3y - x = 2<br><br> -2y - x = -18<br><br> x = y =

line y = 2x+1 is transformed by a dialation with a scale factor of two and centered at (0,-4). what is the equation of the image

Gekata [30.6K]

Answer: y = 2x + 6

Step-by-step explanation:

Here the equation of line,

y = 2x + 1

y-intercept of the line is, (0, 1)

And, the slope of the line is 2.

Since, If a point (x,y) is dilated by a scale factor k about a point (a,b),

Then transformed point are get by,

$(x,y)\rightarrow (k(x-a)+a, k(y-b)+b)$

Thus, The transformed point of point (0,1) when dilation is occur by the scale factor 2 about the point (0,-4),

$(0,-4)\rightarrow (2(0-0)+0, 2(1+4)-4)$

$(0,-4)\rightarrow (0, 6)$

Thus, the point of the new line is (0,6)

And, the slope of the new line is 2 ( because in the dilation, the slope of the line does not change)

Thus, the equation of new line,

(y - 6) = 2 (x - 0)

y - 6 = 2x

y = 2x + 6

5 0

3 years ago

If f(x)=×^2+7x-5 and you divide by x-2, What is the quotient and remainder?

katrin [286]

Answer:

The quotient is : x+9

The remainder is : 13

Step-by-step explanation:

The question requires you to perform the long division method;

This will be;

$x-2\sqrt{x^2+7x-5}$

start with the x term in x-2 and the first term in the function, x², to get x then multiply the x with x-2 to get x²-2x and perform the operation below;

x-2√x²+7x-5 -----------to first get x and then multiply x*[x-2]⇒x²-2x

- x²-2x+0 ------------perform subtraction of like terms

---------------------

9x-5 ----now divide this answer by x-2 ,starting with x and 9x

----------------------This will give , 9 then multiply 9 by x-2 to get 9x-18 and perform the subtraction operation as;

9x-5

- 9x-18

------------------------

13

So the answer will be; x+9 remainder 13

6 0

3 years ago

Dos motos, A y B, toman la salida en una carrera de 90 km. La moto A realiza el recorrido con una velocidad media inferior en 20

aleksandr82 [10.1K]

Answer:

motorcycle A: 180 km/h

motorcycle B: 200 km/h

Step-by-step explanation:

To solve this question we need to write a system of equations for A and B, using the equation:

distance = speed * time

The speed of A is 20 less than the speed of B, so:

speedA = speedB - 20

And the time A traveled is 3 minutes (0.05 hours) more than B's time, so:

timeA = timeB + 0.05

Then, using the distance equation, we have that:

distanceB = speedB * timeB

90 = speedB * timeB

distanceA = speedA * timeA

90 = (speedB - 20) * (timeB + 0.05)

90 = speedB * timeB + 0.05 * speedB - 20*timeB - 1

90 = 90 + 0.05 * speedB - 20*timeB - 1

20*timeB = 0.05 * speedB - 1

timeB = (speedB - 20)/400

using this timeB in the distance equation, we have:

90 = speedB * (speedB - 20)/400

90 * 400 = speedB^2 - 20*speedB

speedB^2 - 20*speedB - 36000 = 0

Solving this quadratic equation, we have speedB = 200 km/h

And the speedA is:

speedA = speedB - 20 = 200 - 20 = 180 km/h

6 0

2 years ago

How many unique ways are there to arrange the letters in the word DEN?

Tatiana [17]

2 is the correct answer I'm almost definite

5 0

2 years ago

Read 2 more answers

A jewelry designer is making a pendant. The pendant will be a circular dis (center O) with a circular hold cut out of it, as sho

antoniya [11.8K]

Answer:

2884.8 millimeters squared

Step-by-step explanation:

Given:

The radius of the disc is 35 millimeters, so the area of it is:

π $r^{2}$ = 3.14* $35^{2}$ = 3846.5

Then, we find out the area of the circular hold cut out of the bigger one, its radius is a haft of the radius of the bigger circle = 35/2 = 17.5

π $r^{2}$ = 3.14* $17.5^{2}$ =961.6

=> the area of the pendant = 3846.5 - 961.6 =2884.8 millimeters squared

6 0

2 years ago

3y - x = 2 -2y - x = -18 x = y =