A tunnel is in the shape of a parabola.if the tunnel is 40 feet wide and has a maximum height of 12 feet. write the equation of the quadratic function that represents the tunnel(let the axis of symmetry be the y-axis)
Answers
9514 1404 393
Answer:
y = -0.03x² +12
Step-by-step explanation:
For "tunnel" or "arch" or "bridge" problems, I like to start with the expression ...
y = 1 - x²
It has a height of 1 and intersects the x-axis at ±1. This can be scaled to give the appropriate height and x-intercepts.
We want the x-intercepts to be ±20, so we can scale this horizontally by a factor of 20:
y = 1 -(x/20)²
We want the height to be 12, so we can scale it vertically by a factor of 12:
y = 12(1 -(x/20)²
y = 12 -12(x²/400)
y = -0.03x² +12
Related Questions
if f(x) =2x/X-5
Find f^-1(x).
Answers
Step-by-step explanation:
Let f(x)=y
y=2x/X-5
y(x-5)=2x
xy-5y=2x
x(y-2)=5y
x=5y/y-2
Apply x=5y/y-2, on f(x)
f(5y/y-2)=2(5y/y-2)/[(5y/y-2)-5]
=(10y/y-2)/[(5y-5y+10)/y-2]
=10y/10
=y
So f^-1(x)=5y/y-2
a
The expression ax²+bx+c is divisible by x-1, has a
remainder of 2 when divided by x+1 and has a remainder of 8 and when divided by x-2 find the values of a, b, and c and
factorise completely.
Answers
Answer:
(x - 1)(3x + 2)
Step-by-step explanation:
By the Remainder theorem
Given expression is divisible by x - 1 then f(1) = 0
when divided by (x + 1) then f(- 1) = 2
when divided by x - 2 then f(2) = 8
Substitute x = 1, x = - 1, x = 2 into the expression , that is
a + b + c = 0 → (1)
a - b + c = 2 → (2)
4a + 2b + c = 8 → (3)
Subtract (1) from (2) to eliminate a and c
- 2b = 2 ( divide both sides by - 2 )
b = - 1
Subtract (1) from (3) to eliminate c
3a + b = 8 ← substitute b = - 1
3a - 1 = 8 ( add 1 to both sides )
3a = 9 ( divide both sides by 3 )
a = 3
Substitute a = 3, b = - 1 into (1) and evaluate for c
3 - 1 + c = 0
2 + c = 0 ( subtract 2 from both sides )
c = - 2
Then a = 3, b = - 1, c = - 2
Thus
ax² + bx + c
= 3x² - x - 2
= (x - 1)(3x + 2) ← in factored form
how to round 8.798 to the nearest cent
Answers
Answer:
8.80
Step-by-step explanation:
Answer:
8.80
Step-by-step explanation:
The hundredths place is occupied by the 9.
First, drop the last 8.
8.79
Since the digit to the right of the dropped 9 is an 8, you round up.
8.79 becomes 8.80
Answer: 8.80
33°
114"
33
A) right scalene
B) acute scalene
C) obtuse isosceles
D) equilateral
Answers
Answer:
b acute I think so ok but that was a weird quistoin
What's the answer to this questions?
Answers
What is the square root of ten rounded to the nearest 100th
Answers
Answer:
3.162
Step-by-step explanation:
√10 = 3.162
Answer:
Step-by-step explanation:
I hope I can use a calculator and not use logs or a type of long division!
√10 = 3.16227
The hundredth place is the 6. The next place is a 2 which does not have any effect on the 6.
Answer: 3.16
PLEASE HELP ILL GIVE YOU BRAINLIST !!! I DONT UNDERSTAND THIS
Answers
Answer:c=2 √1129 or c=−2 √1129
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
c^2=4516
Step 2: Take square root.
c=±√4516
c=2√1129 or c=−2√1129
what is the value of x?
12
15
20
24
Answers
Answer:
15
Step-by-step explanation:
Which of the following represents a polynomial expression? Select one: A. 2x + 3log(x) + 5 B. 10x−−√ − 2 C. (x + 1)(x - 1) D. 4x + 2(3x + 3)
Answers
Answer:
none!
Step-by-step explanation:
Answer:
The answer is C
Step-by-step explanation:
Explanation: I searched up "what don't polynomials have"
Please, somebody, solve this quick and reply with step by step explanation AND provide all steps of working!
If these will be there then I will mark them as BRAINLIEST!
Answers
Answer:
For a trapezium of height H, parallel side 1 X, and parallel side 2 Y, the area is:
A = (1/2)*H*(X + Y)
with this we can complete the table.
a)
Here we know:
X = 7cm
Y = 11cm
H = 6cm
Then: A = (1/2)*6cm*(7cm + 11cm) = 54 cm^2
b)
Here we know:
X = 8 m
Y = 10 m
A = 126 m^2
Then:
126 m^2 = 0.5*H*(8m + 10m)
126 m^2 = H*9m
126 m^2/9m = H = 14m
Then the height of this trapezoid is 14m
c)
Here we know:
X = 5mm
H = 8mm
A = 72 mm^2
Then:
72 mm^2 = 0.5*8mm*(5mm + Y)
72 mm^2 = 4mm*(5mm + Y)
72mm^2/4mm = 5mm + Y
18 mm = 5mm + Y
18mm - 5mm = Y
13 mm = Y
Then the parallel side 2 is 13 mm long.
What is the solution to the equation below? Round your answer two decimal places. 3^x = 9.2
Answers
3x = 9.2 ⇒ x = 2.02000606
Answer:
X=2.02
Step-by-step explanation:
Which property of equality is used to solve the equation 5n = 50?
What property of equality would you use to solve the equation n/4 = 16.
Answers
Answer:
To solve 5n = 50, I would use the property of division.
To solve n/4 = 16, I would use the property of multiplication.
Hope this helped! Have a nice day! Plz mark as brainliest!!! :D
-XxDeathshotxX
A shopkeeper buys a stove from a manufacturer for $100.The selling price if he makes a profit of 15%
Answers
Answer:Selling Price = $115
Step-by-step explanation:
Selling price = Cost price + Profit
Cost price = $100
Profit = 15% = 15% x 100 = $15
Selling Price = $100 + $15= $115
OR
Selling Price = Cost price + Profit
Selling Price =$100 + (15% of $100)
Selling Price = $100+ $15
= $115.
Which of these is the quadratic parent function?
f(x) = x2
f(x) = |x|
f(x) = x
f(x) = 2x
Answers
Answer:
the first one
f(x) = x²
its making me write more
Select the word to make the statement true.
Similar polygons are ____ the same size.
A. always
B. sometimes
C. never
Answers
Answer:
B.
Hope that helps!
Step-by-step explanation:
Answer:
B. Sometimes
Step-by-step explanation:
Hope this helps!
Here is an expression: 4•3^x
a. Evaluate the expression when x = 2
b. Evaluate the expression when x = 4.
Answers
Answer:
First one is 36 and second one is 324!!!
URGENT!!!!
Find Perimeter of the square with the side 15 in.
Use formula P=4s
100 in
60 in
225 in
30 in
Answers
Answer:
It's 60 in
Step-by-step explanation:
P = 4s
P = 4 x 15
P = 60 in
$4000 is compounded annually at a rate of 7% for 7 years.
Answers
Answer:
hey i think its $16,819 i'm so sorry if i get it wrong
Step-by-step explanation:
9 + 15m
factorisation of algebraic expression that contain common factor
Answers
Answer:3(3+5m)
Step-by-step explanation:
Analyze the diagram below and complete the instructions that follow.
Find the value of x.
Answers
Answer: I believe the answer is C.
Step-by-step explanation: In special case isosceles right triangles the hypotenuse is always equal to a · √2. With a=5√2 we can set up the equation 5√2 · √2 = 10.
Find the area of the figure
Answers
Answer:
Answer is 50 m squared
Step-by-step explanation:
Answer: 32.5cm
Step-by-step explanation:
i hope this helps
Isabel has 6.75 bags of coffee. A full bag weighs 5.2 pounds. How many pounds of coffee does Isabel have? *
11.77
11.95
31.5
35.1
which one ^
Answers
Answer:
35.1
Step-by-step explanation:
6.75x5.2=35.1
I have to find the value of x
k so I tried, and honestly I'm not sure what I'm doing wrong but I'm not sure how to solve it. If anyone could help that would be lovely :') thank youu
Answers
Answer:
x = 25
Step-by-step explanation:
A quadrilateral is inscribed in a circle, so it is a cyclic Quadrilateral.
Opposite angles of a cyclic quadrilateral are supplementary.
Therefore,
3x + 21y = 180°.....(1)
2x + 26y = 180°.....(2)
From equations (1) & (2)
3x + 21 y = 2x + 26y
3x - 2y = 26y - 21y
x = 5y
y = 1/5 x
Plug y = 1/5 x in equation (1)
3x + 21*1/5x = 180
15x + 21x = 180*5
(Multiplying both sides by 5)
36x = 900
x = 900/36
x = 25
42
40
x
Find the unknown side length, x. Write your answer in simplest radical form.
A. 2.41
B. 429
C. 48
D. 58
Answers
Answer:
Your answer is D. 58
Step-by-step explanation:
x= [tex]\sqrt{(42^2+40^2)}[/tex]
Help me Please I will give brainliest! (please dont answer if you dont know)
Answers
Answer:
16.5 feet or
about 17 feet long.
Step-by-step explanation:
A = bh
Squares have equal side lengths all around so with there being 4 sides, you will take 66 and divide by 4.
66 ÷ 4 = 16.5
So it is about 17 feet
yall the ones with boxes help
Answers
Answer:
16
Step-by-step explanation:
If the store sells 2 printers for every 5 computers
40/5 is 8. this means there are 8 sets of 5 computers
8x2 is 16 since for every 5computers, 2 printers are sold
i don’t get scientific notation. can someone help me on this?
Answers
Alex was thinking of a number. Alex doubles it the adds 20 to get answer of 22.7. What was his original number.
Answers
Answer:
2.7
Step-by-step explanation:
Let the number alex think be x
Answer = 22.7
According to the question,
x + 20 = 22.7
x = 22.7 - 20
x = 2.7
Therefore, his original number is 2.7
Plz mark me as brainliest
Have a great day
The triangle below are similar find the lengths of the missing side.
Answers
Answer:
The answer is b =9
Step-by-step explanation:
20:12=15:b
5:3=15:b
cross multiply
5×b=3×15
5b=45
divide both sides by 5
b=45÷5
b=9
A store pays $24 for a jewelry box and marks the price up by 20%. What is the amount of
the mark-up?
Answers
Answer:
$4.8
Step-by-step explanation:
$24×20/100=$4.8