The problem says that V(x)
varies directly with its length. This is a proportionality problem. So, V(x) =
kl. If you are given a length of 25 inches and a k (proportionality constant)
of 15, you are required to find its volume V(x).
V(x) = kl
V(x) = (15) (25 inches)
<u>V(x) = 375 cubic inches</u>
<span>
The volume of the box is 375
cubic inches.
</span>
Answer: Since her art and music sections each only had half the number of sheets of paper as a core subject, together the two sections had the same amount of paper as a core subject. Therefore, it is almost like her notebook had five core subjects, rather than four core subjects and two electives. If she divided the 200 sheets equally among the five core subjects, there would be 200 ÷ 5 = 40 sheets in each section. Now we can see that art would actually have half of this amount, or 20 sheets of paper.
Answer:
21440
Step-by-step explanation:
<h2>
Simplify:</h2>
Start by multiplying 7x³ by x² and -5.
- 7x⁵ - 35x³ + (8x² - 3)(x² - 5)
Multiply 8x² by x² and -5.
- 7x⁵ - 35x³ + 8x⁴ - 40x² + (-3)(x² - 5)
Multiply -3 by x² and -5.
- 7x⁵ - 35x³ + 8x⁴ - 40x² -3x² + 15
Combine like terms together.
- 7x⁵ - 35x³ + 8x⁴ - 43x² + 15
Rearrange the terms in descending power order.
- 7x⁵ + 8x⁴ - 35x³ - 43x² + 15
<h2>Verify (I): </h2>
Substitute x = 5 into the above polynomial.
- 7(5)⁵ + 8(5)⁴ - 35(5)³ - 43(5)² + 15
Evaluate the exponents first.
- 7(3125) + 8(625) - 35(125) - 43(25) + 15
Multiply the terms together.
- 21875 + 5000 - 4375 - 1075 + 15
Combine the terms together.
This is the answer when substituting x = 5 into the simplified expression.
<h2>
Verify (II):</h2>
Substitute x = 5 into the expression.
- [7(5)³ + 8(5)² - 3][(5)² - 5]
Evaluate the exponents first.
- [7(125) + 8(25) - 3][(25) - 5]
Multiply the terms in the first bracket next.
Evaluate the expressions inside the brackets.
Multiply these two terms together.
This is the answer when substituting x = 5 into the original (unsimplified) expression.
* J,K,&L are coplanar
* K is the midpoint of JL
* J,K,&L are collinear
* Jk=KL
