A fountain shoots a water arc that can be modeled by the graph of the equation y=-0.006x^2+1.2x+10, where x is the horizontal distance (in feet) from the river's north shore and y is the height (in feet) above the river. Does the water arc reach a height of 50 feet? If so, about how far from the north shore is the water arc 50 feet above the water?
Answers
ANSWER
The water arc is 50 ft above the water approximately 42ft and 158ft from the north shore.
EXPLANATION
The water arc is modeled by the function:
[tex]y = - 0.006 {x}^{2} + 1.2x + 10[/tex]
We write this function in vertex form:
[tex]y = - 0.006 ({x}^{2} - 200x )+ 10[/tex]
[tex]y = - 0.006 ({x}^{2} - 200x + ( - 100)^{2} ) - - 0.006( - 100)^{2} + 10[/tex]
[tex]y = - 0.006 ( x- 100)^{2} ) + 60+ 10[/tex]
[tex]y = - 0.006 ( x- 100)^{2} ) +70[/tex]
The vertex of this function is at
(100,70).
This means that the water arc reached a height of 50ft.
We put y=50 and solve for x.
[tex]- 0.006 ( x- 100)^{2}+70 = 50[/tex]
[tex]- 0.006 ( x- 100)^{2} = - 20[/tex]
[tex]( x- 100)^{2} = \frac{10000}{3} [/tex]
[tex]x = 100 \pm \frac{100 \sqrt{3} }{3} [/tex]
x=42.3 or x=157.7
Hence the water arc is 50 ft above the water approximately 42ft and 158ft from the north shore.
The water arc does reach a height of 50 feet, and it is about 42.27 feet and 157.73 feet from the north shore when it is 50 feet above the water.
1.Set up the equation:
[tex]\[ -0.006x^2 + 1.2x + 10 = 50 \][/tex]
2. Simplify the equation:
Subtract 50 from both sides:
[tex]\[ -0.006x^2 + 1.2x + 10 - 50 = 0 \] \[ -0.006x^2 + 1.2x - 40 = 0 \][/tex]
3. Solve the quadratic equation:
We can use the quadratic formula
[tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = -0.006 \), \( b = 1.2 \), and \( c = -40 \).[/tex]
[tex]\[ a = -0.006, \quad b = 1.2, \quad c = -40 \][/tex]
[tex]\[ \Delta = b^2 - 4ac \] \[ \Delta = 1.2^2 - 4(-0.006)(-40) \] \[ \Delta = 1.44 - 0.96 \] \[ \Delta = 0.48 \][/tex]
[tex]\[ x = \frac{-b \pm \sqrt{\Delta}}{2a} \] \[ x = \frac{-1.2 \pm \sqrt{0.48}}{2(-0.006)} \][/tex]
Calculate the square root of 0.48:
[tex]\[ \sqrt{0.48} \approx 0.6928 \][/tex]
Now, find the two values of x:
[tex]\[ x_1 = \frac{-1.2 + 0.6928}{-0.012} = \frac{-0.5072}{-0.012} \approx 42.27 \] \[ x_2 = \frac{-1.2 - 0.6928}{-0.012} = \frac{-1.8928}{-0.012} \approx 157.73 \][/tex]
Therefore, the water arc reaches a height of 50 feet at approximately [tex]\( x = 42.27 \) feet and \( x = 157.73 \)[/tex] feet from the north shore.
Related Questions
The perimeter of the triangle below is 4x + 3y. Find the measure of the missing side. (Picture of triangle)
Answers
Answer: 2x+3y
Step-by-step explanation: look at picture
To find the missing side in a triangle with a given perimeter, subtract the lengths of the known sides from the total frame. This is based on the sum of the lengths of all sides of a triangle, which equals its circumference.
Explanation:We need to understand a simple rule about triangles to find the missing side of a triangle where the perimeter is 4x + 3y. The sum of all sides of a triangle equals its edge. So, if we know the length of the other two sides, we can subtract their sum from the total circumference to find the size of the missing side.
For example, if we know that the other two sides of the triangle are 2x and y, respectively, the missing side would be calculated by subtracting the sum of these sides from the given perimeter.
4x + 3y = perimeter
2x + y = known sides
missing side = (4x + 3y) - (2x + y)
Note: This method assumes that x and y values are provided. If they're unknown, we will require additional equations to solve for x and y before calculating the length of the missing side.
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A(n) ____ is NOT an example of an agreement.
A) Lease
B) Month-to-month
C) Annual
D) Fine Print
Answers
Answer:
D) Fine Print
Fine print is part of an agreement but technically isnt one.
Final answer:
The correct answer is D) Fine Print. Fine Print is not an agreement but refers to the small, often hard-to-read text in a contract that contains important legal provisions.
Explanation:
The correct answer is D) Fine Print. A lease is a contractual agreement between a lessor and a lessee that gives the lessee the right to use a property owned by the lessor for a specific period in exchange for payment. A month-to-month agreement is a type of lease which automatically renews each month until either party decides to terminate it. An annual agreement typically refers to a contract or lease that is renewed once per year.
Lesson 4 practice problems.
Answers
Answer:
which is the question yours asking help for
Plz help me with this
Answers
Answer: A) 13
Step-by-step explanation:
Mean - 1 SD: 20.2 - 2.4 = 17.8 --> (18)
Mean + 1 SD: 20.2 + 2.4 = 22.6 --> (23)
Now, find the values on the histogram for 18 through 23:
2 + 3 + 4 + 3 + 1 + 1 = 13
Mary and Jane are trying to set up their marmalade selling business. They started off by peeling the oranges. Mary peels 8 oranges in 10 minutes while Jane peels 3 oranges in 5 minutes. If they need to peel 500 oranges for their first batch of marmalade, how long (in hours) will it take them to finish peeling? (round off to nearest hr)
Answers
Answer:
6.0 hours
Step-by-step explanation:
1 hour is the same as 60 minutes.
"Mary peels 8 oranges in 10 minutes"
1 hour = 60 minutes = 6 * 10 minutes
In 1 hour, she peels 6 times as many oranges, so Mary peels 48 oranges in 1 hour.
"Jane peels 3 oranges in 5 minutes"
1 hour = 60 minutes = 12 * 5 minutes
In 1 hour, she peels 12 times as many oranges, so Jane peels 36 oranges in 1 hour.
Combined, the peel 48 + 36 = 84 oranges in 1 hour.
(500 oranges)/(84 oranges/hour) = 5.952 hours
Answer: 6.0 hours
What is the measure of the missing angle?
A. 40
B. 75
C. 35
D. 115
Answers
Answer:
D) 115
the inside angles of a triangle always (ALWAYS) add up to 180, add 75 and 40. You get 65. Then you know that a straight line means it is 180 degrees so you subtract 65 from 180. you get 115 degrees
Missing angle is 115
Chris spent $8 on lunch. 75% was spent on a sub ad the rest was used to buy two cookies. How much was each cookie?
Answers
Answer:
1 dollar.
Step-by-step explanation:
"Chris spent $8 on lunch. 75% was spent on a sub ad the rest was used to buy two cookies. How much was each cookie?"
.75=75%
8*.75=cost of sub=6
total cost- cost of sub=cost of cookies
8-6=2
The cost of 2 cookies is 2 dollars
Now to find the cost per cookie we take the total cost of the cookies, and divide it by the amount of cookies-
2/2=cost per cookie=1
It cost $1 for each cookie.
A right rectangular prism has a length of 10 in., a width of 12 in., and a height of 16 in. The dimensions of the prism are halved. What is the surface area of the reduced prism? Enter your answer in the box. in²
Answers
Answer:
[tex]S.A=236in^2[/tex]
Step-by-step explanation:
The given prism has dimension;
[tex]L=10in.,W=12in.,H=16in.,[/tex]
If the dimensions of the prism are halved then;
[tex]l=5in.,w=6in.,h=8in.,[/tex]
The surface area of the reduced prism will be;
[tex]S.A=2(lw+lh+wh)[/tex]
[tex]S.A=2(5(6)+5(8)+6(8))[/tex]
[tex]S.A=2(30+40+48)[/tex]
[tex]S.A=2(118)[/tex]
[tex]S.A=236in^2[/tex]
Answer:
236in²
Step-by-step explanation:
Given in the question,
length of rectangular prism = 10 in
width of rectangular prism = 12 in
height of the prism = 16 in
Since the dimensions are reduced to half so the new dimensions are
length of rectangular prism = 5 in
width of rectangular prism = 6 in
height of the prism = 8 in
Formula to calculate the surface area
2(lw + lh + wh)
2 ((5x6) + (8x5) + 2(6x8))
236 in²
Helpppppp PLZZZZZZZZZZZZ
Answers
Answer:
Final answer is m∠D = 61°.
Step-by-step explanation:
Given that m∠C = 98°,
m∠B = 140°,
m∠A = m∠D ,
Using those information we need to find the value of m∠D.
We know that sum of all 4 interior angles of a quadrilateral is always 360°.
So we can write equation:
m∠A +m∠B +m∠C +m∠D = 360°
m∠A + 140° + 98° +m∠D = 360°
m∠D + 140° + 98° +m∠D = 360°
2(m∠D) + 140° + 98° = 360°
2(m∠D) + 238° = 360°
2(m∠D) = 360° - 238°
2(m∠D) = 122°
m∠D = 122°/2
m∠D = 61°
Hene final answer is m∠D = 61°.
Answer:
the answer is 61°
Step-by-step explanation:
360- 98- 140 = 122 ÷2 = 61
Which statements are true about polygons?
Answers
The statements that are true about polygons are:
All sides and all angles in a polygon are congruent. In a polygon, all segments with a common endpoint are collinearThe sides of a polygon are segments that intersect exactly two other segments, one at each endpoint.What are polygons?A closed polygonal chain of connected line segments makes up a polygon, a plane shape. The edges or sides of a closed polygonal chain are the individual pieces. The polygon's vertices or corners are the places where two edges converge.
Each side of a polygon is the same length, and each angle is the same size. For instance, in a square, every side is the same length and every angle is 90 degrees. There is at least one interior angle that is more than 180 degrees in a concave polygon. A concave polygon will have at least one point that is inside it if a side or diagonal is expanded.
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Use the distributive property to remove the parentheses.
-5(6y - u - 2)
Answers
Answer:
-30y+5u+10
Hope this helped
Does anyone know this?! Pls help
Answers
Answer:
Step-by-step explanation:
we are given the angles of XYR = 40, ZXY = 130, and SRY = 40 degrees.
angle ZXY is half of angle ZAY, so angle ZXY is 65 degrees.
imagine a line XA (not on the diagram). then ZXA is 32.5 degrees since it is half of YXZ. Angle XZA and ZXA are equal, so XZA is 32.5 degrees. RZA = XZA + RZX = 32.5 + 40 degrees (assuming the upper left stated degree belongs to angle XZA), or simply RZA is 72.5 degrees.
since ZRA = RZA, then ZRA is 72.5 degrees. since angle ZRS = SRY + ZRA, finally ZRA = 40 + 72.5 degrees or simply, ZRS = 112.5 degrees. which visually is blantantly wrong as it appears to be less than 90 degrees.
I’m thinking of a number. The square of this number is the same as the number times 4. What could my number be?
Answers
Answer:
4
Step-by-step explanation:
4 squared equals 16 and 4 times 4 equals 16
a refund of $3.15 on a $8.64 bill
Answers
8.64 - 3.15 = $5.49 if this is what you are asking
Answer:
Step-by-step explanation:
3.15-8.64 is5.49 hope this helps
Write the equation 4x + 2y = 5 in the form y = mx + b.
Answers
Answer:
4x+2y-5=0
Step-by-step explanation:
since you have to put the problem in that order you take 5 from both sides
Answer:
The correct answer is y = -2x + 5/2
Step-by-step explanation:
y = mx + b. is the y intercept form of a line.
To find the y = mx + b. form
It is given that,
4x + 2y = 5
2y = -4x + 5
Dividing both sides by 2 we get,
2y/2 = (-4x + 5)/2
y = -4x/2 + 5/2
y = -2x + 5/2
Here m = -2 and b = 5/2
The leg of a right triangle is 3 units and the hypotenuse is 4 units. What is the length, in units, of the other leg of the triangle . need help !!
Answers
Answer:
[tex]\sqrt{7}[/tex]
Step-by-step explanation:
let the other leg be x
Then using Pythagoras' identity
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² + 3² = 4²
x² + 9 = 16 ( subtract 9 from both sides )
x² = 7 ( take the square root of both sides )
x = [tex]\sqrt{7}[/tex]
Answer:
Square root of 7
Step-by-step explanation:
[WILL GIVE BRAINLIEST ANSWER] f(x)=(x-5)(5x+2) write the smaller solution first and the smaller solutuon second
Answers
Answer:
x = - [tex]\frac{2}{5}[/tex], x = 5
Step-by-step explanation:
Given
f(x) = (x - 5)(5x + 2)
To obtain the solutions set f(x) = 0, that is
(x - 5)(5x + 2) = 0
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5 ← larger x
5x + 2 = 0 ⇒ 5x = - 2 ⇒ x = - [tex]\frac{2}{5}[/tex] ← smaller x
Amy has a triangle with side lengths of 6 and 8. What is the length of the
hypotenuse.
Answers
Hello There!
The length of the hypotenuse is 10.
We know what 2 sides are 6 and 8.
To find the third side we use the formula a^2 + b^2 = c^2
So we multiply 6 by 6 which equals 36 and then multiply 8 by 8 which equals 64.
Next we add 64 and 36 together and we get 100.
Next, we square root 100 and get 10.
10 is the length of the hypotenuse.
Which of the following terms appear in the expansion of (x+y)^10? The letter "a" in each term represents a real constant.
Choices are:
ax^4y^6
ax^5
ax^3y^7
ax^6y^4
Can be multiple
Answers
ANSWER
[tex]ax^4y^6[/tex]
[tex]ax^3y^7[/tex]
[tex]ax^6y^4[/tex]
EXPLANATION.
The given binomial is
[tex]( {x + y)}^{10} [/tex]
One property about all the terms in this binomial expansion is that:
The degree of each term is 10.
[tex]ax^4y^6[/tex]
degree=4+6=10
[tex]ax^3y^7 [/tex]
degree=3+7=10
[tex]ax^6y^4[/tex]
degree=6+4=10
[tex]ax^5[/tex]
degree=5+0=5
All the terms with degree 10 are the correct options
Answer:All of them except for ax^5
Step-by-step explanation:
You add what it’s being squared too and if it equals ten then it’s correct since we’re trying to find (x+y)^10
calculate the slope of the given points (6,2) and (8,2)
Answers
Answer:
0
Step-by-step explanation:
Since both points are on the the line (0,2) there is no slope/the slope is 0
There is no slope it just a straight line
Write the equations of the line contains E and F in:
A) slope-intercept form
B) standard form
C) point-slope form
Answers
Answer:
A) y=4x-12
B) y-4x=-12
C) y+4=4(x-2)
Step-by-step explanation:
Sorry it took you so long to be answered, but I hope this helps! :D
Answer with explanation:
Coordinate of Point E and F are = (4,4) and (2,-4).
Two Point form of line, that is equation of line Passing through two points is given by:
[tex]\rightarrow \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}_x_{1}}\\\\\rightarrow \frac{y-4}{x-4} =\frac{4+4}{4-2}\\\\\rightarrow \frac{y-4}{x-4} =4\\\\ \rightarrow y-4=4 x-16\\\\\rightarrow 4 x-y -16+4=0\\\\\rightarrow 4 x -y-12=0[/tex]
Standard Form : 4 x-y-12=0
Slope-intercept form
[tex]\rightarrow 4 x-y-12=0\\\\\rightarrow 4 x- y=12\\\\\rightarrow \frac{4 x-y}{12}=1\\\\\rightarrow \frac{4x}{12}-\frac{y}{12}=1\\\\\rightarrow \frac{x}{3} +\frac{y}{-12}=1[/tex]
Point-slope form
[tex]\rightarrow \frac{y-4}{x-4} =\frac{4+4}{4-2}\\\\\rightarrow \frac{y-4}{x-4} =4[/tex]
What is the measure of ∠JSM?
A) 12°
B) 17°
C) 23°
D) 31°
Answers
I think it would be “B”
Answer:
Option B.
Step-by-step explanation:
Given information: [tex]m\angle A=48^{\circ},\angle E=90^{\circ},\angle EMS=59^{\circ}[/tex].
According to the angle sum property of a triangles, the sum of interior angles of a triangle is 180°.
Apply angle sum property on triangle AEJ.
[tex]\angle A+\angle E+\angle J=180^{\circ}[/tex]
[tex]48^{\circ}+90^{\circ}+\angle J=180^{\circ}[/tex]
[tex]138^{\circ}+\angle J=180^{\circ}[/tex]
Subtract 138 from both sides.
[tex]\angle J=180^{\circ}-138^{\circ}[/tex]
[tex]\angle J=42^{\circ}[/tex]
The measure of angle J is 42°.
According to exterior angle property, the sum of two interior angles of a triangle is equal to the third exterior angle.
Apply exterior angle property on triangle JMS.
[tex]\angle EJA+\angle JSM=\angle EMS[/tex]
[tex]42^{\circ}+\angle JSM=59^{\circ}[/tex]
Subtract 42 from both sides.
[tex]\angle JSM=59^{\circ}-42^{\circ}[/tex]
[tex]\angle JSM=17^{\circ}[/tex]
The measure of ∠JSM is 17°.
Therefore, the correct option is B.
The denominator of the seventh term is
125
216
343
512
Answers
343 will be your answer
Answer: Thus, Third option is correct.
Step-by-step explanation:
Since we have given that
[tex]1,\dfrac{1}{8},\dfrac{1}{27},\dfrac{1}{64},...............\dfrac{1}{n^3}[/tex]
So, we can see the pattern:
General term of the series is given as
[tex]\dfrac{1}{n^3}[/tex]
So, we just put the value of n = 7, to get the required denominator:
[tex]\dfrac{1}{7^3}=\dfrac{1}{343}[/tex]
Hence, the denominator of the seventh term is 343.
Thus, Third option is correct.
A game is played with a deck of 50 cards numbered from 1 to 50. At the end of each round, players calculate their score by adding the numbers on their cards.
What is the least score a player could have if he or she has 7 cards remaining at the end of a round?
Answers
Answer:
28, 329, 11
Step-by-step explanation:
What is the least score a player could have if he or she has 7 cards remaining at the end of a round?
28 pointsWhat is the greatest score a player could have if he or she has 7 cards remaining at the end of a round?
329 pointsGlenna needs to get 60 points in the next round to win the game. What is the least number of cards Glenna needs to be guaranteed a win?
11The least score a player could have is if he or she has 7 cards remaining at the end of round 28.
What is problem-solving?Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
Calculation:-
Addition of the first 7 natural number (out of 50 cards)
In order to get the minimum value
⇒1+2=3+4+5+6+7=28
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11. Determine whether the triangles are similar. If so, what is the similarity statement and the
postulate or theorem used?
(please answer ASAP if you have the all of the questions for the semester exam I'll take them too please)
A.>TRS~>TPQ;SSS~
B.>TRS~>TPQ;SAS~
C.>TRS~>PQR;SAS~
D.The triangles are not similar
Answers
Answer:
Option B
Step-by-step explanation:
we know that
SAS Similarity Theorem: If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
In this problem
∠STR is congruent with ∠QTP
Verify if the corresponding sides are proportional
[tex]\frac{42}{42+6}=\frac{28}{28+4}[/tex]
[tex]\frac{42}{48}=\frac{28}{32}[/tex]
[tex]42*32=48*28[/tex]
[tex]1,344=1,344[/tex] ----> is true
therefore
The triangles TRS and TPQ are similar by SAS
Find the area of the trapezoid.
Answers
75
15×6÷2+10×6÷2
90÷2+60÷2
45+30
75
The answer is 75.
Hope this helps!
What does this equal to in standard form? (A+bi)
Answers
[tex]
3i(-7+11i)=-28i+33i^2=\boxed{-33-28i}
[/tex]
Answer:
-33 - 21i
Step-by-step explanation:
3i (-7 + 11i)
= -21i + 33i^2 (i^2 = -1)
= -21i + 33(-1)
= -33 - 21i
Could someone check over me? Thanks!
Answers
Answer:
Yes, I agree with A. :)
Step-by-step explanation:
Which of the following are solutions to2x^2-8x-90? Select all that apply. 2
-5
-7
9
15
5
7
Answers
Answer:
9,-5
Step-by-step explanation:
2x^2-8x-90
Factor by 2
2(x^2 -4x-45)
What two numbers multiply to -45 and add to -4
-9*5 = -45
-9+5 = -5
2(x-9) (x+5)
Set this equal to zero
2(x-9) (x+5) =0
Divide by 2
(x-9) (x+5) =0
Using the zero product property
x-9=0 x+5=0
x=9 x=-5
The area of a playground is 160 yd2. The width of the playground is 6 yd longer than its length. Find the length and width of the playground.
Answers
Answer:
length=10\ yd, width=16\ yd
Answer:
Length of the playground is 10 yd and the Width of the playground is 16 yd .
Step-by-step explanation:
Formula
Area of a rectangle = Length × Width
As given
The area of a playground is 160 yd².
The width of the playground is 6 yd longer than its length.
Let us assume that the length be x .
Thus
Width = x + 6
Put all the values in the formula
160 = x × (x + 6)
160 = x² + 6x
x² + 6x - 160 = 0
x² + 16x - 10x - 160 = 0
x (x + 16)-10 (x + 16) = 0
(x -10)(x + 16) = 0
Thus
Either (x - 10) = 0 or (x + 16 ) = 0
x = 10 or x = -16
(Negative value is neglected because sides cannot be negative.)
Thus
x = 10
Length = 10 yd
Width = 10 + 6
= 16 yd
Therefore the length of the playground is 10 yd and the width of the playground is 16 yd .