Answer:
6/7 > 1/2
1/3 < 1/2
Suki rode her bike a longer distance than Clarie
Step-by-step explanation:
Suki's distance = 6/7 miles
Compare with bechmark 1/2
6/7 and 1/2
Make the denominators same
(6*2)/(7*2) and (1*7)/(2*7)
12/14 and 7/14
12/14 is greater than 7/14
12/14 > 7/14
Therefore, 6/7 > 1/2
Clarie distance = 1/3 miles
Compare with bechmark 1/2
1/3 and 1/2
Make the denominators same
(1*2)/(3*2) and (1*3)/(2*3)
2/6 and 3/6
2/6 is less than 3/6
2/6 < 3/6
Therefore,
1/3 < 1/2
Compare Suki's distance with Clarie
compare 6/7 and 1/3
Make the denominators same
(6 * 3)/(7 * 3) and (1 * 7)/(3 * 7)
18/21 and 7/21
18/21 > 7/21
Suki rode her bike a longer distance than Clarie
Answer:
Step-by-step explanation:
We are told that Nita wants to buy a new keyboard for her computer. She will buy the keyboard when it is on sale for under $50.
Let k be the price in dollars at which Nita will buy the keyboard. Nita will buy the keyboard when its price is less than 50. So we can write our inequality as:
Therefore, our desired inequality will be .
Answer:
k = - , k = 2
Step-by-step explanation:
Using the discriminant Δ = b² - 4ac
The condition for equal roots is b² - 4ac = 0
Given
kx² + 2x + k = - kx ( add kx to both sides )
kx² + 2x + kx + k = 0 , that is
kx² + (2 + k)x + k = 0 ← in standard form
with a = k, b = 2 + k and c = k , thus
(2 + k)² - 4k² = 0 ← expand and simplify left side
4 + 4k + k² - 4k² = 0
- 3k² + 4k + 4 = 0 ( multiply through by - 1 )
3k² - 4k - 4 = 0 ← in standard form
(3k + 2)(k - 2) = 0 ← in factored form
Equate each factor to zero and solve for k
3k + 2 = 0 ⇒ 3k = - 2 ⇒ k = -
k - 2 = 0 ⇒ k = 2