1) gradient of line = Δ y ÷ Δ x
= (5 -2) ÷ (3 - (-6))
= ¹/₃
using the point-slope form (y-y₁) = m(x-x₁)
using (3,5)
(y - 5) = ¹/₃ (x -3)
y - 5 = ¹/₃x - 1
⇒ <span> y = ¹/₃ x + 4 [OPTION D]
</span>2) y = 2x + 5 .... (1)
<span> </span>y = ¹/₂ x + 6 .... (2)
by substituting y in (1) for y in (2)
2x + 5 = ¹/₂ x + 6
³/₂ x = 1
x = ²/₃
by substituting found x (2)
y = ¹/₂ (²/₃) + 6
y = ¹⁹/₃
∴ common point is (²/₃ , ¹⁹/₃) thus answer is FALSE [OPTION B]
3) Yes [OPTION A]
This is because the both have a gradient of 5 and if they have the same gradient then that means that the two lines are parallel to each other.
4) No [OPTION B]
Two lines are perpendicular if their gradients multiply to give - 1 and as such one is the negative reciprocal of the other. Since both gradients are ¹/₂ then they are actually parallel and not perpendicular.
Answer:
The additive property of 0; any number added with 0 is going to be that number.
Step-by-step explanation:
Using pythagorean theorem:
![\begin{gathered} c^2=a^2+b^2 \\ b=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{19^2-17^2} \\ b=\sqrt[]{72} \\ b\approx8.5 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20c%5E2%3Da%5E2%2Bb%5E2%20%5C%5C%20b%3D%5Csqrt%5B%5D%7Bc%5E2-a%5E2%7D%20%5C%5C%20b%3D%5Csqrt%5B%5D%7B19%5E2-17%5E2%7D%20%5C%5C%20b%3D%5Csqrt%5B%5D%7B72%7D%20%5C%5C%20b%5Capprox8.5%20%5Cend%7Bgathered%7D)
Answer:
x = Rs 20,833.33
the value of x is Rs 20,833.33
Step-by-step explanation:
Let x,y and z represent the price of the item initially, after one month and after two months respectively.
Given that;
after one month its label price is reduced by 20%
y = x - 20% of x
y = x - 0.20x
y = 0.80x ........1
after 2 months its reduced price is further reduced by 10% and then sold it for Rs 15000.
z = y - 10% of y
z = y - 0.10y
z = 0.90y ........2
Substituting equation 1 into 2;
z = 0.90(0.80x)
z = 0.72x
Also z = Rs 15000
So,
z = 0.72x = Rs 15000
0.72x = Rs 15000
x = Rs 15000/0.72
x = Rs 20833.33333333
x = Rs 20,833.33
the value of x is Rs 20,833.33
Answer:
2. The ratio of the percent increase is not the same as the percent decrease.
3. The ratio for the percent increase has a smaller denominator than the percent decrease.
5. The original amount for the percent increase is different from the original amount for the percent decrease.
Step-by-step explanation:
