Using quadratic function concepts, it is found that:
1) The equation is [tex]y = -0.08x^2 + 4x[/tex]
2) The minimum distance is of 2.64 yards, and the maximum is of 47.36 yards.
A quadratic equation has the following format:
[tex]y = ax^2 + bx + c[/tex]
In this problem:
The ball was kicked from the ground, thus [tex]y(0) = 0[/tex], which means that c = 0.Item 1:
The vertex is: [tex]V(x_v,y_v)[/tex], in which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]
In this problem, it is (25,50). Thus:
[tex]-\frac{b}{2a} = 25[/tex]
[tex]-b = 50a[/tex]
[tex]b = -50a[/tex]
[tex]-\frac{b^2 - 4ac}{4a} = 50[/tex]
[tex]-b^2 = 200a[/tex]
[tex]-(50a)^2 = 200a[/tex]
[tex]-2500a^2 - 200a = 0[/tex]
[tex]200a(-12.5a - 1) = 0[/tex]
Then, as [tex]a \neq 0[/tex]
[tex]a = -\frac{1}{12.5} = -0.08[/tex]
[tex]b = -50a = -50(-0.08) = 4[/tex]
Thus, the equation, in standard form, is:
[tex]y = -0.08x^2 + 4x[/tex]
Item 2:
The distances are the values of x for which:
[tex]y = 10[/tex]
Then
[tex]-0.08x^2 + 4x = 10[/tex]
[tex]-0.08x^2 + 4x - 10 = 0[/tex]
Which is a quadratic equation with [tex]a = -0.08, b = 4, c = -10[/tex]. Then:
[tex]\Delta = 4^2 - 4(-0.08)(-10) = 12.8[/tex]
[tex]x_{1} = \frac{-4 + \sqrt{12.8}}{2(-0.08)} = 2.64[/tex]
[tex]x_{2} = \frac{-4 - \sqrt{12.8}}{2(-0.08)} = 47.36[/tex]
The minimum distance is of 2.64 yards, and the maximum is of 47.36 yards.
A similar problem is given at https://brainly.com/question/24713268
Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.
(Please show your work)
___________
[tex] \: [/tex]
[tex]\boxed{ \rm{answer \: by \: { \boxed{ \rm{☆HayabusaBrainly}}}}}[/tex]
Step by step :x² = (14,4)² - 9²
x² = 207,36 - 81
x² = 126,36
x = 11,2
Twenty students scored the following marks in a history test: 5, 2, 5, 3, 1, 6, 2, 2, 3, 4, 2, 1, 2, 2, 4, 3, 2, 2, 2, 3. What is the mode of distribution. What is the median and mean
Answers:
Mode = 2Median = 2Mean = 2.8===================================================
Work Shown:
Original set = {5, 2, 5, 3, 1, 6, 2, 2, 3, 4, 2, 1, 2, 2, 4, 3, 2, 2, 2, 3}
Sorted set = {1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6}
Do not toss out the duplicates.
The most occurring or most frequent value is 2, so this is the mode.
---------------------------
To find the median, we divide the n = 20 item set into two parts
n/2 = 10
So we'll count to the 10th slot to get to the number "2", which is the second to last "2" in the sorted list shown above.
The number just after this is also "2" in the 11th slot. Average these two values to get (2+2)/2 = 4/2 = 2
The median is 2.
----------------------------
To find the mean, we need to first add up all the data values.
1+1+2+2+2+2+2+2+2+2+2+3+3+3+3+4+4+5+5+6 = 56
Then divide this over n = 20 to get 56/20 = 2.8
The mean is 2.8
The mean being larger than the median tells us we have an outlier that is larger than the main cluster. Those outliers are 5 and 6.
What is the end of your proof? (What are you proving?)
Answer
with
Step-by-step explanation:
Statement Reasons
1.∠1 ≅ 4 Given
2.∠1 = ∠2 Being Vertically opposite angles.
3.∠4 = ∠3 Being Vertically opposite angles.
4.∠2 = 3 From Statement no 2 & 3, Transitive property.
5.∠2 ≅ 3 From Statement 4
Proved.
A woman has a square garden for strawberry planting.2 of the sides have fencing.The fencing is 40m in length.Find the maximum possible area.
Answer:
The maximum possible area is 1,600 m.
Step-by-step explanation:
You already have the two sides so you just multiply 40×40 and that gives you the area.
Please actually help, and don't say random words to get the points
Answer: X=3 Y=2
Step-by-step explanation: just looked it up
What could be the possible one's digit of the square root of 3721 ?
3 , 4
1 , 9
6 , 7
7 , 8
Answer:
6,1 because 61's square root is 3721
HELPPPPP PLEASEEEEEEEEEEE
Answer:
60 students are divided into equal groups of 5 student each.
Groups of 5 students per group totaled up to 60 students.
The quotient in both expression is 60:5 = 12 students per group.
Step-by-step explanation:
The ratio expression is a way of expressing the division of numerator by a denominator.
Here,
The total number of students is the numerator = 60
The denominator is the number of students per group = 5
Hence, the quotient is the value of the divison obtained which is (60/2) = 12
Therefore, there are 12 groups of 5 students.
please somebody answer this last one !!!!!!
Hope this helps :)
need more help just comment :) :)
A bouncy ball is dropped. The function h(n)=300(3/4)^n−1 models the maximum height of the ball, in centimeters, after its nth bounce.
Select EACH true statement about the scenario.
[] The function represents a geometric sequence.
[] The first term in the sequence is 300.
[] The height of the ball after the first bounce is 300 cm.
[] The ball is dropped from a height of 300 cm.
*Multiple Choice*
The true statements about the scenario are;
The function represents a geometric sequence. The first term in the sequence is 300.The standard form of a geometric sequence is expressed as:
[tex]Tn = ar^{n-1}[/tex]
a is the first term
r is the common ratio
n is the number of terms
Given the expression [tex]h(n)=300(\frac{3}{4} )^{n-1}[/tex]
Compare and contrast
a = 300
This shows that the first term of the sequence is 300.
Also, a function represents a geometric sequence
Hence the true statements about the scenario are;
The function represents a geometric sequence. The first term in the sequence is 300.Learn more here: https://brainly.com/question/9300199
The diagonals of a rhombus measure 16 cm and 30 cm .find its perimeter ( in easy way)?
Answer:
68 cmStep-by-step explanation:
Let ABCD be a rhombus, all sides of the rhombus have equal length and its diagonal AC and BD are intersecting each other at a point O.
As we know that the diagonals in the rhombus bisect each other at 90°.
So, AO can be written as (AC/2)
= 16/2
= 8 cm
And, DO can be written as (BD/2)
= 30/2
= 15 cm
Then, consider the triangle AOD and apply Pythagoras theorem,
AD2 = AO2 + DO2
AD2 = 82 + 152
AD2 = 64 + 225
AD2 = 289
AD = √289
AD = 17 cm
Hence, the length of each side of the rhombus is 17 cm
Now,
The perimeter of rhombus = 4 × side of the rhombus
= 4 × 17
= 68 cm
Therefore, the perimeter of the rhombus is 68 cm.
Lucinda spent $95.40 on 4 video games. If each game was the same price, how much did he pay for each
Answer:
If they all cost the same price they should all cost $23.85
What is the answer to -9u for u=-5
Answer:
-9 × u
= -9 × -5
= 45 [(-) × (-) = (+)]
Step-by-step explanation:
brainliest plz
Answer:
45
Step-by-step explanation:
-9(-5)=45
please mark me brainliest
Need help ASAP plz help
- (05.03)
An equation is shown below:
3/2x+ 7/2=2^x
What is the solution to the equation? (4 points)
x = 1
x = 3
x = 5
X = 8
Answer: x = 3
Step-by-step explanation:
Find the missing length to the nearest tenth. Look at the shape.
Answer: [tex]4\sqrt{5}[/tex]/9.0
Step-by-step explanation:
Simple way: Pythagorean Theorem
[tex]a^{2} +b^{2} =c^{2}[/tex]
C being hypotenuse. A and B are bases that are interchangeable.
In this question, you are missing the hypotenuse.
a= 8, b=4 c=?
[tex]8^{2}+4^{2}=c^{2}[/tex]
[tex]64+16=c^{2}[/tex]
To get rid of [tex]c^{2}[/tex]. Square both sides.
[tex]\sqrt{64+16} =\sqrt{c^{2} }[/tex]
[tex]\sqrt{80}=c[/tex]
Simplify [tex]\sqrt{80}[/tex]
[tex]\sqrt{4*4*5} =4\sqrt{5}[/tex]
or 9.0
what is the recurring decimal of 0.68
Answer:
0.68 repeating as a fraction
0.68 repeating as a fraction
When x^3 + kx^2 − 4x + 2 is divided by x + 2 the remainder is 26, find k.
Answer:
k = 6
Step-by-step explanation:
I will Brainlist Who can Answer this 4 Question Math
Match the situation with the corresponding linear system. Write the letter of your answer.
Answer:
6) B
7) D
8) C
9) A
Step by step explanation:
6) Brand A sold 12 notebooks
Brand B sold 28 notebooks
7)
8) 30 pieces of 100-peso bills
10 pieces of 50-peso bills
9) 4 packages have 2 pieces
6 packages have 3 pieces.
In a chemical reaction, Substance A reacts with Substance B and forms a new substance AB. The chemical equation for this reaction is A + B = AB where A and B are the reactants and AB is the product. If you add more and more of only Substance A, there will be
Answer:
More and more of product AB but limited to the amount of B
Step-by-step explanation:
Adding more of one substance which makes up the reactant will increase the number of product AB that will be obtained but limited by the amount of B.
The amount of reacting substances is directly proportional to the amount of product yield. This means that adding more and more of the substance which makes up the reactant increases the amount of atoms reacting to form a product.
Hence, adding more and more of only substance A will increase the product AB, however, the amount of B in the product will be limited.
Learn more :https://brainly.com/question/12373196
the pool at the apartment is 30 feet long 20 feet wide and five feet deep it has been filled to 4 feet how many more cubic inches does it need
Answer:
600 cubic feet
Step-by-step explanation:
HELP PLEASE!!
Write an equation in slope-intercept form for the
graph below:
Answer:
y=4x-3
Step-by-step explanation:
Step 1: plot a new graph cus this one is so hard to read. You know 2 points: (1,1) and (2,5)
Step 2: draw your line
Step 3: find your slope using RISE/RUN: 4/1
Step 4 find your y-int: -3
Hope that helps! Brainliest is appreciated
Saved
Question 11 (5 points)
What's 21-91 - 1-21?
O A) -20
B) 16
C) 20
D) -18
Any one know the answer I don’t know it
A rocket is fired upward from ground level with an initial velocity of 1600ft/sec . When will the rocket be above 1000ft? Show your work. Round your answer to the nearest tenths. Write the answer in set notation.
Answer:
{t: 0.6 < t < 99.4}.
Step-by-step explanation:
Use one of the equations of motion under gravity.
s = ut + 0.5gt^2 where s = distance, u = initial velocity, g = acceleration due to gravity and t = the time.
So we have:
1000 = 1600t + 0.5* -32*t^2 ( acc due to gravity is negative as we are acting against it).
16t^2 - 1600t + 1000 = 0
t = (1660 +/- sqrt(1600^2 - 4*16*1000) / 32
This gives t = 0.629 , 99.371 seconds.
So the time is above 0.6 seconds (to the nearest tenth) and before 99.4 seconds.
What is the change from -1 to 7
A line intersects the points
(8,-10) and (9, 4).
What is the slope of the line in
simplest form?
m = [?]
Answer: 14
Step-by-step explanation:
The s is equal to the change of y/change of x. That means you have to subtract 4 and -10, and the denominator is 9 minus 8. It looks like this:
m=4-(-10)/9-8
m=4+10/9-8
m=14/1
m= 14
A swift is a bird that can fly 3 times faster than a wolf can run. A swift can fly 120 miles per hour. Which equation would be used to find how fast w, a wolf can run
120 x w = 3w
W x 3 =120
3 + w = 120
120 + 3 = 3
Answer:
It would be "W x 3 = 120"
Step-by-step explanation:
Why? Well, since a swift could run 120 miles an hour, that would be a necessity in the problem. It would be needed to find out how fast the wolf ran, but, it cannot be the answer since we are trying to find out "how fast the wolf ran per hour". Right? No. Basically, you need to divide 120 by 3, which is 40. But which equals 40? None. Yes, none. No, to two answers. Why? Because you need to divide, so, the answer could be multiplication, but the opposite. You know if you know... Anyways, 120 x w = 3w is wrong due to the fact that it has no sign of division and the answer is way too large (I tried). 3 + w = 120 is definitely wrong. Why add? 3 + 40 is not 120. It's 43. Also, 120 + 3 is not 3, it's "123". So, the only answer left is "W x 3 = 120". But, how do we know that it's right? Well, think about it backwards. The swift is 3 times faster, so, the wolf times that 3 times faster is 120. And that is exactly what this problem is. By doing the problem backwards, we could find out that a wolf can run 40 miles per hour. Basically, 120 divided by 3, how much faster it is than a wolf, is 40. So, we could find out that a wolf could run 40 miles per hour.
Final Answer: W x 3 = 120
Answer:
The answer will be w×3=120
what is the x-intercept of the line 6x-3y=24
PLSSS HLEPP ME OUTT ITS URGENTTTT
Find each measure! Please please help me!!! 40 points!! No files!!!
Answer:
44º
44º
136º
22º
Step-by-step explanation:
If you want i can explain in the comments.
The figure is a triangle that is divided into two parts. Angle A and angle E are right angles and the measure of angle F is 30 degrees. What is the measure of angle C? Complete the steps below to solve the problem using equations.
Part A
Let the variable g represent the measurement of angle G. Write and equation that you can use to solve for g.
Part B
What is the measurement of angle G?
Part C
Let the variable c represent the measurement of angle C. Use the measurement of angle G to write an equation that you can use to solve for c.
Part D
What is the measurement of angle C?
Answer:
Part A) g + 30 + 90 = 180
Part B) G = 60 degrees
Part C) c + 60 = 180
Part D) C = 120 degrees
Step-by-step explanation:
Part A: If angle F is 30 degrees and E is 90, then we can easily find G using the fact that the sum of a triangle is 180 degrees.
g + f + e = 180
g + 30 + 90 = 180
Part B: g + 30 + 90 = 180
g + 120 = 180
g = 60
Part C: Since G and C are on the same line and just separated by another line, we can use supplementary angles to find C.
c + g = 180
c + 60 = 180
Part D: c + 60 = 180
c = 120
Answer:
A:The sum of the angle measurements in a triangle is 180°. If e, f, and g are the measurements of angles E, F, and G, respectively, e + f + g = 180°.
Angle E is a right angle, so e is 90°. From the given information, f is 30°. Substitute the values of e and f in the equation to solve for g : 90° + 30° + g = 180°.
B:Solve the equation from Part A to find the measurement of angle G:
90° + 30° + g
180° – 90° – 30°
Angle G measures 60°.
C: Angle C and angle G are supplementary angles. The sum of supplementary angles is 180°. If c and g are the measurements of angles C and G, respectively, then c + g = 180°.
The value of g is 60°. Substitute 60° in the equation to get an equation in terms of c:
c + 60° = 180°.
D:Solve the equation from Part C to find the measurement of angle C:
c + 60°
= 180°
c
= 180° – 60°
c
= 120°.
Angle C measures 120°.
the exact answer from edmentum
Step-by-step explanation: