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
rjkz [21]
3 years ago
10

(AM GIVING BRAINLIEST) Find all values of x such that x/(x - 5) =4/(x - 4)

Mathematics
2 answers:
Irina18 [472]3 years ago
4 0

Answer:

x = imaginary number

x₁ = 2<em>i</em>

x₂ = 6<em>i</em>

Step-by-step explanation:

x/(x - 5) =4/(x - 4)

x(x-4) = 4(x-5)

x*x + x*-4 = 4*x * 4*-5

x² -4x = 4x - 20

x² -4x - 4x + 20 = 0

x² - 8x + 20 = 0

x = {-(-8)±√((-8²)-(4*1*20))} / (2*1)

x = {8±√(64-80)} / 2

x = {8±√-16} / 2

√(-16) ∈<em> i</em>

<em>i </em>=  set of imaginary numbers

√-16 = -4<em>i</em>

then:

x = {8±(-4<em>i</em>) } / 2

x₁ = {8+(-4i)}/2 = {8-4i)/2 = 4i/2 = 2i

x₂ = {8-(-4)}/2 = {8+4i}/2 = 12i/2 = 6i

lesya [120]3 years ago
3 0

Answer:

\boxed{\sf x = 4 \pm 2i}

Step-by-step explanation:

\sf Solve  \: for  \: x: \\  \sf \implies \frac{x}{x - 5}  =  \frac{4}{x - 4}  \\  \\  \sf Cross \:  multiply: \\  \sf \implies x(x - 4) = 4(x - 5) \\  \\ \sf Expand  \: out  \: terms \:  of  \: the  \: left \:  hand \:  side: \\  \sf \implies {x}^{2}  - 4x = 4(x - 5) \\  \\  \sf Expand  \: out  \: terms \:  of \:  the \:  right \:  hand  \: side: \\  \sf \implies {x}^{2}  - 4x =  4x  - 20 \\  \\  \sf Subtract \:  4 x   \:  from  \: both  \: sides:\\  \sf \implies {x}^{2}  - 4x  - 4x =  4x  - 20  - 4x  \\ \\   \sf \implies {x}^{2}  - 8x  = - 20\\  \\  \sf Add  \: 16  \: to \:  both \:  sides: \\  \sf \implies {x}^{2}  - 8x + 16  = - 20 + 16 \\  \\  \sf\implies {x}^{2}  - 8x + 16  = -4 \\  \\  \sf Write  \: the \:  left  \: hand \:  side \:  as  \: a  \: square:  \\  \sf\implies {x}^{2}  - 4x - 4x + 16  = -4  \\   \\  \sf\implies x(x - 4)  - 4(x - 4)  = -4  \\   \\  \sf\implies (x - 4)(x - 4) = -4  \\  \\ \sf\implies {(x - 4)}^{2} =  - 4 \\  \\  \sf  Take  \: the  \: square \:  root  \: of \:  both  \: sides: \\  \sf\implies  \sqrt{ {(x - 4)}^{2}} =   \sqrt{ - 4}  \\  \\  \sf\implies x - 4 =  \pm 2i \\  \\  \sf Add \:  4  \: to  \: both \:  sides: \\  \sf\implies x - 4  + 4=  \pm 2i  + 4 \\   \\  \sf\implies x  =  4\pm 2i

You might be interested in
Refer to the Exhibit Student Grades. The professor has informed the class that 7.93 percent of her students received grades of A
Marta_Voda [28]

This question is incomplete, the complete question is;

Refer to the Exhibit Student Grades. A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11.

The professor has informed the class that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A

Answer:

the minimum score needed to receive a grade of A is 88.51

Step-by-step explanation:

Given the data in the question;

Let x represent the grades of the students that were normally distributed with mean μ = 73 and standard deviation σ = 11.

so, The professor has informed the class that 7.93 percent of her students received grades of A

the minimum score needed to receive a grade of A will be:

P( X > x ) = 7.93 %

P( X > x ) = 0.0793

1  - P( X ≤ x ) = 0.0793

- P( X ≤ x ) = 0.0793 - 1

- P( X ≤ x ) = - 0.9207

P( X ≤ x ) = 0.9207

⇒ P( X-μ/σ ≤ x-μ/σ ) = 0.9207

so, x-μ/σ = InvNormal( 0.9207 )  

x-μ/σ = 1.41

(x - 73) / 11 = 1.41

(x - 73) = 1.41 × 11

(x - 73)  = 15.51

x = 15.51 + 73

x = 88.51

Therefore, the minimum score needed to receive a grade of A is 88.51

7 0
2 years ago
Need help fast, will give brainliest!​
hoa [83]

Answer:

Correct answer is A

Step-by-step explanation:

3 0
2 years ago
Pedro gets 8 hours of sleep each night. How many hours does Pedro sleep in a year with 365 days
levacccp [35]
He sleeps 8 times 365 hours, which is 2920 hours
7 0
3 years ago
suppose the circumference of a crop circle is 150.7968 hectometers (hm) what's the radius of the circle? (usett=3.1416)​
gulaghasi [49]

Answer:

The radius of the circle is 24\ hm

Step-by-step explanation:

we know that

The circumference of a circle is equal to

C=2\pi r

In this problem we have

C=150.7968\ hm

\pi=3.1416

substitute and solve for r

150.7968=2(3.1416)r

r=150.7968/(2(3.1416))=24\ hm

7 0
3 years ago
Read 2 more answers
A and B are supplementary angles. If A= (4x – 30)° and m
AfilCa [17]

Answer:

82 degrees

Step-by-step explanation:

Hope this helps! ^^

3 0
3 years ago
Other questions:
  • What is the simplified form of x-2 over x2+x-6 divided x2+5x+4 over x+4
    10·2 answers
  • Morgan charges $12 per hour to babysit. Write an equation to determine how much it would cost,c, for Morgan to babysit for any n
    10·2 answers
  • 4. The distance from lan's home to the museum
    13·1 answer
  • How can you tell the difference between systems with no solution and infinite solutions?
    12·2 answers
  • Classify the four angles of the quadrilateral​
    8·1 answer
  • 9 and a half plus three eighths
    5·2 answers
  • Solve for x: -9x &lt; 27
    11·1 answer
  • What scale factor was applied to the first rectangle to get the resulting image?
    8·1 answer
  • The process for rationalizing a denominator in a variable expression is the same as in a numeric expression. Here’s a real-world
    8·2 answers
  • Help I will give you brainlist with 20 points
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!