Answer:
B) -125a^11
Step-by-step explanation:
(-5a^2)^3·a^5 = (-5)^3·a^6·a^5
= (-5)^3·a^(2·3)·a^5
= (-5)^3·a^6·a^5
= -125·a^(6+5)
= -125·a^11 . . . . matches choice B
_____
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
Given:
0.05181 ÷ 3.14 = 0.0165
i) 0.02
ii) 0.016
iii) 0.0165
<h3>What is a mathematical expression ?</h3>
In mathematics, an expression or mathematical expression is a finite combination of symbols well formed according to context-dependent rules. Mathematical symbols can be used to define numbers (constants), variables, operators, functions, parentheses, punctuation marks, and groupings that help define the order of operations and other aspects of logical syntax.
Many authors distinguish between an expression and a formula, the first meaning a mathematical object and the second a statement about mathematical objects.
To learn more about mathematical expression, visit;
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Answer:
<h2>x = 2</h2>
Step-by-step explanation:
2x + 6 = 6 + 2x
4 + 6 = 6 + 4
10 = 10
Isolate the variable by dividing each side by factors that don't contain the variable.
x = 1
-6+3x+4=2-4x+3
-8+7x+1=0
7x=7
x=1
Answer:
(a) B
(b) $2
Step-by-step explanation:
(a) Let's say the cost of a ticket is t and the cost of popcorn is p. Then we can write the two equations from the table:
12t + 8p = 184
9t + 6p = 138
We need to solve this, so let's use elimination. Multiply the first equation by 3 and the second equation by 4:
3 * (12t + 8p = 184)
4 * (9t + 6p = 138)
We get:
36t + 24p = 552
36t + 24p = 552
Subtract the second from the first:
36t + 24p = 552
- 36t + 24p = 552
________________
0 = 0
Since we get down to 0 = 0, which is always true, we know that we cannot determine the cost of each ticket because there is more than one solution (infinitely many, actually). The answer is B.
(b) Our equation from this, if we still use t and p, is:
5t + 4p = 82
Now, just choose any of the two equations from above. Let's just pick 9t + 6p = 138. Now, we have the system:
5t + 4p = 82
9t + 6p = 138
To solve, let's use elimination again. Multiply the first equation by 6 and the second one by 4:
6 * (5t + 4p = 82)
4 * (9t + 6p = 138)
We get:
30t + 24p = 492
36t + 24p = 552
Subtract the second from the first:
36t + 24p = 552
- 30t + 24p = 492
________________
6t + 0p = 60
So, t = 60/6 = $10. Plug this back into any of the equations to solve for p:
5t + 4p = 82
5 * 10 + 4p = 82
50 + 4p = 82
4p = 32
p = 32/4 = $8
So the ticket costs 10 - 8 = $2 more dollars than the popcorn.
