5a - 2a
16b = 2a
So, 16 times b is equal to 2a
We can write this as:
b/2 = a/16
b = a/8
Then the ratio a to b is:
8:1
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A basketball player made 77 out of 100 attempted free throws. What percentage of free throws was made?
The player made____% of the free throws attempted.
Answers
Answer:
77%
Step-by-step explanation:
Liam had a container of oatmeal that contained 5 and one-half cups of oatmeal. Liam ate StartFraction 4 over 9 EndFraction cups of oatmeal every morning before school for a week. Which is the best estimate of the number of cups of oatmeal that Liam had left in the container at the end of the five-day week?
A.2 1/2
B.3
C.3 1/2
D.5
Answers
Answer: B or 3
Step-by-step explanation:
had this question on my quiz
An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean output of 451 watts with a variance of 144. What is the probability that the mean amplifier output would be greater than 449.8 watts in a sample of 76 amplifiers if the claim is true?
Answers
Answer:
sorry for that i did not about that give a thanks and save water for feuter . jal
A good general rule for this course is to be organized, set a study schedule, and review your work.
True
False
Answers
Answer:
True
Step-by-step explanation:
Being organized, having a study schedule and reviewing your work are all great habits to becoming a well-rounded student and generally succeeding in a course.
Please rate 5 stars and/or say thanks if I was able to help!
Have a good day!
~Roi
Mr. Reed has 114 students. He gives each student ¼ pound of candy in their Halloween bag. How many pounds of candy does he need to buy?
Answers
Answer:
hewo
Step-by-step explanation:
well you need to multiply 1/4*114 and that should give you your answer
which would be 28.5
Find the image of (8,0) after a rotation of 90° about the origin.
Answers
Answer:
(0,8)
Step-by-step explanation:
this is my guess because 90° would move it from axis to axis, switching the x & y numbers. i could be wrong though & my appologies if i am incorrect
what is the answer of this 4:3=a:6
Answers
Answer:
a = 8
Step-by-step explanation:
4 : 3 = a : 6
[tex]\frac{4}{3} = \frac{a}{6}[/tex]
Cross multiply
4*6 = a * 3
[tex]\frac{4*6}{3}=a[/tex]
a = 4 * 2
a = 8
A turkey costs $1.05 per pound. There are going to be fifteen people at Thanksgiving dinner. Plan for each person to eat two, 3/8 pound servings of turkey.
How many pounds of turkey will you need to buy?
Answers
Answer:
I will need to buy 22.5 pounds of turkey and pay $23.63
Step-by-step explanation:
Proportions
Each person is planned to eat 2 x 3/8 pound servings of turkey for thanksgiving dinner. This means each person will eat
[tex]2\cdot\frac{3}{4}=\frac{3}{2}[/tex]
pounds of turkey.
There are going to be 15 people at the dinner, thus the total turkey needed is:
[tex]15\cdot\frac{3}{2}=22.5~pounds[/tex]
The turkey costs $1.05 per pound, thus the total cost is
22.5*$1.05 = $23.63
I will need to buy 22.5 pounds of turkey and pay $23.63
What is the slope of the line whose equation is y-4={(x-2)?
у
-6
5
4
(2,4)
8
N
х
5 -5 -4 -3 -2 -21
2 3 4 5 6
(0, -1)
1
Answers
Answer:
1
Step-by-step explanation:
coefficient if x term is 1
Topic: coordinate geometry
If you like to venture further, do check out my insta (learntionary) where I constantly post math tips! Thanks!
The slope of the line whose equation is y - 4 = (x - 2) is,
⇒ m = 1
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Equation of line is,
⇒ y - 4 = x - 2
Now, We can simplify for slope as;
⇒ y - 4 = x - 2
⇒ y = x + 2
⇒ dy/dx = 1
⇒ m = 1
Thus, The slope of the line whose equation is y - 4 = (x - 2) is,
⇒ m = 1
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A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level and estimates the angle of elevation of the kite to be 55°. If the string is 350 ft long, how high is the kite above the ground? (Round your answer to the nearest foot.)
Answers
The kite is approximately 345 feet above the ground.
The height of the kite above the ground is 287 ft
The length of the string, the height of the kite (h) above ground and the perpendicular distance from the end of the kite string to the man forms a right angled triangle.
Trigonometric shows the relationship between the lengths and angles of a right angled triangle.
Therefore using trigonometric ratios:
sin(55) = h / 350
h = 287 ft
Therefore the height of the kite above the ground is 287 ft.
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How many groups of 2/3 are in 3/5 a 915 B 9/10 C 1 1/3 D 1 1/9
Answers
Answer:
aaa
Step-by-step explanation:
35istohhhaaa bla bla nla
What is the value of f(g(3))
Answers
Answer:
A
Step-by-step explanation:
f(g(3)= f(g(x=3)) = f([tex]\frac{3+1}{3-1}[/tex]) = f(4/2) = f(2) = f(x=2) = 3*2-7 = 6-7 = -1
Answer:
Step-by-step explanation:
A . It is the correct answer
The auxiliary equation for the given differential equation has complex roots. Find a general solution.
y''-4y' +7y =0
Answers
Answer:
y = Ae^2xcos√3 x + Be^2xsin√3 x
Step-by-step explanation:
Given the differential equation
y''-4y' +7y =0
Let my = y' and m²y =y''
The auxiliary equation is expressed as;
m²y - 4my +7y = 0
(m²-4m+7)y =0
Divide through by y;
m²-4m+7= 0
Factorize the auxiliary equation
m = 4±√16-4(7)/2
m = 4±√-12/2
m = 4±2√3 i/2
m = 2+√3i
From the complex number a = 2(real part)
b = √3 (imaginary part)
Substitute into the general solution
y = Ae^axcosbx + Be^axsinbx
y = Ae^2xcos√3 x + Be^2xsin√3 x
Given John's data collection method and findings, what conclusion can be made?
OA.
Only the claim for vehicle B is true because more people agree with their claim.
OB. Neither of the claims are correct.
Ос.
Both SUV manufacturers' claims are true, but the turning radius of vehicle B is sharper than the turning radius of vehicle A.
Only the claim for vehicle A is true because 11 out of 15 people agree with their claim.
OD
Answers
Answer:
b
Step-by-step explanation:
edg2020
I need a tutor or someone that’s willing to help ... but can someone pls answer
Answers
Answer:
1/2
Step-by-step explanation:
Answer:
Your slope is 1/2
Step-by-step explanation:
Slope is rise over run or m=rise/run rise being the Y value and X being the run value. You can count the grid on the graph provided.
rise= 1
run= 2
The figure shows three right triangles. Triangles PQS, QRS, and PRQ are similar. Theorem: If two triangles are similar, the corresponding sides are in proportion. Figure shows triangle PQR with right angle at Q. Segment PQ is 4 and segment QR is 9. Point S is on segment PR and angles QSP a Using the given theorem, which two statements help to prove that if segment PR is x, then x2 = 97? (1 point) Segment PR ⋅ segment PS = 16 Segment PR ⋅ segment SR = 36 Segment PR ⋅ segment PS = 36 Segment PR ⋅ segment SR = 81 Segment PR ⋅ segment PS = 16 Segment PR ⋅ segment SR = 81 Segment PR ⋅ segment PS = 81 Segment PR ⋅ segment SR = 16
Answers
The two statements that help to prove that if segment PR is x, then x² = 97 are:
Segment PR • segment SR = 81Segment PR • segment SR = 16What is a segment?A line segment is a piece or part of a line having two endpoints.
Here, the statements that help to prove that if segment PR is x, then x² = 97 are Segment PR • segment SR = 81 and that Segment PR • segment SR = 16.
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Water flows through a pipe at a rate of 2 fluid ounces per second. Express this rate of flow in quarts per minute.
Answers
Answer:
Step-by-step explanation:
3.75
Water flows through a pipe at a rate of 3.75 fluid quarts per minute.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
Water flows through a pipe at a rate of 2 fluid ounces per second.
2 ounces = 0.0625 quarts
And 1 second = 0.0166667 minutes
So, water flows through a pipe at a rate of 0.0625 quarts per 0.0166667 minutes.
Water flows through a pipe at a rate of 3.75 fluid quarts per minute.
Therefore, the rate is 3.75 fluid quarts per minute.
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Please help me I need to get this right
Answers
Answer:
try the second one on top
Step-by-step explanation:
You are dealt one card from a standard 52-card deck. Find the probability of being dealt a red card
Answers
Answer:
It’s a 50% chance
Step-by-step explanation:
The probability of being dealt a red card is 1/2 or 50% if you are dealt one card from a standard 52-card deck.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
You are dealt one card from a standard 52-card deck.
Total number of red cards = 26
Total number of outcomes = 52
The probability of being dealt a red card = 26/52
The probability of being dealt a red card = 1/2
Or
The probability of being dealt a red card = 0.5 or 50%
Thus, the probability of being dealt a red card is 1/2 or 50% if you are dealt one card from a standard 52-card deck.
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PLEASE HELP ASAP WILL GIVE BRAINLEIST!!
Camila was looking at the architect's blueprint of her house. The scale on the blueprint is shown below the blueprint on the left. What is the PERIMETER on the blueprint if the actual dimensions of her bedroom are 10 feet by 16 feet.
1/4 inch = 1 foot
Answers
Answer:
13 inches
Step-by-step explanation:
10 * 1/4 = 2 1/2 inches
16 * 1/4 = 4 inches
2(2 1/2) + 2(4) = 13 inches
Answer:
Its 4 feet, The other person is wrong and did not explain it the way the question says.
Step-by-step explanation:
Evaluate 8+3e when e = 2
Answers
Answer: 14
Step-by-step explanation: bru is simple
Answer:
8+3e=8+3(2)=8+6=14. aswer is 14
hope this helps u plz give me the brainliest pplzz
Evaluate the integral using the indicated trigonometric substitution. sqrt(x2 − 81)/x dx, x = 9 sec()
Answers
Answer:
C
=
C
'
−
81
2
ln
9
Step-by-step explanation:
What is a slope, because i don't know
Answers
Answer:
The slope of a line is a measure of its steepness. In math, slope is calculated as "rise over run" (change in y divided by change in x).
0 of 1
Does the equation 94=1227
9
4
=
12
27
represent a proportional relationship? Why or why not?
Select the option that correctly answers both questions.
Yes, it is proportional because 94=1227.
9
4
=
12
27
.
No, it is not proportional because 94≠1227.
9
4
≠
12
27
.
Yes, it is proportional because 94≠1227.
9
4
≠
12
27
.
No, it is not proportional because 94=1227.
Answers
Answer:
its 9 4 = 12 27
Step-by-step explanation: