Answer:
The equation modeling the path of the bird in vertex form is [tex]y=2(x-2)^2+2[/tex]
Step-by-step explanation:
General vertex form equation: [tex]f(x) = a(x-h)^2 + k[/tex]
where (h,k) is the vertex
The flight path of a bird can be represented by this equation: [tex]y = 2x^2 - 8x + 10[/tex]
To convert the equation in vertex form
Completing the square :
[tex]y = 2(x^2 - 4x + 5)\\y = 2(x^2 - 4x + 5 +(2)^2-(2)^2)\\y = 2(x^2 - 4x + 5 +(2)^2-4)\\y = 2((x-2)^2-4+5)\\y = 2((x-2)^2+1)\\y=2(x-2)^2+2[/tex]
Where:
(h,k)=(2,2)
a=2
Hence the equation modeling the path of the bird in vertex form is [tex]y=2(x-2)^2+2[/tex]
Una partícula se mueve sobre el eje x de acuerdo con la ecuación del movimiento
s=f(t) donde s es la distancia dirigida al origen en pies a los t segundos.
a) La velocidad v(t) y la aceleración a(t) en el instante t.
b) El instante t en el que la velocidad es cero.
s= 6t-t²
s=t²-6t
s= t²-9t+24
Answer:
a)
s= 6t-t² --> v = 6 -2t --> a = -2
s=t²-6t --> v = 2t-6 --> a = 2
s= t²-9t+24 --> v = 2t -9 --> a = 2
b)
v = 6 -2t = 0 --> t = 3
v = 2t-6 = 0 --> t = 3
v = 2t -9 = 0 --> t = 9/2
Step-by-step explanation:
si s(t) es la distancia, la velocidad es la primera derivada v(t) = s'(t)
y la acceleracion es la segunda derivada : a(t)= v'(t) = s''(t)
s= 6t-t² --> v = 6 -2t --> a = -2
s=t²-6t --> v = 2t-6 --> a = 2
s= t²-9t+24 --> v = 2t -9 --> a = 2
Please help thanks so much for your time !:).
3x +2 = 9x + 20 for x
Answer:
Use a calculator solved :)))
Step-by-step explanation:
Answer:
x=-3
Step-by-step explanation:
3x+2=9x+20
3x-9x=20-2
-6x=18
X=-3
A random sample drawn from a population with mean μ= 66 and standard deviation σ= 6.
Required:
a. Comment on the sampling distribution of the sample mean with n = 16 and n = 36.
b. Can you use standard normal distribution to calculate the probability that the sample mean falls between 66 and 68 for both sample sizes?
c. Report the probability if you answered yes to the previous question for either sample size.
Answer:
In step by step explanation
Step-by-step explanation:
a) Normal distribution N( 0, 1 )
If the sample size is equal n = 16 we have to use t-student distribution since n < 30.
In the case n = 36 we should use normal distribution (z tables)
b) We can´t use the standard normal distribution to calculate the probability that the sample mean falls between 66 and 68 in the first case n < 30 .
We can calculate that probability in the case of the second sample
Suppose the horses in a large stable have a mean weight of 975lbs, and a standard deviation of 52lbs.What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbsif 31horses are sampled at random from the stable
Answer: The required probability = 0.8926
Step-by-step explanation:
Given: [tex]\mu=975\text{ lbs}[/tex], [tex]\sigma= 52\text{ lbs}[/tex]
Let x = weight of horse stable.
Sample size : n= 31
Then, the probability that the mean weight of the sample of horses would differ from the population mean by less than 15 will be:
[tex]P(-15<P(\overline{x}-\mu)<15)=P(\dfrac{-15}{\dfrac{52}{\sqrt{31}}}<\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{15}{\dfrac{52}{\sqrt{31}}})\\\\=P(-1.61<z<1.61)\ \ \ [z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=2(z<1.61)-1\ \ \ [P(-z<Z<z)=2(Z<z)-1]\\\\=2( 0.9463)-1\\\\=0.8926[/tex]
Hence, the required probability = 0.8926
Find the product. Enter your answer in the box.
2.4 x0.87
Answer:2.088
Step-by-step explanation:
2.088
***PLEASE HELP*** What is the remainder in the synthetic division problem below??
Answer:
A. 4
Step-by-step explanation:
1 1 2 -3 3
1 3 0
1 3 0 3
Bring down the first coefficient, 1 and multiply it to 1 and that will be 1
Put the result below 2 and add 2 and 1, that would be 3
Multiply 3 and 1, that would be 3. Put it below -3.
Add -3 and 3 that would be 0.
Multiply 0 and 1, that would be 0. Put 0 below 3.
Add 3 and 0 then that would be 3.
Since the final result is 3, the remainder is 3.
(Sorry for the mistake earlier ;-;)
A small town has two local high schools. High School A currently has 750 students
and is projected to grow by 75 students each year. High School B currently has 900
students and is projected to grow by 25 students each year. Let A represent the
number of students in High School A in t years, and let B represent the number of
students in High School B after t years. Write an equation for each situation, in terms
of t, and determine how many students would be in each high school in the year they
are projected to have the same number of students.
Ok
Answer:
A=750 +75*t
B=900 +25*t
There would be 975 students in each high school in year 3 when they are expected to have the same number of students.
Step-by-step explanation:
You know that High School A currently has 750 students and is projected to grow by 75 students each year. With A being the number of students in High School A in t years, this number will be the number of students it has initially added to the number of students who have joined after t years. This is represented by:
A=750 +75*t
You know that High School B currently has 900 students and is projected to grow by 25 students each year. With B being the number of students in High School B in t years, this number will be the number of students it has initially added to the number of students who have joined after t years. This is represented by:
B=900 +25*t
You want to determine how many students there would be in each high school in the year that they are projected to have the same number of students. That is, in year t the number of students is the same, so
A = B
750 +75*t=900 + 25*t
Solving:
75*t -25*t= 900 - 750
50*t= 150
[tex]t=\frac{150}{50}[/tex]
t=3
This indicates that in year 3 both High Schools are projected to have the same number of students. To get that amount, you simply replace this value in the expressions:
A=750 +75*t= 750 +75*3= 975
B=900 + 25*t=900 + 25*3= 975
There would be 975 students in each high school in year 3 when they are expected to have the same number of students.
Answer: REAL ANSWER
A= 75t +750
B=25t +900
Answer: 975 students
Ellie the elephant has some peanuts. She eats up 49 peanuts. Now Ellie the elephant has 31 peanuts. How many peanuts did she have before?
Answer:
80
Step-by-step explanation:
do: 49+31=Your answer
Ellie had 80 peanuts before she ate 49 of them.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x be the number of peanuts Ellie had before she ate 49 of them.
After eating 49 peanuts, Ellie has 31 peanuts left, so we can write an equation:
x - 49 = 31
To solve for x, we add 49 to both sides of the equation:
x - 49 + 49 = 31 + 49
Simplifying, we get:
x = 80
Therefore, Ellie had 80 peanuts before she ate 49 of them.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
Express 4/5 as a percent. Make sure to label your answer with %.
The auxiliary equation for the given differential equation has complex roots. Find a general solution. y''-10y' 29y=0
Answer:
[tex]y = Acos5x - Bsin5x[/tex]
Step-by-step explanation:
Given the differential equation y''-10y'+29y=0
First, we need to rewrite it as an auxiliary equation as shown:
Let y'' = m²y and y' = my
Substitute the values into the general equation
m²y-10my+29y = 0
Factor out y:
(m²-10m+29)y = 0 [The auxiliary equation]
Solve the auxiliary equation and find the roots of the equation
m²-10m+29 = 0
m = -b±√(b²-4ac)/2a
a = 1, b = -10, c = 29
m = -10±√(10²-4(1)(29))/2(1)
m = -10±√(100-116)/2
m = -10±√-16/2
m = (-10±4i)/2
m = -10/2 + 4i/2
m = -5+2i
Comparing the complex number with a+bi, a = -5 and b = 2
The general solution for complex solution is expressed as:
[tex]y = Acosax + Bsinax[/tex]
Substitute the value of a in the equation
[tex]y = Acos(-5)x + Bsin(-5)x\\y = Acos5x-Bsin5x[/tex]
Hence the general solution to the differential equation is [tex]y = Acos5x - Bsin5x[/tex]
What is the slope of the line passing through the points (0,-5) and (4,2)?
Enter your answer in the box
Answer:
[tex] \huge{ \boxed{ \tt{ \frac{ 7}{4} }}}[/tex]
Step-by-step explanation:
[tex] \text{Let \: the \: points \: be \: A \: and \: B}[/tex]
[tex] \sf{A \:( \: 0 \:, - 5 \: ) \longrightarrow{ \: (x1 \:, y1)}}[/tex]
[tex] \sf{B(4 \:, 2) \: \longrightarrow{ \:( x2 \:, y2)}}[/tex]
[tex] \underline{ \text{Finding \: the \: slope} }: [/tex]
[tex] \boxed{ \sf{Slope = \frac{y2 - y1}{x2 - x1}}} [/tex]
[tex] \sf{➳ \: Slope = \frac{2 - ( - 5)}{4 - 0}} [/tex]
[tex] \sf{➳ \: Slope = \frac{ 2 + 5}{4} }[/tex]
[tex] \sf{➳ \: Slope = \frac{7}{4} }[/tex]
[tex] \text{Hope \: I \: helped!}[/tex]
[tex] \text{Best \: regards!}[/tex]
~[tex] \text{TheAnimeGirl}[/tex]
Write an equation in slope-intercept form for the line with slope 2/5 and y-intercept -6 .
Answer:
[tex] y = \frac{2}{3}x - 6 [/tex]
Step-by-step explanation:
Recall that the the equation of a line in slope-intercept form is given as [tex] y = mx + b [/tex].
m = the slope of the line
b = the y-intercept. This is the point at which the line intercepts the y-axis.
We are given:
slope (m) = ⅖
y-intercept (b) = -6
All you need to do to get an equation of the line is to simply substitute m = ⅔ and b = -6 into [tex] y = mx + b [/tex].
[tex] y = \frac{2}{3}x + (-6) [/tex]
[tex] y = \frac{2}{3}x - 6 [/tex]
The equation for the line is .[tex] y = \frac{2}{3}x - 6 [/tex]
Electrical Resistance The electrical resistance R of a wire varies inversely with the square of its diameter d. If a 25-foot wire with a diameter of 2 millimeters has a resistance of 0.5 ohm, find the resistance of a wire having the same length and a diameter of 3 millimeters.
Answer:
The answer is below
Step-by-step explanation:
The electrical resistance R of a wire varies inversely with the square of its diameter d:
R ∝ 1 / d
Let k represent the constant of proportionality, hence we can represent the statement as an equation:
[tex]R=\frac{k}{d^2}\\ \\when\ R=0.5 \Omega,d=2\ mm\\\\0.5=\frac{k}{2^2} \\\\k=2\\\\The\ equation\ becomes :\\\\R=\frac{2}{d^2}\\ \\When\ d=3, we\ find\ R\\\\R=\frac{2}{3^2} \\\\R=0.22\ \Omega[/tex]
Question 2
2 pts
Two out of every five people who buy ice cream buys vanilla ice cream. If a store sells
65 ice cream cones in one day, about how many will be vanilla?
Question 3
2 pts
Answer:
26
Step-by-step explanation:
Given that :
2 out of every 5 people buys vanilla ice cream;
If Total number of ice cream sold in a day = 65 ; how many will be vanilla ;
Probability of purchasing vanilla ; p(vanilla) = 2/5 = 0.4
Hence, expected number who bought vanilla :
p(vanilla) * total number of icecream sold
0.4 * 65 = 26
Hence, about 26 of the 65 icecream sold are vanilla flavor.
Pendiente 6 y puntos (5, -2)
Step-by-step explanation:
Kira is making ribbon bracelets.
She makes 4 bracelets on Thursday and 3 bracelets on Friday.
She uses 56 yards of ribbon for each bracelet.
Part A
Which of the following equations can Kira use to find how much ribbon she used?
Select all that apply.
A. (4×56)+(3×56)=r
B. 56×(4+3)=r
C. (4+56)+(3+56)=r
D. (4×56)×(3×56)=r
E. (7×56)=r
Part B
How much ribbon did Kira use to make the bracelets?
Kira used
Choose...
yards of ribbon.
Answer:
A. (4x56)+(3x56)=r
B. 56x(4+3)=r
E. (7x56)=r
Step-by-step explanation:
Kira used 392 yards of ribbon.
juan feeds his dog 2 scoops of dry dog food every day. each scoop weighs 1/3 pound. he bought a new 12 pound of dog food. how many days will it last
Pls helpppppp this stuff makes no sense
Answer:
x = 5
Step-by-step explanation:
a || b and a line intersecting them is their transversal.
[tex] \therefore m\angle 1=m\angle 5\\(corresponding \:\angle 's) \\\\
\therefore 60 - 2x = 70 - 4x\\\\
\therefore 4x - 2x = 70 - 60\\\\
\therefore 2x = 10\\\\
\therefore x =\frac{10}{2} \\\\
\huge \orange {\boxed {\therefore x = 5}}[/tex]
I don't believe I was shown how to complete this
−2(−1 1/4) Multiply. Write your answer as a fraction in simplest form.
Answer:
I want to say 2.5
Step-by-step explanation:
The state of Tennessee is shaped like a parallelogram. Its approximate dimensions are a base of 440 miles and a height of 120 miles. The state of Colorado is shaped like a rectangle, with approximate dimensions of 385 miles long and 275 miles wide. Ted works for a geographical company that is working on finding the areas of each state in the Union. Ted asked an assistant to double‐check his answers. Approximate area of Tennessee: 63,000 mi2 Approximate area of Colorado: 106, 000 mi2 11. If you were Ted’s assistant, would you agree with his answers? Explain why you answered yes or no by showing your work and explaining how it helped you come to your answer.
Answer:
Tennessee area we don´t know there is something wrong
Colorado area is ok close to 106000 mi²
Step-by-step explanation:
Tennessee is shaped like a parallelogram base is equal to 440 miles and the height is 120 miles. Therefore
Ap = b*h = 440 * 120 = 52800 mi²
But the area of Tennessee is 63000 mi²
Then there is something wrong because difference in mi² is
10400 mi²
10400/ 63000 = 0,165 % faraway of the real number
In the case of Colorado
Ac = 385 * 275
Ac = 105875 mi² pretty close to 106000 mi²
Then from double check in the areas, we conclude in a high difference in the figures for the state of Tennessee ( one or both of the figures are incorrect ). The state of Colorado area is oK
HELP HELP HELP HELP HELP HELP HELP HELP HELP HELP HELP ASAP ASAP ASAP ASAP ASAP ASAP ASAP ASAP ASAP ASAP ASAP ASAP ASAP ASAP ASAP ASAP HELP
Answer:
Confusing! Where r the instructions?
Step-by-step explanation:
In the diagram, the origin is at the center of a cube that has edges 6 units long. The x-, y-, and z-axes are perpendicular to the faces of the cube. Give the coordinates of the corner at point E.
(3, 3, –3)
(3, –3, –3)
(–3, 3, 3)
(–3, –3, 3)
Answer:
I really think that (3 , -3 , -3) is the answer but I could be wrong.
Step-by-step explanation:
I'm taking the quiz right now and from the graph it looks like point E is in the position (3 , -3 , -3).
Once again, sorry if I'm wrong.
y/4 =12.5
What is Y?
URGENT! NEEDED NOW!
Answer:
y = 50
Step-by-step explanation:
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other.
Multiply 4 to both sides of the equation:
y/4 = 12.5
(y/4)(4) = (12.5)(4)
y = 12.5 * 4
y = 50
y = 50 is your answer.
~
The equation x + y = z relates the whole numbers x, y, and z. How does z compare to x? If it helps, consider an example where you substitute 3 for x, 5 for y, and 8 for z
Answer:
The equation x + y = z relates the whole numbers.
Hopefully, this helps! :D
Ask your question below!
5,049 +48=105
MD Model with Mathematics A comic store sells two rare
comic books for $1,824. The price of one comic book is
11 times as much as the price of the other.
• 'Write an equation to model the price of the less expensive
comic book. Then find the price.
• Write an equation to model the price of the more expensive
comic book. Then find the price.
Let the cost of the less expensive comic book be x .
Then :-
[tex]1284 - 11x = x[/tex]
Using this equation , we can find the cost of the less expensive comic book .
Price of the less expensive book :-
[tex]1284 - 11x = x[/tex]
[tex]11x + x = 1284[/tex]
[tex]12x = 1284[/tex]
[tex]x = \frac{1284}{12} [/tex]
[tex]x = 107[/tex]
Cost of the less expensive book is 107 .
Therefore , the epice of the less expensive book = $ 107 .
Solution (b) :-Cost of the more expensive book = 11x
Which means :-
[tex]1284 - x = 11x[/tex]
[tex]11x + x = 1284[/tex]
[tex]12x = 1284[/tex]
[tex]x = 107[/tex]
[tex]11x = 11 \times 107[/tex]
[tex] = 1177[/tex]
Therefore , the price of the more expensive book = $ 1177 .
Please help me solve What is m
Answer:
a=60
b=85
c=35
Step-by-step explanation:
a is shown to be 60 in the text along with c being 85 with its angle so just add 60 and 85 to get 145 and fill in the remaining to get 180 which gives you c as 35
Please help!!
Square ABCD has vertices A(-2,-3), B(4, -1), C(2,5), and D(-4,3). Find the length of a side
of the square. Round your answer to the nearest tenth if necessary.
Answer:
The length of a side of the square is 6.3 units.
Step-by-step explanation:
When given vertices for a given shape, the length of the side is calculated using the formula:
√(x2 - x1)² + (y2 - y1)²
When given vertices (x1 , y1) and (x2 , y2)
Square ABCD has vertices A(-2,-3), B(4, -1), C(2,5), and D(-4,3). Find the length of a side
Side AB : A(-2,-3), B(4, -1)
√(x2 - x1)² + (y2 - y1)²
= √(4 -(-2))² + (-1 -(-3))²
= √ 6² + 2²
= √36 + 4
= √40
= 6.3245553203
≈ 6.3 units
B(4, -1), C(2,5),
√(x2 - x1)² + (y2 - y1)²
= √ (2- 4)² + (5- (-1))²
= √-2² + 6²
= √4 + 36
= √40
= 6.3245553203
≈ 6.3 units
C(2,5), D(-4,3).
√(x2 - x1)² + (y2 - y1)²
= √(-4 - 2)² + (3 - 5)²
= √-6² + -2²
= √36 + 4
= √40
= 6.3245553203
≈ 6.3 units
A(-2,-3), D(-4,3).
√(x2 - x1)² + (y2 - y1)²
= √(-4 -(-2))² + (3 - (-3))²
= √-2² + 6²
= √4 + 36
= √40
= 6.3245553203
≈ 6.3 units
3. Determine if the graph below is a function.
Explain your reasoning.
Answer:
A function defines one variable in terms of another. The statement "y is a function of x" (denoted y = y(x)) means that y varies according to whatever value x takes on. A causal relationship is often implied (i.e. "x causes y"), but does not *necessarily* exist.
Step-by-step explanation:
