6. The variable x and y vary directly, and y = 40 when x = 5. Which equation relates the variables?
1 answer:
Answer:
The equation relates the variables is y = 8x ⇒ D
Step-by-step explanation:
If x and y vary directly (y ∝ x), then y = k x, where
- k is the constant of variation
- k can be found using the initial value of x and y
∵ The variable x and y vary directly
∴ y ∝ x
→ By using the rule above
∴ y = k x
∵ y = 40 when x = 5
∴ The initial values of x and y are x = 5 and y = 40
→ Substitute them in the equation above to find k
∵ 40 = k(5)
∴ 40 = 5k
→ Divide both sides by 5
∵ =
∴ 8 = k
→ Substitute the value of k in the equation above
∴ y = 8x
∴ The equation relates the variables is y = 8x
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Answer:
In First method : counting up, counting back on a number line,
If we want the quotient after dividing the number by 5 then we count how many 5 we get from 0 to the dividend.
For example :
Since, from 0 to 30 there are six 5's obtained. ( because 5 × 6 = 30 )
Thus,
In Second Method : dividing by 10, and then doubling the quotient.
First we divide the number by 10 then multiply the quotient by 2.
For Example:
Since,
Thus,
Now, when we compare the above methods then we conclude that for the smaller numbers first method is appropriate because for small numbers we can easily count total 5's from 0. While for large numbers Second method is appropriate because it is hard to count the total 5's for the large number.
Answer:
∠ACB = 38°
Step-by-step explanation:
∠ACB is an inscribed angle while arcAB is its intercepted arc
An inscribed angle is equal to half the length of its intercepted arc
Hence, ∠ACB = 1/2 the measure of arc AB
arc AB = 76°
Hence ∠ACB = 1/2 of 76
76/2 = 38
Therefore ∠ACB = 38°
