Answer:
Quad 1
Step-by-step explanation:
AXYZ is in the 2nd quad bc of the rotation, then goes back to 1st quad bc of reflection (y axis). After this, the translation doesn't affect the movement of quadrants. A""X""Y""Z"' lands in quadrant 1.
Answer:
see explanation
Step-by-step explanation:
(a)
Given
x² + 5x + 6
Consider the factors of the constant term ( + 6) which sum to give the coefficient of the x- term ( + 5)
The factors are 3 and 2, since
3 × 2 = 6 and 3 + 2 = 5, hence
x² + 5x + 6 = (x + 3)(x + 2) ← in factored form
(b)
To solve
x² + 5x + 6 = 0 ← use the factored form, that is
(x + 3)(x + 2) = 0
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x + 2 = 0 ⇒ x = - 2
Answer:
x=450
Step-by-step explanation:
1. you cross multiply 1200x3= 3600
2. Divide 3600 by 8
3. Solution is 450
Answer:
x = √47
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Trigonometry</u>
- [Right Triangles Only] Pythagorean Theorem: a² + b² = c²
Step-by-step explanation:
<u>Step 1: Define</u>
We have a right triangle. We can use PT to solve for the missing side length.
<u>Step 2: Identify Variables</u>
Leg <em>a</em> = 5
Leg <em>b </em>= <em>x</em>
Hypotenuse <em>c</em> = √72
<u>Step 3: Solve for </u><em><u>x</u></em>
- Substitute [PT]: 5² + x² = (√72)²
- Exponents: 25 + x² = 72
- Isolate <em>x</em> term: x² = 47
- Isolate <em>x</em>: x = √47
Answer:
72 sq. mi
Step-by-step explanation:
Breaking this down, we have 2 right triangles with sides of 3, 4, and 5 miles, and 3 rectangles with dimensions 3 x 5, 4 x 5, and 5 x 5 miles. Remember that the area of a triangle is 1/2 x b x h , where b and h are the triangle's base and height. The base and height of the triangles at the bases of the figure are 3 and 4, so each triangle has an area of 1/2 x 3 x 4 = 1/2 x 12 = 6 sq. mi, or 6 + 6 = 12 sq. mi together.
Onto the rectangles, we can find their area by multiplying their length by their width. Since the width of these rectangles is the same for all three - 5 mi - we can make our lives a little easier and just "glue" the lengths together, giving us a longer rectangle with a length of 3 + 4 + 5 = 12 mi. Multiplying the two, we find the area of the rectangles to be 5 x 12 = 60 sq. mi.
Adding this area to the triangle's area gives us a total area of 12 + 60 = 72 sq. mi.
