The equation that models the path of the ball is y = -0.05·x² + 5·x.
Given,
The distance where the football landed from where it was kicked = 100 feet
The maximum height that the football reached = 125 feet
We have to write an equation that models the path of the ball while it was in the air.
The path may be parabola.
So, equation is like:
y = a·(x - h)² + k
Where;
(h, k) = The coordinate of the vertex (which is the coordinates of the highest point reached by the ball)
Therefore, taking the x-coordinate of the highest point reached by the ball as midpoint of the horizontal distance moved by the ball, we have;
The x-coordinate of the midpoint of the horizontal distance moved by the ball = (50, 0)
We have;
The coordinate of the highest point reached by the ball = (50, 125)
Therefore;
(h, k) = (50, 125)
Substituting the above values in the equation of the parabola gives;
y = a·(x - 50)² + 125
At x = 100, y = 0, which gives;
0 = a·(100 - 50)² + 125 = a·2500 + 125
0 = a·2500 + 125
a = -125/2500 = -0.05
Therefore, we have;
y = a·(x - h)² + k = y = -0.05 × (x - 50)² + 125 = -0.05·x² + 5·x - 125 + 125
y = -0.05·x² + 5·x - 125 + 125 = -0.05·x² + 5·x
y = -0.05·x² + 5·x
The equation that models the path of the ball is y = -0.05·x² + 5·x.
Learn more about equation here:
https://brainly.com/question/18733124
#SPJ1
Find the measure of the numbered angles
Hello!
This is a parallelogram. It is a quadrilateral with two pairs of parallel sides. Here, the opposite angles are alternate, that is, they have togheter 180°.
Rhombus
This is a rhombus. It is a quadrilateral whose four sides all have the same length. Here, the diagonals of a rhombus intersect at equal angles.
A rhombus has opposite angles equal and the figure formed by joining the midpoints of the sides of a rhombus is a rectangle, and vice versa. It has an inscribed circle.
Good luck:)
What is the slope of a line parallel to the line whose equation is 4x−y=−4. Fully simplify your answer.
Answer:
m=4
Step-by-step explanation:
4x-y=4
y=4x+4
Use the slope intercept form
y=mx+b
y=y
4=m (The slope)
x=x
b=the y intercept
What is the complex conjugate of -2 + 3i?
You burn 20 calories per minute biking for x minutes and 10 calories per minute walking for y minutes. You can spend a total of 90 minutes biking and walking and burn 1300 calories.
A.)write a system of equations to determine how much time you spend on each exercise.
B.) how many minutes did you spend biking?
simplify (csc x)^2 - 1
Answer:
Step-by-step explanation:
\((cscx)^2-1=\frac{1}{sin^2 x} -1\\=\frac{1-sin^2x}{sin^2x} \\=\frac{cos^2x}{sin^2x} \\=(cotx)^2\)
The value of the Australian dolar (A$) today is $0.73. Yesterday, the value of the Australia dollar was $0.69.
The Australian dollar _______ by ______ %.
a.
appreciated; 5.80
b.
appreciated; 5.48
c.
depreciated; 5.80
d.
depreciated; 4.00
This indicates that the Australian dollar appreciated by 5.80%. the correct answer is (a) appreciated; 5.80.
To determine whether the Australian dollar appreciated or depreciated and by what percentage, we can calculate the percentage change in value between today and yesterday.
The formula for calculating the percentage change is:
Percentage Change = (New Value - Old Value) / Old Value * 100
Using this formula, we can calculate the percentage change:
Percentage Change = (0.73 - 0.69) / 0.69 * 100
Percentage Change = 0.04 / 0.69 * 100
Percentage Change ≈ 5.80
The percentage change is approximately 5.80%. This indicates that the Australian dollar appreciated by 5.80%.
Therefore, the correct answer is (a) appreciated; 5.80.
Learn more about Percentage Change here
https://brainly.com/question/14801224
#SPJ4
Researchers were interested in the patterns of alcohol consumption for teenage recorded the number of alcoholic drinks consumed over the previous week for a teenage boys and produced the following SPSS output. Use the following SPSS complete the following description of the distribution of number of drinks consu that a histogram would normally be included with this description) The distribution of number of alcoholic drinks consumed in the past week in a Select teenage boys is displayed in Figure 1. The distrit Select skewed with 50% of the boys consuming Select drinks or less. Typically the boys consumed bety drinks in the past week, with half of values falling [Select this range Hong Dev N20 number of alcoholic drinkstest week
The distribution is positively skewed with 50% of the boys consuming the median number of drinks or less.
Researchers were interested in the patterns of alcohol consumption for teenage boys and recorded the number of alcoholic drinks consumed over the previous week. They analyzed the data using SPSS and found that the distribution of the number of drinks consumed was skewed. A histogram would normally be included with this description to illustrate the distribution.
The distribution of the number of alcoholic drinks consumed in the past week in a select group of teenage boys is displayed in Figure 1. The distribution is skewed, with 50% of the boys consuming 2 drinks or less. Typically, the boys consumed between 1 and 5 drinks in the past week, with half of the values falling in this range. The standard deviation of the number of alcoholic drinks consumed was 2.0, based on a sample size of 20.
The distribution of the number of alcoholic drinks consumed in the past week among a sample of teenage boys is displayed in Figure 1. The distribution is positively skewed with 50% of the boys consuming the median number of drinks or less. Typically, the boys consumed between the first quartile (Q1) and third quartile (Q3) drinks in the past week, with half of the values falling within this interquartile range.
Learn more about histogram at: brainly.com/question/30664111
#SPJ11
Explain why you need to vertically align the decimal points when summing decimal numbers.
Answer: It is irrelevant if multiplying or dividing decimal numbers. For addition and subtraction it is not sufficient: you need to line up the decimal points as well as the digits according to their place values. If you intend to simply align the decimal points then you may as well not bother.
Step-by-step explanation:
Determine if the triangles can be proved congruent, if possible, by sss, sas, asa, aas, or hl.
Each of the triangles can be proved congruent based on the following postulates;
Congruent by AAS.Congruent by SSS Congruence TheoremNot congruentCongruent by HL.Congruent by SAS.Congruent by ASA.What are the properties of similar triangles?In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Furthermore, the lengths of three (3) pairs of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.
Based on the congruence similarity theorem listed above, we can logically deduce that the triangles are both congruent.
Read more on triangle here: brainly.com/question/9858556
#SPJ4
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Determine whether each of the statements are true or false.1.) There exists a function f such that f(x) < 0, f '(x) > 0, and f ''(x) < 0 for all x. True or False.2.) If f '(x) exists and is nonzero for all x, then f(10) ≠ f(0). True or False.
1. True. This statement is true because it is possible for a function to have a negative value, positive derivative, and negative second derivative over all x values.
2. True. This is because the derivative of a function is the rate of change of the function.
1. This kind of function has an example in f(x) = x^3 - 3x^2. This function has a first derivative off'(x) = 3x^2 - 6x that is positive for all x values, a second derivative of f''(x) = 6x - 6 that is negative for all x values, and is negative for all x values.
2. The rate of change of the function is always non-zero if the derivative is non zero for all x, and the value of the function at any two locations will not be the same.
Hence, if f '(x) exists and is nonzero for every x, then f(10) ≠ f(0). Consider the function f(x) = x2 as an illustration of this. This function's derivative with respect to x is given by the expression f '(x) = 2x, which is non zero for every x.
As a result, f(10) = 102 = 100 and f(0) = 0, which are clearly not equal.
To learn more about derivative visit:
https://brainly.com/question/23819325
#SPJ4
Plot the points in a coordinate plane. Then determine whether AB and CD
are congruent
A(-2, 1), B(2, 1), C(3, 2), D(3, -2).
Plz help ASAP
Answer:
need more info bro
Step-by-step explanation:
Find the center and radius for the circle defined by the equation: x2+y2+1/2x-2y-5=0.
x²+y²+1/2x-2y-5=0
x²+1/2x+y²-2y=5
x²+1/2x+1/16+y²-2y+1= 5+1/16+1
(x+1/4)²+(y-1)²= 6 + 1/16
(x+1/4)²+(y-1)²= 16/16 +1/16
(x+1/4)²+(y-1)²= 17/16
(x+1/4)²+(y-1)²= \( (\sqrt{ \frac{17}{16} } )^{2} \)
(x+1/4)²+(y-1)²= \(( \frac{ \sqrt{17} }{4} ) ^{2} \)
-> center of the circle= M(1/4 , -1)
-> radius= \( \frac{ \sqrt{17} }{4} \)
Thomas bought 120 whistles, 168 yo-yos and 192 tops. He packed an equal amount of items in each bag. A) What is the maximum number of bag that he can get?
Thomas can pack the items into a maximum of 20 bags, with each bag containing 24 items after calculated with greatest common divisor.
To find the maximum number of bags Thomas can pack, we need to find the greatest common divisor (GCD) of 120, 168, and 192. The GCD will represent the maximum number of items that can be packed into each bag.
To find the GCD, we can use the Euclidean algorithm. First, we find the GCD of 120 and 168:
168 = 1 * 120 + 48
120 = 2 * 48 + 24
48 = 2 * 24 + 0
Therefore, the GCD of 120 and 168 is 24.
Next, we find the GCD of 24 and 192:192 = 8 * 24 + 0
Therefore, the GCD of 120, 168, and 192 is 24.
So, Thomas can pack 24 items into each bag. To find the maximum number of bags he can get, we divide the total number of items by 24:
Total number of items = 120 + 168 + 192 = 480
Number of bags = 480 / 24 = 20
Therefore, Thomas can get a maximum of 20 bags.
To learn more about Euclidean algorithm Click here:
brainly.com/question/13266751
#SPJ4
Quick algebra question 15 points and will mark brainliest if correct
Answer:
I belive it would be c
Step-by-step explanation:
because if you read the question it says the lowest point altho they are equale it still makes sence to put c
P(Z≤b)=0.0311 b ? a. −1.87 b. −1.86 c. −1.8 d. −1.865
The answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.
In this scenario, P(Z ≤ b) represents the cumulative probability of a standard normal distribution up to the value of b. To find the corresponding value of b, we need to find the z-score that corresponds to a cumulative probability of 0.0311.
By looking up the z-table or using a statistical calculator, we can find that the z-score corresponding to a cumulative probability of 0.0311 is approximately -1.865.
Therefore, the answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.
Learn more about probability:
https://brainly.com/question/31828911
#SPJ11
can someone help with question 19
Answer:
48. 192
Step-by-step explanation:
In order to get from 3/4 to 3/16, one way would be to divide by 4. Another way is to multiply 3/4 by 1/4.
You can test whether multiplying by 4 works by multiplying 3/4 by 4 and 3 by 4.
When 3/4 is multiplied by 4, it would equal 12/3 which will simplify to 3. This can be done again with 3*4=12.
So the answer would be 12*4 = 48 and 48*4 = 192.
Solve for x.
-1/5 (x - 4) = -2
Enter your answer in the box.
x = ________
Answer: x=14
Step-by-step explanation:Simplify both sides of the equation(Distribute),Subtract 4/5 from both sides.Multiply both sides by 5/(-1).
The cone of the volcano has a height of 418 meters and a diameter of 434 meters. Find the volume of the cone. Round your answer to the nearest hundred thousand. Use 3.14 for π.
First, we need to find the radius of the cone. The diameter is given as 434 meters, so the radius is half of that:
radius = 434/2 = 217 meters
Next, we can use the formula for the volume of a cone:
V = (1/3)πr^2h
where r is the radius and h is the height.
Plugging in the values we have:
V = (1/3)π(217)^2(418)
V ≈ 41,796,778.5
Rounding to the nearest hundred thousand, we get:
V ≈ 41,800,000
Therefore, the volume of the cone is approximately 41,800,000 cubic meters.
At Just T-Shirts, tees that normally cost $20 are on sale at 25% off. On tees left over from last year, the store is taking another 30% off. What is the cost of a tee left over from last year? Draw a plan similar to the plan on the previous page to show your work.
The cost of a tee left over from last year is $10.50.
How to calculate the percentage discount?Subtract the final price from the original price then Divide this number by the original price. Finally, multiply the result by 100. You've obtained a discount in percentages.
% discount = 100 × (original price - discounted price) / original price
If the regular price of a t-shirt is $20 and it's on sale at 25% off, then the sale price is:
$20 - (25% x $20) = $20 - $5 = $15
If the leftover t-shirts are discounted an additional 30% off the sale price of $15, then the final price is:
$15 - (30% x $15) = $15 - $4.50 = $10.50
Therefore, the cost of a tee left over from last year is $10.50.
To learn more about the percentage discount click here:
https://brainly.com/question/16524608
#SPJ1
Please help me! thank you
Suppose an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t)=-16t^2+48t+120. Find the average velocity from t=2 to t=4.
Type your answer as a number with no units.
The average velocity from t = 2s to t = 4s would be - 48 ft/s.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.
Average velocity
Average rate of change of velocity with time is called average velocity. Mathematically -
v{avg.} = Δx/Δt .... Eq { 1 }
Δx = x(4) - x(2)
Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}
Δx = - 96
Δt = 4 - 2 = 2
So -
v{avg.} = Δx/Δt = -96/2 = - 48 ft/s
Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.
To solve more questions on functions, visit the link below-
brainly.com/question/17613163
#SPJ1
20 points!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer this please.
Answer:
the answer is 126 or B
Step-by-step explanation:
30 + 30= 60 so 60 + 12= 72 then 72 + 12= 84 after that you add 84 + 36 = 120 so finally you add 120 + 6=126 so 126 is your answer.
Brainliest if you liked the answer.
Gene says that -2 is less than -2.25. Is he correct? Explain why or why not.
Answer:
No
Step-by-step explanation:
-2 is closer to zero than -2.25, which means -2 is greater than -2.25
Answer:
wrong the lower you go the less the nember is.
Can you find the slope and type the correct code?
If p=12 and q=24, evaluate the following expression:p+q/4
Answer:
The answer is 18
Step-by-step explanation:
p+q/4=12+24/4
Since we evaluate the division first: 12+6=18
Thus, the answer is 18
P(Z < -1.02) =0.11510.15390.84610.8849
The probability of a z-value less than -1.02 is similar to getting the area to the left of z = -1.02 in a normal curve.
Using the standard normal distribution table, the area to the left of z = -1.02 is 0.1539. Therefore, P(Z < -1.02) = 0.1539.
9.- Suma de fuerzas
4
45N + SON + 25N
4
4
127N 200N + 1250N
4
1
355N + 40N + 30N + 20N
Answer:
multiply
Step-by-step explanation:
2345567 in the subtract 578431111
Where is the hole for the following function located?f (x) = startfraction x + 3 over (x minus 4) (x + 3) endfractionx = –3y = –3x = 3y = 3
The function f(x) = (x + 3) / ((x - 4)(x + 3)) has a hole at x = -3, where it is undefined due to division by zero. The function is defined for all other values of x.
To determine the location of the hole in the function, we need to identify the value of x where the function is undefined. In this case, the function has a factor of (x + 3) in both the numerator and the denominator. This means that the function is undefined when (x + 3) is equal to zero, as dividing by zero is not possible.
To find the value of x that makes (x + 3) equal to zero, we set (x + 3) = 0 and solve for x:
x + 3 = 0
x = -3
Therefore, the function f(x) has a hole at x = -3. At this point, the function is undefined, as dividing by zero is not allowed. The function is defined for all other values of x except x = -3.
Learn more about function here:
https://brainly.com/question/30721594
#SPJ11
suppose that s is a nonempty set of real numbers that is bounded. prove that infs~sups.
It is given that a set of real numbers s is non-empty and bounded. The objective is to prove that inf s ≤ sup s. This statement can be justified as below.
Firstly, as per the definition of bounded set, it is known that the set s has both lower and upper bounds. Thus, the infimum and supremum of s exist and are denoted as inf s and sup s, respectively.
Since s is non-empty and bounded, it can be observed that every element of the set s is greater than or equal to inf s and less than or equal to sup s.
Therefore, inf s is the greatest lower bound of s and sup s is the least upper bound of s, implying that inf s ≤ sup s. Hence, it is proven that inf s ≤ sup s for a non-empty set s of real numbers that is bounded.
To know more about non-empty visit:
https://brainly.com/question/1581607
#SPJ11
The definition of a circle uses the undefined term____a. Arcb. Linec. planed. Ray
Answer:
c. plane
Step-by-step explanation:
There are three terms generally considered to be undefined in geometry:- Point, Line, Plane.
A circle is the set of all points in a plane the same distance from a given points (i.e center of the circle)
Select the correct difference.
5 d2 + 4 d - 3 less 2 d2 - 3 d + 4
7 d2 + 7 d - 7
3 d2 - 7 d - 7
3 d2 + 7 d - 7
7 d2 + d + 1
Answer:
+ 7 d - 7
7 d2 + d + 1
Step-by-step explanation:
+ 7 d - 7
7 d2 + d + 1