A golfer aims for a hole that is 120 feet away and, when he hits the golf ball off the ground, its highest point reaches 80 feet up in the air. Noemi’s team is working together to write the quadratic equation to model the path of the golf ball in graphing form. She calculated the value of a = - 1/90 . Is she correct?
Answers
Answer:
No she isn't. The value of [tex]a[/tex] is [tex]a=-\frac{1}{45}[/tex]
Step-by-step explanation:
We know that all quadratic equation can be written in the following way :
[tex]y=ax^{2}+bx+c[/tex] (I)
Where [tex]a,b[/tex] and [tex]c[/tex] are real numbers.
I will attach a drawing with the quadratic graph to understand the situation.
We know by looking at the drawing and analyzing it that the parabola passes through the points : [tex](0,0) ; (60,80)[/tex] and [tex](120,0)[/tex]
[tex](0,0)[/tex] because we put our coordinates origin there.
[tex](120,0)[/tex] because that's where the golf hole is.
And [tex](60,80)[/tex] because we know that its highest point reaches 80 feet up in the air at the middle of the distance between its roots (property of a negative parabola).
Finally, we work with the three points and the equation (I) in order to find the values of [tex]a,b[/tex] and [tex]c[/tex] ⇒
The parabola passes through [tex](0,0)[/tex] ⇒
[tex]y=ax^{2}+bx+c[/tex] ⇒
[tex]0=a(0)^{2}+b(0)+c[/tex] ⇒ [tex]c=0[/tex]
The parabola passes through [tex](60,80)[/tex] ⇒
[tex]80=a(60)^{2}+b(60)[/tex] ⇒
[tex]80=3600a+60b[/tex] (II)
The parabola passes through [tex](120,0)[/tex] ⇒
[tex]0=a(120)^{2}+b(120)[/tex] ⇒
[tex]0=14400a+120b[/tex]
[tex]120b=-14400a[/tex]
[tex]b=-120a[/tex] (III)
Now if we use (III) in (II) ⇒
[tex]80=3600a+60(-120a)[/tex]
[tex]80=3600a-7200a[/tex]
[tex]3600a=-80[/tex]
[tex]a=-\frac{1}{45}[/tex] ⇒ [tex]b=\frac{8}{3}[/tex]
Finally the equation of the parabola is
[tex]y=-\frac{x^{2}}{45}+\frac{8}{3}x[/tex]
Where the value of [tex]a[/tex] is [tex]a=-\frac{1}{45}[/tex]
Related Questions
What is the temperature increase in degrees Fahrenheit that is equivalent to a temperature increase of 10 degrees Celsius?
Answers
Answer:
18 degrees Fahrenheit
Step-by-step explanation:
A dishonest shopkeeper has two false balances. One balance weighs 10% more while
buying the goods and other weighs 10% less while selling the goods. Find his gain
percent just by weighing,
Answers
Answer:
Shopkeepers gain just by weighing is 22.22%
Step-by-step explanation:
Explanation:
Assume that the shopkeeper bought x units of goods i.e. actual weight of goods.
As the balance used to buy goods weighs 10% more, he actually bought x×110100=1.1x weight units i.e. although the shopkeeper paid for x units, he actually bought 1.1x units by weight.
Now he has 1.1x units of goods, but for selling he uses another balance, which actually measures 10% less i.e. 1−0.10=0.9 units for each unit weight of goods sold.
So while selling 1.1x becomes 1.1x0.90=1.2222... units.
Hence, shopkeepers gain just by weighing is 22.22%
What is the Ratio of 472 and 482?
Answers
answer: 236/241
❤️❤️!!
If the mean of 50 scores is exactly 26,4, and the mean of 49 of those scores is exactly 26, is the 50 score ?
Answers
Answer:
The 50th score is 46.
Step-by-step explanation:
Given that
[tex]a_{50} = 26.4\\a_{49} = 26\\n_1 = 50\\n_2 = 49[/tex]
In order to find the 50th score we have to find sum of 49 values and 50 values and then subtract them.
Average is given by the formula:
[tex]Average = \frac{Sum}{Number\ of\ values}\\[/tex]
Using this formula, we can calculate sum for both averages
So,
[tex]a_{50} = \frac{s_{50}}{n_1}\\26.4 = \frac{s_{50}}{50}\\26.4*50 = s_{50}\\s_{50} = 1320[/tex]
And
[tex]a_{49} = \frac{s_{49}}{n_2}\\26.4 = \frac{s_{49}}{49}\\26*49 = s_{49}\\s_{49} = 1274[/tex]
Now for the 50th score,
[tex]50th\ score = s_{50} - s_{49} = 1320-1274 = 46[/tex]
Hence,
The 50th score is 46.
A triangle, ABC, has angle measures of 82,75, and 23 and no sides equal (congruent) in length. How would this triangle be classified?
Answers
Answer:
It would be an acute scalene triangle
Step-by-step explanation:
All angles measures are less than 90 so it would be acute. No sides are equal so it would be scalene.
We can classify this triangle as Scalene Acute triangle.
We have a triangle angle measures of 82, 75 and 23 and no sides equal (congruent) in length.
We have to classify this triangle.
What is a Triangle ?A triangle is a plane figure with three straight sides and three angles.
According to question, we have -
A triangle with no side congruent and all angles acute and unequal.
If all the three sides of a triangle are of same length, then the sides are said to be congruent. In an Equilateral triangle all the sides are congruent. Similarly, a triangle with none of its sides equal or congruent is called a Scalene triangle. An acute angle triangle (or acute-angled triangle) is a triangle in which all the interior angles are acute angles i.e. 0 < [tex]\theta[/tex] < 90. Therefore, it is a Scalene acute triangle.
Hence, we can classify this triangle as Scalene Acute triangle.
To solve more questions on Scalene triangle , visit the link below -
brainly.com/question/10651823
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Calculate the simple interest on $600 left in account that pays 7% annual interest for 8 years.
Answers
Answer:
S = $336
Step-by-step explanation:
Given the following data;
Principal, P = $600
Rate, R = 7
Time, T = 8 years
To find the simple interest?
Mathematically, it is given by the formula;
Simple interest, S = (P*R*T)/100
Substituting into the equation, we have;
S = (600*7*8)/100
Simplifying the equation, we have;
S = 6*7*8
S = $336
p2+24p+23 what would the answer be
Answers
Answer:
Step-by-step explanation:
You should factorize so
P2 + 24p + 23
P2 + 23 p + p + 23
P(p + 23) + 1(p + 23)
(p + 23) and ( p + 1) are the factors
Solve for s.
1/2s=7/2
s=1/7
s=2/7
s=3
s=7
Answers
Hello! I have done this test and the answer is!..... D: S=7
Have a great day!!!
Approximate the logarithm using the properties of logarithms, given
logb 2 ≈ 0.3562,
logb 3 ≈ 0.5646,
and
logb 5 ≈ 0.8271.
(Round your answer to four decimal places.)
logb 2/3
Answers
Answer:
-0.2084
Step-by-step explanation:
[tex] log_{b}( \frac{2}{3} ) \\ \\ = log_{b}(2) - log_{b}(3) \\ \\ =0.3562 - 0.5646 \\ \\ = -0.2084[/tex]
HELP ME OUT HERE PLEASEEEEEEEEE
Answers
Answer:
2nd option
Step-by-step explanation:
2 3/8-1 3/10
19/8-13/10
190/80-104/80
86/80
43/40
1 3/40
10. Tell whether the sequence is arithmetic. If it is, what is the common difference? (1 point)
2.7, 13, 20...
A. yes: 5
B. yes; 6
C. yes: 2
D. no
Answers
Answer:
No
Step-by-step explanation:
an airplane moves at a constant speed of 120 miles per hour for 3 hours how many miles does it go
Answers
Answer:
Ok this is super easy
Step-by-step explanation:
120 for every one hour
so 120 x 3 isssss????
120 x 3 = 360 mile per hour
Hope I helped sorry If you get it wrong
2
[tex]2x - 8x = [/tex]
Answers
Answer:
-6x
Step-by-step explanation:
2x - 8x = -6x
Step-by-step explanation:
Question: 2x – 8x
Do, 2 – 8 which is -6
Then just put the x’s next to them
Answer : 2x – 8x = -6x
What’s -10/-1 simplified
What’s -1/-3 simplified
Answers
Answer:
10 and 1/3
Step-by-step explanation:
Answer:
10
1/3
Step-by-step explanation:
Write an equation in point-slope form and slope-intercept form for
each line.
the line passes through (4, 7), slope = 2
Answers
Answer: y=2x-1
Step-by-step explanation:
Equation of a line that passes through (a,b) and have slope m is given by :-
[tex](y-b)=m(x-a)[/tex] [point slope form]
Given, Point = (4,7) , m= 2
Equation in point slope form : [tex](y-7)=2(x-4)[/tex]
To write in slope intercept form (y=mx+c) , we need to simplify it
[tex]y-7= 2x-8\\\\\Rightarrow\ y-2x=-8+7\\\\\Rightarrow\ y-2x=-1\\\\\Rightarrow\ y=2x-1[/tex]
Hence, y=2x-1
what does 100+100 equal
Answers
Answer:
100+100=200 it's an mathmatecial answer
What is the equation for slope -2,point (-1,4) in y=Mx+b form
Answers
Answer:
y=-2×+2
Step-by-step explanation:
Hope this helped you out and sorry if it is wrong!
What is the value of sin(80%)cos(20°) - cos(80°)sin(20°)?
Answers
Answer:
[tex]\frac{\sqrt{3} }{2}[/tex]
Step-by-step explanation:
edge 2020
The value of sin(80) cos(20°) - cos(80°) sin(20°)= √3/2
What is Trigonometry?Trigonometry the area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations.
Given:
sin(80) cos(20°) - cos(80°) sin(20°)
Using Trigonometric identity
sin ( A- B) = sin A cos B - cos A sin B
So, sin(80) cos(20°) - cos(80°) sin(20°)
= sin (80 - 20)
= sin 60
= √3/2
Hence, sin(80) cos(20°) - cos(80°) sin(20°)= √3/2
Learn more about trigonometry here:
https://brainly.com/question/26719838
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The box plots show the weights, in pounds, of animals at two different zoos,
Animals in City Zoo
120 125 130 135 140 145 150 155 160 165 170
Animals in Country Zoo
What is the difference between the median weights of the animals in City Zoo and in Country Zoo in pounds
Answers
Answer:
it is 10 pounds
Step-by-step explanation:
Please help!!! ASAP
Answers
Step-by-step explanation:
19,800 is your answer because you want to subtract the number 14 and divide 14,900 plus 3,309
Which inequality can be used to represent this problem? A company spent $15,000 developing a new graffiti repelling paint. The company makes $10 on the sale of each gallon of paint after subtracting manufacturing costs. How many gallons, x, will they need to sell to have a profit of at least $50,000?
A 10x — 15000 ≥ 50000
B 10x — 15000 > 50000
C 10x + 50000 > 15000
D 10x + 50000 ≥ 15000
Answers
Answer:
The correct answer is:
Option A: A 10x — 15000 ≥ 50000
Step-by-step explanation:
Given that the total cost of manufacturing by the company is $15000.
Let x be the number of gallons the company sells.
It is also mentioned that the company earns $10 on each gallon.
So the total profit will be the the difference of the selling cost of gallons and manufacturing cost
Mathematically,
[tex]10x-15000[/tex]
Now it is mentioned that the profit should be at least 50000 dollars which means the profit can be minimally 50000 and also can be greater than it so
[tex]10x-15000 \geq 50000[/tex]
The number of gallons can be found by solving the obtained inequality.
Hence,
The correct answer is:
Option A: A 10x — 15000 ≥ 50000
Which expressions have a value of 60 when h=3? Choose two correct answers.
Group of answer choices
1....(h+1)^3 - 4
2.....(4h)^2 + 36
3....4h^2+ 24
Answers
Answer:
(1) & (3)
Step-by-step explanation:
Given
List of options
Required
Select which is equal to 60 when h = 3
To do this, we simply substitute 3 for h in all of the options.
1.
[tex](h + 1)^3 - 4[/tex]
[tex](3 + 1)^3 - 4[/tex]
[tex]4^3 - 4[/tex]
[tex]64 - 4[/tex]
[tex]60[/tex]
Hence:
[tex](h + 1)^3 - 4= 60[/tex]
2.
[tex](4h)^2 + 36[/tex]
[tex](4*3)^2 + 36[/tex]
[tex](12)^2 + 36[/tex]
[tex]144 + 36[/tex]
[tex]180[/tex]
Hence:
[tex](4h)^2 + 36=180[/tex]
3.
[tex]4h^2 + 24[/tex]
[tex]4*3^2 + 24[/tex]
[tex]4 * 9 + 24[/tex]
[tex]36 + 24[/tex]
[tex]60[/tex]
Hence:
[tex]4h^2 + 24 = 60[/tex]
If it is 2 o'clock and you take away 25 minutes, what time would it be?
Answers
Answer:
1:35
Step-by-step explanation:
Answer:
It will be 1:35
Step-by-step explanation:
2:00 - 25 = 1:35.
At Mr. McNeely's farm, there were 75 sheep and 60 cows. What is the ratio of the number of cows to the number of sheep at Mr. McNeely's farm? 5/4 4/9 5/9 or 4/5
Answers
Answer:
5/4
Step-by-step explanation:
At McNeely farm there are 75 sheep and 60 cow
Therefore the number of ratio of cow to sheep can be calculated as follows
= 75/60
=5/4
Answer:
4/5
Step-by-step explanation:
Complete the table below to find solutions to the linear equation y=−4x−12.
Answers
Answer:
y= -4x-12
-4x
y= -12
Step-by-step explanation:
So Y is equal to -4x minus 12. You subtract the -4x by itself that will leave you with zero. And then you bring down Y and -12, and it will say that Y is equal to -12.
Answer:
X Y
0 -12
3 -24
-3 0
Step-by-step explanation:
Help please I’ll mark brailiest
Answers
Answer:
DB,AB,AD,CD,AC
Martin and Sue are collecting clothes for a clothing drive. Sue collected 1/5 as many clothes as Martin did. If Martin collected 2 1/2 bags of clothes, how many bags of clothes did Sue collect?
Answers
Answer:
Sue collected 1/2 bags of clothes.
Step-by-step explanation:
Fractions
Let's solve the problem from end to beginning.
Martin collected 2 1/2 bags of clothes for a clothing drive. This mixed fraction can be expressed as:
[tex]2\frac{1}{2}= 2+\frac{1}{2}=\frac{5}{2}[/tex]
Sue collected 1/5 as many clothes as Martin did. This means she collected:
[tex]\frac{1}{5}\cdot \frac{5}{2}[/tex]
Multiplying:
[tex]\frac{1}{5}\cdot \frac{5}{2}=\frac{1}{2}[/tex]
Sue collected 1/2 bags of clothes.
Need help please now
Answers
Answer:
Step-by-step explanation:
m = - 5
i need help asap math sucks and is hard
8th grade math
Answers
Answer:
Slope = [tex]\frac{-1}{3}[/tex]
Step-by-step explanation:
(x₁ , y₁) = (-9 , -4) & (x₂ ,y₂) = (-3, -6)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{-6-[-4]}{-3-[-9]}\\\\= \frac{-6+4}{-3+9}\\\\= \frac{-2}{6}\\\\= \frac{-1}{3}[/tex]
Convert 68 from hexadecimal to binary.
Answers
Answer:
68 = 01101000 (binary)
Answer:
1101000 Sorry i didnt put the right value here now its binary
Step-by-step explanation:
Hex 68 to decimal explained:
The value of HEX 68 in decimal is 104.
The value of HEX 68 in binary is 1101000.
8 8 X 160 = 8
6 6 X 161 = 96
HEX 68 = 104
the binary value is: 1101000
HOPE THIS HELPS!
PLEASE MARK BRAINLIEST