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
Ronch [10]
3 years ago
6

The standard form of the equation of a parabola is y = 5x2 + 20x + 14.

Mathematics
2 answers:
Irina-Kira [14]3 years ago
8 0
The vertex form of quadratic equation is expressed as:

y = a (x - h)² + k

We manipulate the given equation to be the same as the vertex form. First we transpose the constants to the left-hand side.

y - 14 = 5x² + 20x

Then, we factor out in right hand side the coefficient of the x² term.

y- 14 = 5 (x² + 4x)

We divide the coefficient of the x term with 2 and take its square. We add this value to both sides of the equation but we should remember that in the left-hand side we should multiply this value with five to keep it balanced.

y - 14 + 20 = 5 (x² + 4x +4)

We simplify the right-hand side as:

y + 6 = 5 (x + 2)²

We can now manipulate further the equation above in the vertex form. Thus,

y= 5 [ x- (-2)]² - 6
Ber [7]3 years ago
7 0

Answer:

y = 5(x+2)^2 - 6

Step-by-step explanation:

You might be interested in
Jason and Alison are hiking in the woods when they spot a rare owl in a tree. Jason stops and measures an angle of elevation of
Shalnov [3]

Answer:

Owl= 67.14ft

Step-by-step explanation:

<em>See comment for complete question.</em>

The given information is represented in the attached figure.

First convert 22°8'6'' and 30° 40’ 30” to degrees

22^{\circ} 8'6'' = 22 + \frac{8}{60} + \frac{6}{3600}

22^{\circ} 8'6'' = 22.135^{\circ}

30^{\circ} 40'30'' = 30 + \frac{40}{60} + \frac{30}{3600}

30^{\circ} 40'30'' = 30.675^{\circ}

Considering Jason's position:

tan(22.135^{\circ}) = \frac{H}{x + 48}

Where x = distance between the tree and Alison

Make H the subject

H = (x + 48)tan(22.135^{\circ})

Considering Alison's position

tan(30.675^{\circ}) = \frac{H}{x}

Make H the subject

H = xtan(30.675^{\circ})

H = H

(x + 48)tan(22.135^{\circ}) = xtan(30.675^{\circ})

(x + 48) *0.4068 = x* 0.5932

Open bracket

x *0.4068 + 48 *0.4068 = 0.5932x

0.4068x + 19.5264 = 0.5932x

Collect Like Terms

-0.5932x+0.4068x = -19.5264

-0.1864x = -19.5264

0.1864x = 19.5264

Make x the subject

x = \frac{19.5264}{0.1864}

x = 104.76

Substitute 104.76 for x in H = xtan(30.675^{\circ})

H = 104.76 * tan(30.675^{\circ})

H = 104.76 * 0.5932

H = 62.14

The above represents the height of the tree.

The height of the owl is:

Owl= H + 5

Owl= 62.14 + 5

Owl= 67.14ft

7 0
2 years ago
Please help. i don't understand
zaharov [31]

78×.33=25.74 busses are new

25.74+15=40.74 new busses

78+15=93 total busses

40.74/78=0.5223076923= 52% will be new with the new 15 busses

4 0
3 years ago
Someone please explain transforming liner equations for me and help me with this question.
PilotLPTM [1.2K]
Sorry hope you find the answer that you’re looking for I am not much help
7 0
3 years ago
What is the basic metric unit of capacity <br> meter<br> gallon<br> gram <br> liter
Advocard [28]
Hoi!

The basic metric unit of capacity is a liter. :)
8 0
3 years ago
Read 2 more answers
I need this for a geometry assignment........please help
anastassius [24]

All three are similar

In ∆SUT and ∆VWX

  • Two sides are similar and one angle is similar

So by SSA they are similar

In ∆PRQ and rest two

All angles are.

  • 80,80,20°

So

They are similar by AAA congruence

6 0
2 years ago
Other questions:
  • Need answers for 2,3 and 4
    9·2 answers
  • Help please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11
    15·1 answer
  • Which of the following can be represented by the equation y = 2x?
    13·1 answer
  • If you roll a 6-sided die 4 times, what is the probability of one roll being a multiple of 3? A)2/3 B)16/81 C)145/1296 D)65/81 E
    14·2 answers
  • What is the circumference of a circle with a radius of 56 inches
    8·1 answer
  • What is the equation of a parabola that has a vertex at ( 0,4 ) and passes through points ( 2,0 )?
    8·1 answer
  • How do you do this and what is it called
    10·1 answer
  • Please help!! This is urgent.
    14·1 answer
  • Eric's cell phone service costs $40.00 a month for unlimited calls. He also pays $0.02 for each text message he sends Which equa
    14·1 answer
  • Deanna borrowed $650 at 8% 0 simple interest. How much - 52 interest did she pay for 1 year?​
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!