We need Pythagoras theorem here
a^2+b^2 = c^2
a, b = legs of a right-triangle
c = length of hypotenuse
Let S=shorter leg, in cm, then longer leg=S+2 cm
use Pythagoras theorem
S^2+(S+2)^2 = (10 cm)^2
expand (S+2)^2
S^2 + S^2+4S+4 = 100 cm^2 [collect terms and isolate]
2S^2+4S = 100-4 = 96 cm^2
simplify and form standard form of quadratic
S^2+2S-48=0
Solve by factoring
(S+8)(S-6) = 0 means (S+8)=0, S=-8
or (S-6)=0, S=6
Reject nengative root, so
Shorter leg = 6 cm
Longer leg = 6+2 cm = 8 cm
Hypotenuse (given) = 10 cm
Answer:
Box 2 has 3 times the volume of Box 1....
Answer:
Step-by-step explanation:
Given
-- total
--- defective
--- selected
Required
The probability of rejecting the batch
This means that at least one of the selected piece is defected.
So, we first calculate the probability that all the selected piece are accepted.
So, we have:
The denominator decreases by 1 because it is a probability without replacement; 180 is subtracted from the numerator to represent the number of non-defective CDs
So, we have:
Using the complement rule, the probability that the batch will be rejected is:
The shape consists of 5 faces. One on the front, one on the back, one on the left of the shape, the other on the right, and of course the one on the bottom :)
Hope it helped.
Answer:
see below
Step-by-step explanation:
A: 2x² - 3x - 5
(2x - 5)(x + 1)
B: Set the factored equation equal to zero and solve for x.
(2x - 5)(x + 1) = 0
2x - 5 = 0
2x = 5
x = 5/2
x + 1 = 0
x = -1
The x-intercepts are 5/2 and -1
C) To find the end behavior, you need to look at the term in the unfactored equation with the highest exponential number. For this equation, that is 2x². Since the exponent is positive, both ends of the graph will point in the same direction. Because the leading coefficent is positive, the graph will point upwards. The end behavior of the graph is that as the x-values approach both ∞ and -∞, the function approaches ∞.
D) Since we know that the x-intercepts are 5/2 and -1, you can plot these points. You also know that the graph will be in an upward U shape. Plug in a couple x-values and plot them to make the graphing of the equation more accurate.
