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ozzi
2 years ago
11

The expression (27y^-2)^1/3 / y^-2/3 can be simplified and written without negative exponents as

Mathematics
1 answer:
Phoenix [80]2 years ago
4 0

Answer:

3

Step-by-step explanation:

\displaystyle\tt \frac{(27y^{-2})^{\frac{1}{3}}}{y^{-\frac{2}{3}}}=\frac{(3^3\cdot y^{-2})^{\frac{1}{3}}}{y^{-\frac{2}{3}}}=\frac{3\cdot y^{-\frac{2}{3}}}{y^{-\frac{2}{3}}}=3

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Simplify 9 exponent 2
STatiana [176]

Answer:

81

Step-by-step explanation:

9^2 = 81 bc 9x9=81

3 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
2 years ago
I need help fast! This is polynomials help
antiseptic1488 [7]

Answer:

  • incorrect
  • correct
  • incorrect

Step-by-step explanation:

A + B = (-4x^2 +2x -5) +(3x^2 +6) = x^2(-4+3) +x(2) +(-5+6) = -x^2 +2x +1

  The given sum is Incorrect.

__

A - C = (-4x^2 +2x -5) -(-5x -4) = -4x^2 +x(2+5) +(-5+4) = -4x^2 +7x -1

   The given difference is Correct.

__

B + C = (3x^2 +6) +(-5x -4) = 3x^2 -6x +2

  The given sum is Incorrect.

5 0
3 years ago
Simplify 36*3.<br> O A. 35<br> B. 36<br> O C. 37<br> O D. 96<br> HELP ME
Lelu [443]

Answer:

12/1

Step-by-step explanation:

hope this helped if not sorry

6 0
2 years ago
PLSS helpp <br><br> btw have a nice day
Natali5045456 [20]
It’s the first one! The table shows X going up and Y going down, so the slope would be negative!
8 0
3 years ago
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