The market equilibrium is the point where the demand and supply functions are equal
The producer's surplus at market equilibrium for a product is #105
How to determine the producer's surplusThe functions are given as:
[tex]p = 121 - x^2[/tex]
[tex]p = x^2 + 6x + 65[/tex]
Equate both functions
[tex]x^2 + 6x + 65 = 121 - x^2[/tex]
Collect like terms
[tex]x^2 + x^2 + 6x + 65 - 121 = 0[/tex]
Evaluate the like terms
[tex]2x^2 + 6x -56 = 0[/tex]
Divide through by 2
[tex]x^2 + 3x -28 = 0[/tex]
Expand
[tex]x^2 + 7x - 4x - 28 = 0[/tex]
Factorize
[tex]x(x + 7) - 4(x +7)= 0[/tex]
Factor out x + 7
[tex](x - 4)(x +7)= 0[/tex]
Solve for x
x = 4 or x = -7
The number of units cannot be negative,
So, we have:
x = 4
Substitute 4 for x in [tex]p = 121 - x^2[/tex]
[tex]p = 121 - 4^2[/tex]
p = 105
Hence, the producer's surplus at market equilibrium for a product is #105
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One angle in an obtuse isosceles triangle measures 40°. What are the measures of the other two angles?
40° and 120°
70° and 70°
40° and 100°
80° and 80°
Answer:
40° and 100°
Step-by-step explanation:
An obtuse triangle has one obtuse angle, or an angle that measures more than 90° but less than 180°. Options 1 and 2 are not correct, because these are acute angles.
So, one of the angles must be 40°, and the other may be 100° or 120°.
The measures of the angles in a triangle add up to 180°
40° + 40° + [tex]x[/tex] = 180°
80° + [tex]x[/tex] = 180°
[tex]x[/tex] = 180° - 80°
[tex]x[/tex] = 100°
The other two angles are 40° and 100°.
The mechanic does 4 oil changes in 2 hours. How many oil changes can the mechanic do in 8 hours?
Answer:
16.
Step-by-step explanation:
^
Answer:
The mechanic does 4 oil changes in 2 hours. How many oil changes Can the mechanic do in 8 hours. My answer is16 oil changes. 4 x 2 =8 and 8+8=16.
Step-by-step explanation:
A shipping company charges a flat rate of $3 and 1 cent for every mile traveled. What is the initial value and the rate of change?
Answer:
initial value = 3
rate of change = 0.01
Step-by-step explanation:
we can represent this as a linear equation:
y = 0.01x + 3
the initial value is the value of y when x = 0; we can find this by setting x to zero and evaluating for y, which gives us 3. Our initial value is 3.
The rate of change, of slope of this graph, is 0.01, as it is the constant multiplier of x.
Hare Krishna! :)
A field is divided into three senion A, B and C ratio 2:3:5. If section A covers an area 3.5 acres. Calculate the area of field
Answer:
17.5 acres
Step-by-step explanation:
Let the areas of A, B, and C be 2x, 3x, and 5x, respectively,
then 2x = 3.5 acrea, x = 3.5/2 acres
Total area is 2x + 3x + 5x = 10x = 10 * 3.5/2 = 17.5 acres
Could anyone help me / giving crowns away
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I messed up, so here's the answer.
can somebody help me with this question? please and thank you
the answer to your question is 72
Change 39 square yard to feet
Answer:
351 squared feet
Step-by-step explanation:
multiply by 9
A cyclist bikes a certain distance in 25 minutes,
How long would it take a pedestrian to travel the same distance
if he travels 2 = times slower than the cyclist?
Answer:
12.5 minutes
Step-by-step explanation:
Since the cyclist is biking a certain distance in 25 minutes, (which we don't know), and the pedestrian is traveling 2 times slower,
the speed of the pedestrian would be 25/2
25 / 2 = 12.5 minutes
simplify (2x+4÷3) ×6x÷x+2
Answer:
12x+10
Step-by-step explanation:
pls mark brainliest
Which of the following is not a linear function?
Answer: B
Step-by-step explanation:
This is a vertical line, meaning it fails the vertical line test, and thus cannot be a function.
How many grams in 3.2 tons
Answer:
2 902 991.17 grams in 3.2 tons
Original price of an SUV: $34,400.00
Discount: 25%
Step-by-step explanation:
Step 1- convert 25% into a decimal
Step 2- Multiply 34,400.00 x 0.25
Which should give you $8600.00
Step 3- Then subtract 34,400.00 from 8600.00
Which will give you $25800.0
The The thing to remember is Multiply with the discount then subtract your answer from the original price of the item.
Hope This Helps !!
In triangle ABC, m∠B=a, Find the measure of the angle, in degrees, between the altitudes dropped from the vertices A and C. WILL GIVE BRAINLIEST
The value of the angles between the altitudes dropped from the vertices A and C equals [tex]180^{\circ} - \alpha[/tex].
How to determine an angle between two heights inside a triangle
In this question we must apply definitions and theorems of Euclidean geometry to derive the value of all required angles.
Based on geometry we know that heights are perpendicular to sides opposite to an angle, sum of internal triangles equals 180°, sum of supplementary angles equals 180°.
If we know that [tex]m\angle B = \alpha[/tex], then the value of the angles between the altitudes dropped from the vertices A and C equals [tex]180^{\circ} - \alpha[/tex]. [tex]\blacksquare[/tex]
To learn more on triangles, we kindly invite to check this verified question: https://brainly.com/question/25813512
don't spam answer only if you know What is the measure of angle x? Enter your answer in the box
Answer:
The angle of x is 83°
Step-by-step explanation:
A straight line has a total of 180°. That means if you can figure out what the third angle on the bottom is (the one in the middle) you can add 41 to it and subtract that from 180. Since all the lines are straight you can say that the middle angle on the bottom is the same as the middle angle on the top. So:
180° - (41° + 56°) = 83°
11(u-4)
remove the parentheses
Answer: 11u - 44
Step-by-step explanation:
11u - 44.
You have to distrubute the 11 to everything inside the parenthesis. So it becomes 11*u or 11u and 11*-4 or -44.
Answer:
11u - 44
Step-by-step explanation:
11(u - 4)
We have to distribute
(11 × u) + (11 × -4)
11u - 44
A basket contains 8 oranges and 2 pears, the fruit are picked at random from one after assuming the fruits are not replaced. (a). Draw a probability tree to show the possible outcome to show the 3 picks. (b). Show the probability of picking all oranges and pears and an orange in that order. (c). Find the probability of picking at least two orange
Answer:
StepStep-by-step-by-step explanation:
........
.........................
Answer:
"." is a symbol called a period, it is typically used to mark the end of a sentence that has a main clause which contains a subject and a verb. In informal conversations that involve visible text ".....", which is a combination of many periods, is often used to show a long pause. This is the type seen in the question you asked.
Hope this helps!
Help fast will give Brainlyest
Answer: 64
Step-by-step explanation:
Which equation represents the graphed function?
A survey determined that 39% of the students at Lake Middle like math. There were 400 students in the cafeteria on Thursday. What is a good estimate for the number of students in the cafeteria who like math?
Answer:
math organization and the other one day is the best way to get a runner up
One graphic designer takes 3 hours to design a logo. Her less experienced
colleague takes 4 hours to design a logo. How many hours would it take them to
design a total of 7 logos if they both
start working at the same time?
It takes them 12 hours to design a total of 7 logos if they both start working at the same time
RateThis is the amount per unit time.
Since one graphic designer takes 3 hours to design a logo. Her less experienced colleague takes 4 hours to design a logo, we need to find the rate at which the work is done.
The rate at which the first graphic designer works is 1 logo/3 hours = 1/3 logo/hr.Also, the rate at which the less experienced colleague works is 1 logo/4 hours = 1/4 logo/hr.So, their combined rate r = 1/3 logo/hr + 1/4 logo/hr = (4 + 3)/12 logo/hr = 7/12 logo/hr.Time to design 7 logosNow, since we require the time to desigh 7 logos, this time is T = number of logos/combined rate
= 7 logos ÷ 7/12 logo/hr
= 12 hr
So, it takes them 12 hours to design a total of 7 logos if they both start working at the same time
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Can someone help me with this
Answer:
Some right angles
Step-by-step explanation:
What is the value of 5a when a=7 ?
Answer:
35
...
....
....
....
...
.
.
Select the correct answer.
A team of researchers is monitoring the population of crickets in a particular town. They do not know exactly how many crickets are remaining, but the model they use represents the minimum number of crickets remaining in the town.
According to their model, the minimum number of the species remaining, in thousands, multiplies by 10 every month. The researchers determine that right now, the population of crickets is at least 5 thousand. Once the minimum population reaches 1 million, measures are taken to stop the increase in population.
If P represents the actual population of crickets in the town, in thousands, and t represents the time, in months, which of the following systems of inequalities can be used to determine the possible number of crickets in the town over time?
Answer:
P>_5(10)^t
P<_1,000
Step-by-step explanation:
What is the range for the possible side length AB of ABC?
Answer:
2 < AB < 18
Step-by-step explanation:
Answer:
The range is from [tex]18[/tex] to [tex]2[/tex] (greatest to least)
[tex]2 < x < 18[/tex]
Step-by-step explanation:
we know that
The triangle inequality theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
Let
x-----> the length of the third side AB of triangle ABC
Applying the triangle inequality theorem
case A)
[tex]8+10 > x[/tex]
[tex]18 > x[/tex]
Rewrite
[tex]x < 18[/tex]
case B)
[tex]8+x > 10[/tex]
[tex]x > 10-8[/tex]
[tex]x > 2[/tex]
The solution for the range of possible side lengths of the third side is the interval
[tex](2,18)[/tex]
so
[tex]2 < x < 18[/tex]
All real numbers greater than [tex]2[/tex] and less than [tex]18[/tex]
The number [tex]2[/tex] and the number [tex]18[/tex] are not included in the solution
Solve the following proportion for u. u/10 = 3/17 Round your answer to the nearest tenth.
Step-by-step explanation:
To solve for u, remove the fraction.
Multiply each side by 10 to remove the fraction;
[tex]u = \frac{30}{17} = 1 \frac{13}{17} = 0.8[/tex]
What is the distance between (2, -4) and (9,-4)?
8 units
11 units
O units
7 units
Answer:
7 units
Step-by-step explanation:
If you want to get from (2, -4) to (9, -4) you have to move 7 units to the right. (9 - 2 = 7)
Answer:
7 units.
Step-by-step explanation:
pls help i need help
8 Connor the fruiterer sells two fruit packs.
Pack 1: 10 apples and 5 mangoes ($12)
Pack 2: 15 apples and 4 mangoes ($14.15)
Determine the cost of 1 apple and 5 mangoes.
(Simultaneous equations) pleaseeee help me test tomorrow
The cost of 1 apple and 5 mangoes is $6.15.
Let's look at how to form and solve simultaneous equations in a word problem.
State assumption and define variables:Assuming that the cost of each apple and mango is equal in both packs.
Let the cost of an apple be a and that of a mango be m.
Write equations based on given information:10a +5m= 12 -----(1)
15a +4m= 14.15 -----(2)
Solve by elimination:Steps for solving equations with two variables
Ensure that the magnitude of the coefficients of one of the term is equal in both equationsEliminate the term with the chosen term through subtraction or additionSolve for the other termSubstitute the value of the term found in (3) to find the value of the second termWorking
Here, I am making the value of the coefficient of m constant.
(1) ×4:
40a +20m= 48 ----(3)
(2) ×5:
75a +20m= 70.75 -----(4)
Moving on to step 2, we can eliminate the m term by subtracting equation (3) from (4). When the sign of the terms are equal, we use subtraction to eliminate the term. On the other hand, if one of the sign is positive and the other is negative, adding the two equations together will eliminate the term (provided that you have already ensured that the magnitude of the coefficient is equal).
(4) -(3):
75a +20m -(40a +20m)= 70.75 -48
Expand:
75a +20m -40a -20m= 22.75
Simplify:
35a= 22.75
Let's continue with step 3, where we solve for a.
a= 22.75 ÷35
a= 0.65
The cost of an apple is $0.65.
Now, moving on to step 4!
Substitute a= 0.65 into (1):
10(0.65) +5m= 12
6.5 +5m= 12
5m= 12 -6.5
5m= 5.50
5 mangoes costs $5.50.
Cost of 1 apple and 5 mangoes
= $0.65 +$5.50
= $6.15
Thus, the cost of 1 apple and 5 mangoes is $6.15.
How many cubes with edge lengths of 1/4 in. will it take to fill the prism?
56 cubes
375 cubes
6000 cubes
Answer:
1560
Step-by-step explanation:
First (2 1/2)/(1/4) = (5/2)(4) = 20/2 = 10
Next, 3/(1/4) = 3(4) = 12
Lastly, (3 1/4)/(1/4) = (13/4) x 4 = 52/4 = 13
This means we need 10 rows of 12, 13 high. 10(12)(13) = 1560 cubes.
Another way is to multiply 2 1/2 x 3 x 3 1/4 = 5/2 x 3 x 13/4 = 195/8
A 1/4 inch cube is 1/4 x 1/4 x 1/4 for a volume of 1/64
(195/8)/(1/64) = (195/8)(64) = 1560 cubes.