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Answer:
(5, 3 ) and (- , - 10 )
Step-by-step explanation:
Given the 2 equations
2x - y = 7 → (1)
xy = 15 → (2)
Rearrange (1) expressing y in terms of x , that is
y = 2x - 7 → (3)
Substitute y = 2x - 7 into (2)
x(2x - 7) = 15
2x² - 7x = 15 ( subtract 15 from both sides )
2x² - 7x - 15 = 0 ← in standard form
(x - 5)(2x + 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = -
Substitute these values into (3) for corresponding values of y
x = 5 : y = 2(5) - 7 = 10 - 7 = 3 ⇒ (5, 3 )
x = - : y = 2(-
) - 7 = - 3 - 7 = - 10 ⇒ (-
, - 10 )
Answer:
a) i) The probability depends on the total number of counters not on the number of colors.
ii) There are 10 number of counters not 4
b)
Step-by-step explanation:
Given that:
Total number of counters in a bag = 10
Number of red counters = 4
Number of green counters = 3
Number of pink counters = 2
Number of blue counters = 1
a) Ella writes: "There are four colors, so the probability of selecting a green is , so the probability is
"
Ella has considered the total type of counters here, which is 4.
But Ella must have considered total number of counters which is 10.
i) The probability depends on the total number of counters not on the number of colors.
ii) There are 10 number of counters not 4
b) There are 4 colors in the bag.
Formula for probability of an event E can be observed as:
To select 2 counters of the same color:
The required probability will be the sum of all 4 above probabilities: