Answer:
This is a convergent geometric series. The sum is 30.
Step-by-step explanation:
In your series, the ratio of terms is 3/5, a value whose magnitude is less than 1. That means the series is convergent. The sum is given by the formula ...
S = a1/(1 -r)
where a1 is the first term (12) and r is the common ratio (3/5). This gives ...
S = 12/(1 -3/5) = 12·5/2 = 30
The series is convergent and has a sum of 30.
The correct answer is C. This is because
10^-2 = 1/10^2 which is 0.01
Answer: V = (12in - 2*x)*(8 in - 2*x)*x
Step-by-step explanation:
So we have a rectangular cardboard sheet, and we cut four squares of side length x in each corner so we can make a box.
Remember that for a box of length L, width W and height H, the volume is:
V = L*W*H
In this case, the length initially is 12 inches, but we remove (from each end) x inches of the length, then the length of the box will be:
L = 12 in - 2*x
For the width we have a similar case:
W = 8in - 2*x
And te height of the box will be equal to x, then:
H = x
This means that the volume is:
V = (12in - 2*x)*(8 in - 2*x)*x
Here we can see the connection between the cutout and the volume of the box
Answer:
A. the first one
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Since BD and AE are parallel lines, then
∠BDC = ∠AED ( corresponding angles ), thus
4x - 5 = 97 - 2x ( add 2x to both sides )
6x - 5 = 97 ( add 5 to both sides )
6x = 102 ( divide both sides by 6 )
x = 17, hence
∠AED = 97 - 2x = 97 - (2 × 17) = 97 - 34 = 63°
∠BDE and ∠AED are same side interior angles and are supplementary, thus
10y - 3 + 63 = 180
10y + 60 = 180 ( subtract 60 from both sides )
10y = 120 ( divide both sides by 10 )
y = 12 → D
