Answer:
18
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Step-by-step explanation:
<u>Step 1: Define</u>
4a - 2
a = 5
<u>Step 2: Evaluate</u>
- Substitute in <em>a</em>: 4(5) - 2
- Multiply: 20 - 2
- Subtract: 18
Answer:
C) a = 10√3, b = 5√3, c = 15 , d = 5
Step-by-step explanation:
Here we use the ratio of 30, 60, 90 degree triangle.
The ratio of sides, 1:√3:2
2x = 10
x = 5
d = 5
b = 5√3
c = 5√3√3
c = 5*3 = 15
c = 15
a = 2(5√3)
a = 10√3
Therefore, a = 10√3, b = 5√3, c = 15 and d = 5
Thank you.
Answer: (f·g)(x) = -5x³ - 31x² + 62x + 18
(f·g)(-1) = -70
(fog)(x) = 25x² - 130x + 155
(fog)(-1) = 310
<u>Step-by-step explanation:</u>
f(x) = x² + 8x + 2 g(x) = -5x + 9
(f·g)(x) = (x² + 8x + 2)(-5x + 9)
= -5x³ + 9x²
- 40x² + 72x
<u> - 10x + 18</u>
= -5x³ - 31x² + 62x + 18
(f·g)(-1)= -5(-1)³ - 31(-1)² + 62(-1) + 18
= -5(-1) - 31(1) - 62 + 18
= 5 - 31 - 62 + 18
= -70
****************************************************************************************
(fog)(x) = (-5x + 9)² + 8(-5x + 9) + 2
= 25x² - 90x + 81
- 40x + 72
<u> + 2</u>
= 25x² - 130x + 155
(fog)(-1) = 25(-1)² - 130(-1) + 155
= 25 + 130 + 155
= 310
<em>It wasn't clear if you wanted multiplication or composition so I solved both.</em>
Begin by finding the lowest point the quadratic equation can be, the vertex;
x²-1= is just a translation down of the graph x²
vertex; (0, -1) and since the graph of x² would extend to infinity beyond that point, we can say {x| x≥0} for domain and {y| y≥-1}.
For the linear equation, it is possible to have all x and y values, therefore range and domain belong to all real numbers.
Hope I helped :)