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Mathematics

1 answer:

Ad libitum [116K]2 years ago

5 0

Answer:

The equation of this line is therefore y = 2x + 3.

Step-by-step explanation:

this line passes thru the points (0, 3) and (3, 9). As we move from (0, 3) to (3, 9), x increases by 3 and y increases by 6. Thus, the slope of this line is

m = rise / run = 6/3, or m = 2. Inserting the known info (m = 2, x = 0, y = 3) into y = mx + b, we get: 3 = 2(0) + b, so we see that b = 3.

The equation of this line is therefore y = 2x + 3.

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Solve 3x² + 4x = 2. (2 points)

uysha [10]

Answer:

Step-by-step explanation:

As it is a second order equation, it means that it has two possible answers and they are $x_1$ and $x_2$ .

The famous quadratic formula for solving any second order equation is the following:

$x_{1} = \frac{-b + \sqrt{b^2 - 4 ac}}{2a}\\x_{2}=\frac{-b - \sqrt{b^2 - 4 ac}}{2a}$

Where a is the coefficient of $x^2$ , b is the coefficient of x, and c is the free term. In other words,

$a = 3\\b=4\\c=-2$

as the equation should be in the following form:

$a x^2 + bx+c = 0$

Therefore the possible answer should be the following,

$\frac{-4 + \sqrt{4^2 - 4*3*(-2)}}{2*3}=\frac{-4 +\sqrt{16 + 24}}{6} =\frac{-4 + \sqrt{40}}{6}=\\ \frac{-4 + \sqrt{4*10}}{6} = \frac{-4 + 2\sqrt{10}}{6}$ $\frac{2*(-2 + \sqrt{10})}{2*3} = \frac{-2 + \sqrt{10}}{3}$

by dividing the numerator and denominator by 2, we can deduce the following,

6 0

2 years ago

Nancy’s morning routine involves getting dressed , eating breakfast, making her bed , and driving to work . Nancy spends 1/3 of

grin007 [14]

Answer: Nancy needs 26 minutes to driving to work.

Explanation:

Since we have given that

Time taken in eating breakfast = 10 minutes

Time taken in making her bed = 5 minutes

Let the total time taken by her in doing routine activities be x

Time taken in getting dressed is given by

$\frac{1}{3}x$

So, According to question,

$\frac{x}{3}+10+5=35\frac{1}{2}\\\\\frac{x}{3}+15=\frac{71}{2}\\\\\frac{x}{3}=\frac{71}{2}-15\\\\\frac{x}{3}=\frac{71-30}{2}=\frac{41}{2}\\\\x=\frac{123}{2}$