<span>6b^3 (2a+7b)
</span>
<span><span>(<span>6b^3</span>)</span><span>(<span>2a+7b</span><span>)
</span></span></span>
<span><span><span>=(<span>6b^3</span>)</span><span>(2a)</span></span>+<span><span>(<span>6b^3</span>)</span><span>(7b)
</span></span></span>
<span><span>=12ab^3</span>+<span>42<span>b^4]
Answer: </span></span></span>
<span><span><span>12a</span><span>b^3</span></span>+<span>42<span>b^4</span></span></span>
ANSWER
93 and 70
EXPLANATION
We have that one number is 23 more than another.
Let the first number be x.
Let the second number be y.
This means that:
x = 23 + y ____(1)
The sum of the two numbers is 163. This means that:
x + y = 163 ____(2)
Put (1) in (2):
23 + y + y = 163
23 + 2y = 163
2y = 163 - 23
2y = 140
y = 140 / 2
y = 70
From (1):
x = 23 + 70
x = 93
The two numbers are 93 and 70.
First, you must distribute 2(3x-1).
To do that, you will multiply 2•3x, and 2•-1 because you are taking the number outside of the parentheses and multiplying (distributing) it to all the numbers inside
After distributing, the left side of your inequality will be 6x-2
Now you have

To find the value of x, you must subtract an x value from both sides of the equation, as well as a constant from each side.
so you have

And that will make the equation

Now, divide the variable side, ***BUT, because you are dividing by a negative number in an inequality, the inequality will switch sides.
Then, the value of x is greater than or equal to 2
I'll try to explain in the simplest way possible:
Total cost for a single widget: $32 + $44 = $76 for one widget.
So, since we know the cost of one widget is $76, then the price of 350 widgets would be = $76 x 350 = $26,600.
The <em><u>correct answers</u></em> are:
The inequality is 75+4t ≥ 400, and they must sell at least 82 tickets.
Explanation:
t is the number of tickets sold. They start out with $75, so that is where our inequality begins. Each ticket is $4; this gives us the expression 4t. Together with the $75 carry over, we have 75+4t.
They must make at least $400 to pay for the dance. This means it must be more than or equal to 400; this gives us 75+4t ≥ 400.
To solve this, first subtract 75 from each side:
75+4t-75 ≥ 400-75
4t ≥ 325
Divide both sides by 4:
4t/4 ≥ 325/4
t ≥ 81.25
We cannot sell a portion of a ticket, so we round. While mathematically this number would "round down," if they only sell 81 tickets, they will not have enough money. Therefore we round up to 82.