The quadratic function to represent the given situation is y=-(1/312)x²+x+3
A quadratic function is of the form y=g(x) where g(x) is a polynomial in x with degree 2.
The baseball is hit at a initial height of 3 feet. The baseball follows a path of a parabola.
Maximum height=81 feet
Distance from home plate =156 feet
So, (156,81) is the vertex of the parabolic path.
We know that when vertex is at (h,k) then the vertex form of the parabola is y=a(x-h)²+k
So the quadratic equation is of the form
y=a(x-156)²+81
Now the initial height is given as 3 feet.
So at x=0, y=3
Putting the values in the equation we get:
3=a(0-156)²+81
or, -78=a×156²
or, a=-(78÷156²)
or, a=-(1/312)
So the quadratic equation can be written as
y=-(1/312)(x-156)²+81
Simplifying we get : y=-(1/312)x²+x+3
The quadratic function to represent the path of the baseball is given by y=-(1/312)x²+x+3
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The CFO of International Hardware expects to invest $50,000 of the firm's funds in a long-term investment vehicle at the end of each year for the next five years. She expects that the company will earn 7% interest that will compound annually. What is the value of these funds at the end of the five-years
The future value of these funds at the end of the five-years is $287,536.95
What is the future value of an annuity?
The future value of annuity , which is a stream of level of cash flows of $50,000 each year is determined using the future value formula of an ordinary annuity bearing in mind that that investment for an ordinary annuity is made at the end of each year rather than at the beginning of each year
FV=PMT*(1+r)^N-1/r
FV=future value of the annuity=unknown
PMT=annual investment=$50,000
r=annual interest rate=7%
N=number of annual investments to be made over 5 years=5
FV=$50,000*(1+7%)^5-1/7%
FV=$50,000*(1.4025517307-1)/0.07
FV=$50,000*0.4025517307/0.07
FV=$287,536.95
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Evaluate 3x2+8x+8 when x=3.
Answer:
Step-by-step explanation: since X=3 replace X
3 (3)2 +8 (3)+8
18+24+8 =50
Zeke made $10,200 last year working at a fast food restaurant. How much did Zeke make per month?
Two travelers riding camels are lost in the desert, so they split up to try to find help. One traveler goes east, while the other goes north. The traveler going east goes 7 miles per hour faster than the traveler going north, and after 3 hours, they are 39 miles apart. How fast are the travelers going? Show your work.
Answer:
which one is a factor that effects temperature between Tanzania and Netherlands ?
A+B=C make B the subject
Answer:
C - A = B
Step-by-step explanation:
B is now what we are solving for.
Answer:
Flip the equation so B is the sum and also the subject.
Step-by-step explanation:
[tex]A - C = B[/tex]
Scrie numerele impare cuprinse între
695 și 707
Answer:
997
999
701
703
705
Sper că am ajutat <3
What is f_x (0,0) if
Hint: use Limit
[tex]f_x(0,0)[/tex] is the partial derivative of [tex]f[/tex] with respect to [tex]x[/tex] evaluated at the origin. By definition of derivative, this is the limit
[tex]\displaystyle f_x(0,0) = \lim_{x\to0} \frac{f(x,0) - f(0,0)}{x-0} = \lim_{x\to0} \frac{f(x,0)}x[/tex]
We have by definition of [tex]f[/tex],
[tex]f(x,0) = \dfrac{x^5}{x^4+0^4} = \dfrac{x^5}{x^4}[/tex]
so
[tex]\displaystyle f_x(0,0) = \lim_{x\to0} \frac{\frac{x^5}{x^4}}x = \lim_{x\to0} \frac{x^5}{x^5} = \lim_{x\to0} 1 = \boxed{1}[/tex]
The perimeter of a pool is 150 m. the rectangle at the right is a scale drawing of the pool. The length of each square on the grid represents 1 cm. draw another scale drawing of the pool using the scale 25 m to 2 cm. Explain why your drawing is accurate.
The dimensions of the another rectangle is 2 cm and 4 cm.
According to the statement
We have to find that the perimeter of another rectangle.
So, For this purpose, we know that the
The perimeter of a shape is defined as the total length of its boundary.
From the given information:
The perimeter of a pool is 150 m. the rectangle at the right is a scale drawing of the pool. The length of each square on the grid represents 1 cm. draw another scale drawing of the pool using the scale 25 m to 2 cm.
Then
From the given rectangle,
Length of the rectangle = 5 cm
Width of the rectangle = 10 cm
Ratio of length : width = 1 : 2
Perimeter of the rectangle = 2(l + b)= 150 cm
l + b = 75 -----(1)
Since, l : b = 1 : 2
l/b = 1/2
b = 2l ------(2)
From equations (1) and (2),
l + 2l = 75
3l = 75
l = 25 m
Width 'b' = 2(25) = 50 m
Now we've to draw a rectangle with a scale = 25 : 2
Therefore, multiplier factor = 25/l = 25/2
l = 2 cm
Similarly,
50/w = 25/2
w = 4 cm
Now we are able to draw a rectangle with length = 2 cm and width = 4 cm.
So, The dimensions of the another rectangle is 2 cm and 4 cm.
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help pls, the cut off part at the bottom is L
Answer:
∠ON = 5
Making even jumps, I was able to determine that angles O and N were 5 units apart.
Information given:∠LM is twice the length of ∠ON ∠LN = 7∠OP = 4If you need me to put it in radical form or have concerns about this, please inform me. Have a good day!
Determine whether the following procedure results in a binomial distribution or a distribution that
can be treated as binomial (by applying the 5% guideline for cumbersome calculations). If it is not
binomial and cannot be treated as binomial, identify at least one requirement that is not satisfied.
In a Pew Research Center survey of 150 subjects, the ages of the respondents are
recorded.
From the given parameters in the survey; It is not binomial because the probability of success does not remain the same in all trials.
How to identify a binomial distribution problem?
The conditions for a distribution to be called binomial distribution are as follows;
1. The number of observations n is fixed.
2. Each observation is independent.
3. Each observation represents one of two outcomes (either a success or failure).
4. The probability of success (p) is the same for each outcome.
Now, from the given question, we can see that the number of observations is fixed and that each observation is independent. However, we don't know the probability of success for each person and as such we can't call this a binomial distribution.
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Can you think of any other shapes that are always similar? If you can explain why they are always similar.
Answer:
Step-by-step explanation:
All you need is angles that are the same in each shape.
For example, all squares are similar. They all have 4 ninety degree angles.
All polygons with equal angles are similar. All regular hexagons have interior angles of 120 degrees. So all regular hexagons are similar.
All regular octagons are similar. All regular octagons (8 sides) have interior angles of 135 degrees.
To get more, just look up the names of all regular polygons from 3 to 10. I've given you three of them.
The graph of the parent function f(x) = x is translated to form the graph of g(x) = (x+3)³-4. The point (0, 0) on the
graph of f(x) corresponds to which point on the graph of g(x)?
Answer:
f(x) + n - shift a graph of f n units up
f(x) - n - shift a graph of f n units down
f(x + n) - shift a graph of f n units left
f(x - n) - shift a graph of f n units right.
f(x) = x³, g(x) = (x + 3)³ - 4 = f(x + 3) - 4
3 units left and 4 units down.
(x, y) → (x - 3, y - 4)
therefore
(0, 0) → (0 - 3, 0 - 4) = (-3, -4).
Answer: (-3, -4).
Step-by-step explanation:
hope it helpsssss
Skylar is the youngest of four siblings whose ages are consecutive integers. if the sum of their ages is 70, find skylars age
Answer: 16
Step-by-step explanation:
Let Skylar is x year old
Hence, they ages is (x+1), (x+2), (x+3)
Thus,
x+(x+1)+(x+2)+(x+3)=70
x+x+1+x+2+x+3=70
4x+6=70
4x+6-6=70-6
4x=64
Divide both parts of the equation by 4:
x=16
The age of Skylar is 16.
What is algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the ages of the siblings be x, x+1, x+2 and x+3.
and, the sum of the ages be 70.
So, x+ x+1 + x + 2 +x+ 3 = 70
4x + 6 = 70
4x = 70 - 6
4x = 64
x= 64/4
x = 16.
Then, the age of siblings be 16. 17, 18 and 19.
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chapter 8
2.Find the volume of each figure. Round your answers to the nearest hundredth, if necessary.
The volume of the given figure is 267.95 mi³.
What is the volume?The given object is a sphere. A sphere is a three-dimensional object that has all its surface points at equal distances from the center. A sphere is round in shape.
The volume of an object is the amount of space in the three-dimensional object. The radius of a sphere is a straight line from the circumference of the sphere to the center of the sphere.
Volume of a sphere = 4/3 × π × r³
Where:
π = pi = 22/7
r = radius = 4
4/3 x 22/7 x 4³ = 267.94667 mi³
267.95 mi³
To round off to the nearest hundredth, if the thousandth digit is equal to 5 or greater than 5, add 1 to the hundredth digit and change all the digits after the hundredth digit to 0.
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What is $20 for 8 bottles as a unit rate
Answer:
$2.50
Step-by-step explanation:
20 ÷ 8 = 2.50
Can someone please help with my question?
The required line representing the rise and the run of the line is created.
And the slope of the line in its simplest form is 9/-18.
Given a line is represented on the graph.
we need to create lines representing the rise and run of the line.
To find the slope of the line we need to determine the rise and run of the line.
The slope of a line is defined as the rise divided by the run, or the ratio of the rise to the run. It gives information about a line's slope in the coordinate plane. Finding the slope between two separate places is comparable to calculating the slope of a line.
The coordinates of the points are:
(9,0) = (x₁ , y₁)
(₋9 , 9) = (x₂ , y₂)
we know that slope (m) = rise/ run
rise = y₂ ₋ y₁
= 9 ₋ 0
= 9
run = x₂ ₋ x₁
= ₋9 ₋ 9
= ₋18
hence the slope is 9/₋18
The required slope of the line is 9/-18.
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Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
3,\, 12,\, 48,\, ...
3,12,48,...
This is
sequence and the
is equal to
.
The given sequence is an arithmetic sequence and the common difference is 4.
Given, the sequence is :
3,12,48
we need to determine the common difference.
common ratio = a₂/a₁
a₂/a₁ = 12/3
a₂/a₁ = 4
a₃/a₂ = 48/12
a₃/a₂ = 4
hence the common difference is 4.
Therefore, the common difference indicates arithmetic sequence.
There are two approaches to define an arithmetic sequence. It is a "series where the differences between every two succeeding terms are the identical" (or) In an arithmetic sequence, "each term is obtained by adding a fixed number (positive or negative or zero) to its preceding term."
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2. Choose Yes or No to tell if the Distributive
Property is being used.
2a. 4 x (2+3)=
4x244x3
2b. (4+5) x2 =
4x2+5X2
2c. 2x4=
2x (3+1)
2d. 7 x (5-2)=
7x5-7x2
O Yes No
O Yes O No
O Yes O No
O Yes O No
Answer: Yes
Step-by-step explanation:
Determine the value of expression one
5(x+2)-7 When X equals 4
Analyze the diagram below and answer the question that follows.
Which statement describes the shaded region in the Venn diagram?
The statement that describes the shaded region in the Venn diagram is (a) (P u Q)' n S
How to determine which statement describes the shaded region in the Venn diagram?The Venn diagram represents the given figure
On the Venn diagram, we can see that:
All region that contains set P and Q are not shaded
This means that
(P u Q)'
The only region that is shaded in the diagram is the region of set S
This is then represented as
(P u Q)' n S
Hence, the statement that describes the shaded region in the Venn diagram is (a) (P u Q)' n S
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Please help me I’m begging you
Answer: 6 : 3 = 8 : 4 = 1 : 2
Step-by-step explanation:
Here are 3 equivalent ratios
6 : 3 = 8 : 4 = 1 : 2
The musical last 42 minutes it ends at 159 pm what time did the musical start
Answer:
1:17 PM
Step-by-step explanation:
1:59 has 59 minutes
42 minutes is what we must subtract by to find the time of the musical, M
[tex]M = 59 - 42\\M = 17\\M = 1:17[/tex]
.
A gold coin is worth $800 per oz. A silver coin is worth $50 per oz. How many ounces of gold can I purchase if I have $5600?
10 ounces
4000 ounces
7 ounces
Not enough information
Answer:
7 oz.
Step-by-step explanation:
$800 x 7 = $5600.
Answer:
7 ounces
Step-by-step explanation:
5600/800=7
4x-3y=3
- 8x+6y=-6
solve for x and y
The system of equation 4x - 3y = 3and -8x + 6y = -6 has no solution as they are parallel lines.
What is system of equation?When two or more linear equations are there we call them a system of equations.
Given a system of equations 4x - 3y = 3...(i) and -8x + 6y = -6...(ii) this is solvable as the number of variables is not more than the number of equations.
Now to solve for x or y first we have to eliminate one of the varibales by any arithmetic operation.
By observing we conclude that if we multiply equation(i) by 2 and then add both of them the x variable will cancel out and we can solve for y which is
8x - 6y = 6
(+) -8x + 6y = -6
----------------------
As we can see here that both x and y are getting canceled therefore these two equations have no solution and hence they are parallel to each other(lines).
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What are the alternate exterior angle pairs in the picture below?
A. ∠1 and ∠7, ∠2 and ∠8
B. ∠1 and ∠8, ∠2 and ∠7
C. ∠1 and ∠2, ∠7 and ∠8
D. ∠1 and ∠3, ∠5 and ∠7
A. 1 and 7 and
2 and 8 alternate exteriora
Answer:
∠1 and ∠7, ∠2 and ∠8
Step-by-step explanation:
Alternate exterior angles are on the exterior of the lines and on opposite sides of the transversal.
1. find three consecutive integers such that twice the lease integer is 12 more than the greater integer.
2. The perimeter of a rectangle is 150 cm the length is 15cm greater than the width. Find all of the dimensions, please.
the sum of 15 and the product of 5 and z
Answer:
Step-by-step explanation: 15 divided by 5 is 3
so the answer is 3
Mario was asked by his teacher to express 33% in ratio, fraction, and decimal. Which of the following table do you think is an equivalent value of 33% expressed in a ratio, fraction, and decimal? Compute and solve a problem of Mario
The equivalent value of 33% expressed in a ratio, fraction, and decimal is 33 : 100, 33/100 and 0.33 respectively
Ratio, Fraction and decimal33%
In ratio:
33%
= 33 / 100
= 33 : 100
In fraction:
33%
= 33/100
In decimal:
33%
= 33/100
= 0.33
Therefore, the equivalent value of 33% expressed in a ratio, fraction, and decimal is 33 : 100, 33/100 and 0.33 respectively
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5. Write two numbers so that the value of the digit 9 in the second
number is 10 times the value of the digit 9 in the first number.
The two numbers with the value of 9 in the first digit being 10 times the value of 9 in the second digit are 98 and 9.
The first number will be 9 and the second number will be 98.
In the second number, the 9 is in the tens position which means that it has the value of 90.
In the first number, the value of 9 is simply 9.
therefore,90 is 10 times the value of 9 which means that 9 and 98 satisfy the requirements.
The “tens” digit is the digit in the second place to the left of the decimal point. The tens digit of 42936.875 is “3”. The “tenths” digit is the digit directly to the right of the decimal point.Each digit is a different place value. The left digit is the tens' place. It tells you that there are 8 tens. The last or right digit is the ones' place which is 4 in this example
In our decimal number system, the value of a digit depends on its place, or position, in the number. Each place has a value of 10 times the place to its right. A number in standard form is separated into groups of three digits using commas.
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kindly assist in answering these question
Answer:
4. 7
5. a=7 d=31.5
Step-by-step explanation: