Please help u don't get it #begging

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

Gala2k [10]

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)

3 0

4 years ago

Assume that when Human Resource managers are randomly selected, 62% say job applicants should follow up within two weeks. If 25

stellarik [79]

Using the binomial distribution, it is found that there is a 0.1008 = 10.08% probability that exactly 18 of them say job applicants should follow up within two weeks.

<h3>What is the binomial distribution formula?</h3>

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

The values of the parameters are given as follows:

n = 25, p = 0.62.

The probability that exactly 18 of them say job applicants should follow up within two weeks is P(X = 18), hence:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 18) = C_{25,18}.(0.62)^{18}.(0.38)^{7} = 0.1008$

0.1008 = 10.08% probability that exactly 18 of them say job applicants should follow up within two weeks.

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1

6 0

2 years ago

Triangle ABC has vertices at A(−3, 4), B(4, −2), C(8, 3). The triangle translates 2 units up and 1 unit right. Which rule repres

Nataly [62]

Answer:

The translation statement is given by:

$(x,y)\rightarrow (x+1,y+2)$

After the translation, the coordinates of vertex A is (-2,6).

Step-by-step explanation:

Given :

Vertices of a triangle ABC are:

A(−3, 4), B(4, −2), C(8, 3)

The triangle is translated 2 units up and 1 unit right.

To find the co-ordinates of point A after translation.

Translation rules.

For shift of $c$ units up, the translation is given as:

$(x,y)\rightarrow (x,y+c)$

For shift of $k$ units right, the translation is given as:

$(x,y)\rightarrow (x+k,y)$

So, it says the triangles is translated 2 units up and 1 unit right.

The translation statement is given by:

$(x,y)\rightarrow (x+1,y+2)$

So, co-ordinates of point A after translation is given by :

$(-3,4)\rightarrow (-3+1,4+2)=(-2,6)$

After the translation, the coordinates of vertex A is (-2,6).

4 0

4 years ago

2. Solve this: f(x) = 2x^2 + 5x - 12

MAVERICK [17]

A n s w e r:

(x+4)(2x−3)

7 0

3 years ago

Consider the regular octagon below with a center at the organ and a vertex at 4,0

Elan Coil [88]

Reflection on y=0

Step-by-step explanation:

The property to note when a point is reflected on the line y=0 is that the object figure will be congruent to the image figure.Here the distance of the object from the axis of reflection will equal that distance of image from the axis of reflection.In this case, the object point (0,-4) will reflect at (0,-4). The same will occur for object point (0,4) which will reflect at (0,-4). Doing the same for all the points, the image formed will be carried onto the polygon itself.

Learn More

Reflection of objects along x-axis :brainly.com/question/5017530

Keywords: octagon, reflection, vertex

#LearnwithBrainly

8 0

3 years ago

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