Answer:
x = - 
, x = 2
Step-by-step explanation:
To find h(g(x)) substitute x = g(x) into h(x) , that is
h(g(x))
= h(x + 1)
= (x + 1)²
= x² + 2x + 1
For h(g(x)) = 3x² + x - 5 , then
3x² + x - 5 = x² + 2x + 1 ← subtract x² + 2x + 1 from both sides
2x² - x - 6 = 0 ← in standard form
(2x + 3)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = -
x - 2 = 0 ⇒ x = 2
Answer:
25/30 and 28/30
Step-by-step explanation:
1. To find the least common denominator, you need to find the least common multiple of the two denominators which are 6 and 15. Prime factorization of these numbers gives:
6 = 2 x 3
15 = 5 x 3
A number that would evenly divide both 6 and 15 must contain 2 x 3 x 5 which is 30.
Thus 30 is the least common denominator.
2. Now we need to somehow change both fractions to make them have a denominator of 30. To do this we can multiply by fractions with same numerator and denominator since that would be like multiplying by 1.
So, 5/6 x 5/5 = 25/30
And 14/15 x 2/2 = 28/30
Answer:
28.3
Step-by-step explanation:
9x3.142=28.27800 and if you round that it is 28.3
Answer:
1. a) Square
2. c) Rectangle
Step-by-step explanation:
1. If you cut this rectangular prism in way to be PERPENDICULAR to the base, that means you're cutting it straight down, from the top to the bottom, in a vertical line. The cross-section obtained will be just like an end of the prism, which in this case is a square. Because it's a regular rectangular prism, no matter where you cut it, as long as it's vertical, perpendicular to the base, you'll get a square due to this particular form. Technically, the answer could also be a rectangle, since a square is a rectangle.
2. you cut this rectangular prism in way to be PARALLEL to the base, that means you're cutting it straight, from the front to the back, in an horizontal line. The cross-section obtained will be just like an top of the prism, which in this case is a rectangle. Because it's a regular rectangular prism, no matter where you cut it, as long as it's an horizontal line, parallel to the base, you'll get a rectangle due to this particular form.
