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
madreJ [45]
3 years ago
10

A science teacher told his students that the expression 4m^4/144n^4 represents the area in square units of the contaminated squa

re region in their activity. What is the width of the region in simplest form?
Mathematics
2 answers:
Bond [772]3 years ago
8 0
Given that the contaminated region is a square, the area is given by the formula:
Area=length*width
since in a square length=width
the 
area=length×length
or
area=width×width

thus given that area=4m^4/144n^4 sq. units let the width be w units
thus
area=w×w=4m^4/144n^4 
w²=4m^4/144n^4 
solving for w we get:
w=√(4m^4/144n^4 )
w=2m²/12n²
Hence the width,w=2m²/12n²
Anon25 [30]3 years ago
8 0

Answer:

The answer is 100% <u>B. m^2/6n^2 units</u>

I took the test and it was correct :)

You might be interested in
A rectangular tank that is 5324 ft cubed with a square base and open top is to be constructed of sheet steel of a given thicknes
marishachu [46]

Answer:

Side of 22 and height of 11

Step-by-step explanation:

Let s be the side of the square base and h be the height of the tank. Since the tank volume is restricted to 5324 ft cubed we have the following equation:

V = s^2h = 5324

h = 5324 / s^2

As the thickness is already defined, we can minimize the weight by minimizing the surface area of the tank

Base area with open top s^2

Side area 4sh

Total surface area A = s^2 + 4sh

We can substitute h = 5324 / s^2

A = s^2 + 4s\frac{5324}{s^2}

A = s^2 + 21296/s

To find the minimum of this function, we can take the first derivative, and set it to 0

A' = 2s - 21296/s^2 = 0

2s = 21296/s^2

s^3 = 10648

s = \sqrt[3]{10648} = 22

h = 5324 / s^2 = 5324 / 22^2 = 11

4 0
3 years ago
The equation 2x2 − 12x + 1 = 0 is being rewritten in vertex form. Fill in the missing step. Given 2x2 − 12x + 1 = 0 Step 1 2(x2
Bezzdna [24]

Answer:

Part 1) 2(x-3)^{2}-17=0  (the missing steps in the explanation)

Part 3) (8, 4); The vertex represents the maximum profit

Part 4) x = 3.58, 0.42

Part 5) x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made

Part 6) 2(x − 7)2 + 118; x = $7

Part 7) The maximum height of the puck is 4 feet. −(x − 4)^2 + 6

Part 8) (x + 3)^2 − 4

Part 9) 2(x − 1)^2 = 4

Part 10) 8(x − 4)^2 + 592

Step-by-step explanation:

Part 1) we have

2x^{2} -12x+1=0

Convert to vertex form

step 1  

Factor the leading coefficient and complete the square

2(x^{2} -6x)+1=0

2(x^{2} -6x+9)+1-18=0

step 2

2(x^{2} -6x+9)+1-18=0

2(x^{2} -6x+9)-17=0

step 3

Rewrite as perfect squares

2(x-3)^{2}-17=0

Part 3) we have

f(x)=-x^{2}+16x-60

we know that

This is the equation of a vertical parabola open downward

The vertex is a maximum

Convert to vertex form

f(x)+60=-x^{2}+16x

Factor the leading coefficient

f(x)+60=-(x^{2}-16x)

Complete the squares

f(x)+60-64=-(x^{2}-16x+64)

f(x)-4=-(x^{2}-16x+64)

Rewrite as perfect squares

f(x)-4=-(x-8)^{2}

f(x)=-(x-8)^{2}+4

The vertex is the point (8,4)

The vertex represent the maximum profit

Part 4) Solve for x

we have

-2(x-2)^{2}+5=0

-2(x-2)^{2}=-5

(x-2)^{2}=2.5

square root both sides

(x-2)=(+/-)1.58

x=2(+/-)1.58

x=2(+)1.58=3.58

x=2(-)1.58=0.42

Part 5) we have

f(x)=-x^{2}+50x-264

we know that

The zeros or x-intercepts are the value of x when the value of the function is equal to zero

so

In this context the zeros represent the number of monthly memberships where no profit is made

To find the zeros equate the function to zero

-x^{2}+50x-264=0

-x^{2}+50x=264

Factor -1 of the leading coefficient

-(x^{2}-50x)=264

Complete the squares

-(x^{2}-50x+625)=264-625

-(x^{2}-50x+625)=-361

(x^{2}-50x+625)=361

Rewrite as perfect squares

(x-25)^{2}=361

square root both sides

(x-25)=(+/-)19

x=25(+/-)19

x=25(+)19=44

x=25(-)19=6

Part 6) we have

-2x^{2}+28x+20

This is a vertical parabola open downward

The vertex is a maximum

Convert the equation into vertex form

Factor the leading coefficient

-2(x^{2}-14x)+20

Complete the square

-2(x^{2}-14x+49)+20+98

-2(x^{2}-14x+49)+118

Rewrite as perfect square

-2(x-7)^{2}+118

The vertex is the point (7,118)

therefore

The video game price that produces the highest weekly profit is x=$7

Part 7) we have

f(x)=-x^{2}+8x-10

Convert to vertex form

f(x)+10=-x^{2}+8x

Factor -1 the leading coefficient

f(x)+10=-(x^{2}-8x)

Complete the square

f(x)+10-16=-(x^{2}-8x+16)

f(x)-6=-(x^{2}-8x+16)

Rewrite as perfect square

f(x)-6=-(x-4)^{2}

f(x)=-(x-4)^{2}+6

The vertex is the point (4,6)

therefore

The maximum height of the puck is 4 feet.

Part 8) we have

x^{2}+6x+5

Convert to vertex form

Group terms

(x^{2}+6x)+5

Complete the square

(x^{2}+6x+9)+5-9

(x^{2}+6x+9)-4

Rewrite as perfect squares

(x+3)^{2}-4

Part 9) we have

2x^{2}-4x-2=0

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert to vertex form

Factor 2 the leading coefficient

2(x^{2}-2x)-2=0

Complete the square

2(x^{2}-2x+1)-2-2=0

2(x^{2}-2x+1)-4=0

Rewrite as perfect squares

2(x-1)^{2}-4=0

2(x-1)^{2}=4

The vertex is the point (1,-4)

Part 10) we have

8x^{2}-64x+720

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert to vertex form

Factor 8 the leading coefficient

8(x^{2}-8x)+720

Complete the square

8(x^{2}-8x+16)+720-128

8(x^{2}-8x+16)+592    

Rewrite as perfect squares    

8(x-4)^{2}+592

the vertex is the point (4,592)

The population has a minimum at x=4 years ( that is after 4 years since 1998 )

6 0
3 years ago
in a pottery class, a teacher has 2/3 pound of clay for 6 students. If she gives each student a equal amount of clay, how much w
Jlenok [28]
She will give 1/9 pound of clay to each student
8 0
3 years ago
Read 2 more answers
How many times greater is 130,000,000 than 64,800,000?
insens350 [35]
\frac{130,000,000}{64,800,000} = \frac{1,300}{648} =\boxed {2.00617283951}
4 0
3 years ago
Slove for y show all your work 12y + 4 = 8y-12​
Vedmedyk [2.9K]

Answer:

y = -4

Step-by-step explanation:

12y + 4 = 8y-12​

Subtract 8y from each side

12y - 8y +4 = -12

4y +4 = -12

Subtract 4 from each side

4y +4-4 = -12 -4

4y = -16

Divide by 4

4y/4 = -16/4

y = -4

8 0
3 years ago
Read 2 more answers
Other questions:
  • (6x?+ 5) - (4x - 3)<br> A. 6x2 - 4x + 2<br> B. 2x2 + 2<br> C. 2x2 + 8<br> O D. 6x2 - 4x + 8
    10·2 answers
  • Please Help !!! Picture shown.
    13·2 answers
  • An animal shelter has two purebred Labradors among the 81 dogs available for adoption. It is also known that 7/9 of the
    15·1 answer
  • 10. For the equation 3x – 4 = 8, which
    5·2 answers
  • What is the area of the shaded region?
    13·1 answer
  • You and your friend drive toward each other. The equation 50h = 190 – 45h represents the number h of hours until you and your fr
    8·1 answer
  • Need help on this please help
    5·1 answer
  • Please help...<br><br> Will someone please help on the questions circled in black...
    7·2 answers
  • Estimate the product of 45.67and 1.42​
    14·1 answer
  • Find x please :) pleaseeee
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!