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hjlf
2 years ago
5

Use the distance formula and/or the Pythagorean Theorem to find the area of the triangle.

Mathematics
1 answer:
Free_Kalibri [48]2 years ago
8 0

Answer:

<h2>B. 20.5 square units</h2>

Step-by-step explanation:

Area of a triangle = 1/2 * Base * Height

For the given triangle, the value for the sides will be the distance between adjacent points on the triangle. Look at the attached file for the explanation of the diagram.

Using the formula for finding the distance between two points to get the base and the height of the triangle.

D = √(x2-x1)²+(y2-y1)²

For side AB where A = (-3, -4) and B(2, 0)

AB = √(2-(-3))²+(0-(-4))²

AB = √5²+4²

AB = √25+16

AB = √41

AB = Height

For side BC where B = (2, 0) and C = (6, -5)

√(x2-x1)²+(y2-y1)²

BC = √6-2)²+(-5-0)²

BC= √4²+(-5)²

BC = √16+25

BC= √41

BC = base of the triangle

Area of the triangle = 1/2 * √41 * √41

Area of the triangle = 1/2 * 41

Area of the triangle =20.5square units

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seropon [69]

Answer: a) x = 5 or -1 b) x = √3+2

c) x = -1/2 or -3/2

Step-by-step explanation:

a) (x − 2)² = 9

First step is to take the square root of both sides to eliminate the square

√ (x − 2)² = √9

x-2 = +-3

x = +3+2

x = 5 and;

x = -3+2

x = -1

x = 5 or -1

b) 3(x-2)² = 9

First we divide both sides by 3 to get;

(x-2)² = 9/3

(x-2)² = 3

Second step is to take the square root of both sides to eliminate the square

√(x-2)² = √3

x-2 = √3

x = √3+2

c) 6 = 24(x+1)²

Dividing both sides by 24, we have

6/24 = (x+1)²

1/4 = (x+1)²

Taking the square root of both sides we have

√1/4 = √(x+1)²

= +-1/2 = x+1

x = +1/2-1 = -1/2 and;

x = -1/2-1 = -3/2

x = -1/2 or -3/2

4 0
3 years ago
Your job pays $8 per hour. (a) Write an algebraic expression for your pay in dollars for working h hours. (b) What is your pay i
Korvikt [17]
P = 8h.....where P stands for pay

if u work 36 hrs...
P = 8(36)
P = 288 <==
4 0
3 years ago
Read 2 more answers
Marina has $145 to spend. She spends $68. 50 on jeans. T-shirts cost $12. 75. Write and solve an inequality to find the greatest
Kruka [31]

Answer:

6

Step-by-step explanation:

145-68.50 = 76.50

76.20/12.75 = no of t-shirts she can buy

ans= 6

6 0
2 years ago
The Martinez family went to play and paid $13 for 1 adult and 4 children. The Hernandez family went to the same place and paid $
andrey2020 [161]

Answer: the price for an adult ticket is $3

Step-by-step explanation:

Let x represent the price of one adult ticket.

Let y represent the price of one child ticket.

The Martinez family went to play and paid $13 for 1 adult and 4 children. This means that

x + 4y = 13 - - - - - - - - - - -1

The Hernandez family went to the same place and paid $14 for 3 adults and 2 children. This means that

3x + 2y = 14 - - - -- - - - - - - -2

Multiplying equation 1 by 3 and equation 3 by 1, it becomes

3x + 12y = 39

3x + 2y = 14

Subtracting, it becomes

10y = 25

y = 25/10 = 2.5

Substituting y = 2.5 into equation 1, it becomes

x + 4 × 2.5 = 13

x + 10 = 13

x = 13 - 10

x = 3

6 0
3 years ago
X(x+7)=0 solve whatever this id
Anit [1.1K]

Step-by-step explanation:

x(x + 7) = 0

By Zero Product rule,

either x = 0 or (x + 7) = 0.

=> x = 0 or x = -7.

5 0
2 years ago
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