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
vodka [1.7K]
3 years ago
8

what positive number satisfies the condition that twice the number minus three times the reciprocal of the number is equal to 1?

Mathematics
1 answer:
marshall27 [118]3 years ago
8 0
Solve:

"<span>twice the number minus three times the reciprocal of the number is equal to 1."
                                                     3(1)
Let the number be n.  Then 2n - ------- = 1
                                                       n

Mult all 3 terms by n to elim. the fractions:

2n^2 - 3 = n.  Rearranging this, we get 2n^2 - n - 3 = 0.

We need to find the roots (zeros or solutions) of this quadratic equation.

Here a=2, b= -1 and c= -3.  Let's find the discriminant b^2-4ac first:

disc. = (-1)^2 - 4(2)(-3) = 1 + 24 = 25.

That's good, because 25 is a perfect square.
                -(-1) plus or minus 5         1 plus or minus 5
Then x = ------------------------------ = --------------------------
                            2(2)                                  4

x could be 6/4 = 3/2, or -5/4.

You must check both answers in the original equation.  If the equation is true for one or the other or for both, then you have found one or more solutions.</span>
You might be interested in
G(x) = -2x^3 – 15x^2 + 36x
shusha [124]

Consider the function G(x) = -2x^3 - 15x^2 + 36x. First, factor it:

G(x) = -2x^3 - 15x^2 + 36x=-x(2x^2+15x-36)=\\ \\=-x\cdot 2\cdot \left(x-\dfrac{-15-\sqrt{513}}{4}\right)\cdot \left(x-\dfrac{-15+\sqrt{513}}{4}\right).

The x-intercepts are at points \left(\dfrac{-15-\sqrt{513} }{4},0\right),\ (0,0),\ \left(\dfrac{-15+\sqrt{513} }{4},0\right).

1. From the attached graph you can see that

  • function is positive for x\in \left(-\infrty, \dfrac{-15-\sqrt{513} }{4}\right)\cup \left(0,\dfrac{-15+\sqrt{513} }{4}\right);
  • function is negative for x\in \left(\dfrac{-15-\sqrt{513} }{4},0\right)\cup \left(\dfrac{-15+\sqrt{513} }{4},\infty\right).

2. Since

G(-x) = -2(-x)^3 - 15(-x)^2 + 36(-x)=2x^3-15x^2-36x\neq G(x)\ \text{and }\neq -G(x) the function is neither even nor odd.

3. The domain is x\in (-\infty,\infty), the range is y\in (-\infty,\infty).

8 0
3 years ago
Read 2 more answers
Obtuse angles measure greater than 90 degrees
Harman [31]

yes obtuse angles measure over 90 degrees and less 180 degrees

4 0
3 years ago
50 Points!
Advocard [28]
Well, 50 points total given, 25 points per user  and 13 bonus for brainliest

anyway


1.
add them equations, the y's will cancel
x+2y=4
<span>3x-2y=4 +</span>
4x+0y=8

4x=8
divide by 4 both sides
x=2
sub back
x+2y=4
2+2y=4
minus 2
2y=2
divide 2
y=1
x=2
y=1
(x,y)
(2,1) is solution


2.
the solution is where they intersect
multiply 2nd equation by 2 and add to first
4x-14y=6
<span>-4x+14y=-6 +</span>
0x+0y=0
0=0
infinite solutions

that is because they are actually the same line
the solutions are (x,y) such that they satisfy -2x+7y=-3 or 4x-14y=6 (same equaiton)
infinite solutions



3.
multiply first equation by 2 and add to first
4x+2y=-6
<span>1x-2y=-4 +</span>
5x+0y=-10

5x=-10
divide by 5 both sides
x=-2
sub bac
x-2y=-4
-2-2y=-4
add 2
-2y=-2
divide by -2
y=1

x=-2
y=1
(x,y)
(-2,1)


4.
coincident means they are the same line
so

we see that we have to multiply 4 by 2 to get 8
multiply top equation by 2
8x+10y=16
8x+By=C
B=10 and C=16


5.
a. false, either 0, 1, or infinity solutions
change the word 'two' to 'one' or 'zero' or 'infinite', or change 'can' into 'can't'

b.false
 'sometimes' to 'always'

c. true

d. false, change 'sometimes' to 'always'


EC
total cost=150
TC=childC+adultC
TC=3c+5a
150=3c+5a


40 tickets, c+a
40=c+a

the equations are
150=3c+5a and
40=c+a

eliminate
multiply 2nd equaton by -3 and ad to first one

150=3c+5a
<span>-120=-3c-3a +</span>
30=0c+2a

30=2a
divide by 2
15=a

sub back
40=c+a
40=c+15
minus 15
25=c

25 children tickets and 15 adult tickets were sold


ANSWERS:

1.
(2,1) is solution

2.
infinite solutions

3.
(-2,1)

4.
B=10 and C=16

5.
a. false,
change the word 'two' to 'one' or 'zero' or 'infinite', or change 'can' into 'can't'

b.false
 'sometimes' to 'always'

c. true

d. false, change 'sometimes' to 'always'

EC
the equations are
150=3c+5a and
40=c+a
25 children tickets and 15 adult tickets were sold
7 0
3 years ago
Read 2 more answers
You earn $8.50 per hour. Then you receive a raise to $9.35 per hour. Find the percent increase. Then find your pay per hour if y
netineya [11]
Subtract $8.50 by $9.35
4 0
3 years ago
sophie was 28 years old when daughter Nichole was born. In how many years will Sophie be two years less than still times Nichole
Kamila [148]
It will take 6 years for that to happen. 

You can find this by setting Nichole's age as x and Sophie's age as x + 28 since she will always be 28 years older. 

Now we are looking for a time that Sophie's age is equal to 2 less than 6 times Nichole's age. So we can set up the below equation. 

6(x) - 2 = x + 28
6x - 2 = x + 28
5x - 2 = 28
5x = 30
x = 6

This let's us know that it needs to be when Nichole is 6, which is 6 years in the future. 
6 0
3 years ago
Other questions:
  • If MNO = PQR, which of the following can you conclude as being true?
    11·2 answers
  • What is the solution of the equation?<br>6/7 x - 8 = 7
    15·1 answer
  • A standard number cube is rolled once, what is the probability that the upturned face is three or less?
    7·1 answer
  • What is [4-{8x÷4x}]×8​
    12·1 answer
  • Can someone please help me
    6·1 answer
  • For all values of x,
    14·1 answer
  • A water container was 1/4 full. Two litres of water was added. The container was then 1/3 full. How much did the container hold?
    9·1 answer
  • The price of printing digital photos is $1.40 for 7 prints. If Louie wants to have 48 digital photos printed, what will be the c
    11·1 answer
  • An animal shelter has 36 pets available for adoption. 1/4 of them are puppies. How many are puppies?
    10·1 answer
  • Find the theoretical probability of rolling a number cube labeled 1-12 and<br> it landing on 7.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!