Answer:
The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches
Step-by-step explanation:
We have that:
Let the dimension of the paper be x and y;
Such that:
So:
Substitute 128 for Area
Make x the subject
When 1 inch margin is at top and bottom
The length becomes:
When 2 inch margin is at both sides
The width becomes:
The New Area (A) is then calculated as:
Substitute for x
Open Brackets
Collect Like Terms
To calculate the smallest possible value of y, we have to apply calculus.
Different A with respect to y
Set
This gives:
Collect Like Terms
Multiply through by
Divide through by 2
Take square roots of both sides
Recall that:
Recall that the new dimensions are:
So:
To double-check;
Differentiate A'
The above value is:
This means that the calculated values are at minimum.
<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>
Answer:
A. 7
Step-by-step explanation:
Since the triangle sides are not defined, therefore let the base side have the 12 unit and one of the slant side be 7 unit.
Therefore height of the triangle, h can gotten from the Pythagoras theorem as thus:
7² = (12/2)² + h²
49 = 36 + h²
h² = 49 - 36 = 13
h = √13
knowing the height of the triangle, we can apply same rule to the other unknown slant side, x as thus:
x² = (12/2)² + h²
x² = 36 + 13 = 49
x = √49
x = 7
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - x + 4 ← is i slope- intercept form
with slope m = -
Parallel lines have equal slopes, thus
y = - x + c ← is the partial equation
To find c substitute (6, 5) into the partial equation
5 = - 2 + c ⇒ c = 5 + 2 = 7
y = - x + 7 ← equation of parallel line
Answer:
D.) rational numbers are associative under subtraction
Step-by-step explanation:
rational numbers are closed under subtraction
↳ TRUE
zero is the identity for addition of rational numbers
↳ TRUE
subtraction is the inverse of the addition
↳ TRUE
rational numbers are associative under subtraction
↳ FALSE
The number of miles in day at which the rental cost for the company A and Company B are the same is 200 miles
The Company A rented the truck for $40 a day plus $0.40 per miles
The expression will be
40+0.40x
Where x is the number of miles
The company B rented the truck for $20 a day plus $0.50 per miles
20+0.50x
To find the number of miles in a day at which the rental costs for Company A and Company B are the same, the linear equation will be
40+0.40x = 20+0.50x
40-20 = 0.50x-0.40x
0.1x = 20
x = 200 miles
Hence, the number of miles in day at which the rental cost for the company A and Company B are the same is 200 miles
Learn more about linear equation here
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