Mathematics: Are the graphs of y=3/8x -5 and y=3/8x +2 parallel

Are the graphs of y=3/8x -5 and y=3/8x +2 parallel, №12638016, 23.04.2020 09:57

Mathematics

1. write the equation in standard form. identify the important features of the graph: x^2+y^2-9x+10y+15=0 2. write the equation in standard form. identify the important features of the graph: y^2+4y-8x+4=0 3. write the equation of the conic section with the given properties: a hyperbola with vertices, (0, -6) and (0,6), asymptotes, y=3/4 x and y = -3/4 x 4. write the equation of the conic section with the given properties: an ellipse with vertices, (0,-5) and (0,5), and a minor axis of length 8.

Step-by-step answer

P Answered by PhD

3

(x-4.5)^2 +(y +5)^2 = 30.25x = (1/8)y^2 +(1/2)y +(1/2)y^2/36 -x^2/64 = 1x^2/16 +y^2/25 = 1

Step-by-step explanation:

1. Complete the square for both x and y by adding a constant equal to the square of half the linear term coefficient. Subtract 15, and rearrange to standard form.

(x^2 -9x +4.5^2) +(y^2 +10y +5^2) = 4.5^2 +5^2 -15

(x -4.5)^2 +(y +5)^2 = 30.25 . . . . . write in standard form

Important features: center = (4.5, -5); radius = 5.5.

__

2. To put this in the form x=f(y), we need to add 8x, then divide by 8.

x = (1/8)y^2 +(1/2)y +(1/2)

Important features: vertex = (0, -2); focus = (2, -2); horizontal compression factor = 1/8.

__

3. We want y^2/a^2 -x^2/b^2 = 1 with a=36 and b=(36/(3/4)^2) = 64:

y^2/36 -x^2/64 = 1

__

4. In the form below, "a" is the semi-axis in the x-direction. Here, that is 8/2 = 4. "b" is the semi-axis in the y-direction, which is 5 in this case. We want x^2/a^2 +y^2/b^2 = 1 with a=4 and b=5.

x^2/16 +b^2/25 = 1

_____

The first attachment shows the circle and parabola; the second shows the hyperbola and ellipse.

1. write the equation in standard form. identify the important features of the graph: x^2+y^2-9x+10

Mathematics

1. write the equation in standard form. identify the important features of the graph: x^2+y^2-9x+10y+15=0 2. write the equation in standard form. identify the important features of the graph: y^2+4y-8x+4=0 3. write the equation of the conic section with the given properties: a hyperbola with vertices, (0, -6) and (0,6), asymptotes, y=3/4 x and y = -3/4 x 4. write the equation of the conic section with the given properties: an ellipse with vertices, (0,-5) and (0,5), and a minor axis of length 8.

Step-by-step answer

P Answered by PhD

3

(x-4.5)^2 +(y +5)^2 = 30.25x = (1/8)y^2 +(1/2)y +(1/2)y^2/36 -x^2/64 = 1x^2/16 +y^2/25 = 1

Step-by-step explanation:

1. Complete the square for both x and y by adding a constant equal to the square of half the linear term coefficient. Subtract 15, and rearrange to standard form.

(x^2 -9x +4.5^2) +(y^2 +10y +5^2) = 4.5^2 +5^2 -15

(x -4.5)^2 +(y +5)^2 = 30.25 . . . . . write in standard form

Important features: center = (4.5, -5); radius = 5.5.

__

2. To put this in the form x=f(y), we need to add 8x, then divide by 8.

x = (1/8)y^2 +(1/2)y +(1/2)

Important features: vertex = (0, -2); focus = (2, -2); horizontal compression factor = 1/8.

__

3. We want y^2/a^2 -x^2/b^2 = 1 with a=36 and b=(36/(3/4)^2) = 64:

y^2/36 -x^2/64 = 1

__

4. In the form below, "a" is the semi-axis in the x-direction. Here, that is 8/2 = 4. "b" is the semi-axis in the y-direction, which is 5 in this case. We want x^2/a^2 +y^2/b^2 = 1 with a=4 and b=5.

x^2/16 +b^2/25 = 1

_____

The first attachment shows the circle and parabola; the second shows the hyperbola and ellipse.

Mathematics

Estimate the minimum value of the system by graphing. -x+y -3 -8x + 2y 4 -5 21 y C—X+ 4 2 2

Step-by-step answer

P Answered by Master

Answer is in the images THIS IS NO LINK ITS THE GRAPHS

Step-by-step explanation:

mark my answer the brainliest

so i can tell you the 4 algebra math calculators :)

Estimate the minimum value of the system by graphing.

-x+y> -3
-8x + 2y <4
-5 21
y C—X+
4 2
2

Mathematics

Estimate the minimum value of the system by graphing. -x+y -3 -8x + 2y 4 -5 21 y C—X+ 4 2 2

Step-by-step answer

P Answered by Specialist

Answer is in the images THIS IS NO LINK ITS THE GRAPHS

Step-by-step explanation:

mark my answer the brainliest

so i can tell you the 4 algebra math calculators :)

Mathematics

Which of the following describes the graph of y-3/8x-64-5 compared to the parent cube root function? stretched by a factor of 2 and translated 64 units right and 5 units down stretched by a factor of 8 and translated 8 units right and 5 units down stretched by a factor of 2 and translated 8 units right and 5 units down stretched by a factor of 8 and translated 64 units right and 5 units down

Step-by-step answer

P Answered by PhD

66

Stretched by a factor of 2 and translated 8 units right and 5 units down

Step-by-step explanation:

$y = \sqrt [3]{8x - 64} - 5 = \sqrt [3]{8(x - 8)} - 5$

A general form of a cube root function has four parameters: a, b, c, and d:

$y = a\sqrt[3]{b(x - c)} + d$

The effects of each parameter are

a — stretches in the y direction by a factor of a

b — stretches in the y direction by a factor of ∛b

c — translates c units in x direction

d — translates d units in y direction

In your function, a = 1, b = 8, c = 8, and d = -5, so it is

stretched vertically by a factor of 2 translated 8 units to the right translated 5 units down

The diagram below shows you function (purple graph) and the parent cube root function (blue). The parent function is translated eight units to the right and five units own (red arrows).The blue arrows show that the function is stretched vertically by a factor of two.

Mathematics

Which of the following describes the graph of y-3/8x-64-5 compared to the parent cube root function? stretched by a factor of 2 and translated 64 units right and 5 units down stretched by a factor of 8 and translated 8 units right and 5 units down stretched by a factor of 2 and translated 8 units right and 5 units down stretched by a factor of 8 and translated 64 units right and 5 units down

Step-by-step answer

P Answered by PhD

66

Stretched by a factor of 2 and translated 8 units right and 5 units down

Step-by-step explanation:

$y = \sqrt [3]{8x - 64} - 5 = \sqrt [3]{8(x - 8)} - 5$

A general form of a cube root function has four parameters: a, b, c, and d:

$y = a\sqrt[3]{b(x - c)} + d$

The effects of each parameter are

a — stretches in the y direction by a factor of a

b — stretches in the y direction by a factor of ∛b

c — translates c units in x direction

d — translates d units in y direction

In your function, a = 1, b = 8, c = 8, and d = -5, so it is

stretched vertically by a factor of 2 translated 8 units to the right translated 5 units down

The diagram below shows you function (purple graph) and the parent cube root function (blue). The parent function is translated eight units to the right and five units own (red arrows).The blue arrows show that the function is stretched vertically by a factor of two.

Mathematics

1. the width w of a rectangular swimming pool is x+4. the area a of the pool is 2x^3-29+12. what is an expression for the length of the pool? a. 2x^2+8x+3 b. 2x^2-8x-3 c. 2x^2-8x+3 d. 2x^2+8-3 2. simplify x/6x-x^2 a. 1/6-x; where x = 0,6 b. 1/6-x; where x=6 c. 1/6; where x=0 d. 1/6 3. simplify -12x4/x4+8x^5 a. -12/1+8x; where x= -1/8 b. -12/1+8x; where x= -1/8,0 4. simplify x+5/ x^2+6x+5 a. 1/x+1; where x= -1 b. 1/x+1; where x=-1, -5 5. simplify x^2-3x-18/x+3 a. x-3 b. x-6; where x= -3 c. x-6; where x= 6 d. 1/x+3; where x= -3 6. simplify 2/3a .

Step-by-step answer

P Answered by PhD

20

Question 1

To find the width of the rectangle, we divide the area by the length
$2x^{3}-29x+12$ ÷ x+4

We use the method of long division to get the answer. The method is shown in the first diagram below

$2x^{2}-8x+3$

Question 2:
$\frac{x}{6x-x^{2} } = \frac{x}{x(6-x)} = \frac{1}{6-x}$

Question 3:
$\frac{-12 x^{4} }{x^{4}+8 x^{5} }= \frac{-12 x^{4} }{ x^{4}(1+8x)}= \frac{-12}{1+8x}$

Question 4:
$\frac{x+5}{x^{2}+6x+5}= \frac{x+5}{(x+1)(x+5)}= \frac{1}{x+1}$

Question 5:
$\frac{x^{2}-3x-18} {x+3}= \frac{(x-6)(x+3)}{x+3}= \frac{x-6}{1}=x-6$

Question 6:
$\frac{2}{3a}$ × $\frac{2}{a^{2}}$ = $\frac{4}{3a^{3} }$ where $a \neq 0$

Question 7: (Question is not written well)
$\frac{x-5}{4x+8}$ × $(12x^{2}+32x+8)$
$\frac{12 x^{3}-28 x^{2} -152x-40 }{4x+8}$
By performing long division we get an answer $3 x^{2} -x-36$ with remainder of 248

Question 8:
$( \frac{x^{2}-16} {x-1})$ ÷ (x+4)

$( \frac{ x^{2}-16 }{x-1})$ × $\frac{1}{x+4}$
$\frac{(x+4)(x-1)}{x-1}$ × $\frac{1}{x+4}$
Cancelling out x+4

we obtain $\frac{x+1}{x-1}$

Question 9:
$\frac{x^{2}+2x+1} {x-2}$ ÷ $\frac{x^{2-1} }{x^{2}-4 }$
$\frac{ x^{2}+2x+1 }{x-2}$ × $\frac{x^{2}-4 }{x^{2}-1}$
Factorise all the quadratic expression gives
$\frac{(x+1)(x+1)}{x-2}$ × $\frac{(x-2)(x+2)}{(x+1)(x-1)}$
Cancelling out (x+1)

and

gives a simplest form
$\frac{(x+1)(x+2)}{x-1}$

Question 10:

$\frac{24 w^{10}+8w^{12} }{4 x^{4} }= \frac{24w^{10} }{4 x^{4} } + \frac{8 w^{12} }{4 x^{4} }$
Cancelling out the constants of each fraction
$\frac{6w^{10} }{x^{4} }+ \frac{2w^{12} }{x^{4}}= \frac{6w^{10}+2w^{12} }{ x^{4}}$

Question 11:

$\frac{-6m^{9}-6m^{8}-16m^{6} }{2m^{3} } = \frac{-2m^{6}(3m^{3}-3m^{2}-8)}{2m^{3} }$
Cancelling $2m^{3}$ gives us the simplified form
$-m^{3}(3m^{3}-3m^{2}-8) = -3m^{6}+3m^{5}+8m^{3}$

Question 12:

$\frac{-4x}{x+7} - \frac{8}{x-7} = \frac{-4x(x-7)-8(x+7)}{(x+7)(x-7)}$
$\frac{-4 x^{2} +28x-8x-56}{(x+7)(X-7)}= \frac{-4 x^{2} +20x-56}{(x+7)(x-7)}$
Factorising the numerator expression
$\frac{(-4x+28)(x-2)}{(x+7)(x-7)} = \frac{-4(x-7)(x-2)}{(x+7)(x-7)}$
Cancelling out x-7

gives the simplified form
$\frac{-4x+8}{x-7}$

Question 13:

$\frac{3}{x-3} - \frac{5}{x-2}= \frac{x3(x-2)-5(x-2)}{y(x-3)(x-2)}$
$\frac{3x-6-5x+15}{(x-3)(x-2)}= \frac{-2x+9}{(x-3)(x-2)}$

Question 14:

$\frac{9}{x-1}- \frac{5}{x+4}= \frac{9(x+4)-5(x-1)}{(x-1)(x+4)}$ $\frac{9x+36-5x+5}{(x-1)(x+4)}= \frac{4x+41}{(x-1)(x+4)}$

Question 15:

$\frac{-3}{x+2}- \frac{(-5)}{x+3}= \frac{-3(x+3)-(-5)(x+2)}{(x+2)(x+3)}$
$\frac{-3x-9+5x+10}{(x+2)(x+3)}= \frac{2x+1}{(x+2)(x+3)}$

Question 16:

$\frac{4}{x}+ \frac{5}{x}=-3$
$\frac{9}{x}=-3$
x=-3

Question 17:

$\frac{1}{3x-6}- \frac{5}{x-2}=12$
$\frac{(x-2)-5(3x-6)}{(3x-6)(x-2)} = \frac{x-2-15x+30}{(3x-6)(x-2)}= \frac{-14x+28}{(3x-6)(x-2)}$

Question 18

1. the width w of a rectangular swimming pool is x+4. the area a of the pool is 2x^3-29+12. what is

Mathematics

1. the width w of a rectangular swimming pool is x+4. the area a of the pool is 2x^3-29+12. what is an expression for the length of the pool? a. 2x^2+8x+3 b. 2x^2-8x-3 c. 2x^2-8x+3 d. 2x^2+8-3 2. simplify x/6x-x^2 a. 1/6-x; where x = 0,6 b. 1/6-x; where x=6 c. 1/6; where x=0 d. 1/6 3. simplify -12x4/x4+8x^5 a. -12/1+8x; where x= -1/8 b. -12/1+8x; where x= -1/8,0 4. simplify x+5/ x^2+6x+5 a. 1/x+1; where x= -1 b. 1/x+1; where x=-1, -5 5. simplify x^2-3x-18/x+3 a. x-3 b. x-6; where x= -3 c. x-6; where x= 6 d. 1/x+3; where x= -3 6. simplify 2/3a .

Step-by-step answer

P Answered by PhD

20

Question 1

To find the width of the rectangle, we divide the area by the length
$2x^{3}-29x+12$ ÷ x+4

We use the method of long division to get the answer. The method is shown in the first diagram below

$2x^{2}-8x+3$

Question 2:
$\frac{x}{6x-x^{2} } = \frac{x}{x(6-x)} = \frac{1}{6-x}$

Question 3:
$\frac{-12 x^{4} }{x^{4}+8 x^{5} }= \frac{-12 x^{4} }{ x^{4}(1+8x)}= \frac{-12}{1+8x}$

Question 4:
$\frac{x+5}{x^{2}+6x+5}= \frac{x+5}{(x+1)(x+5)}= \frac{1}{x+1}$

Question 5:
$\frac{x^{2}-3x-18} {x+3}= \frac{(x-6)(x+3)}{x+3}= \frac{x-6}{1}=x-6$

Question 6:
$\frac{2}{3a}$ × $\frac{2}{a^{2}}$ = $\frac{4}{3a^{3} }$ where $a \neq 0$

Question 7: (Question is not written well)
$\frac{x-5}{4x+8}$ × $(12x^{2}+32x+8)$
$\frac{12 x^{3}-28 x^{2} -152x-40 }{4x+8}$
By performing long division we get an answer $3 x^{2} -x-36$ with remainder of 248

Question 8:
$( \frac{x^{2}-16} {x-1})$ ÷ (x+4)

$( \frac{ x^{2}-16 }{x-1})$ × $\frac{1}{x+4}$
$\frac{(x+4)(x-1)}{x-1}$ × $\frac{1}{x+4}$
Cancelling out x+4

we obtain $\frac{x+1}{x-1}$

Question 9:
$\frac{x^{2}+2x+1} {x-2}$ ÷ $\frac{x^{2-1} }{x^{2}-4 }$
$\frac{ x^{2}+2x+1 }{x-2}$ × $\frac{x^{2}-4 }{x^{2}-1}$
Factorise all the quadratic expression gives
$\frac{(x+1)(x+1)}{x-2}$ × $\frac{(x-2)(x+2)}{(x+1)(x-1)}$
Cancelling out (x+1)

and

gives a simplest form
$\frac{(x+1)(x+2)}{x-1}$

Question 10:

$\frac{24 w^{10}+8w^{12} }{4 x^{4} }= \frac{24w^{10} }{4 x^{4} } + \frac{8 w^{12} }{4 x^{4} }$
Cancelling out the constants of each fraction
$\frac{6w^{10} }{x^{4} }+ \frac{2w^{12} }{x^{4}}= \frac{6w^{10}+2w^{12} }{ x^{4}}$

Question 11:

$\frac{-6m^{9}-6m^{8}-16m^{6} }{2m^{3} } = \frac{-2m^{6}(3m^{3}-3m^{2}-8)}{2m^{3} }$
Cancelling $2m^{3}$ gives us the simplified form
$-m^{3}(3m^{3}-3m^{2}-8) = -3m^{6}+3m^{5}+8m^{3}$

Question 12:

$\frac{-4x}{x+7} - \frac{8}{x-7} = \frac{-4x(x-7)-8(x+7)}{(x+7)(x-7)}$
$\frac{-4 x^{2} +28x-8x-56}{(x+7)(X-7)}= \frac{-4 x^{2} +20x-56}{(x+7)(x-7)}$
Factorising the numerator expression
$\frac{(-4x+28)(x-2)}{(x+7)(x-7)} = \frac{-4(x-7)(x-2)}{(x+7)(x-7)}$
Cancelling out x-7

gives the simplified form
$\frac{-4x+8}{x-7}$

Question 13:

$\frac{3}{x-3} - \frac{5}{x-2}= \frac{x3(x-2)-5(x-2)}{y(x-3)(x-2)}$
$\frac{3x-6-5x+15}{(x-3)(x-2)}= \frac{-2x+9}{(x-3)(x-2)}$

Question 14:

$\frac{9}{x-1}- \frac{5}{x+4}= \frac{9(x+4)-5(x-1)}{(x-1)(x+4)}$ $\frac{9x+36-5x+5}{(x-1)(x+4)}= \frac{4x+41}{(x-1)(x+4)}$

Question 15:

$\frac{-3}{x+2}- \frac{(-5)}{x+3}= \frac{-3(x+3)-(-5)(x+2)}{(x+2)(x+3)}$
$\frac{-3x-9+5x+10}{(x+2)(x+3)}= \frac{2x+1}{(x+2)(x+3)}$

Question 16:

$\frac{4}{x}+ \frac{5}{x}=-3$
$\frac{9}{x}=-3$
x=-3

Question 17:

$\frac{1}{3x-6}- \frac{5}{x-2}=12$
$\frac{(x-2)-5(3x-6)}{(3x-6)(x-2)} = \frac{x-2-15x+30}{(3x-6)(x-2)}= \frac{-14x+28}{(3x-6)(x-2)}$

Question 18

1. the width w of a rectangular swimming pool is x+4. the area a of the pool is 2x^3-29+12. what is

Mathematics

Will mark brainiest 1. what is the equation of the line that goes through the point (-5,-2) and is parallel to the line represented by the equation below? 4x+5y=12 a. y=4/5x+2 b. y=4/5x+7=6 c. y=-4/5x-2 d. y=-4/5x-6 2. what is the equation of the line that goes through the point (-8,-6) and is perpendicular to the line represented by the equation below? y=8/3x-2 a. y= -3/8x+3 b. y= -3/8x+9 c. y= -3/8x-3 d. y= -3/8x-9 3. which equation produces a line that is parallel to the line represented by the function below? y=2/5x+9 a.5x+2y=4 b.2x-5y=8 c.5x-2y=-3

Step-by-step answer

P Answered by Specialist

7

1.D y=-4/5x-6

2.D y=-3/8x-9

3.C 5x-2y=-3

4. A 3x-5y=-1 and y=-5/3x-8

Mathematics

Will mark brainiest 1. what is the equation of the line that goes through the point (-5,-2) and is parallel to the line represented by the equation below? 4x+5y=12 a. y=4/5x+2 b. y=4/5x+7=6 c. y=-4/5x-2 d. y=-4/5x-6 2. what is the equation of the line that goes through the point (-8,-6) and is perpendicular to the line represented by the equation below? y=8/3x-2 a. y= -3/8x+3 b. y= -3/8x+9 c. y= -3/8x-3 d. y= -3/8x-9 3. which equation produces a line that is parallel to the line represented by the function below? y=2/5x+9 a.5x+2y=4 b.2x-5y=8 c.5x-2y=-3

Step-by-step answer