MATHEMATICS HIGH SCHOOL

What is the area of a triangle with vertices at (0, −2) ,(8, −2) , and (9, 1) ?
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Answers

Answer 1

Answer:

The area of a triangle with vertices at (0, −2) ,(8, −2) and (9, 1) is 12 square units

Solution:

Given, vertices of the triangle are A(0, -2), B(8, -2) and C(9, 1).

We have to find the area of the given triangle.

The area of triangle when vertices are given is:

$\text { Area of triangle }=(1)/(2)\left|x_(1)\left(y_(2)-y_(3)\right)+x_(2)\left(y_(3)-y_(1)\right)+x_(3)\left(y_(1)-y_(2)\right)\right|$

$\text { Where, }\left(x_(1), y_(1)\right),\left(x_(2), y_(2)\right),\left(x_(3), y_(3)\right) \text { are vertices of the triangle. }$

Here in our problem,

$\left(\mathrm{x}_(1), \mathrm{y}_(1)\right)=(0,-2),\left(\mathrm{x}_(2), \mathrm{y}_(2)\right)=(8,-2) \text { and }\left(\mathrm{x}_(3), \mathrm{y}_(3)\right)=(9,1)$

Now, substitute the above values in the formula:

$\text { Area of triangle }=(1)/(2)\left|x_(1)\left(y_(2)-y_(3)\right)+x_(2)\left(y_(3)-y_(1)\right)+x_(3)\left(y_(1)-y_(2)\right)\right|$

$\begin{array}{l}{=(1)/(2)|0(-2-1)+8(1-(-2))+9(-2-(-2))|} \n\n {=(1)/(2)|0+8(1+2)+9(2-2)|} \n\n {=(1)/(2)|0+24+0|} \n\n {=(24)/(2)} \n\n {=12 \text { square units }}\end{array}$

Hence, the area of the triangle is 12 square units.

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Answers

Answer:

Express as exponents) 1) 81 / 2) 4/9 3) -64

Challange: Use parenthesis) 1) 3b 2) 8x^3y^3 3)15x^2y^2

Evaluate) 1) 125 2) 81/256

Challenge) 9a^2b^2

True or flase) 1) flase 2) false 3) true 4) false

Step-by-step explanation:

Question 2 An exponential model y = a.6 passes through the points (0,9) and (3,243). What are the values of a and b?

Answers

Answer:

a = 9, b = 3

Step-by-step explanation:

The exponential function is

y = a $b^(x)$

Find a and b by using the points it passes through

Using (0, 9 ) then

9 = a $b^(0)$ ( $b^(0)$ = 1 )

a = 9

y = 9 $b^(x)$

Using (3, 243 ) then

243 = 9b³ ( divide both sides by 9 )

27 = b³ ( take the cube root of both sides )

b = $\sqrt[3]{27}$ = 3

y = 9 $(3)^(x)$ ← exponential equation

What is the value of x in 3x+7y=27

Answers

Answer:

$x = (-7y)/(3) +9$

Step-by-step explanation:

Note the equal sign, what you do to one side, you do to the other side. Do the opposite of PEMDAS. Isolate the variable, x.

PEMDAS is the order of operation, and =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, subtract 7y from both sides:

3x + 7y (-7y) = 27 (-7y)

3x = -7y + 27

Next, divide 3 from all terms on both sides:

(3x)/3 = (-7y + 27)/3

x = (-7y/3) + 9

$x = (-7y)/(3) +9$

Find the square root of 0.81 a. 0.9 b. 9 c. 81 d. 0.09

Answers

The square of 0.9 will result to 0.81, and the squareroot of 0.81 is equal to 0.9.

What is square and square root

Squares are the numbers gotten after multiplying a value by itself. While the squareroot of a number is a number whose square is the given number. Hence, both are vice versa methods.

We shall solve for the square root of the number 0.81 as follows;

0.81 = (0.9 × 0.9)

by taking the squareroot of both sides we have;

√0.81 = √(0.9 × 0.9)

√0.81 = √(0.9)²

√0.81 = 0.9

Therefore, the square of 0.9 will result to 0.81, and the squareroot of 0.81 is equal to 0.9

Know more about square and squareroot here:brainly.com/question/428672

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