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:
you never showed the number line sir
Step-by-step explanation:
Step-by-step explanation:
I'll do one for you.
Using the formula for turning exponents into radicals
![(b) {}^{ \frac{x}{y} } = \sqrt[y]{b} {}^{x}](https://tex.z-dn.net/?f=%28b%29%20%7B%7D%5E%7B%20%5Cfrac%7Bx%7D%7By%7D%20%7D%20%20%3D%20%20%20%20%5Csqrt%5By%5D%7Bb%7D%20%7B%7D%5E%7Bx%7D%20%20)
where b is the base
This means that the numerator in the exponet form becomes the power under the radical in radical form and
the denominator in exponet form becomes the nth root in radical form.
For example 5,
That becomes in radical form
![\sqrt[5]{5 {}^{ - 3} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B5%20%7B%7D%5E%7B%20-%203%7D%20%7D%20)
or if you want to write it using positive exponents
![\frac{1}{ \sqrt[5]{5 {}^{3} } }](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B%20%5Csqrt%5B5%5D%7B5%20%7B%7D%5E%7B3%7D%20%7D%20%7D%20)
I'll do one more for you
For example 6,
That becomes in radical form
![\sqrt[3]{11 {}^{4} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B11%20%7B%7D%5E%7B4%7D%20%7D%20)
Answer:
f(x) = 4x² - 1
Step-by-step explanation:
The given function is; f(x) = x²
Now, when stretched vertically by a factor of 4, we have;
f(x) = 4x²
It's now shifted 1 unit down.. Thus, the final function will be;
f(x) = 4x² - 1
I think it is 36^2+12ab+b^2
