1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
vodomira [7]
2 years ago
6

Which expression is equivalent to the following complex fraction?

Mathematics
1 answer:
svlad2 [7]2 years ago
4 0

Consider the <em>fraction</em> first ;

{:\implies \quad \sf \dfrac{\dfrac{3}{(x-1)}-4}{2-\dfrac{2}{(x-1)}}}

{:\implies \quad \sf \dfrac{\dfrac{3-4(x-1)}{\cancel{(x-1)}}}{\dfrac{2(x-1)-2}{\cancel{(x-1)}}}}

{:\implies \quad \sf \dfrac{3-4x+7}{2(x-1-1)}}

{:\implies \quad \boxed{\bf{\dfrac{-4x+7}{2(x-2)}}}}

<em>Hence, Option B) is </em><em>required</em><em> </em><em>answer</em>

You might be interested in
A rock is thrown upward from a bridge that is 57 feet above a road. The rock reaches its maximum height above the road 0.76 seco
bekas [8.4K]

answer:

f(t) = -9.9788169(t -0.76)^2 +57

Step-by-step explanation:

On this question we see that we are given two points on a certain graph that has a maximum point at 57 feet and in 0.76 seconds after it is thrown, we know can say this point is a turning point of a graph of the rock that is thrown as we are told that the function f determines the rocks height above the road (in feet) in terms of the  number of seconds t since the rock was thrown therefore this turning point coordinate can be written as (0.76, 57) as we are told the height represents y and x is represented by time in seconds. We are further given another point on the graph where the height is now 0 feet on the road then at this point its after 3.15 seconds in which the rock is thrown in therefore this coordinate is (3.15,0).

now we know if a rock is thrown it moves in a shape of a parabola which we see this equation is quadratic. Now we will use the turning point equation for a quadratic equation to get a equation for the height which the format is f(x)= a(x-p)^2 +q  , where (p,q) is the turning point. now we substitute the turning point

f(t) = a(t-0.76)^2 + 57, now we will substitute the other point on the graph or on the function that we found which is (3.15, 0) then solve for a.

0 = a(3.15 - 0.76)^2 + 57

-57 =a(2.39)^2  

-57 = a(5.7121)

-57/5.7121 =a

-9.9788169 = a      then we substitute a to get the quadratic equation therefore f is

f(t) = -9.9788169(t-0.76)^2 +57

4 0
2 years ago
A population has the following characteristics. (a) A total of 75% of the population survives the first year. Of that 75%, 25% s
Artemon [7]

Answer:

= \left[\begin{array}{ccc}1344\\84\\28\end{array}\right]  \left \begin{array}{ccc}{0 \  \leq  age   \leq  1 }\\{ 1 \  \leq  age   \leq  2 }\\{2 \  \leq  age  \leq 3}\end{array}\right

i.e after the first year ;

there 1344 members in the first age class

84 members for the second age class; and

28 members for the third age class

Step-by-step explanation:

We can deduce that the age distribution vector x represents the number of population members for each age class; Given that in each class of age there are 112 members present.

The current age distribution vector is as follows:

x = \left[\begin{array}{ccc}1&1&2\\1&1&2\\1&1&2\end{array}\right] \left[\begin{array}{ccc}{0 \  \leq  age   \leq  1 }\\{ 0 \  \leq  age   \leq  2 }\\{0 \  \leq  age   \leq 3}\end{array}\right]

Also , the age transition matrix is as follows:

L = \left[\begin{array}{ccc}3&6&3\\0.75&0&0 \\0&0.25&0\end{array}\right]

After 1 year ; the age distribution vector will be :

x_2 =Lx_1 = \left[\begin{array}{ccc}3&6&3\\0.75&0&0 \\0&0.25&0\end{array}\right]  \left[\begin{array}{ccc}1&1&2\\1&1&2\\1&1&2\end{array}\right]

= \left[\begin{array}{ccc}1344\\84\\28\end{array}\right]  \left \begin{array}{ccc}{0 \  \leq  age   \leq 1 }\\{ 1 \  \leq  age   \leq  2 }\\{2 \  \leq  age   \leq  3}\end{array}\right

6 0
2 years ago
What is f(-2) of the function given below? *<br> f(x) = 3x2 - 4x + 1
slava [35]

Answer:

f(-2) = 21

Step-by-step explanation:

Step 1: Define

f(x) = 3x² - 4x + 1

f(-2) is x = -2

Step 2: Substitute and Evaluate

f(-2) = 3(-2)² - 4(-2) + 1

f(-2) = 3(4) + 8 + 1

f(-2) = 12 + 9

f(-2) = 21

5 0
2 years ago
Find a ·<br> b. |a| = 4, |b| = 7, the angle between a and b is 2π/3
galben [10]

Answer:

-14

Step-by-step explanation:

a·b = |a|×|b|×cos(angle between them)

= 4×7×(-1/2)

= -14

5 0
3 years ago
Caswell started studying how the number of branches on his tree grows over time. The relationship between the elapsed time ttt,
ipn [44]

Answer:

t =log(20) / 0.3 = 10*log(20) / log(1,000) - years - when the tree will have 100 branches.

Step-by-step explanation:

100 = 5 * 10^(0.3t), solve for t

Divide both sides by 5:

20 =10^(0.3t)

Take the log of both sides:

0.3t =log(20)

Divide both sides by 0.3:

Multiply the RHS by 10 / 10

t =log(20) / 0.3 = 10*log(20) / log(1,000) - years - when the tree will have 100 branches.

8 0
3 years ago
Read 2 more answers
Other questions:
  • Which phrase best describes the translation from the graph y=(x-5)^2+7 to the graph of y=(x+1)^2-2
    8·2 answers
  • Find the slope and Y-intercept of the graph of this equation <br><br> y-9x=1/2
    9·1 answer
  • 758 round to the nearsest hundred
    13·2 answers
  • A rectangular prism has dimensions of 3x, 5x, and 6x. Write an expression for the total volume of the prism.
    6·2 answers
  • A box has a length of 15 in., a width of 7 in., and a height of 9 in. If Tara plans to cover the box with wrapping paper, how mu
    13·1 answer
  • Need help wit number 60 plz. Math.
    10·1 answer
  • What is the absolute value of 9?<br>need it for tomorrow
    9·2 answers
  • Which of the following is a parent function?
    11·1 answer
  • True or False: The following set of points could represent a function:
    12·1 answer
  • Over a 30-day period, the mean temperature in Morristown was 56°F with a standard deviation of 8.4°F and the mean temperature in
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!