<h3>
Answer: Largest value is a = 9</h3>
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Work Shown:
b = 5
(2b)^2 = (2*5)^2 = 100
So we want the expression a^2+3b to be less than (2b)^2 = 100
We need to solve a^2 + 3b < 100 which turns into
a^2 + 3b < 100
a^2 + 3(5) < 100
a^2 + 15 < 100
after substituting in b = 5.
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Let's isolate 'a'
a^2 + 15 < 100
a^2 < 100-15
a^2 < 85
a < sqrt(85)
a < 9.2195
'a' is an integer, so we round down to the nearest whole number to get 
So the greatest integer possible for 'a' is a = 9.
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Check:
plug in a = 9 and b = 5
a^2 + 3b < 100
9^2 + 3(5) < 100
81 + 15 < 100
96 < 100 .... true statement
now try a = 10 and b = 5
a^2 + 3b < 100
10^2 + 3(5) < 100
100 + 15 < 100 ... you can probably already see the issue
115 < 100 ... this is false, so a = 10 doesn't work
B is the answer hope I helped u out!!!
What do we know about those two lines?
They are perpendicular, meaning they have the same slope.
We know the slope of both is not zero (neither is vertical).
Therefore either
1) Both slopes are positive and therefore the product is positive
2) Both slopes are negative and therefore the product is positive (minus by a minus is a plus)
For the y intercepts, we know that the line P passes through the origin.
Therefore its Y intercept is zero.
[draw it if this is not obvious and ask where does it cross the y axis]
Therefore the Y intercept of line K and line P is zero.
[anything multiplied by a zero is a zero]
So we know that the product of slopes is positive, and we know that the product of Y intercepts is zero.
So the product of slopes must be greater.
Answer A
Answer:
D.
Step-by-step explanation:
y = (x - 5)^2 + 16
= x^2 - 5x - 5x + 25 + 16
= x^2 - 10x + 41
That corresponds with answer choice D.
Hope this helps!
Answer:
The lateral area is 392.5 sq. inches.
Step-by-step explanation:
The pipe is in a shape of a cylinder. The lateral area formula for a cylinder is:
Lateral Area = 
Where
r is the radius (half of diameter)
h is the height
Given, diameter = 5
so,
radius = 5/2 = 2.5
Also,
height = 25 inches (same as length, here)
Now we use 3.14 for 
and substitute the values to get the lateral area:
Lateral Area = 
The lateral area is 392.5 sq. inches.
