Please answer with clear instructions so that i can apply this to other questions

Mathematics

1 answer:

marishachu [46]2 years ago

4 0

Answer:

1 and - 1

Step-by-step explanation:

The equation of a line passing through the origin is

y = mx ( m is the slope ( gradient ) )

y = x ← is in this form

with gradient m = 1

Parallel lines have equal gradients

Then the gradients of lines parallel to the given line is 1

Given a line with gradient m then the gradient of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{1}$ = - 1

Then the gradients of lines perpendicular to this line is - 1

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Kieth ran a marathon. It took 3 hours and 2 mins to run 26 miles. If he ran at the same rate for the whole race, how many minute

baherus [9]

It took him 7 minutes to run each mile.

Firstly, covert the time into minutes.
3 * 60 = 180 minutes
180 + 2 = 182 minutes

Now in order to find how long he ran each mile,
divide 182 by 26
182/26 = 7 minutes

7 0

3 years ago

Suppose a and b are the solutions to the quadratic equation 2x^2-3x-6=0. Find the value of (a+2)(b+2).

KonstantinChe [14]

Answer:

(a+2)(b+2) = 4

Step-by-step explanation:

We are given the following quadratic equation:

$2x^2-3x-6=0$

Let a a and b be the solution of the given quadratic equation.

Solving the equation:

$2x^2-3x-6=0\\\text{Using the quadratic formula}\\\\x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{Comparing the equation to }ax^2 + bx + c = 0\\\text{We have}\\a = 2\\b = -3\\c = -6\\x = \dfrac{3\pm \sqrt{9-4(2)(-6)}}{4} = \dfrac{3\pm \sqrt{57}}{4}\\\\a = \dfrac{3+\sqrt{57}}{4}, b = \dfrac{3-\sqrt{57}}{4}$

We have to find the value of (a+2)(b+2).

Putting the values:

$(a+2)(b+2)\\\\=\bigg(\dfrac{3+\sqrt{57}}{4}+2\bigg)\bigg(\dfrac{3-\sqrt{57}}{4}+2\bigg)\\\\=\bigg(\dfrac{11+\sqrt{57}}{4}\bigg)\bigg(\dfrac{11-\sqrt{57}}{4}\bigg)\\\\=\dfrac{121-57}{156} = \dfrac{64}{16} = 4$