Check the picture below, that'd be more or less the pattern of the sprinklinkg, so when we find it's vertex, we'd find how far along the ground at the maximum and its maximum height.
[tex]h(x)=160x-16x^2\implies h(x)=-16x^2+160x+0 \\\\\\ \textit{vertex of a vertical parabola, using coefficients} \\\\ h(x)=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+160}x\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left( -\cfrac{160}{2(-16)}~~,~~0-\cfrac{160^2}{4(-16)} \right)\implies \left( \cfrac{160}{32}~~,~~\cfrac{25600}{64} \right) \\\\\\ (\stackrel{\stackrel{\textit{along the ground}}{\downarrow }}{5}~~,~~\underset{\stackrel{\uparrow }{\textit{maximum height}}}{400})[/tex]
well, as you may notice from the picture, the water will hit the ground again when h(x) = 0 or namely y = 0, so let's do that to find out
[tex]h(x)= 160x-16x^2\implies \stackrel{h(x)}{0}= 160x-16x^2 \\\\\\ \stackrel{\textit{common factoring}}{0=16x(10-x)} \implies x = \begin{cases} 0&\leftarrow \textit{hits the ground first}\\ 10&\leftarrow \textit{hits \underline{the ground again}} \end{cases}[/tex]
answer.plsssssssssssssssssssssssssssssssssss
Answer:
see explanation
Step-by-step explanation:
(1)
4(m + 7) = 4 ( divide both sides by 4 )
m + 7 = 1 ( subtract 7 from both sides )
m = - 6
(2)
let the number be n , then
[tex]\frac{3}{5}[/tex] n - 2 = 40 ( multiply through by 5 to clear the fraction )
3n - 10 = 200 ( add 10 to both sides )
3n = 210 ( divide both sides by 3 )
n = 70
The required number is 70
(3)
The 4 sides of a square are congruent , then
length of side = 36 cm ÷ 4 = 9 cm
4z-2 when z=3
plz help
Answer:
10
Step-by-step explanation:
4 times 3 = 12
12-2=10
what is it called when a constant and variable are combined (math)
Answer:
a 'term'
Step-by-step explanation:
3r means the constant 3 multiplied by the variable 'r'
Guided Practice
The graph of y = 2(x + 1)2 − 4 is a translation 1 unit horizontally and 4 units vertically of the function y = 2x2. Graph this function in your notebook.
Type your answer and then click or tap Done.
The vertex of the parabola is (Fill in the blank text field 1
, Fill in the blank text field 2
( , )
Answer:
Step-by-step explanation:
hmm
The graph of a quadratic function is always a parabola. The vertex of the parabola after transformation is (-1,-4).
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The graph of the two functions can be made as shown below. Therefore, the two functions are,
y=2x² → Drawn by the red line
y = 2(x + 1)² − 4 → Drawn by the blue line
Now, the vertex of a quadratic function or a parabola is the point at which the function or the parabola changes its slope, it's either the maximum of the function or the minimum of the function, depending on which side the parabola opens.
Hence, The vertex of the parabola after transformation is (-1,-4).
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Complete the equation to show how many tenths are equivalent to 1/2
Answer:
5/10
Step-by-step explanation:
A simple pendulum is made from a 0.864-m-long string and a small ball attached to its free end. The ball is pulled to one side through a small angle and then released from rest. After the ball is released, how much time elapses before it attains its greatest speed?
Answer:
Step-by-step explanation:
The period of a simple pendulum is
T = 2π√(L/g)
as going from zero velocity to max velocity takes 1/4 of a period
t = ¼(2π)√(L/g)
t = ½π√(L/g)
t = ½π√(0.864/9.81)
t = 0.466 s
Ahh can someone helpppp
1. In the expression at aⁿ,n is called
a. exponent
b.base
c. variable
d.number
If the area of a rectangle is 12[tex]b^{7}[/tex]b[tex]b^{4}[/tex] and the width of the rectangle is 4[tex]a^{2}[/tex][tex]b^{2}[/tex] , what is the length of the rectangle?
[tex]\text{Given that,}\\\\\text{Area} = 12 b^7 b b^4 =12 b^{12}\\\\\text{Width} = 4a^2 b^2\\\\\text{Now,}\\\\\text{Length} \times \text{Width} =\text{Area} \\\\\implies \text{Length} = \dfrac{\text{Area}}{\text{Width}}=\dfrac{12b^{12}}{4a^2 b^2} = \dfrac{3b^{10}}{a^2}[/tex]
Select the table of values that you would use to graph f(x) = 3x2 – 4.
Hello Please help.
The the table of values that you would use to graph [tex]f(x) = 3x^{2} -4[/tex] is option "B"
What is point on graph?A point is the basic relationship displayed on a graph. Each point is defined by a pair of numbers containing two coordinates. A coordinate is one of a set of numbers used to identify the location of a point on a graph.
According to the question
Points on graph for equation :
[tex]f(x) = 3x^{2} -4.[/tex]
Now,
Table of points on graph
x y
-2 8
-1 -1
0 -4
1 -1
2 8
Hence, The the table of values that you would use to graph [tex]f(x) = 3x^{2} -4[/tex] is option "B" .
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Introduction to Dividing Whole Numbers
Five friends shared $87 and kept this record of how they did it. What does the 2
represent?
Answer:
probably a
Step-by-step explanation:
what is the numerical answer?
Answer:
x = 3
Step-by-step explanation:
In a parallelogram the diagonals bisect each other , then
6x + 11 = 5x + 14 ( subtract 5x from both sides )
x + 11 = 14 ( subtract 11 from both sides )
x = 3
A spherical tank has a circular orifice in its bottom through which the liquid flows out. The following data is collected for the flow rate through the orifice as a function of time:
Hi small cats and cats and dogs have a great experience with the evening of the evening of 6th century the morning of this
The rabbit will never go over 75 pounds. If this rabbit is bom in July weighing 2 pounds, in which month will it weigh around 46 pounds?
help ??? on edu math review
Answer:
It must be C.
Step-by-step explanation:
x² - 9 = 16
=> 16 + 9 = x²
=> 25 = x²
=> x = 5
Referring to the options, C is the only one that is accurate to me. Hoped this helped.
Solve for x.
100°
(2x+3)
51°
Answer:
23
Step-by-step explanation:
Exterior angle property: Exterior angle equals sum of opposite interior angles
51 + 2x +3 = 100
2x + 54 = 100
2x = 100 - 54
2x = 46
x = 46/2
x = 23
What is 2+2=?
PLS HEP ME
I in kindergarden.
Answer:
4
Step-by-step explanation:
You want a cookie?
Answer:
2+2 = 4
Step-by-step explanation:
1+1+1+1 = 4
Hope this helped!
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Step-by-step explanation:
My favorite movie would have to be the Pirates of the Caribbean collection. Captain Jack sparrow aka Johnny Depp is is just great at his character.
Answer:
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Step-by-step explanation:
Original price of a puppy $159.95 Discount 15% Tax 8.725%?
Answer:
$124.095
Step-by-step explanation:
Discounted Price= $159.95- 15%of $159.95=$135.9575
Final Price= Discounted price + Tax
= $135.9575+ 8.725% of $135.9575
= $135.9575-$11.8622
=$124.095
If 2x = 3y + 11 and 2^x = 2^4(y+1), determine the value of x+y
Answer:
3^7
Step-by-step explanation:
https://dlsfile.com/dd/MTQ1ODE5a3Bjd2hiaGxmXzM0MTMyNQ
it will tell you why hear
What number should be placed in the box to help complete the division calculation? (1 point) Long division setup showing an incomplete calculation. 19 is in the divisor, 8216 is in the dividend, and 4 hundreds and 3 tens is written in the quotient. 7600 is subtracted from 8216 to give 616. An unknown value represented by a box is being subtracted from 616.
Answer:
The unknown value is being subtracted from 702 is 650
Step-by-step explanation:
Long division setup showing an incomplete calculation
13 is in the divisor
3302 is in the dividend
2 hundreds and 5 tens is written in the quotient
2600 is subtracted from 3302 to give 702
An unknown value represented by a box is being subtracted from 702
We need to find this number
Lets write the steps above
∵ The dividend = 3302
∵ The divisor = 13
- 2 hundreds means 200 and 5 tens means 50
∵ The quotient = 200 + 50 + x
∵ Dividend = divisor × quotient
∴ (13 × 200) + (13 × 50) + (13 × x) = 3302
∵ 13 × 200 = 2600
- Subtract 2600 from the dividend
∴ 3302 - 2600 = 702
∵ 13 × 50 = 650
∴ 702 - 650 = 52 ⇒ 650 is the unknown value
∵ 13 × x = 13x
∵ 52 - 13x = 0
- Add 13 x to both sides
∴ 52 = 13x
- Divide both sides by 13
∴ x = 4
∴ 3302 ÷ 13 = 200 + 50 + 4
∴ 3302 ÷ 13 = 254
∴ From the steps above the missing number subtracted from
702 is 650
PLEASE HELP, PIC IS ATTACHED
Answer:
1. 1
2. 14
3.9
4. 15
5.17
step-by-step explanation:
take X and times it by 4 then add 9
A swimming coach needs to choose a team for a relay race. The coach must select 4 of 6 available swimmers
and put them in a strategic sequence.
How many unique ways are there to arrange 4 of the 6 swimmers?
The number of unique ways is given by the number of possible
combination having distinct members.
The number of unique ways there are to arrange 4 of the 6 swimmers are 15 ways.
Reasons:
The given parameters are;
The number of swimmers available = 6 swimmers
The number of swimmers the coach must select = 4 swimmers
Required:
The number of unique ways to arrange 4 of the 6 swimmers.
Solution:
The number of possible combination of swimmers is given as follows;
[tex]_4C_6 = \dfrac{6!}{4! \times (6 - 4)!} = 15[/tex]
Therefore, the coach can select 4 of the 6 available swimmers in 15 unique ways
Learn more here:
https://brainly.com/question/23589217
Answer:
360
Step-by-step explanation:
6!/(6-4)!
Please please help please help me help please help me
f(x)=x^2-(7/2)x-.5 and g(x)= 2-(2/x)
Answer:
23
Step-by-step explanation:
what is the domain and range?
Suppose Steve changed $250 into 200 Euros. How many Euros did he receive per US dollar?
Answer:
0.8 Euros
Step-by-step explanation:
Per US Dollar means its a proportion that the question is asking for. So, you can do 200/250 and get the answer.
Which of the following shows the
Commutative Property?
A 3 + 6 = 6-3
B 3X 6 = 6 = 3
C 3X 6 = 6 - 3 X (3 X 2)
D 3 X 6 = 6 X 3
Answer:
D
Step-by-step explanation:
Commutative switchs the numbers but not with subtraction or divion
Answer:
it is D I know because it is the opposite
Use substitution to determine which value of x makes the equation x– 5 = 7.4 true
x=2.4
X= 6.9
X= 7.9
X = 12.4
HELPPPP
Step-by-step explanation:
I'm not sure if I'm using substitution method but I guess it's x = 12.4
5. A 32 foot tree casts a 60 foot shadow as shown below. A man next to the tree casts a 12 foot shadow. How tall
is the man? Justify your solution
Answer:
Step-by-step explanation:
The shadow length will be proportional to height
12 / 60 = h / 32
h = 12(32)/60 = 6.4 ft or 6 ft 4.8 inches