If f(x) = −2(x + 3)(x + 5), complete the square and determine the minimum or maximum value of the function.

Given triangle abc with vertices A(2,-1), B(5,6), C(-1,4) as shown. Find the number of square units in the area of triangle abs

Roman55 [17]

Answer:

The area of the triangle is 18 square units.

Step-by-step explanation:

First, we determine the lengths of segments AB, BC and AC by Pythagorean Theorem:

AB

$AB = \sqrt{(5-2)^{2}+[6-(-1)]^{2}}$

$AB \approx 7.616$

BC

$BC = \sqrt{(-1-5)^{2}+(4-6)^{2}}$

$BC \approx 6.325$

AC

$AC = \sqrt{(-1-2)^{2}+[4-(-1)]^{2}}$

$AC \approx 5.831$

Now we determine the area of the triangle by Heron's formula:

$A = \sqrt{s\cdot (s-AB)\cdot (s-BC)\cdot (s-AC)}$ (1)

$s = \frac{AB+BC + AC}{2}$ (2)

Where:

$A$ - Area of the triangle.

$s$ - Semiparameter.

If we know that $AB \approx 7.616$ , $BC \approx 6.325$ and $AC \approx 5.831$ , then the area of the triangle is:

$s \approx 9.886$

$A = 18$

The area of the triangle is 18 square units.

7 0

3 years ago

Solve the linear programming problem.

larisa [96]

Answer:

1. Objective function is a maximum at (16,0), Z = 4x+4y = 4(16) + 4(0) = 64

2. Objective function is at a maximum at (5,3), Z=3x+2y=3(5)+2(3)=21

Step-by-step explanation:

1. Maximize: P = 4x +4y

Subject to: 2x + y ≤ 20

x + 2y ≤ 16

x, y ≥ 0

Plot the constraints and the objective function Z, or P=4x+4y)

Push the objective function to the limit permitted by the feasible region to find the maximum.

Answer: Objective function is a maximum at (16,0),

Z = 4x+4y = 4(16) + 4(0) = 64

2. Maximize P = 3x + 2y

Subject to x + y ≤ 8

2x + y ≤ 13

x ≥ 0, y ≥ 0

Plot the constraints and the objective function Z, or P=3x+2y.

Push the objective function to the limit in the increase + direction permitted by the feasible region to find the maximum intersection.

Answer: Objective function is at a maximum at (5,3),

Z = 3x+2y = 3(5)+2(3) = 21

7 0

3 years ago

Write a whole number that rounds to

dimaraw [331]

1999

hope this answer helps!!!!

please rate, thank, and mark as brainliest!!!! :D

6 0

3 years ago

Read 2 more answers

A farmer sells 6.6 kilograms of apples and pears at a farmers market.4/5 of this weight is apples,the rest is pears.How many kil

Ad libitum [116K]

Answer:

1.32 kg

Step-by-step explanation:

Given a fraction of the market goods, we can find the remaining fraction by subtracting the given fraction from 1.

The fraction of the goods the farmer sells that is pears will be ...

(apples +pears) = (apples) +(pears)

pears = (apples +pears) -(apples)

pears = 1 - 4/5 = 1/5 . . . . . of the total goods

One-fifth of the goods sold will have a weight of ...

(1/5) × (6.6 kg) = 1.32 kg

The farmer sold 1.32 kg of pears at the market.

6 0

2 years ago

How do i find the area

Alexus [3.1K]

Hi there!

The formula for the area of a kite is A = 1/2(d1 x d2). Using this formula, all we need to do to find the area is to plug in each diagonal length, then solve the equation.

WORK:
A = 1/2(15 x 16)
A = 1/2(240)
A = 120cm^2

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

6 0

3 years ago