<em>Answer:</em>
<em>r = -</em>
<em />
<em>Step-by-step explanation:</em>
<em>Rewrite the equation as </em>
<em> = m</em>
<em>Remove the radical on the left side of the equation by squaring both sides of the equation.</em>
<em>(</em>
<em> = m^2</em>
<em>Then, you simplify each of the equation. </em>
<em>Rewrite: (</em>
<em> as </em>
<em />
<em>Remove any parentheses if needed.</em>
<em>Solve for r. </em>
<em>Multiply each term by r and simplify."</em>
<em>Multiply both sides of the equation by 5.</em>
<em>6a+r= m^2r⋅(5)</em>
<em>Remove parentheses.</em>
<em>Move 5 to the left of (m
^2) r
</em>
<em>6a+r=5m^2)r</em>
<em>Subtract 5m^2)r from both sides of the equation.</em>
<em>6a+r-5m^2)r=0</em>
<em>Subtract 6a from both sides of the equation.</em>
<em>r-5m^2)r=-6a</em>
<em>Factor r out of r-5m^2)r </em>
<em>r(1-5m^2)=-6a</em>
Divide each term by 1-5m^2 and simplify.
r = - 
There you go, hope this helps!
Answer:
f(x) is negative and g(x) is positive
Step-by-step explanation:
f(x) = 4-x
Rewriting
f(x) = -x+4
We recognize this as
y= mx+b or the representation of a line with slope -1 and y intercept 4
f(x) is linear
g(x) as we increase x by 1 we increase g(x) by 2
The slope is 2, and the y intercept is 1
y = 2x+1
Lets check a point
(2,5)
5 = 2(2)+1
5=5 so we are correct
f(x) is negative and g(x) is positive
2^3:
a) 2 x 2 x 2
b) 8
3^2 x e^3:
a) 3 x 3 x e x e x e
b) 9e^3
Answer:
The rule of dilation is
.
The vertices of the dilated triangle are
,
and
, respectively.
Step-by-step explanation:
From Linear Algebra, we define the dilation by the following definition:
(1)
Where:
- Center of dilation, dimensionless.
- Scale factor, dimensionless.
- Original point, dimensionless.
- Dilated point, dimensionless.
If we know that
,
,
,
and
, then dilated points of triangle ABC are, respectively:
(2)
![A'(x,y) = (0,0) + 3\cdot [(-7,-6)-(0,0)]](https://tex.z-dn.net/?f=A%27%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B%203%5Ccdot%20%5B%28-7%2C-6%29-%280%2C0%29%5D)

(3)
![B'(x,y) = (0,0) + 3\cdot [(-5,-2)-(0,0)]](https://tex.z-dn.net/?f=B%27%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B%203%5Ccdot%20%5B%28-5%2C-2%29-%280%2C0%29%5D)

(4)
![C'(x,y) = (0,0) +3\cdot [(-1,-5)-(0,0)]](https://tex.z-dn.net/?f=C%27%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B3%5Ccdot%20%5B%28-1%2C-5%29-%280%2C0%29%5D)

The rule of dilation is:
(5)
The vertices of the dilated triangle are
,
and
, respectively.