Answer:
r = {-8, -4}
Step-by-step explanation:
Simplifying
r2 = -32 + -12r
Solving
r2 = -32 + -12r
Solving for variable 'r'.
Reorder the terms:
32 + 12r + r2 = -32 + -12r + 32 + 12r
Reorder the terms:
32 + 12r + r2 = -32 + 32 + -12r + 12r
Combine like terms: -32 + 32 = 0
32 + 12r + r2 = 0 + -12r + 12r
32 + 12r + r2 = -12r + 12r
Combine like terms: -12r + 12r = 0
32 + 12r + r2 = 0
Factor a trinomial.
(8 + r)(4 + r) = 0
Subproblem 1
Set the factor '(8 + r)' equal to zero and attempt to solve:
Simplifying
8 + r = 0
Solving
8 + r = 0
Move all terms containing r to the left, all other terms to the right.
Add '-8' to each side of the equation.
8 + -8 + r = 0 + -8
Combine like terms: 8 + -8 = 0
0 + r = 0 + -8
r = 0 + -8
Combine like terms: 0 + -8 = -8
r = -8
Simplifying
r = -8
Subproblem 2
Set the factor '(4 + r)' equal to zero and attempt to solve:
Simplifying
4 + r = 0
Solving
4 + r = 0
Move all terms containing r to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + r = 0 + -4
Combine like terms: 4 + -4 = 0
0 + r = 0 + -4
r = 0 + -4
Combine like terms: 0 + -4 = -4
r = -4
Simplifying
r = -4
Solution
r = {-8, -4}
Yes!! the line AED is cut with a perpendicular line. The rule for perpendicular lines is that the angles made =90.
-This can also be proven by the fact that lines =180, 90+90=180
Answer: 8 cupcakes per box
Step-by-step explanation: "Per box" means in 1 box, so we can rewrite the given statement using fractions as
<em>48 cupcakes/6 boxes</em> = <em>__ cupcakes/1 box</em>.
To find out what goes in the blank, notice that we
have a 1 in the denominator of our second fraction.
So we want to find a fraction that is equivalent
to 48/6 that has a 1 in the denominator.
If we divide the numerator and denominator of 48/6 by 6,
we get the equivalent fraction 8/1 or <em>8 cupcakes/1 box</em>.
So now we have <em>8 cupcakes/1 box = __cupcakes/1 box</em>.
So an 8 must go in the blank which means that the unit rate
for 48 cupcakes in 6 boxes is <em>8 cupcakes per box</em>.
Answer:
x^2 + (y+1)^2 = 10^2
Step-by-step explanation:
Centre (p,q) = (0, -1)
radius, r = 10
General Equation of a circle
(x-p)^2 + (y-q)^2 = r^2
(x-0)^2 + (y- -1)^2 = 10^2
x^2 + (y+1)^2 = 10^2
