Round 425 feet in hours
2 answers:
You might be interested in
Answer:
Step-by-step explanation:
Given: 8x² + 10x - 7 = 0
<u>When factoring trinomials of the form ax² + bx + c</u>:
- multiply the leading coefficient and the last term.
- find the product factors that add to give you the coefficient of the middle term.
- rewrite the polynomial with those factors replacing the middle term.
1. Split the middle term:
⇒ 8 × -7 = -56 [multiply the leading coefficient and the last term]
⇒ 14, -4 [find the product factors that add to the middle term's coefficient]
⇒ 8x² + 14x - 4x - 7 = 0 [rewrite with those factors replacing the middle term.]
2. Factor by grouping:
⇒ 8x² + 14x - 4x - 7 = 0 [factor out 2x]
⇒ 2x(4x + 7) - 4x - 7 = 0 [factor out -1 or the negative sign]
⇒ 2x(4x + 7) -1(4x + 7) = 0 [factor out 4x + 7]
⟹ (4x + 7)(2x - 1) = 0
3. Separate into 2 cases:
- 4x + 7 = 0
- 2x - 1 = 0
<u><em>Case 1:</em></u>
⇒ 4x + 7 = 0 [subtract 7 from both sides]
⇒ 4x + 7 - 7 = 0 - 7
⇒ 4x = -7 [divide both sides by 4]
⇒ 4x ÷ 4 = -7 ÷ 4
⟹ x =
<u><em>Case 2:</em></u>
⇒ 2x - 1 = 0 [subtract 1 from both sides]
⇒ 2x - 1 + 1 = 0 + 1
⇒ 2x = 1 [divide both sides by 2]
⇒ 2x ÷ 2 = 1 ÷ 2
⟹ x =
Solutions:
Learn more about quadratic equations here:
Answer:
Approximately 3.5 feet - Option B
Step-by-step explanation:
Imagine that you have this walkway around the garden, with dimensions 30 by 20 feet. This walkway has a difference of x feet between it's length, and say the dimension 30 feet. In fact it has a difference of x along both dimensions - on either ends. Therefore, the increases length and width should be 30 + 2x, and 20 + 2x, which is with respect to an increases area of 1,000 square feet.
( 30 + 2x ) ( 20 + 2x ) = 1000 - Expand "( 30 + 2x )
( 20 + 2x )"
600 + 100x + 4 = 1000 - Subtract 1000 on either side, making on side = 0
4 + 100x - 400 = 0 - Take the "quadratic equation formula"
( Quadratic Equation is as follows ) - ,
,
There can't be a negative width of the walkway, hence our solution should be ( in exact terms ) . The approximated value however is 3.5081...or approximately 3.5 feet.