Answer in the attachment.
The answer is: "
y = −
x − 4 " .
_________________________________________________________Explanation:_________________________________________________________Given a linear equation in "slope-intercept form" ; that is:
"
y = mx + b " ;
________________________________________________A line that is PARALLEL to the aforementioned equation has the same slope (i.e the same value for "m" ) ; and the given the [x and y coordinates of any particular point] on the parallel line; " (x₁ , y₁)" ; we can write the equation of the parallel line—in "slope-intercept format" — by using the following equation/formula:
y − y₁ = m(x − x₁<span>) ;
</span>
in which: "m = the slope"
and plug in the values for: "m" ; and "x₁" and "y₁" ;
We are given the coordinates of a particular point on the line that is parallel:
" (-4, 1) " ;
as such: x₁ = -4 ; y₁ = 1 ;
& we are given: "m = −

" .
_____________________________________________So:
→ y − y₁ = m(x − x₁) ;
→ y − 1 = −

[x − (-4) ] ;
→ y − 1 = −

(x + 4) ;
→ y − 1 = −

(x + 4) ;
Now; let us examine the "right-hand side of the equation" ;
We have: −

(x + 4) ;
__________________________________________________Note the "distributive property" of multiplication:__________________________________________a(b + c) = ab + ac ;a(b – c) = ab – ac .__________________________________________As such:
__________________________________________ −

* x + (−

* 4) ;
= −

* x + (−

*

) ;
Note: Examine the
" (−

*

) " ;
→ EACH of the 2 (TWO) "4's" cancel out to "1"s" ;
{ since: "4 ÷ 4 = 1" } ;
and we can rewrite the: "(−

*

) " ;
as: " (−

*

) " ;
Note that: "{-5 ÷ 1 = -5} ; and: "{1 ÷ 1 = 1} ;
so, rewrite the: "" (−

*

) " ;
as: "{-5 * 1}" → which equals: = " -5" ;
So:
−

* x + (−

*

) ;
= -

x + (-5) ;
= -

x − 5 ;
______________________________________________→ Now, bring down the "y −1" ; which goes on the left hand side;
→ y − 1 = -

x − 5 ;
Add "1" to EACH SIDE of the equation; to isolate "y" as a single variable on the "left-hand side" of the equation ; & to write the equation of the particular parallel line in "slope-intercept format" ;
→ y − 1 + 1 = -

x − 5 + 1 ;
_______________________________________________________to get:
_______________________________________________________→ "
y = −
x − 4 " .
_______________________________________________________
A decagon has 10 sides (think decade and decathlon). From the center of the decagon we draw the radii and in doing so we take the area of the decagon and divide it into 10 congruent Triangles.
The angles around the center add up to 360 because they form a circle and since there are 10, they each measure 36 degrees. So the answer to the first part (the angle between the radii) is 36 degrees.
Each of these triangles has two equal sides (both radii) so is Isosceles. That means that the base angles are congruent. So the two angles that are left in each triangle must measure the same. Since the angles in a triangle add up to 180 degrees, we know that the two remaining angles are together equal to 180-36=144 degrees. Since they are equal in measure they each measure 72 degrees.
Thus the answer to the second part, trhe measure of the angle between a radius and the side of the polygon is 72 degrees.
Answer:
It's very simple. In 4 decimal digits there are 10,000 (0000 to 9999) possible values. The odds of any one of them coming up randomly is one in 10,000. A specific "4 digit number" would have 1/9000 chance, since there are 9000 4 digit numbers (1000-9999).
Step-by-step explanation:
Answer:
1603
Step-by-step explanation:
3^3*4^3-5^3
__________
3*3*3=9*3=27
4*4*4=16*4=64
5*5*5=25*5=125
(27*64)-125
1728-125
1603