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2 years ago

Solve for x: 1 over 3 (2x − 8) = 4. (1 point)

Mathematics

1 answer:

garik1379 [7]2 years ago

6 0

Answer:

x=6

Step-by-step explanation:

$2x - 8 = 4 \\ 2x = 4 + 8 \\ 2x = 12 \\ x = \frac{12}{2} \\ x = 6$

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Is the given point interior , exterior, or on the circle k (x+2)2 + (y-3)2 =18 P (8,4)

Mnenie [13.5K]

One way would be to find the distance from the point to the center of the circle and compare it to the radius

for
$(x-h)^2+(y-k)^2=r^2$
the center is (h,k) and the radius is r

and the distance formula is
distance between $(x_1,y_1)$ and $(x_2,y_2)$ is
$D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

r=radius
D=distance form (8,4) to center

if r>D, then (8,4) is inside the circle
if r=D, then (8,4) is on the circle
if r<D, then (8,4) is outside the circle

so
$(x+2)^2+(y-3)^2=18$
$(x-(-2))^2+(y-3)^2=(\sqrt{18})^2$
$(x-(-2))^2+(y-3)^2=(3\sqrt{2})^2$

the radius is $3\sqrt{2}$
center is (-2,3)

find distance between (8,4) and (-2,3)

$D=\sqrt{(8-(-2))^2+(4-3)^2}$
$D=\sqrt{(8+2)^2+(1)^2}$
$D=\sqrt{10^2+1}$
$D=\sqrt{100+1}$
$D=\sqrt{101}$

$r=3\sqrt{2}$ ≈4.2
$D=\sqrt{101}$ ≈10.04

do r<D

(8,4) is outside the circle

6 0

3 years ago

What would be the coordinates of triangle A'B'C' if triangle ABC was dilated by a factor of

notsponge [240]

Answer:

$A(0,0)\rightarrow A'(0,0) \\ B(2,0)\rightarrow B'(\frac{2}{3},0) \\ C(0,2)\rightarrow C'(0,\frac{2}{3})$

Step-by-step explanation:

The question is as following:

The verticies of a triangle on the coordinate plane are

A(0, 0), B(2, 0) and C(0, 2).

What would be the coordinates of triangle A'B'C' if triangle ABC was dilated by a factor of 1/3 ?

=============================================

Given: the vertices of a triangle ABC are A(0, 0), B(2, 0) and C(0, 2).

IF the triangle is dilated by a factor of k about the origin, then

(x,y) → (kx , ky)

that triangle ABC was dilated by a factor of 1/3 to create the triangle A'B'C'.

It is given that triangle ABC was dilated by a factor of 1/3 to create the triangle A'B'C'.

If a figure dilated by a factor of 1/3 about the origin

So, $(x,y)\rightarrow (\frac{1}{3}x,\frac{1}{3}y)$

<u>So, The coordinates of the triangle A'B'C' are:</u>

$A(0,0)\rightarrow A'(0,0) \\ B(2,0)\rightarrow B'(\frac{2}{3},0) \\ C(0,2)\rightarrow C'(0,\frac{2}{3})$

6 0

3 years ago

What are the first three terms of the sequence represented by the recursive formula

AnnyKZ [126]

Explecit formula
hmm, seems to be a geometric sequence
so
an=a1+d(n-1)
d=common differnce
a1=first term

given
a1=firstterm=9.2

and the difference between each tierm is 1.8

an=9.1-1.8(n-1) is da equation

so 4th option

5 0

3 years ago

1.01 an rational number

insens350 [35]

No its not an rational number.The answer is no

8 0

3 years ago

Read 2 more answers

Sophia and Quinn were picking apples at the farm.

vazorg [7]

Answer: I think Sophia

Step-by-step explanation:

5 apples for 25 min and 3 for every 12 min which would mean both can go to 300 which means 12 goes to 300 25 times then do 25x5 to get 125 and the do 12x5 to get 60...

4 0

3 years ago