Kathy designed a square patio. She made the sides of the patio 15 feet. What is the area of the patio?

Find the area of triangle ABC with vertices A(2,1), B (12,2), C (12,8). Hence, or otherwise find the perpendicular distance from

Lapatulllka [165]

<h2>The area of a triangle is =54 square units</h2><h2>The perpendicular distance from B to AC is = $\frac{108}{\sqrt{149} } units$ </h2>

Step-by-step explanation:

Given a triangle ABC with vertices A(2,1),B(12,2) and C(12,8)

$x_1=2,y_1=1,x_2=12,y_2=2,x_3=12 and y_3=8$

The area of a triangle is= $\frac{1}{2} [x_1(y_2-y_3) +x_2 (y_3- y_1)+x_3(y_1-y_2)]$

= $|\frac{1}{2} [2(2-8+12(8-1)+12(1-2)]|$

= $|-54|$ = 54 square units

The length of AC = $\sqrt{(x_1-x_3)^{2} +(y_1-y_3)^2}$

= $\sqrt{(2-12)^{2} +(1-8)^2}$

= $\sqrt{149}$ units

Let the perpendicular distance from B to AC be = x

According To Problem

$\frac{1}{2} \times x \times \sqrt{149} = 54$

⇔ $x =\frac{108}{\sqrt{149} }$ units

Therefore the perpendicular distance from B to AC is = $\frac{108}{\sqrt{149} } units$

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Inverse of f(x) = 3 + 2 In x?

JulsSmile [24]

This is the inverse of f(x)= -3 - (-2)

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Help please..! I need the answer to this thank you.

torisob [31]

1. The additive identity is 0. This is because adding 0 to anything leads to the same value. Example: 0+3 = 3.

2. An equation is where you have two expressions separated by an equal sign. In your case it would be "a mathematical sentence whose verb is 'equal' (=)"

3. The multiplicative identity is 1. Multiply 1 with any number and the result is that same number. Example: 1*7 = 7.

4. An open sentence is an equation that contains one or more variables. An example would be x+2 = 4. The reason why we call it open is because the true or false nature of the sentence is up in the air until we know what x is. If we knew that x = 3 for instance, then x+2 = 4 would be false since 3+2 = 4 is false. If we nailed down what x was then it would go from open to closed.

5. The symmetric property is that if a = b then b = a. Think of a mirror how the image reverses.

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The answer is 24.32 is the difference

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A rectangular piece of metal is 25 in longer than it is wide. Squares with sides 5 in long are cut from the four corners and the

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