1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
IRISSAK [1]
3 years ago
15

PLs help 50 PTS!!!!! PLEASE ILL GIVE BRAINLIEST!!!!!

Mathematics
1 answer:
Nookie1986 [14]3 years ago
3 0

Answer:

\large\boxed{y=\dfrac{1}{4}x^2-x-4}

Step-by-step explanation:

The equation of a parabola in vertex form:

y=a(x-h)^2+k

<em>(h, k)</em><em> - vertex</em>

The focus is

\left(h,\ k+\dfrac{1}{4a}\right)

We have the vertex (2, -5) and the focus (2, -4).

Calculate the value of <em>a</em> using k+\dfrac{1}{4a}

<em>k = -5</em>

-5+\dfrac{1}{4a}=-4        <em>add 5 to both sides</em>

\dfrac{1}{4a}=1           <em>multiply both sides by 4</em>

4\!\!\!\!\diagup^1\cdot\dfrac{1}{4\!\!\!\!\diagup_1a}=4

\dfrac{1}{a}=4\to a=\dfrac{1}{4}

Substitute

a=\dfrac{1}{4},\ h=2,\ k=-5

to the vertex form of an equation of a parabola:

y=\dfrac{1}{4}(x-2)^2-5

The standard form:

y=ax^2+bx+c

Convert using

(a-b)^2=a^2-2ab+b^2

y=\dfrac{1}{4}(x^2-2(x)(2)+2^2)-5\\\\y=\dfrac{1}{4}(x^2-4x+4)-5

<em>use the distributive property: a(b+c)=ab+ac</em>

y=\left(\dfrac{1}{4}\right)(x^2)+\left(\dfrac{1}{4}\right)(-4x)+\left(\dfrac{1}{4}\right)(4)-5\\\\y=\dfrac{1}{4}x^2-x+1-5\\\\y=\dfrac{1}{4}x^2-x-4

You might be interested in
A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.10.
HACTEHA [7]

Answer:

Option B. $0.70

Step-by-step explanation:

First day fine = $0.10

Second day fine (doubled or $0.30 which is lesser)

= $0.10 + $0.10           [$0.10 is lesser than $0.30]

= $0.20

Third day fine = $0.20 + $0.20           [ $0.20 is lesser than $0.30]

                      = $0.40

Fourth day fine = $0.40 + $0.30  = $0.70

[$0.30 is cheaper than doubling the amount $0.40 + $0.40]

Therefore, the total fine for a book on the fourth day is $0.70

4 0
3 years ago
A volleyball league organizer collected $2,040 for both divisions of volleyball teams.teams.the blue division costs &amp;160 per
evablogger [386]

A volleyball league organizer collected $2,040 for both divisions of volleyball teams. The Blue division costs $160 per team and the Red division cost $180 per team. How many teams will play in each division.

<h3><u>Answer:</u></h3>

6 teams will play in each division

<h3><u>Solution:</u></h3>

Given that volleyball league organizer collected $2,040 for both divisions of volleyball teams

The blue division costs $160 per team

The Red division cost $180 per team.

Let the number of blue teams be "b"

Let the number of red teams be "r"

Total cost = number of blue teams x cost of blue division per team + number of red teams x cost of red division per team

Total cost = 160b + 180r

2040 = 160b + 180r

Assuming both divisions have the same number of teams, we substitute b = r = x

2040 = 160x + 180x

2040 = 340x

x = 6

So 6 teams will play in each division

4 0
3 years ago
Maci and I are making a small kite. Two sides are 10". Two sides are 5". The shorter diagonal is 6". Round all your answers to t
Art [367]

Answer:

A. 4".

B. Approximately 9.54".

C. Approximately 13.54".

Step-by-step explanation:

Please find the attachment.

Let x be the distance from the peak of the kite to the intersection of the diagonals and y be the distance from the peak of the kite to the intersection of the diagonals.

We have been given that two sides of a kite are 10 inches and two sides are 5 inches. The shorter diagonal is 6 inches.

A. Since we know that the diagonals of a kite are perpendicular and one diagonal (the main diagonal) is the perpendicular bisector of the shorter diagonal.

We can see from our attachment that point O is the intersection of both diagonals. In triangle AOD the side length AD will be hypotenuse and side length DO will be one leg.

We can find the value of x using Pythagorean theorem as:

(AO)^2=(AD)^2-(DO)^2

x^{2}=5^2-3^2

x^{2}=25-9

x^{2}=16

Upon taking square root of both sides of our equation we will get,

x=\sqrt{16}

x=\pm 4

Since distance can not be negative, therefore, the distance from the peak of the kite to the intersection of the diagonals is 4 inches.

B. We can see from our attachment that point O is the intersection of both diagonals. In triangle DOC the side length DC will be hypotenuse and side length DO will be one leg.

We can find the value of y using Pythagorean theorem as:

(OC)^2=(DC)^2-(DO)^2

Upon substituting our given values we will get,

y^2=10^2-3^2

y^2=100-9

y^2=91

Upon taking square root of both sides of our equation we will get,

y=\sqrt{91}

y\pm 9.539392

y\pm\approx 9.54

Since distance can not be negative, therefore, the distance from intersection of the diagonals to the top of the tail is approximately 9.54 inches.

C. We can see from our diagram that the length of longer diagram will be the sum of x and y.

\text{The length of the longer diagonal}=x+y

\text{The length of the longer diagonal}=4+9.54

\text{The length of the longer diagonal}=13.54

Therefore, the length of longer diagonal is approximately 13.54 inches.

3 0
3 years ago
If an angle of 96 degrees is rotated 90 degrees clockwise. what the measure?
Natali [406]

Answer:

The measure is 6°.

Step-by-step explanation:

If an angle of 96 degrees is rotated 90 degrees clockwise then the measure of the new angle will be given by

= 96° - 90° = 6°

3 0
2 years ago
If there are 7,674,000,000 people in the world and 80,000 of them have a Reh, what is the probability at least one person has a
9966 [12]

Answer:

its not 80k/3000 someone answer

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • What is an equivalent expression of 28p^9q^-5/12p^-6q^7
    15·1 answer
  • What is the equation of the graph below?<br> PLEASE HELP!
    5·1 answer
  • Solve by using the quadratic formula: x^2 - 6x + 7 = 0 Please enter any square root values using "sqrt" or the decimal answer ro
    11·1 answer
  • Plz help with this question!
    13·1 answer
  • What is the slope intercept equation of the line below
    7·1 answer
  • The lifespan of a hamster is 6 years less than that of a rabbit. The lifespan of a raccoon is 3 times that of the hamster. If th
    12·1 answer
  • If the volume of the cone is 120 cm", what is the volume of the cylinder?
    6·1 answer
  • An automobile manufacturer claims that its car has a 37.2 miles/gallon (MPG) rating. An independent testing firm has been contra
    13·1 answer
  • What expressions are equivalent to 4x + 12?
    11·2 answers
  • Help please:)need asap
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!