Answer:
To determine the common ratio of a geometric sequence. You just need to divide any two consecutive terms on it. You can see below that all of them have the same quotient.
1.2 / 1.5 = 0.8
0.96 / 1.2 = 0.8
0.768 / 0.96 = 0.8
.
Decimal form = 0.8
Fraction form = 4/5
.
Check:
1.5 x 0.8 = 1.2
1.5 x 4/5 = 6/5 = 1 1/5 = 1.2
Therefore, the common ratio between successive terms in the sequence? 1.5, 1.2, 0.96, 0.768 is 0.8 or 4/5.
Given:
Point A (-3.0,-5.4)
Point B (-3.0,5.4)
reflection across y-axis ⇒ (a,b) reflected (-a,b)
reflection across x-axis ⇒ (a,b) reflected (a,-b)
reflection across the origin ⇒ (a,b) reflected (-a,-b)
reflection on y = x ⇒ (a,b) reflected (b,a)
Point B is a reflection of Point A across the x-axis.
To solve this problem, all we have to do is to thoroughly
analyze the situation step by step.
First let us work on the remaining 10 gallons of water in
the tank. We are given that 2 / 3 of the water initially in the tank leaked
out. Therefore this means that we are left with 1 / 3 the original amount of
water which is 10 gallons, hence:
(1 / 3) Vi = 10 gallons
where Vi is the initial volume of water inside the tank,
calculating for Vi:
Vi = 3 (10 gallons)
Vi = 30 gallons
We are also given that this initial volume of water is
just 3 / 4 of the total capacity of the tank, therefore:
(3 / 4) Vc = Vi
where Vc is the volume capacity of the tank, calculating
for Vc:
Vc = 4 Vi / 3
Vc = 4 (30 gallons) / 3
Vc = 40 gallons
Answer:
<span>Capacity of the fish tank is 40 gallons</span>
The answer is 0 < x <span>≤ 7
</span>
First, we know that width = x
Which means that length = x +18
So, the possible equation for the Table's area is
X (X + 18) ≤ 175
X^2 + 18x - 175 <span>≤ </span>0
Next, we need to calculate is by using complete square method
x^2 + 18x + 81 <span>≤ 175 + 81
(x + 9)^2 </span><span>≤ 256
|x + 9| </span><span>≤ sqrt(256)
|x + 9| </span><span>≤ +-16
-16 </span>≤ x + 9 <span>≤ 16
</span>-16 - 9 ≤ x <span>≤ 16 - 9
</span>-25 ≤ x <span>≤ 7
Since the width couldn't be negative, we can change -25 with 0,
so it become
</span> 0 < x ≤ 7
