The equation of the parabolic arc that accomplishes this task is:
y = (-k/256)(x - 16)² + k.
In which k is the maximum height of the arc.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For this problem, the arc has these following characteristics:
Parabolic.Concave down.The peak is at half the road.The road under the arc is 20 feet wide with a 6-foot sidewalk on both sides of the road, hence it's total length is of 20 + 2 x 6 = 32 feet, and the peak of the arc will be at h = 16.
Hence:
y = a(x - 16)² + k.
The height is of 0 at x = 0 and x = 32, hence:
0 = 256a + k.
a = -k/256
y = (-k/256)(x - 16)² + k.
In which k is the maximum height of the arc.
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Find the sum of (4.9 × 10^−9) and (7.4 × 10^−10). Write the final answer in scientific notation.
5.64 × 10^−9
5.64 × 10^−10
1.23 × 10^−18
12.3 × 10^−19
Taking into account the scientific notation, the result of the sum is 5.64×10⁻⁹.
Scientific notationScientific notation is a quick way to represent a number using powers of base ten.
The numbers are written as a product:
a×10ⁿ
where:
a is a real number greater than or equal to 1 and less than 10, to which a decimal point is added after the first digit if it is a non-integer number.n is an integer, which is called an exponent or an order of magnitude. Represents the number of times the comma is shifted. It is always an integer, positive if it is shifted to the left, negative if it is shifted to the right.Sum in scientific notationTo add two numbers in scientific notation, when the numbers to be added do not have the same base 10 exponent, the base 10 power with the highest exponent must be found. In this case, the highest exponent is -9.
Then all the values are expressed as a function of the base 10 exponent with the highest exponent. In this case: 7.4×10⁻¹⁰= 0.74×10⁻⁹
Taking the quantities to the same exponent, all you have to do is add what was previously called the number "a". In this case:
4.9×10⁻⁹ + 0.74×10⁻⁹= (4.9 + 0.74)×10⁻⁹= 5.64×10⁻⁹
Finally, the result of the sum is 5.64×10⁻⁹.
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Can someone please find x ?
[tex]\frac{4}{3} x- \frac{1}{3} = x + 7[/tex]
the value of x in the question is 22
How to determine the value of x?The equation is given as
4/3x - 1/3 = x + 7
Multiply through by 3
4x - 1 = 3x + 21
Collect the like terms
4x - 3x = 1 + 21
Evaluate
x = 22
Hence. the value of x in the question is 22
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Find the amount of simple interest earned for depositing the given principle in an account. if $4200 is invested at 4.5 % for 4 months
Simple interest: $
well, keeping in mind a year has 12 months, thus 4 months is really 4/12 of a year
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$4200\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ t=years\to \frac{4}{12}\dotfill &\frac{1}{3} \end{cases} \\\\\\ I = (4200)(0.045)(\frac{1}{3}) \implies I=63[/tex]
Complete the statement.
x(y + 5) = x(__) + x(__)
Answer:
x(y + 5) = x(y) + x(5)
Step-by-step explanation:
Multiply the x to the variable and number in the parenthesis.
Can also be written xy + x5.
Rieko has 10 pounds of nails. She divides the nails equally among 3 bags. How many pounds of nails does Rieko place in each bag?
A division is a process of splitting a specific amount into equal parts. The number of pounds Rieko place in each bag is 3.33 pounds.
What is division?A division is a process of splitting a specific amount into equal parts.
We have,
Rieka has 10 pounds of nails and wants to divide it equally among 3 bags.
We need to divide the 10 pounds by 3.
The number of pounds in each bag:
= 10 pounds / 3
= 3.33 pounds
Thus the number of pounds in each bag is 3.33 pounds.
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can u guys please help me with is problem!! (ᗒᗩᗕ|||)
Answer: 4 miles per hour
Explanation: Put in the calculator 1/7 divided by 1/28 and then you get 4. Also can I get the brainliest pls?
PLS HELP IM TIMED!!!
Answer:
MDS/GDS
10....../9.6
8......./7.6
4.75./4.69
4......./3.6
(I hope so)
Help!! Find the domain of the graphed function.
A parking lot is shaped like a parallelogram and bounded on four sides by streets, as shown in the figure to the right. How much asphalt (in square yards) is needed to pave the parking lot?
The amount of asphalt needed to pave the parking lot is __ yd^3, yd, or yd^2
Amount of Asphalt needed = 27000 square yards
The shape of the parking lot is a parallelogram.
In the figure, the base of the parking lot is of length 180 yd and the height of the parking lot is 150 yd.
If 'b' is the base of the parallelogram and 'h' its height, then area of the parallelogram, A = bh
So here, base length, b = 180 yd
and height, h = 150 yd.
Therefore, area of the parking lot which is parallelogram, A = bh
= 180 x 150
= 27000 yd² (square yards)
Amount of Asphalt needed to pave the parking lot = Area of the parking lot
= 27000 square yards
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8. Gavin goes to the market and buys one rectangle shaped board. The
length of the board is 16 cm and width of board is 10 cm. If he wants to add
a 2 cm wooden border around the board, what will be the area of the
rectangle board?
160 cm² is the area of the rectangle.
What do we mean by rectangles?A rectangle is a closed two-dimensional shape with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel. Because a rectangle is a 2-D shape, it has two dimensions: length and width. The word rectangle is derived from the Latin word rectus, which means "right" or "straight." A rectangle has straight sides due to its right angles.Rectitude, which means moral uprightness, is another word with the same root.The formula for the area of a rectangle:
l × bPut values in the formula:
= 16 × 10= 160 cm²Therefore, the area of a rectangle is 160 cm².
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At Gabby's family reunion, Gabby hands out watermelon for the annual seed-spitting contest
She gives a watermelon slice to each kid at the reunion. She also gives a slice to 25 adults.
Gabby hands out 55 watermelon slices in all.
Which equation can you use to find how many kids k are at the reunion?
k - 25 = 55
k
25
= 55
k + 25 = 55
25k = 55
Solve this equation for k to find how many kids are at the reunion.
The equation which can be used to find how many kids k are at the reunion is :k + 25 = 55
There are 30 kids at the reunion
What is algebraic expression?
Algebraic expressions are based on expressing numbers using letters without indicating their actual values, such that we can determine the unknown variables by solving the expression or equation.
The total number of watermelons in this case is 55, if 25 slices are handed to the adults in the reunion gathering, the remaining one is the difference between 55 and 25 already served, which is known as k in this case.
total number of watermelons=55
number of adults=25
number of kids given watermelon=k
i.e k+25=55
k=55-25
k=30
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3) A closed rectangular box with volume 12 cubic feet is such that the length of its base is twice
the width. Express the surface area of the box as a function of the width.
Point Breakdown
1) 8 points (4/4)
2) 6 points
3) 6 points
A closed rectangular box with volume 12 cubic feet is such that the length of its base is twice the width.The surface area of the box as a function of the width is (4b³ +36)/b.
volume 12 cubic feet
volume =(l)(b)(h)=12
l=2b
(2b)(b)(h)=12
h=6/b²
Surface area = 2 (lb + bh + lh)
= 2((2b)(b) + b(6/b²) + 2b(6/b²))
=4b² + 12/b + 24/b
= (4b³ +36)/b
A three-dimensional object's surface area is the sum of all of its faces. Real-world applications of the notion of surface areas include wrapping, painting, and finally constructing things to get the greatest potential design.
An object's surface area is the total area that all of its surfaces occupy. The formulae we will learn in this post make it simple to determine the various surface areas that various 3D forms in geometry have. There are two groups for the surface area:
The surface area that is laterally oriented or curved
Surface area overall
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w = 5x² + 3
x = -3
Work out the value of w.
Answer:
48
Step-by-step explanation:
w = 5x² + 3
x = -3
w = 5(-3)² + 3
w = 5(9) + 3
w = 45 + 3
w = 48
50 points please show your work and answer all of them
Answer/Step-by-step explanation:
Convert:
8m to _800_cm
K H D B D C M
8 -> 80 -> 800
---------------------------------------------------------------------------------------------------
Interpret and simplify:
1 added to the difference of 12 and 9
1 + (12 - 9)
1 + (3) = 4
---------------------------------------------------------------------------------------------------
Write a positive or negative integer that represents the following:
A football team loses 14 yards on a play.
loses indicated a negative
-14
------------------------------------------------------------------------------------------------------
Evaluate:
4 3
------- + -------
20 12
4 (3) 3 (5)
------- + -------
20 (3) 12 (5)
12 15 27
------- + ------- = -------
60 60 60
27 ÷ 3 9
------- = --------
60 ÷ 3 20
----------------------------------------------------------------------------------------------------------
Write the Prime Factorization of 24.
24
/ \
2 × 12
/ \
2 × 6
/ \
2 × 3
Prime factorization = 2 × 2 × 2 × 3 or 2³ × 3
----------------------------------------------------------------------------------------------------------
Tell whether the ordered pair is a solution of the equation:
y = x + 7; (1, 6)
(x, y)
6 = 1 + 7
6 = 8
Not a solution
----------------------------------------------------------------------------------------------------------
Simplify and Graph the following:
x = -2 - 3
x = -5
↑
<-----|--------------------------------->
-5
↓
Don't worry about the other numbers. Put a dot on -5 and draw a line vertically (up and down).
----------------------------------------------------------------------------------------------------------
If the weight of a package is multiplied by (5/7). The result is 40.5 pounds. find the weight of the package.
x(5/7) = 40.5
--------- --------
÷(5/7) ÷(5/7)
x = 56.7
----------------------------------------------------------------------------------------------------------
A = (1/2)bh
A= (1/2)(8)(5)
A = (1/2)(40)
A = (20)
A = 20in²
----------------------------------------------------------------------------------------------------------
I hope this helps!
What are the vertex and x-intercepts of the graph of y = x2 – 4x – 21? Select one answer for the vertex and one for the x-intercepts. A. x-intercepts: (–3, 0), (7, 0) B. x-intercepts: (3, 0), (7, 0) C. x-intercepts: (3, 0), (–7, 0) D. Vertex: (2, 13) E. Vertex: (2, –25) F. Vertex: (–2, –9)
Answer:
To find x-intercept ,let y=0
0=x²-4x-21
(x+3)(x-7)=0
x=-3 or x=7
(-3;0) or (7;0)
To find vertex
x=
[tex] \frac{ - b}{2a} = x[/tex]
x=4/2=2
y=(2)²-4(2)-21=-25
(2;-25)
choose A and E
Round 34608 to the nearest hundred
Answer:
3460800.00
explanation:
13.95 + 0.49x = 50 - 13.95 - x
Whats the value of x please i have a test today
Answer:
14.832
Step-by-step explanation:
I hope this helps good luck
7.8 x 10 3
--------------
1.2 x 10 4
Step-by-step explanation:
7.8 ×1000=7800.
1.2×10000=12000.
7800÷12000=0.65.
What is the ones digit in the number 2^2076Hint: Start with smaller exponents to find a pattern.
Answer
Answer:
Step-by-step explanation: i think 9 the 9 is in one digits
g(x)=3x+1
f(x) =x^2 + 3x^2
Find g(2)•f(2)
Answer:
112
Step-by-step explanation:
Just plug in 2 into the equations and then multiply them together at the end.
g(2) = 3(2) + 1
= 6 + 1
= 7
f(2) = (2)² + 3(2)²
= 4 + 3(4)
= 4 + 12
= 16
g(2) × f(2)
7 × 16 = 112
Estimate using compatible numbers then find quotient 62÷1178
Answer:
the answer would be 0.05
PLEASE HELP DUE SOON!
I'm so confused, help determine the 100th line segment from question below!
Answer:
20200
Step-by-step explanation:
As you're in a hurry, I can give it later? xx
B is between A and C. If
AB=x+4 , BC=2x−2 , and AC=4x−1 , what is AB?
AB= (geometry someone help)
If B is between A and C and AB= x+4,BC= 2x-2 and AC= 4x-1, then the length of the AB is 3 units
The point B is between A and C
AB = x+4
BC = 2x-2
AC = 4x-1
We know,
AC = AB + BC
Substitute the value in the equation and find the value of x
4x-1 = x+4 + 2x-2
4x-1 = 3x-2
4x-3x = -2+1
x = -1
Then,
AB= x+4
Substitute the value of x in the equation
AB = -1+4
AB = 3 units
Hence, If B is between A and C and AB= x+4,BC= 2x-2 and AC= 4x-1, then the length of the AB is 3 units
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Help please .
I can’t figure out magnitude . Can anyone help me ASAP ?
Answer:
|-20| |12.3| |8| |-6| |-4| |2 3/10|
Step-by-step explanation:
Magnitude in this context means that they want you to order the values from greatest to least. These are all absolute values and that means distance from zero without regard to sign. So if you just stripped the signs and absolute value symbols off of each value, then ordered them from largest to smallest, and THEN added the signs and absolute value symbols back, you have the answer.
Answer:
From greatest to least magnitude
|-20|
|12.3|
|8|
|-6|
|-4|
[tex]\lvert {2 \frac{3}{10}}\rvert[/tex]
Step-by-step explanation:
The absolute value of a number |x| is the positive value of x. So if x is positive then it's the number itself and if x is negative it is the positive value of the number
Ex. |5| = 5 and |-5| = 5
Take the absolute values of each of the numbers first
|12.3| = 12.3
|-20| = 20
|2 3/10 | = 2 3/10 = 23/10 = 2.3
|-4| = 4
|8| = 8
|-6| = 6
Now arrange these numbers from greatest to least. The order is
20, 12.3, 8, 6, 4, 2.3
So in terms of the original numbers this corresponds to
|-20| , |12.3| , |8|, |-6| , |-4| , |2 3/10|
determine a series of transformations that would map polygon abcd onto polygon a'b'c'd
Answer: a reflection across the y-axis and scaling it by a factor of 1/2
Step-by-step explanation: First, you need to reflect the shape over the y-axis to move it into the neighboring quadrant. After that, you scale the polygon down by a factor of 1/2, because the lengths of the line segments of A'B'C'D' are half the length of the original polygon, ABCD.
I don’t know how to do this -2(-5+n)=6 ?
Answer:
n = 2
Step-by-step explanation:
So all you have to do is solve:
-2(-5 + n) = 6
= 10 + -2n = 6
= -2n = -4
= n = 2
This means that n = 2.
But what if I'm wrong? So lets see if it works.
-2(-5 + 2) = 6
10 - 4 = 6
6 = 6
So n = 2 is right.
Hope this helped! :D
Answer:
n = 2Step-by-step explanation:
I don’t know how to do this -2(-5+n)=6 ?
-2*(-5+n)=6
10 -2n = 6
10 - 6 = 2n
4 = 2n
2 = n
-----------------
check
-2 ( -5 * 2) = 6
10 - 4 = 6
6 = 6
HELP PLEASE
The absolute value inequality 5 <= I x l — n is graphed below. What is the value of n?
Answer:
I think the answer is 7
Step-by-step explanation:
Function yes or no whag is the domain and range?
Step-by-step explanation:
to be a function every value of x must have exactly one value of y.
in other words, if you create a vertical line and move it across the whole chart (e.g. from left to right), this line must not even once intersect the function curve more or less than once.
so, this is clearly a given here. yes, it is a function.
the domain is the interval or set of all valid x (input) values. and that starts on the right with x = 5 (included in the function indicated by the filled dot). and it goes endlessly to the left. that means -infinity (but not included as "infinity" is only a symbol but not a number).
-infinity < x <= 5
the range is the interval or set of all valid y (function result) values.
and that starts on the top with y = 2 (included). and it goes endlessly down. that means again -infinity (not included).
-infinity < y <= 2
I need help for the Wednesday one
Answer:
Seth is correct.
Step-by-step explanation:
Complementary means that they add to 90 degrees. Supplemental means that they add to 180. 147 + 33 equals 180 so they are supplemental.
Connor missed 12 out of his last 18 free throws. What is the experimental probability that
Connor will miss his next free-throw attempt?
Write your answer as a fraction or whole number.
The experimental probability that Connor will miss his next free-throw attempt is 2/3.
How to calculate the probability?From the information, Connor missed 12 out of his last 18 free throws.
Therefore, the probability will be:
= Number of missed throws / Total throws
= 12/18
= 2/3
Therefore, the experimental probability that Connor will miss his next free-throw attempt is 2/3.
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