Answer:
Step-by-step explanation:
Pythagorean theorem: base ² +altitude² = hypotenuse²
1) hypotenuse² = base² + altitude²
x² = 6² + 3²
= 36 + 9
= 45
x = √45
x = 6.7 cm
4) base ² +altitude² = hypotenuse²
x ² + 3.7 ² = 4.2 ²
x ² + 13.69 = 17.64
x ² = 17.64 - 13.69 = 3.95
x = √3.95
x = 1.99 cm
10)c ² = a ² + b ²
= 3 ² +4 ²
= 9 + 16
c ² = 25
c = √25 = 5
11) a ² + b ² = c ²
9 ² +b² = 13 ²
81 + b² = 169
b² = 169 - 81 = 88
b = 9.38
12) a² + b² = c²
12² + b² = 22²
144 + b² = 484
b² = 484 - 144 = 340
b =√340 = 18.44
Answer:
40 m^3
Step-by-step explanation:
Volume of a pyramid = 1/3 * base area * height
base area = 4 x 4
1/3 * (4x4) * 7.5 = 40 m^3
Answer:
w = -3/8
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define Equation</u>
-6(w + 2) = w - 9 + 3(3w + 1)
<u>Step 2: Solve for </u><em><u>w</u></em>
- Distribute: -6w - 12 = w - 9 + 9w + 3
- Combine like terms: -6w - 12 = 10w - 6
- Add 6w to both sides: -12 = 16w - 6
- Isolate <em>w</em> term: -6 = 16w
- Isolate <em>w</em>: -3/8 = w
- Rewrite: w = -3/8
Answer:
Step-by-step explanation:
Answer:
-20x +52
Step-by-step explanation:
To solve this, we put the function g(x) into the function f(x) in the place of x
Put 5x-3 in for x in -4x
f(g(x)) = -4 (5x-13)
= -4*5x -4(-13)
= -20x +52
