Johnny kicks a ball into the air. Assume the path of the ball can be modeled with a quadratic function. The ball reaches a height of 10 feet and lands on the ground 3 seconds later. Draw and label a graph that models the path of the ball. Write an equation that models the path of Johnny’s ball.
An equation that models the path of Johnny’s ball is [tex]y = -\frac{40}9(x - 1.5)^2 + 10[/tex]
The maximum height is given as:
[tex]h_{max}= 10ft[/tex]
And the time spent is:
[tex]t = 3s[/tex]
So, the vertex of the ball would be:
[tex]Vertex = (t/2,h_{max})[/tex]
This gives
[tex]Vertex = (3/2,10)[/tex]
[tex]Vertex = (1.5,10)[/tex]
Rewrite properly as:
[tex](h,k) = (1.5,10)[/tex]
The ball is on the floor after 3 seconds.
So, another point on the graph is:
[tex](x,y) = (3,0)[/tex]
A quadratic equation is represented as:
[tex]y=a(x - h)^2 + k[/tex]
Substitute [tex](x,y) = (3,0)[/tex] and [tex](h,k) = (1.5,10)[/tex] in [tex]y=a(x - h)^2 + k[/tex]
[tex]0=a(3 - 1.5)^2 + 10[/tex]
[tex]0=a(1.5)^2 + 10[/tex]
Evaluate the exponent
[tex]0=2.25a + 10[/tex]
Subtract 10 from both sides
[tex]2.25a =- 10[/tex]
Divide both sides by 2.25
[tex]a = -\frac{10}{2.25}[/tex]
Multiply by 4/4
[tex]a = -\frac{40}{9}[/tex]
Substitute [tex]a = -\frac{40}{9}[/tex] and [tex](h,k) = (1.5,10)[/tex] in [tex]y=a(x - h)^2 + k[/tex]
[tex]y = -\frac{40}9(x - 1.5)^2 + 10[/tex]
See attachment for the graph that models the path
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Write an absolute value inequality to represent the situation.
What is the range of the number for calories in the chicken.
The menu at Jeanne's favorite restaurant states that the roasted chicken with vegetables entree typically contains 480 Calories. Based on the size of the chicken, the actual number of Calories in the entree can vary by as many as 40 Calories from this amount.
Answer:
|x-480|<=40
Step-by-step explanation:
The absolute distance on the number-line from x to 480 has to be 40.
|x-val| <= error-margin
|x-480| <= 40
helpppppppppppppppppp
Answer:
IP information is attached to each packet, and this information helps routers to send packets to the right place. Every device or domain that connects to the Internet is assigned an IP address, and as packets are directed to the IP address attached to them, data arrives where it is needed.
Step-by-step explanation:
hope i helped!
A survey of 2,541 American households discovered that 64% of the households own one car.
what is the population?
what is the sample?
Answer:
See below
Step-by-step explanation:
The population is all American households
The sample is 2,541 of those American households
Graph the line with the equation
y = -1/3x + 4.
Answer:
Answer in the image
Step-by-step explanation:
How do I find the percentage of two column data table?
Answer:
a) 47.7%
b) 87.2%
Step-by-step explanation:
Find the ratio of interest, and convert it to a percentage.
a)(messy right-handed writers)/(right-handed writers)
= 31/65 = 31/65 × 100% ≈ 47.7%
__
b)(neat right-handed writers)/(neat writers)
= 34/39 = 34/39 × 100% ≈ 87.2%
help please RSM problem -need anwser please
Answer:
1/8 + 1/4 = 3/8
Step-by-step explanation:
The linear parent function, f(x) = x, was transformed to create a graph g(x) = f(x + 4).
Which statement about the graphs is true?
O The graph of fis steeper than the graph of g.
O The graph of fis shifted 4 units left to create the graph of g.
O The graph of fis less steep than the graph of g.
O The graph of fis shifted 4 units right to create the graph of g.
Answer:
2nd option
Step-by-step explanation:
Given f(x) then the graph of f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift left of a units
• If a < 0 then a shift right of a units
g(x) = f(x + 4)
Is the graph of f(x) shifted 4 units to the left
Marla was given the point (1, 3), (2, 1), and (-2, -15). She was asked to find a quadratic function that fit these 3 given points. Marla created a system of three equations with three variables to solve the problem and then used the matrix functions on her graphing calculator to find the equation. Which equation can be written given these 3 points?
The quadratic equation is given by y = -2x² + 4x + 1
The standard form of a quadratic equation is given by:
y = ax² + bx + c
At point (1, 3):
3 = a(1)² + b(1) + c
a + b + c = 3 (1)
At point (2, 1):
1 = a(2)² + b(2) + c
4a + 2b + c = 1 (2)
At point (-2, -15):
-15 = a(-2)² + b(-2) + c
4a - 2b + c = -15 (3)
Solving equations 1, 2 and 3 simultaneously gives:
a = -2, b = 4, c = 1
The quadratic equation is given by y = -2x² + 4x + 1
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d20) A department store buys 200 shirts at
of $2,400 and sells them at a selling price of $20
each. Find the percent markup.
Pls answer now I need it pls
Evaluate the figure below.
Find the value of x.
Formula for area of a rectangle: A = lw
Answer:
x=9,-7
Step-by-step explanation:
(x+3)(x-5)=48
x^2-2x-15-48=0
x^2-2x-63=0
(x-9)(x+7)=0
x=9,-7
dont use the negative number becuase it would not make sense in this scenario
width = 12
length=4
Consider the numbers 54.162 and 5,416.2. Which statements accurately reflect the relationship between the "6" in each number?
Select two (2) that apply.
The 6 in 54.162 has a greater value than the 6 in 5,416.2
The 6 in 54.162 has a smaller value than the 6 in 5,416.2.
a
The value of the 6 in 5,416.2 is 10 times greater than the value of the 6 in 54.162.
The value of the 6 in 54.162 is 10 times greater than the value of the 6 in 5, 416.2.
The value of the 6 in 5,416.2 is 100 times greater than the value of the 6 in 54.162.
The value of the 6 in 54.162 is 100 times greater than the value of the 6 in 5,416.2.
Answer:
1) The value of the 6 in 5,416.2 is 100 times greater than the value of the 6 in 54.162.
2) The 6 in 54.162 has a smaller value than the 6 in 5,416.2.
Step-by-step explanation:
1) 0.06 times 100 equals 6
2) 0.06 < 6
What is 7x(-4) ? Please
[tex]\mathfrak{7x(-4)} [/tex]
[tex]\mathfrak{=7x*-4} [/tex]
[tex]\boxed{\mathfrak{=-28x}} [/tex]
[tex]\mathbb{MIREU} [/tex]
pls help this a math question. image below
Answer:
D
Step-by-step explanation:
Same X, but different Y value, it is five apart in D
Can someone help me with this please.
Answer:
x = 29
Step-by-step explanation:
(x + 3) + (x - 1) + (x + 1) = 90
3x + 3 = 90
3x = 87
x = 29
Answer:
x = 29
Step-by-step explanation:
(x+3)+(x-1)+(x+1) = 90
90 = 3x +3
3x = 87
x = 29
The number of international tourist arrivals in Russia in 2012 was 13.5% greater than in 2011. The number of international tourist arrivals in Russia was k million more in 2012 than in 2011. What is the value of k to the nearest integer
The value of k to the nearest integer is 21
Let the number of international tourist arrivals in Russia in 2011 be kIf the number of international tourist arrivals in Russia in 2012 was 13.5% greater than in 2011 will be expressed as:
k = 24.7 - (13% of 24.7)
k = 24.7 - (0.135 * 24.7)
k = 24.7 - 3.3345
k = 21.3655
Hence the value of k to the nearest integer is 21
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Find the equation of a line perpendicular to y - 1= -x that passes through the
point (-4,-8).
1.) y = x - 4
2.) y = -x - 4
3.) y = -x - 1
4.) y = x - 1
Answer:
4
Step-by-step explanation:
firstly you separate y
y=-x-1
which means that the slope is equal to -1
then you flip the slope so -1 over -1 which is equal 1
a √(x^2-n/m)= a^2/b make x subject
[tex]\sqrt{x^2 -\dfrac nm} = \dfrac{a^2}b\\\\\implies x^2 - \dfrac nm = \dfrac{a^4}{b^2}\\\\\implies x^2 = \dfrac{a^4}{b^2} + \dfrac nm}\\\\\implies x = \pm \sqrt{ \dfrac{a^4}{b^2} + \dfrac nm}}[/tex]
Hi! Please help me!
Lightbulbs act as resistors. Janine is building a circuit that contains two lightbulbs in parallel. One of the lightbulbs has a
resistance of 120 ohms, but the resistance of the second lightbulb is unknown. She models the total
resistance in the
circuit, t, with this equation, in which r represents the resistance of the second lightbulb.
t =
1207
+ 120
Find the inverse of Janine's equation.
Look at photo below
Thank you have a nice day:)
Answer:
The answer is t^-1 (r)=120r/120-r
i hope this is right sry if im wrong have a good day :)
The inverse of Janine's equation is [tex]r = \frac{120t}{120-t}[/tex] .
What is resistance?Resistance is a measure of the opposition to current flow in an electrical circuit. Resistance is measured in ohms, symbolized by the Greek letter omega (Ω).
According to the question
Janine is building a circuit that contains two lightbulbs in parallel.
One of the lightbulbs has a resistance of 120 ohms.
R = 120ohms
r = resistance of the second lightbulb
t = total resistance in the circuit
[tex]t = \frac{120r}{r+120}[/tex]
Now,
The inverse of Janine's equation in which we will make r independent
[tex]t = \frac{120r}{r+120}[/tex]
[tex]t(r+120) = 120r[/tex]
[tex]tr + 120t = 120r[/tex]
[tex]120t = 120r - tr[/tex]
[tex]120t = r(120-t)[/tex]
[tex]r = \frac{120t}{120-t}[/tex]
Hence, the inverse of Janine's equation is [tex]r = \frac{120t}{120-t}[/tex] .
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Find the greatest common factor and the least common multiple of 16 and 20. The prime factorizations of each number are given.
.
Answer:
GCF 4, LCM 80
Step-by-step explanation:
Since both 16 and 20 have two 2s as factor, their greatest common factor is 4.
The LCM is found by multiplying all of the remaining factors by the LCM:
16 still has (2 x 2), 20 still has (5), times the GCF (4) so 2 x 2 x 5 x 4 = 80.
what are Two numbers that can add to 7 but multiply to -30
[tex]x + y = 7~~~.....(i)\\\\xy=-30~~~~......(ii)\\\\\\\text{From (ii):}\\\\y= -\dfrac{30}x~~~~....(iii)\\\\\\\text{Substitute equation (iii) in equation (i):}\\\\\\x- \dfrac{30}x = 7\\\\\implies x^2 -30 = 7x\\\\\implies x^2 -7x -30 =0\\\\\implies x^2 -10x +3x -30 =0\\\\\implies x(x-10) +3(x-10) =0\\\\\implies (x+3)(x-10)=0\\\\\implies x = -3 ~~\text{or}~~ x=10\\\\\text{Substitute x = 10 in equation (iii):}\\\\\\y= -\dfrac{30}{10} =-3\\\\[/tex]
[tex]\text{Substitute x = -3 in equation (iii):}\\\\y = \dfrac{-30}{-3} =10\\\\\\\text{So, (x,y) =(10,-3) and (x,y)=(-3,10)}\\\\\\\text{Hence, the two numbers are}~ 10~ \text{and}~ -3.[/tex]
Evaluate.
[2−∣∣−14−2(−35)∣∣]÷(−6)
What is the value of the expression?
Enter your answer as a simplified fraction in the box.
-7/40
/////
I honestly didn't know how to do this one. But thats the correct answer.
The solution of the mathematical expressions will be 0.175.
What is Number system?
A system of writing to express the number is called number system.
Given that;
The mathematical expressions are,
⇒ [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6
Now,
Solve the mathematical expression as;
⇒ [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6
Using the BODMAS rule to solve the expressions as;
⇒ [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6
⇒ [ 2 - | - 1/4 + 6/5 | ÷ -6
⇒ [ 2 - 19/20 ] ÷ -6
⇒ [ 21/20] ÷ -6
⇒ 21/20 x 1/-6
⇒ - 7 / 40
Therefore,
The solution of the mathematical expressions will be 0.175.
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The product of a binomial and a trinomial is x 3 3 x 2 âÂ’ x 2 x 2 6 x âÂ’ 2. Which expression is equivalent to this product after it has been fully simplified? x3 5x2 5x â€"" 2 x3 2x2 8x â€"" 2 x3 11x2 â€"" 2 x3 10x2 â€"" 2.
The product of given binomial and trinomial is given by below polynomial:
[tex]x^5 + 9x^4 + 15x^3 -10x^2 + 14x - 4[/tex]
Given polynomials:Trinomial : [tex]x^3+3x^2-x+2[/tex]Binomial: [tex]x^2+6x-2[/tex]Explanation:The expression formed by the sum of sub expressions which are product of constant integers with variables raised to some exponent is called polynomial.
Their product is given by:
[tex](x^3 + 3x^2 - x + 2) \times (x^2 + 6x -2)\\= x^5 + 6x^4 - 2x^3 + 3x^4 + 18x^3 - 6x^2 -x^3 -6x^2 + 2x +2x^2 + 12x - 4\\= x^5 + 9x^4 + 15x^3 -10x^2 + 14x - 4[/tex]
Thus the product of given binomial and trinomial is given by below polynomial:
[tex]x^5 + 9x^4 + 15x^3 -10x^2 + 14x - 4[/tex]
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Someone please help me with this question And you can get 20 points
[tex]\text{Consider the slope - intercept form} ~y = mx +c,\\\\ \text{where m is the slope and and c is the y-intercept.}\\\\(a) \\\\y = -\dfrac 12 x +8 \\\\\text{This is in a form of y = mx +c, so}\\\\\text{Slope, m =}-\dfrac 12 ~ \text{and}~ \text{y - intercept , c =8}\\\\(b)\\\\y = 9x -2 \\\\\text{This is in a form of y = mx +c, so}\\\\\text{Slope, m =9}~ \text{and}~ \text{y - intercept ,}~ c =-2\\\\[/tex]
someone please explain this
Answer:
HOPE THIS HELPS
Step-by-step explanation:
[tex]x^{2}[/tex]-14x-32 =(X+2)(X-16)
A=1
B=2
C=1
D=-16
How i can answer this question
Answer:
B
D
C
Glad I coild help you out.
Answer:
B,C and D
Step-by-step explanation:
They all expand back to 16x + 20.
5w+4w=18 simplify
how do you do this??
Answer:
Solved: w = 2
Step-by-step explanation:
Combine like terms
5w+4w = 9w
Isolate or make w alone
9w= 18 so divide both sides by 9 to make w alone
9w ÷ 9 = w
18 ÷ 9 = 2
w = 2
Answer:
you just add 5w and 4w and taht is 9w
[tex]9x = 18 \\ w = 18 \div 9 \\ w = 2[/tex]
Help please, I don't know how to get the measurements for the angles.
the only one i could figure out was that q= 24 and i think r=48
A text font fits 12 characters per inch. Using the same font, how many characters can be expected per yard of text? 36 characters 144 characters 360 characters 432 characters.
Answer:
432 characters
Step-by-step explanation:
There are 36 inches in a yard, so there will be 36 times 12 characters:
(36 in/yd)(12 char/in) = 432 char/yd
432 characters can be expected per yard of text.
i cant fail this class
Answer:
what are you asking?
Step-by-step explanation: