Answer:
Producer's surplus = (1/2) x (2) x (10) = 10
Step-by-step explanation:
To find the producer's surplus, we need to first determine the equilibrium quantity and price at which the supply and demand functions intersect.
Setting the supply function S(x) equal to the demand function D(x) and solving for x, we get:
4x + 2 = 14 - x^2
Rearranging and simplifying, we get a quadratic equation in standard form:
x^2 + 4x - 12 = 0
Using the quadratic formula, we get:
x = (-4 ± √(4^2 - 4(1)(-12))) / (2(1))
x = (-4 ± √64) / 2
x = -2 ± 4
x = -6 or x = 2
Since we're interested in a positive quantity, we'll take x = 2 as the equilibrium quantity.
To find the equilibrium price, we substitute x = 2 into either the supply or demand function:
D(2) = 14 - 2^2 = 10
So the equilibrium price is P = 10.
The producer's surplus is the area above the supply curve and below the equilibrium price. Since the supply function is linear, we can find the producer's surplus by calculating the area of a triangle with base x = 2 and height S(2) = 10:
Producer's surplus = (1/2) x (2) x (10) = 10
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8% of x is 20.
Plz help
Answer: 250 im not sure if its correct though
Step-by-step explanation: 8% = 8/100
8 /100 × x = 20
Multiplying both sides by 100 and dividing both sides by 8,
we have x = 20 × 100 /8
x = 250
If you are using a calculator, simply enter 20×100÷8, which will give you the answer.
Select all of the following that are true. *
sinA=18/30
sinA=3/5
cosA=10/6
cosA=8/10
cosA=5/3
tanF=24/18
tanF=3/4
tanD=3/4
sinD=18/30
Answer:
Step-by-step explanation:
sin A = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{6}{10}[/tex] = [tex]\frac{3}{5}[/tex]
cos A = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex]
tan F = [tex]\frac{DE}{FE}[/tex] = [tex]\frac{24}{18}[/tex] = [tex]\frac{4}{3}[/tex]
tan D = [tex]\frac{FE}{DE}[/tex] = [tex]\frac{18}{24}[/tex] = [tex]\frac{3}{4}[/tex]
sin D = [tex]\frac{FE}{FD}[/tex] = [tex]\frac{18}{30}[/tex] = [tex]\frac{3}{5}[/tex]
PLEASE ANSWERRRRRRRRRRRRRRRRRRRRRRRRR
Sara and 3 of her friends went to lunch one day. Each person paid for her own lunch, but they agreed to split the tip. If the tip amount was 15% of the total, and the 4 lunches totaled $60, what was the portion of each person’s tip amount?
Answer:
Step-by-step equation:
15% of 60 is nine.
Percentage is equivalent to the portion of a quantity present in the whole. The portion of each person’s tip amount shared by Sara and 3 of her friends is $2.65.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
To convert percentage into a fraction it is divided by 100.
Given that,
The amount of tip is 15% of the total amount A.
The total amount of 4 lunches = $60.
As per the question, the total amount can be written as,
15% of A = A - 60
=> 15 / 100 × A = A - 60
=> A - (3 / 20) × A = 60
=> A - (3 / 20) × A = 60
=> (17 / 20) × A = 60
=> A = (60 × 20) / 17
=> A = 70.58
Now, the total amount of tip is,
15% of 70.58
(15 / 100) × 70.58 = 10.58
The tip shared by each friend = 10.58 ÷ 4
= 2.65
Hence, the portion of each person’s tip amount is $2.65.
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Can somebody help me out ? Please
Answer:
52 sq mm
Step-by-step explanation:
you can break it into a long rectangle in the middle with dimensions of 2(6+8) or 2(14) = 28 sq mm
the triangle on the bottom has a base of (8-4) x height of 3, which gives 6 sq mm (you have to divide by 2)
the upper left rectangle is 6 x 3 = 18 sq mm
add: 28 + 6 + 18 = 52
Anyone pls help on this
Please find X ASAP. You’ll find it on the picture
Answer:
51°
Step-by-step explanation:
so lets all know that the sum of a trapezoid is 360°
so lets find x
360-83-115-111=51
so your answer is 51°
Hope this helped :)
HELP I NEED HELP ASAP
Answer:
I think the answer is letter C
4 When a ball bounces, the heights of consecutive bounces form
a geometric sequence. The height of the first bounce is
121 centimeters and the height of the third bounce is
64 centimeters. To the nearest centimeter, what is the height of the
fifth bounce?
Answer:
34 cm
Step-by-step explanation:
The nth term of a geometric progression Tₙ = arⁿ⁻¹ where a = first term, and r = common ratio.
Given that our first term, T₁ = ar¹⁻¹ = a = 121 cm and our third term T₃ = ar³⁻¹ = ar² = 64 cm
Then, T₃/T₁ = ar²/a = r²
r² = T₃/T₁
r² = 64 cm/121 cm
r = √64/121
r = 8/11
So, the height of our fifth bounce T₅ = ar⁵⁻¹
= ar⁴
= 121 cm × (8/11)⁴
= 121 × 4096/14641
= 4096/121 cm
= 33.9 cm
≅ 34 cm to the nearest cm
Using a geometric sequence, it is found that the height of the fifth bounce is of 33.85 cm.
In a geometric sequence, the quotient between consecutive terms is always the same, and it is called common ratio r.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1r^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
In this problem:
The height of the first bounce is of 121 cm, hence [tex]a_1 = 121[/tex].The height of the third bounce is of 64 cm, hence [tex]a_3 = 64[/tex], and this is used to find r.[tex]a_n = a_1r^{n-1}[/tex]
[tex]64 = 121r^{2}[/tex]
[tex]r^2 = \sqrt{\frac{64}{121}}[/tex]
[tex]r = \frac{8}{11}[/tex]
Hence:
[tex]a_n = 121\left(\frac{8}{11}\right)^{n-1}[/tex]
The height of the fifth bounce is of [tex]a_5[/tex], hence:
[tex]a_5 = 121\left(\frac{8}{11}\right)^{4} = 33.85[/tex]
The height of the fifth bounce is of 33.85 cm.
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I NEED HELP NOW ITS 100 points!!!!!
You are going to paint 3 rooms in your house. Two of the rooms measure 12 ft. by 15 ft. and the third is 15 ft. by 20 ft. The ceilings are 9 ft. high. You are going to paint the 2 rooms the same size the same color. The third room will be a different color. You will paint the ceilings in all three rooms with ceiling white paint. This ceiling paint costs $39.99 per gallon and will cover 250 square ft.. The paint for the two rooms will be tan and costs $27.95 per gallon and covers 320 sq. ft. The paint for the third room will be waterfall blue and will cost $32.50 per gallon and covers 288 sq.ft. How much will it cost to paint these three rooms if the store has a 20% off your entire purchase and sales tax is 7.35%?? *
40 points
Answer:
im sorry i dont know
Step-by-step explanation:
Help please ASAP
Brainiest answer to whoever is correct
The measure of angle 1 is (10x+8) and the measure of angle 3 is (12x-10)
What is the measure of angle 2 in degrees?
9
98
82
16
Answer:
The answer is C. 82 degrees!
Step-by-step explanation:
Hope this helped! Have a fantastic rest of ur day/ night! :)))
hey hons, i'd love some help here if you could take a look and see if you could help i'd be grateful! <33333
Step-by-step explanation:
A function is a rule that relates how one quantity depends on other quantities
Hey, guys I need help :D
Answer:
D
Step-by-step explanation:
Dilating BC to B'C' by a factor of 1/2 makes each side of the triangle halved. Originally BC is 16, so when it's halved, it becomes 8
We know when triangle are similar and are changed only by a scale factor, the angle will not change. Angle A' = 28 degrees
For part (a), determine whether the triangles are congruent by SSS or SAS. If not congruent, write “not congruent.” If congruent, write a congruency statement for part (b).
The congruency rules is as follows;
4)a) The triangles are congruent by SSS Congruency Postulate
b) Triangle PQR is congruent to Triangle PQS
5a) The triangles are not congruent
b) Triangle VWZ is not congruent to Triangle YXZ
6a) The triangles are congruent by SAS Congruency Postulate
b) ΔACB is congruent to ΔDBC by SAS Congruency Postulate
7) The triangles are not congruent
b) ΔKLJ is not congruent to ΔMNL
How to Identify Congruent Triangles?There are different congruency postulates or theorems as it pertains to congruent triangles and they are;
AAS theorem which denotes Angle-Angle-Side Theorem
HL theorem which denotes Hypotenuse-Leg Theorem
SSS Postulate which denotes Side-Side-Side Postulate
ASA postulate which denotes Angle-Side-Angle Postulate
SAS Postulate which denotes Side-Angle-Side Postulate
5) We can see that we are given two sides of one triangle that are congruent to two sides of another triangle. However, the third side is also congruent by reflexive property of congruency and as such we now have three sides congruent by SSS Congruency Postulate.
5) We can see that we are given two sides of one triangle that are congruent to two sides of another triangle. Now, the angle where the transverse lines intersect is not given but we can see that they are opposite angles by definition of opposite angles. Thus, the triangles are congruent by SSA Congruency Theorem because it has a non-included angle but SSA Congruency is not valid and so this is not congruent.
6) We can see that one side is given to be congruent. However, by reflexive property of congruence, we see that BC is congruent to itself and also the included right angle being congruent to each other. Thus, this is congruent by SAS Congruency postulate.
7) The triangles are not congruent because we are not given any third congruent side nor the angles and we can't use the given data to prove congruency.
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Please help I'm giving 50 points I don't have time to do assignment as of now so can someone do me the favor of doing it?
Answer:
Step-by-step explanation:
1. Not a function
2. Function
3. Function
4. Not a function
5. Not a function
6. Function
7. Function
8. Not a Function
9. Function
10. Not a Function
Answer:
1. Not a function
2. A function
3. A function
4. Not a function
5. Not a function
6. A function
7. A function
8. Not a function
9. A function
10. Not a function
Step-by-step explanation:
The only rule for a relationship to be a function is...
Only ONE output for ONE input
1. There is more than one output for one input
2. Each input has only one output
3. Each input has only one output
4. There is more than one output for one input
5. There is more than one output for one input
6. Each input has only one output
7. Each input has only one output
8. There is more than one output for one input
9. Each input has only one output
10. There is more than one output for one input
Hope this helps :)
Let me know if there are any mistakes!!
Which set of numbers could represent the lengths of the sides of a right triangle?
12, 18, 22
8. 15. 17
10. 15.20
7.9.11
Answer:
8, 15, 17
Step-by-step explanation:
The 2nd option. You know this by using this math formula: a^2 + b^2 = c^2. That is the formula to find a right triangle. So if you square 8 and 15 you get 64 and 225, and if you add them together you get 289, which is 17^2. Hope this helps! :)
is a(t) = 1200(1 + .03)t a decay function?
Answer:
Step-by-step explanation:
No, it is an exponential growth function because 1.03>1. An exponential decay function would have a rate less than 1.
Please helppppp!!!!!!
Answer:
$7.44
Step-by-step explanation:
4.96/8= .62 per ounce
.62 x 12 = $7.44
4(5.8 - 9x) + 8.2 + 22x
Answer:
157 - 70x
—————————
5
Step-by-step explanation:
Answer:
31.4 - 14x
Step-by-step explanation:
4(5.8 - 9x) = 23.2 - 36x
23.2 - 36x + 8.2 + 22x
23.2 + 8.2 - 36x + 22x
only add/subtract LIKE terms
31.4 - 14x
i really need help wit this pleasee help and show work pleasee
Answer:
4000π cm^2
Step-by-step explanation:
first we change the 1.6m to cm:
1.6m = 160cm
Now we can use the formula:
V = πr^2h
where π is just π, r is the radius (not the diameter) and h is the height
V = π * 5^2 * 160 = 4000π cm
Answer:
Step-by-step explanation:
[tex]\text{They give you the equation for the volume.}\\ \\ V=\pi r^2h\\ \\ \text{You simply need to plug in the values given to you for r and h.}\\ \\ r=10/2=5cm,\ h=1.6m(100cm/m)=160cm\\ \\
V=\pi 5^2(160)\\ \\ V=160(25)\pi\\ \\ V=4000\pi cm^3\\ \\ V\approx 12566.37 cm^3[/tex]
Ellen Greenberg loves to make and fly kites. Ellen is planning to open a shop that
sells custom-made kites. She asks for your advice to help her set financial goals.
Ellen estimates that after expenses, she can make a $15 profit on each kite she
sells. If her annual income goal is $15,400, how many kites will she have to sell?
Answer:
She must sell 1026.66666667 kites
Step-by-step explanation:
15,400/15
The number of kites that Ellen needs to sell to complete her annual goal is 1027.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that Ellen can make a $15 profit on each kite she sells. Also, Ellen's annual income goal is to have $15,400. Therefore, the number of kites that Ellen needs to sell is,
Number of kites that Ellen will sell = Annual income goal/Profit on each kite
Number of kites that Ellen will sell = $15,400 / $15
= 1026.6667
Since Ellen can not sell half kites, therefore, she needs to sell 1027 kites to complete her annual income goal.
Hence, the number of kites that Ellen needs to sell to complete her annual goal is 1027.
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Problem situation:
Janelle is at the movie theater and has $20
to spend.
She spends $8 on a ticket and wants to buy some snacks. Each snack costs $4.99.
How many snacks, x, can Janelle buy?
Inequality that represents this situation:
20 > 8 + 4.99x
Drag each number to show if it is a solution to both the inequality and the problem
situation, to the inequality only, or if it is not a solution.
Answer:
Rewrite so x is on the left side of the inequality.
8 + 4.99x < 20
Move all terms not containing x to the right side of the inequality.
4.99x < 12
Divide each term by 4.99 and simplify.
x < 2.405
The result can be shown in multiple forms.
Inequality Form:
x < 2.405
Interval Notation:
( −∞ , 2.405 )
Step-by-step explanation:
Answer:
Both:
1
2
Inequality Only:
-4
3/4
2.3
Neither:
2.5
Help me with this please!!!
this question answer is 4.25
2(6x + 1) - 4(x - 5) = -2
Answer:
x=−3
Step-by-step explanation:
2(6x+1)−4(x−5)=−2
Step 1: Simplify both sides of the equation.
2(6x+1)−4(x−5)=−2
(2)(6x)+(2)(1)+(−4)(x)+(−4)(−5)=−2(Distribute)
12x+2+−4x+20=−2
(12x+−4x)+(2+20)=−2(Combine Like Terms)
8x+22=−2
8x+22=−2
Step 2: Subtract 22 from both sides.
8x+22−22=−2−22
8x=−24
Step 3: Divide both sides by 8.
8x/8=−24/8
4. Simplify the expression
2(10) + 2(x-4).
(A) 2x + 16
(B) x+12
© 2x + 12
(D) x + 16
Answer:
C. 2x + 12
Step-by-step explanation:
2(10) + 2(x-4)
= 20 + 2x - 8
= 2x + 20 - 8
= 2x + 12
find the distance of each the following lines from the origin.
(a),4x_3y=10
b,x_5y+2=0
c,3x+y_7=0
Answer:
Step-by-step explanation:
3x+y−7=0 and x+2y+9=0
write in the form y=mx+c
i.e.y=−3x+7,y=
2
−x
−
2
9
∴m
1
=−3 and m
2
∓−
2
1
tan(A−B)=
∣
∣
∣
∣
∣
1+tanAtanB
tanA−tanB
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
1+(−3)(−y
2
)
−3−(−y
2
)
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
5/2
−5/2
∣
∣
∣
∣
∣
=1
∴ Angle b/w then is tan
−1
(1)=45
∘
=
4
π
write : what’s the algebraic expression for the difference of 9 and x
Answer:
9-x
Step-by-step explanation:
ez dub
Answer:
9-x
Step-by-step explanation:
the difference of (tells you to subtract) 9 and x (9-x)
hope this helps have a blessed
How is a "series" different than a "sequence"?
Answer:
See below
Step-by-step explanation:
A series is the terms added together and a sequence is the list of terms. When you add the terms of a sequence, then you have formed a series.
Given that ƒ(x) = x2 + 1 and g(x) = –3, multiply the functions (g · ƒ)(x).
Answer:
(2+1×-3)(x) = 3×(-3)(x) =-9x
Answer:
(g · ƒ)(x) = –3x2 – 3
Step-by-step explanation:I took the test
plz answer the picture below fast and correctly!
Answer:
a) BOC = 80⁰
b) COD = 60⁰
Step-by-step explanation:
..................
Answer:
BOC is 80 and COD is 60
Step-by-step explanation:
If DOF is 120 you subtract 40 from it because of of AOB then COD is the remaining of 180