To figure out the common denominator for these fractions, I'll first need to factor that quadratic in the denominator on the right-hand side of the rational equation. This will also allow me to find the disallowed values for this equation. Factoring gives me:

x2 – 6x + 8 = (x – 4)(x – 2)

The factors of the quadratic on the right-hand side "just so happen" to be duplicates of the other denominators. This often happens in these exercises. (So often, in fact, that if you get completely different factors, you should probably go back and check your work.)

Step-by-step explanation:

4 0

3 years ago

The table shown below shows some values for functions f(x) and g(x). What is/are the solution(s) to f(x)=g(x)? Explain your answ

salantis [7]

Answer:

x = -1

Step-by-step explanation:

Both tables show a function value of 9 for x = -1.

x = -1 is the solution to f(x) = g(x), since f(-1) = 9 = g(-1).

5 0

3 years ago

The formula that describes an object's motion is given by S=ut+1/2at^2 , where S is the distance traveled, u is the initial velo

RSB [31]

S = ut + (1/2)a(t²) Subtract ut from both sides
(1/2)a(t²) = S - ut Multiply both sides by 2
a(t²) = 2s - 2ut Divide both sides by t²
a= 2s/t² - 2u/t

a= (2S - 2ut)/t²

Answer is C) but there should be parentheses around the term (2S-2ut)

5 0

3 years ago

A water well is to be drilled in the desert where the soil is either rock, clay or sand. The probability of rock P(R)equals=0.

GaryK [48]

The tree diagram for the probability is shown below

P(Clay|Positive) is read 'Probability of Clay given the result is Positive'.

This is a case of conditional probability.

The formula for conditional probability is given as
P(Clay|Positive) = P(Clay∩Positive) ÷ P(Positive)

P(Clay∩Positive) = 0.21×0.48 = 0.1008

P(Positive) = P(Rock∩Positive) + P(Clay∩Positive) + P(Sand∩Positive)
P(Positive) = (0.53×0.53) + (0.21×0.48) + (0.26×0.75)
P(Positive) = 0.2809 + 0.1008 + 0.195
P(Positive) = 0.5767

Hence,
P(Clay|Positive) = 0.1008÷0.5767 = 0.175 (rounded to 3 decimal place)

5 0

3 years ago