Answer:
N80
Step-by-step explanation:
One ruler is N60 and one pencil is N20.
The function f(x) = −x2 + 18x − 72 models the daily profit, in dollars, a gym makes for selling memberships, where x is the number of memberships sold, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
(10 points)
Answer:
Step-by-step explanation:
The way to do this so as to streamline both the vertex and finding the zeros is to complete the square. That method will provide us with the vertex, and then we can continue on to factor from that form to find the zeros. Completing the square requires us to set the quadratic equal to 0 then move over the constant, giving us
[tex]-x^2+18x=72[/tex] The leading coefficient HAS to be a positive 1; ours is negative 1 so we factor out the negative to get:
[tex]-(x^2-18x)=72[/tex] Now we're ready to complete the square.
Take half the linear term, square it, and add it to both sides. Our linear term is 18 (from -18x; don't worry about the negative because squaring it makes it positive anyway). Half of 18 is 9, and 9 squared is 81.
BUT on the left we have that -1 sitting out front that refuses to be ignored. What we actually added on to the left side, inside the parenthesis, is -1(81) which is -81. -81 is what we add to the right since that turns out to be what we added to the left:
[tex]-(x^2-18x+81)=72-81[/tex] and we clean that up.
The reason we complete the square is because when we simplify the left side, we end up with a perfect square binomial found from taking the square root of x-squared, the first sign we come to, then the square root of 81:
[tex]-(x-9)^2=-9[/tex]. Move the constant back over to get
[tex]-(x-9)^2+9=y[/tex] telling us that the vertex is (9, 9). In the context of the problem that means that the gym sells on average 9 memberships a day and the profit it makes on average per day is $9.
To factor, we will go back one step to
[tex]-(x-9)^2=-9[/tex] and begin by dividing both sides by -1 to get
[tex](x-9)^2=9[/tex] and undo the squaring by taking the square root of both sides to get
x - 9 = ±3 so
x = 9 + 3 and
x = 9 - 3 so
x = 6 and 12
Those are the zeros. This means that if they sell either 6 or 12 memberships they have a 0 profit. That may sound strange, but in business it does often work like that...selling too many of something makes your company lose money (this is often due to the cost required by you to produce or manufacture the product).
Use differentials to estimate the amount of material in a closed cylindrical can that is 10 cm high and 4 cm in diameter if the metal in the top and bottom is 0.1 cm thick, and the metal in the sides is 0.05 cm thick.
Answer:
dv = attached below
dr = 0.05 cm
dh = 0.2 cm
Approximate volume of metal = 2.8 * π cm^3
Step-by-step explanation:
height of can ( h ) = 10 cm
diameter = 4 cm ; r = 4/2 = 2cm
thickness of metal in top and bottom = 0.1 cm
thickness of metal in sides = 0.05 cm
attached below is the detailed solution
A popular beach erodes 4 inches per year on average.
An eroding beach.
A. How many years will it take for the coastline to erode one foot?
Answer:
3 years
Step-by-step explanation:
4 inches per year on average
1 foot = 12 inches
12 divided by 4 equals 3
therefore it is 3 years
Rose walks 2 2/3 km in three-fifths of an hour. If her speed remains unchanged, how many kilometres can she walk in one and three quarters of an hour? Express your answer as a mixed number in lowest terms
Answer:
Distance = 7 7/9 Km
Step-by-step explanation:
Given the following data;
Distance = 2⅔ = 8/3 Km
Time = ⅗ hour
First of all, we would find her speed;
Speed = distance/time
Speed = (8/3)/(3/5)
Speed = 8/3 * 5/3
Speed = 40/9 km/h
Next, we would find the distance covered when time = 1¾ hours
Distance = speed * time
Distance = 40/9 * 1¾
Distance = 40/9 * 7/4
Distance = 10/9 * 7
Distance = 70/9
Distance = 7 7/9 Km
Plz help me find x and y on the triangle big thanks
Answer:
This is a 30-60-90 right triangle.
The ratio of sides:
a : b : c = 1 : √3 : 2Compare with the given values:
a = 3√3, b = y, c = xy = 3√3*√3 = 9x = 2*3√3 = 6√3I NEED HELP ASAP PLEASE!!!
Answer:
Hello the answer is A <!!
Answer:
c
Step-by-step explanation:
pi/ 3 * (180/pi)= 180/3
pi/3 = 60 degrees
11. Find the 5th term of the sequence defined by the given rule. (1/2 point)
f(n) = 6n + 4
Answer:
34
Step-by-step explanation:
n = 5
f(5) = 6(5)+4
f(5)=34
The fifth term of the sequence is equal to 34.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is f(n) = 6n + 4. The value of the fifth term will be calculated as,
n = 5
f(5) = 6(5)+4
f(5)=34
Therefore, the fifth term of the sequence is equal to 34.
To know more about arithmetic progression follow
https://brainly.com/question/6561461
#SPJ2
What is the length of the missing leg??
Answer:
12.04 cm
Step-by-step explanation:
Pythagoras in general :
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90 degree angle).
a and b are the side legs.
so, in our example here
17² = 12² + b²
289 = 144 + b²
145 = b²
b = sqrt(145) = 12.04 cm
(WILL GIVE YOU 30 POINTS!!!)
The graph shows the functions f(x), p(x), and g(x):
Graph of function g of x is y is equal to 3 multiplied by 1.2 to the power of x. The straight line f of x joins ordered pairs minus 3, minus 3 and 4, 4 and is extended on both sides. The straight line p of x joins the ordered pairs minus 6, 1 and minus 3, minus 3 and is extended on both sides.
Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points)
Part B: Write any two solutions for f(x). (3 points)
Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (4 points)
Answer:
(a) No solution
(b)
[tex](x_1,y_1) =(-3,-3)\\(x_2,y_2) =(4,4)[/tex]
(c) [tex](-6,1)[/tex]
Step-by-step explanation:
Given
See attachment for graph
Solving (a): Solution to p(x) and f(x)
Curve p(x) and line f(x) do not intersect.
So, there is no solution to the pair of p(x) and f(x)
Solving (b): Two solutions to f(x)
This means that we select any two point on straight line f(x)
From the line of f(x), we have:
[tex](x_1,y_1) =(-3,-3)\\(x_2,y_2) =(4,4)[/tex]
Solving (c): Solution to p(x) = g(x)
Here, we write out the point of intersection of p(x) and g(x)
From the graph, the point of intersection is: [tex](-6,1)[/tex]
This figure shows △ABC. BD¯¯¯¯¯ is the angle bisector of ∠ABC.
What is AD?
Answer:
AD = 8/3 units
Step-by-step explanation:
Based on the angle bisector theorem, angle bisector BD divides AC into AD and CD such that they are proportional to AB and CB.
This implies:
AB/AD = CB/CD
AB = 8
CB = 10
Set AD equal to x
AD = x
CD = 6 - x
Substitute the values
8/x = 10/(6 - x)
8(6 - x) = 10(x)
48 - 8x = 10x
48 - 8x + 8x = 10x + 8x
48 = 18x
48/18 = 18x/18
8/3 = x
x = 8/3
AD = 8/3 units
Answer:8/3
Step-by-step explanation:
I just took the quiz
The formula for finding the area of a square that has a side length, s, is A= 52. If a square has an area of 40 square
units, what is the length of a side?
20
10/
2 /10
Answer:
2√10
Step-by-step explanation:
Given the following data;
Area of square = 40
Mathematically, the area of a square is calculated by using the formula;
Area, A = s²
Where;
s is the length of sides of a square.
Substituting into the formula, we have;
40 = s²
s = √40
s = √4 * √10
s = 2 * √10
s = 2√10
HELP ASAP!!!! i need the answer immediately
Answer:
Option C, half the circumference, or πr
Answered by GAUTHMATH
i need help on 8-9 plss :))
Answer:
8. SU = 24
9. TU = 16√3
Step-by-step explanation:
Recall: SOH CAH TOA
8. Reference angle (θ) = 30°
Opposite = 8√3
Adjacent = SU
Apply TOA,
Tan θ = Opp/Adj
Substitute
Tan 30° = 8√3/SU
Tan 30° × SU = 8√3
SU = 8√3/Tan 30°
SU = 8√3/(1/√3) (tan 30° = 1/√3)
SU = 8√3*√3/1
SU = 8*3
SU = 24
9. Reference angle (θ) = 30°
Opposite = 8√3
Hypotenuse = TU
Apply SOH,
Sin θ = Opp/Hyp
Substitute
Sin 30° = 8√3/TU
Sin 30° × TU = 8√3
TU = 8√3/sin 30°
TU = 8√3/(½) (sin 30° = ½)
TU = 8√3 × 2/1
TU = 16√3
Fo quality control purposes, we collect a sample of 300 items and find 36 defective items in it. Construct a 90% confidence interval [a, b] for the proportion of defective items in the whole shipment.
Answer:
(0.089 ; 0.151)
Step-by-step explanation:
Given :
Sample size, n = 300
Number of defective items, x = 36
The confidence interval required here is that for a one sample proportion :
The confidence interval is defined thus :
Phat ± Zcritical * √[Phat(1 - phat) / n]
Zcritical at 90% = 1.645
Phat = x / n = 36 / 300 = 0.12
Hence,
C.I = 0.12 ± 1.645 * √[0.12(1 - 0.12) / 300]
C.I = 0.12 ± (1.645 * 0.0187616)
C.I = 0.12 ± 0.0308629
C.I = (0.089 ; 0.151)
Which equation shows that the Pythagorean identity is true for 0 = 27? Select
the equation that is in the form sin?(27) + cos2(27) = 1.
A. 02 + (-1)2 = 1
B. 02 + 12 = 1
C. (-1)² + 02 = 1
D. 12 + 02 = 1
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Answer:
B. 0^2 +1^2 = 1
Step-by-step explanation:
For θ = 2π, the trig identity is ...
sin(2π)² +cos(2π)² = 1
0² +1² = 1
which data is represented by this plot?
a)2,4,0,4,6,3,1,7,8,1,1
b)0,1,2,3,4,5,6,7,8,0,1
c)0,2,3,0,2,4,4,5,7,8,7
d)1,2,6,4,7,7,2,2,0,1
D. Rom has just given an insurance company $35,000. In return, he will receive an annuity of $3,700 for 20 years. At what
rate of return must the insurance company invest this $35,000 in order to make the annual payments?
Answer:
0.53%
Step-by-step explanation:
hope it is well understood
Find the value of z.
54°
X
2049
(32+1)°
A. 25.25
OB. 129
Answer:
Step-by-step explanation:
(z)° + (3z + 1)° = 360° - ( 54° + 204° )
z + 3z + 1 = 360 - 258
4z = 101
z = 25.25
At basketball practice, you made 59 out of 80 shots.
Which choice is closest to the percentage of shots you mad
Answer:
73.5 Percent ...........
Answer:
The closest percentage of shots you made is 75%. Please mark brainliest.
I believe the choices are:
60%
70%
75%
80%
Therefore the answer 75%
Step-by-step explanation:
59/80 = 0.7375
Rounded up is 0.75
0.75 x 100 = 75%
Hope this helps.
Have a nice day amazing person there.
MAY GOD RICHLY BLESS YOU!!
Zoe is a party planner. She orders cupcakes and sheet cakes from Creative Cakes whenever she needs beautiful cakes to serve. One sheet cake serves 24 people and 2 dozen cupcakes serve 24 people. For the Benson's bridal shower she ordered 8 dozen cupcakes and 3 sheet cakes and paid $160.81. For the Nygaard's 50th wedding anniversary she ordered 6 dozen cupcakes and 15 sheet cakes and paid $342.33. She is planning a graduation party for her niece's high school class. She wants the party to be nice but she offered to pay for the cakes herself so she wants to choose the most economical plan. Zoe estimates 250 people will attend the party.
Full question:
Zoe is a party planner. She orders cupcakes and sheet cakes from Creative Cakes whenever she needs beautiful cakes to serve. One sheet cake serves 24 people and 2 dozen cupcakes serve 24 people. For the Benson's bridal shower she ordered 10 dozen cupcakes and 4 sheet cakes and paid $186.44. For the Nygaard's 50th wedding anniversary she ordered 2 dozen cupcakes and 15 sheet cakes and paid $259.66. She is planning a graduation party for her niece's high school class. She wants the party to be nice but she offered to pay for the she wants to choose the most economical plan. Zoe estimates 250 people will attend the party
Select the most economical choice below:
Zoe should buy sheet cakes because they cost $12.38 for one sheet cake.
Zoe should buy sheet cakes because they cost $15.66 for one sheet cake.
Zoe should buy cupcakes because they cost $12.38 for one dozen cupcakes.
Zoe should buy cupcakes because they cost $15.66 for one dozen cupcakes.
Zoe should buy cupcakes because they cost $12.38 for two dozen cupcakes.
Answer:
Zoe should buy cupcakes because they cost $12.38 for two dozen cupcakes.
Explanation:
If there are 250 people attending the high school class graduation party, then 24 people each within 250 people in total would get 2 dozen cupcakes worth $12.38 each.
Therefore there are 250/24 = 10.41 groups (10 groups approximately or 10.41×2=20.82 dozens of cupcakes required)
Zoe would need to spend 10.41×$12.38= $128.88 to buy the cupcakes for the party
The height of a triangle is 2 times the base. The area is 4 square inches. Find the base.
The base of the triangle is
inches.
Answer:
2 Inches
Step-by-step explanation:
Area of a triangle = (1/2)* Base * Hight
lets consider the base of the triangle is X inches,
then, Hight of the triangle is 2X
Then the Area of the Angle is = (1/2)*X*2X
4 = x^{2}
X = 2
The isosceles triangle and rectangle have the same perimeter find the value of x
Answer:
x=15
Step-by-step explanation:
x+2+x+2+2x-2=9+8+9+8
2x+4=34
2x=30
x=15
The graph is that of a fourth-degree polynomial function. Which of the following correctly shows three factors of the function? Image included, please help!
C.
Observe that the roots of polynomial are [tex]-3,2,5[/tex]
We have a polynomial in a factored form,
[tex](x+3)(x-2)(x-5)[/tex]
If you substitute x for any of [tex]-3,2,5[/tex] the product will always equal to zero that is these numbers are roots of polynomial.
Hope this helps :)
Do this please helpppp
Answer:
y = [tex]\frac{20}{9}[/tex]
Step-by-step explanation:
Since the figures are similar then the corresponding sides are in proportion, that is
[tex]\frac{JH}{PQ}[/tex] = [tex]\frac{FM}{ST}[/tex] , substitute values
[tex]\frac{6}{4}[/tex] = [tex]\frac{7}{3y-2}[/tex] ( cross- multiply )
6(3y - 2) = 28
18y - 12 = 28 ( add 12 to both sides )
18y = 40 ( divide both sides by 18 )
y = [tex]\frac{40}{18}[/tex] = [tex]\frac{20}{9}[/tex]
Answer:
20/9
Step-by-step explanation:
since the 2 are similar,
JH/PQ = FM/ST
6/4 = 7/(3y-2)
6(3y-2) = 7*4
18y-12=28
18y = 40
y = 40/18 = 20/9 = 2 2/9
The diameter of a circle has endpoints P(-12, -4) and Q(6, 12).
Write an equation for the circle. Be sure to show and explain all work.
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Answer:
(x +3)² +(y -4)² = 145
Step-by-step explanation:
The center of the circle is the midpoint of the given segment PQ. If we call that point A, then ...
A = (P +Q)/2
A = ((-12, -4) +(6, 12))/2 = (-12+6, -4+12)/2 = (-6, 8)/2
A = (-3, 4)
The equation of the circle for some radius r is ...
(x -(-3))² +(y -4)² = r² . . . . . . where (-3, 4) is the center of the circle
The value of r² can be found by substituting either of the points on the circle. If we use Q, then we have ...
(6 +3)² +(12 -4)² = r² = 9² +8²
r² = 81 +64 = 145
Then the equation of the circle is ...
(x +3)² +(y -4)² = 145
(a) Express the prime number 3 as the difference of two squares? 3=
Answer:
2^2 - 1^2
Step-by-step explanation:
1^1 = 1
2^2 = 4
4-1 =3
2^2 - 1^1 = 3
Fiona invested $1000 at 7% compounded continuously. At the same time, Maria invested $1100 at 7% compounded daily. How long will it take for their investments to be equal in value? Assume there are 365 days in every year.
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Answer:
14,201 years
Step-by-step explanation:
The two compound interest formulas are ...
A = P·e^(rt) . . . . . continuous compounding at rate r for t years
A = P·(1 +r/365)^(365t) . . . . . daily compounding at rate r for t years
We went the amounts to be equal:
1000·e^(0.07t) = 1100·(1+0.07/365)^(365t)
Dividing by 1000(1 +0.07/365)^(365t), we have ...
((e^0.07)/(1+0.07/365)^365)^t = 1.1
The base of the exponential on the left is ...
( e^0.07)/(1+0.07/365)^365 ≈ 1.00000671149321522
Taking logs, we have ...
t×ln(1.00000671149321522) = ln(1.1)
t = ln(1.1)/ln(1.00000671149321522) ≈ 0.09531018/(6.7114704·10^-6)
t ≈ 14,201.09 . . . . . years
It will take about 14,201 years for the investments to be equal.
_____
Additional comment
The investment value at that time will be about $5.269·10^434. (That's a larger number than anything countable in the known universe, including energy quanta.)
These calculations are beyond the ability of many calculators, so might need to be carefully rewritten if the calculator only keeps 10 significant digits, or only manages exponents less than 100.
This shows that daily compounding is very close in effect to continuous compounding. It would take almost 150 years to make a difference of 0.1% in value.
what is the answer to EVAULATE 8+-9+-6
Answer:
11
Step-by-step explanation:
8 + 9 + -6
8 + 9 = 17
17 + (-6) = 11
Answered by Gauthmath
Find the length of AC again
Answer:
B
Step-by-step explanation:
side Ac is the opposite of angle B, therefore use the sin ratio to find ac since the hypotenuse is also given
sin B=opposite/hypotenuse
sin 27=ac/15
ac=sin27×15
=6.81
I hope this helps
Answer:
AC = 6.81
Step-by-step explanation:
∠BAC = 90° - 27° = 63°
Cos 63° =[tex]\frac{AC}{AB}[/tex] = 0.454
AC = cos 63° * AB = 0,454 * 15 = 6.81
any polynomial of degree 2 can have at most two zero is
true and false
Answer:
True
Step-by-step explanation:
Answer is true, the degree of a function tells you at most how many zeroes the function can have.
