step-by-step explanation:
every time we see "a number" or "the same number," we can add a variable (we'll use x here). rewriting the problem, we get: 8 less than 2 times x is gr8er than the sum of x and 9.
next, we can work backwards to write an inequality. we know from the word problem above that the number on the left side of the equation is 8 less than 2x, so we can rewrite that part like this: 2x-8.
for the right side of the equation, all we have to do is simplify "the sum of x and 9" to x + 9. so now the inequality should look like this: 2x - 8 > x + 9.
now we'll solve the inequality just like an equation: subtract x from both sides of the inequality, so now we have: x - 8 > 9.
then, we can add 8 to both sides to get the x by itself, and we get the answer: x > 15
hope this helps! <em>:)</em>
Remark
If the lines are parallel, there are no solutions to the system of equations. Start with the equation you know the most about.
x + 6y = 7 Subtract x from both sides
x - x + 6y = 7 - x Combine
6y = - x + 7 Switch and divide by 6
y = -x / 6 + 7/6
The general equation for a line is y = mx + b where m is the slope of the line.
m = - 1/6
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Now look at the second equation
10ay - 5x = 32 Add 5x to both sides
10ay = 5x + 32 Divide by 10a
y = (5/10a)x + 32/(10a)
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Now you must make
5/10a = - 1/6 Cross Multiply
5* 6 = - 10a * 1
30 = - 10a Divide by - 10
a = 30 / - 10
a = - 3
So these two equations will have no solution when a = - 3
The dimension of the box of the greatest volume that can be constructed in this way is 12x12x3 and the volume is 432.
<h3>
How to s
olve the d
imens
ion?</h3>
Let x be the side of the square to remove. Then the volume of the box is:
V(x) = (18 - 2x)² * x = 324x - 72x² + 4x³
To find the maximum volume, differentiate and set it to 0:
V'(x) = 324 - 144x + 12x²
0 = x² - 12x + 27
0 = (x - 9)(x - 3)
x = 3 or 9
When x = 3,
V"(x) =-144+24x
V"(3) =-144+72=-72<0
so volume is maximum at x=3
Therefore the box is 12x12x3 and the volume is 432.
Learn more about dimension on:
brainly.com/question/26740257
