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
kolezko [41]
3 years ago
5

Point p(a,b) is in the first quadrant on the graph of the line x+y=4. A triangular region is shown on the diagram. What is the m

aximum area of the triangular region?

Mathematics
1 answer:
Gala2k [10]3 years ago
3 0

Answer:

The maximum area of the triangular region is 2 square units

Step-by-step explanation:

we know that

The area of the triangular region is equal to

A=\frac{1}{2}(x)(y) -----> equation A

where

x is the x-coordinate of point P

y is the y-coordinate of point P

we have

The equation of the graph of the line is

x+y=4

y=-x+4 -----> equation B

substitute equation B in equation A

A=\frac{1}{2}(x)(-x+4)

A=-\frac{1}{2}x^2+2x

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The y-coordinate of the vertex represent the maximum area of the triangular region

Find the vertex

Convert the quadratic equation in vertex form

Factor -1/2

A=-\frac{1}{2}(x^2-4x)

Complete the square

A=-\frac{1}{2}(x^2-4x+4)+2

Rewrite as perfect squares

A=-\frac{1}{2}(x-2)^2+2

The vertex is the point (2,2)

so

The maximum area is the y-coordinate of the vertex

The maximum area of the triangular region is 2 square units

Find the coordinates of point P for the maximum area

x=2 (x-coordinate of the vertex)

Find the y-coordinate of point P

substitute in equation B

y=-2+4=2

The coordinates of point P for the maximum area is P(2,2)

You might be interested in
Expand and simplify <br> (x + 1) (x + 4) (x + 3)
dedylja [7]

x^{3} + 8x^{2} + 19x + 12

Step-by-step explanation:

expanded and simplified

6 0
3 years ago
A zoo has 2 male lion one sixth of the lion are male lion how many lions are there at the zoo
pishuonlain [190]

If 1/6 of the population of the zoo are males and there are 2 males, then there must be 12 lions in all. 2 males and 10 females.

4 0
3 years ago
What is the volume of the shape below?
Yakvenalex [24]

Answer:

the answer is 147

Step-by-step explanation: Basicly with volume, you have to time all the sides so it would be 7x7x3, 7 is the heigh, 7 is the length and 3 is the width

6 0
2 years ago
Read 2 more answers
The function {(-1, 2), (-2, 1), (0, 2)} has the function rule y = x + 3. HELPPPPPP
Komok [63]
Answer: True
Explanation: hope this help
7 0
3 years ago
-8x-27=-7\left(1+2x\right)+2x
Darina [25.2K]

Answer:

x=5

Step-by-step explanation:

-8x-27=-7\left(1+2x\right)+2x

Expand:

-8x-27=-7\times 1-7\times 2x+2x

-8x-27=-7-12x

Add 27 to both sides:

-8x-27+27=-7-12x+27

-8x=-12x+20

Add 12x to both sides:

-8x+12x=-12x+20+12x

4x=20

Divide both sides by 4:

\frac{4x}{4}=\frac{20}{4}

x=5

5 0
3 years ago
Other questions:
  • f(x) g(x) ​ =x 2 =x 2 −8 ​ We can think of ggg as a translated (shifted) version of fff. Complete the description of the transfo
    10·1 answer
  • PLEASE HELP!!!!!!!
    14·1 answer
  • Muriel has kept track of her income and expenses for the week in the spreadsheet below. How much was Muriel’s restaurant bill? A
    9·1 answer
  • PLEASE PLEASE HELP ME PLEASE
    13·1 answer
  • the ratio of the fourth to the first term of a geometric sequence is ⅛. if the first term exceeds the second term by 5, find the
    13·1 answer
  • Rita ran 4 miles on Wednesday. The number of miles that Rita ran on Saturday can be represented by this expression.
    14·2 answers
  • Kiran is going to see a movie and is taking his 3 kids. Each movie ticket costs $13 and there are an assortment of snacks availa
    7·1 answer
  • What is the slope between the points (-2,7) and (2,1)
    8·1 answer
  • 48 / 48 hrs Completed, Read watch every Single thing and answer it in comments.<br><br> 48 / 48 = ?
    6·1 answer
  • For the graph shown, determine which letter represents the mean, the median, and the mode. Letters may be used more than once.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!