Using the vertex of a quadratic equation, it is found that the company should charge each customer $15 per day to maximize revenue.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the number of bikes rented per day is given by:
n(p) = 300 - 10p.
Hence, the revenue function is given by:
R(n) = p x n(p)
R(n) = 300p - 10p².
Which is a quadratic function with coefficients a = -10, b = 300. Hence, the price in dollars that will maximize the revenue is given by:
[tex]x_v = -\frac{300}{-20} = 15[/tex]
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A company produces circular drink coasters. the equation x2 y2 = 18.0625, with units in inches, represents the size of a coaster. each coaster is cut from a square piece of cardboard. what is the minimum possible area of each cardboard piece? 4.25 in2 8.5 in2 18.0625 in2 72.25 in2
The minimum possible area of each square cardboard piece which is used to produce circular drink coasters is 72.25 in².
What is the equation of circle?The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.
The standard form of the equation of the circle can be given as,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here (h,k) is the center of the circle and (r) is the radius of the circle.
A company produces circular drink coasters. the equation which represents the size of a coaster is,
[tex]x^2+ y^2 = 18.0625[/tex]
The units are in the inches. This equation can be written as,
[tex]x^2+ y^2 = \dfrac{289}{16}\\x^2+ y^2 =\left( \dfrac{17}{4}\right)^2[/tex]
Compare it with the equation of the circle, we get,
[tex]h=0\\k=0\\r=\dfrac{17}{4}\rm\; in[/tex]
The radius of the circular coaster is 17/4. The diameter of it is,
[tex]d=2\times\dfrac{17}{4}\\d=\dfrac{17}{2}\rm \; in[/tex]
Now, each coaster is cut from a square piece of cardboard. The diameter of the circular coaster will be equal to the side of the square piece of cardboard.
[tex]a=d=\dfrac{17}{2}\rm\; in[/tex]
The area of the square is the square of its side. Thus, the area of a square piece of cardboard is,
[tex]A=a^2\\A=\left(\dfrac{17}{2}\right)^2\\A=72.25\rm\; in^2[/tex]
Thus, the minimum possible area of each square cardboard piece which is used to produce circular drink coasters is 72.25 in².
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Working alone, it takes Castel 12 hours to pick forty bushels of apples. Mei can pick the same amount in 10 hours. If they worked together how long would it take them?
Answer:
5.5 hours
Step-by-step explanation:
dibide by 2 one is 5 and one is 6, middle. is 5.5,
Write an equation for the line passing through the given pair of points. Give the final answer in (a) slope-intercept form and (b) standard form.
(-5.--3) and (1. -8)
(a) The equation of the line in slope-intercept form is
(Use integers or fractions for any numbers in the equation)
The equation of the line in slope-intercept form and standard form that passes through the line are y = -5 / 6x - 43 / 6 and 5x + 6y = -43 respectively.
Slope intercept equationThe Slope intercept equation is use to represent a linear table or graph. Therefore, the formula is represented as follows
y = mx + b
where
m = slope
b = y-intercept
Hence,
(-5, -3)(1, -8)
m = -8 + 3 / 1 + 5 = - 5 / 6
Using (1, -8) let's find b
-8 = -5 / 6 (1) + b
-8 + 5 / 6 = b
-48 + 5/6 = b
b = -43 / 6
Therefore, the slope intercept equation is y = -5 / 6x - 43 / 6
The equation in standard form is represented as Ax + By = C. Therefore,
y + 5 / 6 x = - 43/6
5x + 6y = -43
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The perimeter of the figure below is 84.6 ft. Find the length of the missing side.
Answer:
7.3 ft.
Step-by-step explanation:
The perimeter of a geometrical figure is calculated by adding all side lengths up:
The perimeter of the figure in question is 84.6 ft.
2*(3.4) + 2*(11.3) + 6*(6.8) + (7.1) + ? = 84.6 (it's easier if we write equal terms in multiplying form)
77,3 + ? = 84.6 subtract 77.3 from both sides
? = 7.3 is the length of the missing side
PLEASE HELP AND ANSWER CORRECTLY
I know the axis of symmetry but I don't know how to put it in an equation
please review the graph and answer you may use the other answers to help
Answer:
standard form: y = x² - 2x - 8
vertex form: y = (x − 1)² - 9
factorized form: y = (x + 2)(x - 4)
Step-by-step explanation:
From inspection of the graph:
Axis of symmetry: x = 1Vertex = (1, -9)x-intercepts = (-2, 0) and (4, 0)y-intercept = (0, -8)Standard quadratic form: y = ax² + b x + c
Vertex form of a quadratic equation: y = a(x − h)² + k
If a > 0 then the parabola opens upwards
If a < 0 then the parabola opens downwards
(h, k) is the vertex
c is the y-intercept
Inputting the vertex into the vertex form gives:
y = a(x − 1)² - 9
= a(x² - 2x + 1) - 9
= ax² - 2ax - 8
Using the x-intercepts to create a quadratic equation:
y = a(x + 2)(x - 4)
= a(x² - 2x - 8)
= ax² - 2ax - 8a
Comparing the y-intercepts:
-8 = -8a ⇒ a = 1
Therefore, y = x² - 2x - 8
Sketch the graph of y = 5 sin 2x° + 12
Function: y = 5 sin (2(x))+ 12
Find y-intercept:
y = 5 sin 2(0)+ 12
y = 12
[tex]\sf Y\:Intercepts}:\:\left(0,\:12\right)[/tex]
→ Formula for maximum: M = A + |B|
Maximum:
12 + |5|
17
When y = 17
[tex]\rightarrow \sf 17 = 5 sin (2(x))+ 12[/tex]
[tex]\rightarrow \sf \sf 5 sin (2(x)) = 5[/tex]
[tex]\rightarrow \sf sin (2(x)) = 1[/tex]
[tex]\rightarrow \sf 2x = sin^{-1}(1)[/tex]
[tex]\rightarrow \sf 2x = 90^{\circ \:}, \ \ 450^{\circ \:}[/tex]
[tex]\rightarrow \sf x = 45^{\circ \:}, \ \ 225^{\circ \:}[/tex]
maximum: ( 45° , 17 ), (225° , 17), .....
==========================================================
→ Formula for minimum: m = A ‐ |B|
Minimum:
12 - |5|
7
When y = 7
[tex]\rightarrow \sf 7 = 5 sin (2(x))+ 12[/tex]
[tex]\rightarrow \sf 5 sin (2(x)) = -5[/tex]
[tex]\rightarrow \sf 2(x) = sin^{-1}(-1)[/tex]
[tex]\rightarrow \sf x = -45^{\circ \:} , \ \ 135^{\circ \:}[/tex]
minimum: ( -45°,7), (135°, 7), .....
Repeat the same process for finding more values on the x-axis, or just follow the trend of the curve from the points found and sketch the graph easily.
[tex]\sf Domain\:\left(-\infty \: < x < \infty )[/tex]
[tex]\sf Range : 7\le \:f\left(x\right)\le \:17[/tex]
Sketched below:
help me i need this grade but im bad at math
Answer:
B
C/15=3
Step-by-step explanation:
They devided the coconuts among 15 children
3x15 =45
45÷3 =15
So the number of coconut the kids gathered is 45
C/15=3 multiply by 15 on both side
15/1 ×c/15=3×15
C=3×15
C=45
What is the sale price of jeans which regularly cost $32, but now are 10% off?
Answer:
$28.80
Step-by-step explanation:
32 x 0.1 = 3.2
32 - 3.2 =28.8
Hope this helps :)
Answer:
$28.8
Step-by-step explanation:
10% of 32 is 3.2
32 - 3.2 = 28.8
Jeff volunteers his time by working at an animal shelter. Each year he works for a total of 240 hours. So far this year he has worked 97 hours. Which equation will solve for how many more hours (h) Jeff will volunteer for?
Answer: h + 97 = 240
Step-by-step explanation:
Total hours worked per year: 240 hours
Current hours worked so far: 97 hours.
The variable h represents hours
Therefore, h + 97 = 240
Identify the value of y.
-6×2×9y = 7y-4+4-690
Hey there!
-6×2×9y = 7y-4+4-690
=> Let's solve your equation step-by-step.
(((−6)(2))(9))(y)=7y−4+4−690
Step 1: Simplify both sides of the equation.
(((−6)(2))(9))(y)=7y−4+4−690
−108y=7y+−4+4+−690
−108y=(7y)+(−4+4+−690)(Combine Like Terms)
−108y=7y+−690
−108y=7y−690
Step 2: Subtract 7y from both sides.
−108y−7y=7y−690−7y
−115y=−690
Step 3: Divide both sides by -115.
−115y/−115 = −690/−115
y=6
Answer:
y=6
Therefore, the value of y = 6
Answer:
y=6
Step-by-step explanation:
(((−6)(2))(9))(y)=7y−4+4−690
−108y=7y+−4+4+−690
−108y=(7y)+(−4+4+−690)
−108y=7y+−690
−108y=7y−690
Subtract 7y from both sides.
−108y−7y=7y−690−7y
−115y=−690
Step 3: Divide both sides by -115.
−115y -690
−115 -115
y=6
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7.5
A
7
10
12.5
3. sin A:
COS A:
tan A:
What is Sin
Answer:
sin is something that we say, think, or do, that displeases God
Step-by-step explanation:
hoped this helped! :)
helppppppppp please
thanks
Answer:
Here is the answer
Step-by-step explanation:
4^4/(6^6)
factorise: 6x^2 – 5 x – 6
Step-by-step explanation:
I think it will help you.
Look at the example
Let's use mid-term splitation
[tex]\\ \rm\rightarrowtail 6x^2-5x-6[/tex]
[tex]\\ \rm\rightarrowtail 6x^2+4x-9x-6[/tex]
[tex]\\ \rm\rightarrowtail 2x(3x+2)-3(3x+2)[/tex]
[tex]\\ \rm\rightarrowtail (2x-3)(3x+2)[/tex]
A board game that normally costs $30 is on sale for 25 percent off. What is the sale price of the game?
$22.50
$27.50
$32.50
$37.50
Answer:
22.50
Step-by-step explanation:
25% of 30 is 7.50
30-7.50 is 22.50
Answer: A: $22.50
Step-by-step explanation:
The original price of the game, $30, is 100%.
If the game if 25% off, then it will be, (100 - 25), 75% of its original price.
All we need to do is 75% x 30:
0.75 x 30 = 7.5 x 3 = $22.50
So your answer is A: $22.50
STOP WITH THE LINKS! please? Help? NO LINKS!?????
Answer:
The answer is 24
just multiply 6 and 4 together
what is x (its a parralleligram)
Check the picture below.
The radius of a circle is 13 in. Find its circumference in terms of T(pi)
Answer: 40.82
Step-by-step explanation: You have to multiply pi and 13 to get the answer
Hi! Im stuck on this question please help, thanks
Answer:
I guess it is 43.57 Hope it helps!!!
If f and f ◦ g are onto, does it follow that g is onto? justify your answer
The functions f, g and f ◦ g are illustrations of relations and functions
If f and f ◦ g are onto, it does not necessarily follow that g is onto
How to complete the statement?The onto functions are given as:
Function fFunction f ◦ gConsider the functions f and g.
The function f is an onto function, if for every element of function f, there is at least one matching element with function g.
The above definition implies that the following definition is not a condition for the two functions to be an onto function
If for every element of function g, there is at least one matching element with function f.
Hence, it does not necessarily follow that function g is onto
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Find the value of x. Round to the nearest tenth.
I’m going to Mcshoot myself pls help
Answer:
x = 10.8
Explanation:
[tex]\sf \sf cos(x)= \dfrac{adjacent}{hypotensue}[/tex]
using cosine rule:
[tex]\rightarrow \sf cos(26)= \dfrac{x}{12}[/tex]
[tex]\rightarrow \sf x = cos(26) *12[/tex]
[tex]\rightarrow \sf x =10.8[/tex]
Answer:
The answer is rounded 10.8
Step-by-step explanation:
Cosine is the adjacent side over the hypotenuse, or a/h. So, cos 26=x/12. To solve for x, isolation of the variable is necessary. If both sides are multiplied by 12, the equation becomes 12 (cos 26)=x. The cosine of 26 is 0.8988, which multiplied by 12 is 10.8.
Hope this helps!
A husband and wife are building a tiny house for a vacation getaway, and they want to measure the height of the roof of the house to see if they will be able to have a bedroom on the second floor. One side of the house is 18 ft long and the slant height of the roof along this side is 13 ft. The point on the roof's peak is above the center of the house. What is the height of the roof of the house? Round your answer to the nearest hundredth. Question 4 options: 9.38 ft 11.28 ft 15.21 ft 9.4
By using a right triangle as a model, we will see that height of the roof is 9.38 ft.
What is the height of the roof of the house?The slant height is equivalent to the hypotenuse of a right triangle, so we know the length of the base and the hypotenuse of a right triangle. The cathetus will be half of 18ft
We need to find the other cathetus, so we can use the Pythagorean theorem, if X is the other cathetus we will get:
X^2 + (9ft)^2 = (13 ft)^2
X = √( (13 ft)^2 - (9 ft)^2) = 9.38ft
So the height of the roof is 9.38 ft.
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x + 3y = 3
x - 5y = -29
solve by elimination
Answer:
x=-9
y=4
Step-by-step explanation:
x + 3y = 3
x - 5y = -29
Multiply the second equation by -1
-x + 5y = 29
Add the two equations together to eliminate x
x + 3y = 3
-x + 5y = 29
---------------------
0x +8y = 32
Divide each side by 8
8y/8 = 32/8
y = 4
Now solve for x
x+3y =3
x+3(4) = 3
x+12 = 3
Subtract 12 from each side
x+12-12 = 3-12
x = -9
Sam has been running his swimming pool cleaning business now for five years. He is considering enlarging his service area to a 100 mile radius, which would require two new offices in different parts of town. He would like to take out a business loan to cover the cost of expansion. The profits for Sam's business over the last 5 years are outlined in the table below. According to this information, what would be the best estimate for Sam to quote as expected profits in the next year in his new business plan? Business Year Net Profit 1 $43,502. 25 2 $47,417. 45 3 $51,685. 02 4 $56,336. 68 5 $61,406. 98 a. $66,477. 28 b. $66,933. 60 c. $72,003. 91 d. $72,957. 63.
Thus, the best estimate for Sam to quote as expected profits in the next year in his new business plan is $66,933.60.
What is net profit?Net profit is the amount of a business earn after deducting all the expenditure over it.
Sam has been running his swimming pool cleaning business now for five years. He is considering enlarging his service area to a 100 mile radius, which would require two new offices in different parts of town.
He would like to take out a business loan to cover the cost of expansion. The profits for Sam's business over the last 5 years are outlined in the table below.
Business Year Net Profit 1 $43,502.25 2 $47,417.45 3 $51,685.02 4 $56,336.68 5 $61,406.98Using the regression graph, the quadratic equation we get for this data as,
[tex]y=192.4493x^2+3318.1733x+39998.214[/tex]
For the 6 year value,
[tex]y=192.4493(6)^2+3318.1733(6)+39998.214\\y\approx 66835.43[/tex]
This value is much near to the option b which is $66,933.60.
Thus, the best estimate for Sam to quote as expected profits in the next year in his new business plan is $66,933.60.
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Lacie bought a $20 shirt that was marked down 30%. what did she pay after tax of 6% was added to the price of the shirt?
Answer:
14.84
Step-by-step explanation:
20*(6%+1)*(1-30%)
20*(0.06+1)*1-0.3)
20*1.06*0.7
14.84
Solve: log2(3x 8) = 5 which is an equivalent equation? 25 = 3x 8 52 = 3x 8 25 = [log2(3x 8)]2 52 = [log2(3x 8)]5
The value of the equivalent equation will be 32=3x+8
What will be the value of x?It is given in the question that
[tex]\rm Log_2(3x+8)=5[/tex]
Now from the antilog property property
[tex]\rm x=Log_by[/tex] can be written as below
[tex]b^x=y[/tex]
So the value of [tex]\rm Log_2(3x+8)=5[/tex] will be
[tex]2^5=3x+8[/tex]
[tex]3x+8=32[/tex]
Thus the value of the equivalent equation will be 32=3x+8
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Answer:
I did it on edgeinuity
Step-by-step explanation:
X 12. Find the volume of the composite solid. Use 3.14 for . 5.5 ft Find the volume of the cone using the formula.
Answer: 74.61 ft^3
Step-by-step explanation:
pls help! no links
A spy realizes his cover is blown and flees toward his secret
evacuation spot at a speed of 60 mph. Two hours later, a special
agent in a helicopter starts chasing the spy. The special agent travels
the same route at a speed of 90 mph.
What distance does the spy cover in t hours?
Answer:
60t = y
t; time in hours
60: Speed of the spy fleeing
y: how far he has gone in t hours
Hope this helps!
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Have a great day!!
what is the quotient?
Answer:
[tex]x^{2}[/tex] - 2x + 4
Step-by-step explanation:
What is the smallest number by which 256 may be divided so that the quotient is perfect cube?
Answer:
The smallest number by which 256 must be divided so that the quotient is a perfect cube is 4.
Step-by-step explanation:
There are 9 members on a board of directors. if they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible? a. 504 c. 729 b. 84 d. 362,880
Answer:
A. 504
Step-by-step explanation:
on edge 2022
Answer:
A.
Step-by-step explanation:
EDG 2022