Problem 13
10p+10q factors to 10(p+q). If we apply the distributive property, we can distribute the 10 to each term inside (p and q) to get
10(p+q) = (10 times p)+(10 times q) = 10*p + 10*q = 10p+10q
so we get the original expression again. Here 10 is the GCF of the two terms.
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Plug p = 1 and q = 2 into the factored form
10*(p+q) = 10*(1+2) = 10*(3) = 30
As a check, let's plug those p,q values into the original expression
10*p+10*q = 10*1+10*2 = 10+20 = 30
We get the same output of 30
Answer:
Step-by-step explanation:
Given the circumference of Circle K = π
circumference of Circle L = 4π
Ratio of their circumferences = Ck/Cl
Ratio of their circumferences = π/4π
Ratio of their circumferences = 1/4 = 1:4
For their radii
C = 2πr
for circle k with circumference π
π = 2πrk
1 = 2rk
rk = 1/2
for circle l with circumference 4π
4π = 2πr
4 = 2r
r = 4/2
rl = 2
ratio
rk/rl = 1/2/2
rk/rl = 1/4 = 1:4
for the areas
Area of a circle = πr²
for circle k
Ak = π(1/2)²
Ak = π(1/4)
Ak = π/4
for circle l
Al = π(2)²
Al = 4π
Ratio of their areas
Ak/Al = π/4/(4π)
Ak/Al = π/16π
Ak/Al = 1/16 = 1:16
The answer is forty four 44
60/100 / 60 are shaded out of the hundred. Simplified would be 3/5. The decimal would be 0.6.
Answer: Reformatting the input :
Changes made to your input should not affect the solution:
(1): "y3" was replaced by "y^3". 1 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
(23x2 • y3) - 5
STEP
2
:
Trying to factor as a Difference of Cubes
2.1 Factoring: 8x2y3-5
Theory : A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)
Proof : (a-b)•(a2+ab+b2) =
a3+a2b+ab2-ba2-b2a-b3 =
a3+(a2b-ba2)+(ab2-b2a)-b3 =
a3+0+0+b3 =
a3+b3
Check : 8 is the cube of 2
Check : 5 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
Final result :
8x2y3 - 5
