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Llana [10]
3 years ago
6

Write the expression 2a+b in the form of a fraction with the given denominator. Check if the domain of the expression changed. I

f yes, state the changes explicitely.
3a
Mathematics
1 answer:
Ymorist [56]3 years ago
6 0

Answer:

See below

Step-by-step explanation:

I will assume the given denominator is 3a as there is nothing attached to the statement.

Lets first look at the domain of 2a+b. As it is a polynomial with unknowns a and b, we know it has its domain in all real numbers for both  a and b as every polynomial does. For verifying it replace a and b by any real number you can think of.

Domain = a, b belonging to R

Now, if we divide 2a+b by 3a we will have:

(2a+b)/3a

As know we don not have a polynomial we cant state that the domain will still be all the real numbers for sure. We need to go further.

We have a fraction and as every fraction the denominator CAN'T be equal to 0, so 3a MUST be different to 0. This means that a MUST be different to 0. So, now our domain changes:

domain' = a, b belonging to R and a different to 0.

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Law Incorporation [45]
164+56−(3+4+1) =220−(3+4+1) =220−(7+1) =220−8 =212
7 0
3 years ago
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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
solve each equation. Round your answers to the nearest ten-thousandth. Show your work please. Part 2A​
Reika [66]

Answer:

16. x = 3.0822, -3.0822

17. x = 1.6432, -1.6432

18. x = 1, -1

Step-by-step explanation:

16. log5[(4x²+2)/8] = 1

(4x²+2)/8 = 5¹

4x² + 2 = 40

4x² = 38

x² = 38/4

x² = 19/2

x = +/- sqrt(19/2)

x = 3.0822, -3.0822

17. log7[(2x²-4)(5)] = 1

10x² - 20 = 7¹

10x² = 27

x² = 2.7

x = +/- sqrt(2.7)

x = 1.6432, -1.6432

18. log5[(2x²+8)/2] = 1

x² + 4 = 5¹

x² = 1

x = +/-1

4 0
3 years ago
In parallelogram LMNO, what are the values of x and y?
Norma-Jean [14]
In a parallelogram, if two opposites are congruent, then the two opposites are equal. We apply this description to solve the problem.
∠O = ∠M since they are opposite
2x = 3x - 55
55 = 3x - 2x
55 = x

Total of all angles in the parallelogram is 360°
∠L + ∠N +∠O +∠M=360°
360° - ∠O -∠M = ∠L + ∠N note that ∠L =∠N
360° -110° -110° = 2∠N
70° = ∠N

Solving for Y,
∠N = 5Y = 70°
Y=70/5
Y=14

Therefore, the value of "x" is 55 and the value of "y" is 14. The answer is the letter "C".
6 0
3 years ago
Read 2 more answers
Can u guys help me with this show all work that is the main thing
pochemuha
12x7x3=Volume recipe, the dirt they have to remove is within that volume so just do that formula and bam you got your answer
6 0
3 years ago
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