Answer:
The vertex form will be:
[tex]y(x)=(x-2)^{2}+1[/tex]
Step-by-step explanation:
The equation of the vertex form of a quadratic equation is given by:
[tex]y(x)=a(x-h)^{2}+k[/tex]
Where:
a is a coefficient
h is the x value of the vertex
k is the y value of the vertex
To completing the square we just need to add and subtract the square of the term with x divided by 2.
[tex]y(x)=x^{2}-4x+(\frac{4}{2})^{2}-(\frac{4}{2})^{2}+5[/tex]
[tex]y(x)=x^{2}-4x+4-4+5[/tex]
[tex]y(x)=(x-2)^{2}-4+5[/tex]
Finally, the vertex form will be:
[tex]y(x)=(x-2)^{2}+1[/tex]
I hope it helps you!
Help me out please an thank you
Given:
The graph of a parabola.
To find:
The equation of the parabola.
Solution:
From the given graph, it is clear that the vertex of the parabola is at point (0,0) and it is a horizontal parabola.
The general equation of a horizontal parabola is:
[tex]x=ay^2[/tex]
Where, a is a constant.
If a<0, then the parabola opens left and if a>0, then the parabola opens right.
Equations in options B and D are of the form [tex]x=ay^2[/tex] but a<0 in option B and a>0 in option D.
In the given graph the parabola opens right, so the value of a mus be a positive number. So, the required equation is:
[tex]x=\dfrac{1}{6}y^2[/tex]
Therefore, the correct option is D.
If the initial velocity stays the same, but the height the projectile is launched from changes , how would the amount of time change that it takes for the projectile to reach its maximum height? How would its maximum height change?
Answer:
Part A
The height to which the projectile reaches is given by the following formula;
[tex]\Delta y = y-y_0 = v_{0y} \times t-\dfrac{1}{2} \times g \times t^2[/tex]
Where;
[tex]v_{0y}[/tex] = The initial velocity of the projectile = Stays the same
y = The height the projectile reaches
y₀ = The height from which the projectile is launched
g = The acceleration due to gravity
t = The time taken
Given that the projectile has the same initial velocity, the variation of Δy with time, 't', will be the same when the project is launched from a different height, and the time change that it takes for the projectile to reach the maximum height will be the same for the previous launch height
Part B
From the change in eight of the projectile, Δy = y - y₀, the maximum height reached, 'y', is therefore given as follows;
y = Δy + y₀
The maximum height will increase by 'y₀', where 'y₀' is the difference between new height and the previous height, [tex]y_i[/tex]
That is, if y₀ > [tex]y_i[/tex], the maximum height reached increases and if y₀ < [tex]y_i[/tex], y₀ will be added as y = Δy - y₀ and the maximum height reached decreases
Step-by-step explanation:
(p -√ 5 ) (p + √ 5 )
Answer:
p² -5
Step-by-step explanation:
pxp + p√ 5 -p√ 5 -√ 5√ 5
pxp -√ 5√ 5
pxp -√ 5√ 5
p² -5
the relationship between a and b if a + b = 0
Answer:
a=-b
Step-by-step explanation:
a+b=0a=-bOr,
b=-a
Subject:Mathematics
I need help asap thank you
Answer:
Thisis your answer ☺️☺️☺️
Can someone help me with this ( pls don't use links) the first one who answers this gets 5 stars
Answer: 4 = 90
Step-by-step explanation:
90
Answer:
1. 135° = obtuse angle
2. 245° = Reflex angle
3. 62° = acute angle
4. 110° = obtuse reflex angle
What are the coordinates of the point?
(−4, −2)
(−2, 4)
(2, 4)
(4, −2)
Answer:
-2,4 is the answer x,y is the formula
Answer:
hey if I can get some of your social network to send you homework, they won't here?
The cylindrical canister of a fire extinguisher
has a diameter of 4 inches and is 12 inches
high. About how many square inches of
metal (total surface area) would be needed
to manufacture one fire extinguisher?
Step-by-step explanation:
2*22/7*48=301.714 .This the answer
Answer:
Yeah, what they said above.
Step-by-step explanation:
help anyone? please?
Answer:
x=11.2
Step-by-step explanation:
Set up a proportion:
x+11/36 = 37/60
Cross multiply:
1332=60(x+11)
Distribute:
1332=60x+660
Subtract 660 from 1332
672=60x
Divide:
x=11.2
I'm not sure if this is the correct answer but I hope this helps! :)
Correct me if I'm wrong!
which of the following trigonometric expressions are equal? a. sin(theta) b. cos(theta)tan(theta) c. 1/sec(theta) d. csc(theta) (1-cos^2(theta))
Answer:
A & B
Step-by-step explanation:
cos(theta)tan(theta) can be expressed as;
cos(theta)tan(theta) = cos(theta) × (sin(theta))/cos(theta).
cos(theta) cancels out to give; sin(theta)
Thus is equivalent to option A
PLEASE HELP ME
In the coordinate plane, the point X(3,2) is translated to the point X (−1, 5). Under the same translation, the points Y( 6,− 1) and Z( 5 ,5) are translated to Y′ and Z′, respectively. What are the coordinates of Y′ and Z′?
Y': ( , )
Z': ( , )
Answer:
y=(2,1)
z=( 1,7)
Step-by-step explanation:
Because from their original point you would have to count to the left four unit and up two units
Álgebra/help
There are 3 consecutive integers that add up to 15. What is the least of these integers?
Answer:
The answers are 4,5,6,
the answer you are looking for is 4
Step-by-step explanation:
the first thing you have to do is define a variable for stuff that you don't know. In this problem, you don't know any of the integers, so you should assign a variable to them.
will put the first integer as n. The second integer, since it is right after the first, will be n+1. The third integer, since it is right after the second, will be (n+1)+1=n+2. consider the integers 1, 2, and 3. 2 is one more than 1, or in other words, 2=1+1. same for 3, except 3 is two more than 1, so 3=1+2. Since the integers are consecutive, each is one more than the last.We're told that the sum of our three integers is 15. Therefore, n+(n+1)+(n+2)=15 Solving this equation is pretty straightforward:
3n+3=15
3n=12
n=4 That means our first integer is 4. Our second integer is 4+1, or 5, and our third integer is 5+1, or 6. Our answer is confirmed because 4+5+6=15
i hope I helped!!
Need help :::::::::::::::::
Answer:
2/3
Step-by-step explanation:
First, we read the two points with circles off the graph.
They are (-4, -5) and (5, 1).
slope = (y2 - y1)/(x2 - x1) = (-5 - 1)/(-4 - 5) = -6/(-9) = 2/3
Answer: 2/3
A new road was added near Riana's neighborhood. The road is 5 miles long, and the city plans 1/10 to place a streetlight every mile. There already is a streetlight at the beginning of the new road. How many streetlights will be placed on the new road?
Answer:
= 49
Answer.
Step-by-step explanation:
Solution:-
Length of the road = 5 miles
Distance between every two streetlights = 1/10 miles
Total number of streetlights placed on the new road = 5 ÷ 1/10
= 5*10
= 50 streetlights
As there is already a streetlight at the beginning of the new road, so the number streetlights will be = 50 - 1
Answer:
49 is correct answer
Step-by-step explanation:
please mark me as brainliest
What is the multiplicative identity of the complex number 4 + 8i
Answer:
1
Step-by-step explanation:
when you multiply an complex number by its multiplicatuive identity, in case 4+8i, you would multiply both the top and the bottom by 4-8i which is actually the value one since we cannot actually change the whole value of the number. By multiplying it by 1 and we get the same value without the imaginary number
(sorry if this doesn't make sense but I hope it helps)
about that did you forget to put -4 + 8i just to make sure about it because I am not sure if you forget it or not just making sure
Answer:
1
Step-by-step explanation:
In a survey of 2,000 people who owned a certain type of car, 1,200 said they would buy that type of car again. what percent of the people surveyed where satisfied with the car
Answer:
1200÷2000=0.6
0.6×100%= 60%
The answer is 60%
Graph the function
f(x) = -log - 6. You must plot the
asymptote and any two points with whole number coordinates.
Answer:
To graph a rational function, you find the asymptotes and the intercepts, plot a few points, and then ... graphing showing vertical asymptote at x = 1 ... Next, I'll find any x- or y- intercepts.
I need help please ):
Answer:
yes, 3:4
Step-by-step explanation:
The ratio of the side lengths is 6:8 and 18:24 both of which simplify to 3:4
A kid at the bus stop is tossing a coin. He tosses the coin 19 times and it lands on heads eight times. If the kid tosses the coin an 20th time, what is the probability that it will land on heads?
Answer:
I honestly dont know
Step-by-step explanation:
Jiro borrows $48000 from a bank that charges simple interest at a rate of 6% per year. Find the total amount of money he has to pay the bank at the end of 2 years.
Answer:
$53760
Step-by-step explanation:
Rui Feng borrows $48 000 from a bank that charges simple interest at a rate of 6% per annum.
Now, we have to calculate the total amount he has to pay the bank at the end of 2 years.
Now, using the formula of simple interest the total amount after 2 years will be
dollars. (Answer)
a sign in front of a roller coaster say '' you must be 40 inches tall to ride" what percentage of 54 inches of this is?
help me asap please :)
Find the measure of segment `DE.`
Answer:
DE=24
Step-by-step explanation:
We can see clearly that the two angles, angle A and angle F are congruent with one another, and since they are, we know the two triangles are shifted in a growth, not in an adjustment of angles. the hypotenuse doesnt matter, what does matter is the 5 and the 10, clearing showly the transition of Triangle ABC to Triangle DEF is times 2. Therefore, 12 times 2 is 24.
Answer:
Step-by-step explanation:
segment DE is what we want to find
notice that the two triangles are similar, similar here just means one is an exact copy of the other, except for scale. One is an exact scale copy of the other. sooooo we can make some scaling of one side of one.. to the same side of the other. here we want DE so .. see that BC is the same side on the other , smaller triangle?
now notice AB on the small triangle and FE on the bigger one... sooo just by observation we can see, that the bigger triangle is 2X bigger than the small one , b/c 5 * 2 = 10 . 5 is the AB side of the smaller triangel and 10 is the same side but on the bigger triangle and 2 is our scaling factor.. got it?
So do the same on BC to find DE
12 * 2 = DE
24 = DE
see? :)
Of the $2400 Mr Calvin earned, he spent 3/8 on food, 1/3 on taxes and 1/6 on other expenses. Find out how much all this is in dollars. Then find out how much he saved.
Answer: $300
Step-by-step explanation:
Mr. Calvin earned [tex]\$2400[/tex]
He spent [tex]\frac{3}{8}[/tex] on food i.e.
[tex]\Rightarrow \dfrac{3}{8}\times 2400=\$900[/tex]
[tex]\dfrac{1}{3}\quad \text{on taxes i.e.}\\\\\Rightarrow \dfrac{1}{3}\times 2400=\$800[/tex]
[tex]\dfrac{1}{6}\ \text{on other expenses i.e.}\\\\\Rightarrow \dfrac{1}{6}\times 2400=\$400[/tex]
Remaining money = [tex]2400-900-800-400=\$300[/tex]
So, he saved $300 after expenses
2{x+8}+5{x-1}=60 answer
Answer:
x=7
Step-by-step explanation:
2{x+8}+5{x-1}=60
Distribute
2x+16+5x-5 = 60
Combine like terms
7x +11 = 60
Subtract 11 from each side
7x+11-11 = 60-11
7x = 49
Divide each side by 7
7x/7 = 49/7
x = 7
what is the average monthly ranfall?
Help
I costs $50 to make 10 calculators
Answer: so but 10 calculators
Step-by-step explanation:
The movie you chose is 2 hours long. After only 1 /2 of an hour, you look and "Oh no!" you have already eaten a third of your popcorn! If you continue eating popcorn at this speed, do you think you will have enough for the rest of the movie? Include a mathematical explanation to support your thinking.
Answer:
no
at every 30 minutes, a third of the popcorn is consumed.
After an hour, 1/3 + 1/3 = 2/3 of popcorn would be consumed.
At one hour 30 minutes, 2/3 + 1/3 = 3/3 or 1 or all of the popcorn would have been consumed
Step-by-step explanation:
The rate at which popcorn is consumed is 1/3 in 30 minutes
so, in 1 and a half hours, all the popcorn would be finished
1/3 + 1/3 + 1/3 = 1
b) After allowing 16 % discount on the marked price of an article and levying 13 % value
added tax, the price of the article becoipes Rs 9,492. Find the value added tax.
Answer:
135.15
Step-by-step explanation:
let SP be x
sp with vat=sp + vat % of sp
9492=x+13/100*x
x=1039.6
vat=vat% of sp
=13/100*1039.6
=135.15
The diameter of a circle is 22 miles. What is the circle's circumference?
Answer:
69.12
Step-by-step explanation:
