Ask question

Ask question

All categories

3 years ago

12

The line representing the equation x+y=3 is dilated by a scale factor of 2.5, with the center of dilation (3,0). Which statement

is true?
A- the dialated line lies on the original line

b- the dilated line is perpendicular to the original line

c- the dilated line is parallel to the original line and to its left

d- the dilated line is parallel to the original line and to its right

1 answer:

creativ13 [48]3 years ago

3 0

Answer:

A- the dialated line lies on the original line

Step-by-step explanation:

The center of dilation is invariant (doesn't move). Hence the line through it still goes through it after dilation. The direction of the line is not changed by dilation, so the dilated line lies on the original line.

You might be interested in

HURRYYYYYYYYY!! What is the equation of the quadratic function with a vertex at (2, 25) and an x-intercept at (7,0)?

tangare [24]

Answer:

$y=-(x-7)(x+3)$

which is none of the choices provided.

Are you sure the question is right or even the choices?

You can even write it as:

$y=-(x+3)(x-7)$ but this is still not a choice.

Step-by-step explanation:

The vertex form of a quadratic is $y=a(x-h)^2+k$ .

This is called vertex form because it gives you the vertex is $(h,k)$ .

We are given that $(h,k)=(2,25)$ which makes our equation:

$y=a(x-2)^2+25$ .

We can find the value of $a$ by plugging in the x-intercept (7,0) for $(x,y)$ into:

$y=a(x-2)^2+25$

$0=a(7-2)^2+25$

$0=a(5)^2+25$

Subtract 25 on both sides:

$-25=a(5)^2$

$-25=a(25)$

Divide both sides by 25:

$\frac{-25}{25}=a$

$-1=a$ .

So the equation for the quadratic is:

$y=-1(x-2)^2+25$

Let's put this into factored form since all the choices are in factored form.

This will require us to multiply the (x-2)(x-2) out:

$y=-1(x-2)(x-2)+25$

$y=-1(x^2-2x-2x+4)+25$

$y=-1(x^2-4x+4)+25$

$y=-x^2+4x-4+25$

$y=-x^2+4x+21$

Factor out -1:

$y=-(x^2-4x-21)$

WE need to find two numbers that multiply to be -21 and add to be -4:

$y=-(x-7)(x+3)$

8 0

3 years ago

Read 2 more answers

Please help 12+2x-14x+8=

bulgar [2K]

Answer:

-12x+20

Step-by-step explanation:

12+2x-14x+8

Add constants: 20+2x-14x

Add variables: 20-12x

Reorder: -12x+20

8 0

3 years ago

Read 2 more answers

Expanded form of (-ab)6

Tcecarenko [31]

Answer:

it is ,

-6ab

hope it helps!

8 0

2 years ago

the gross income is $215 per week the deductions are $15.16,$29.33,2%,1%,and 3% what is the net income

Naddik [55]

State tax = 2% of $215 = 0.02 x $215 = $4.30
city tax = 1% of $215 = 0.01 x $215 = $2.15
retirement fund = 3% of $215 = 0.03 x $215 = $6.45

Total deductions = $15.16 + $29.33 + $4.30 + $2.15 + $6.45 = $57.39

Net income = $215 - $57.39 = $157.61

8 0

3 years ago

Determine the two ordered pair solutions of the equation y = 2x2 + 3x , given (0, ), and (-2, ).

Rudiy27

Answer:

We conclude that the two ordered pairs (0, 0) and (-2, 2) are the solutions of the equation y = 2x² + 3x.

Step-by-step explanation:

Given the expression

y = 2x² + 3x

Substituting x = 0

y = 2(0)² + 3(0)

y = 0+0

y = 0

so when x = 0, y = 0

Thus, the ordered pair is: (0, 0)

Now, substituting x = -2

y = 2x² + 3x

y = 2(-2)² + 3(-2)

y = 8 - 6

y = 2

so when x = -2, y = 2

Thus, the ordered pair is: (-2, 2)

Therefore, we conclude that the two ordered pairs (0, 0) and (-2, 2) are the solutions of the equation y = 2x² + 3x.

3 0

3 years ago