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Mathematics

1 answer:

sergij07 [2.7K]3 years ago

3 0

Answer:

Step-by-step explanation:

Draw a picture!

You have a right triangle with legs of 5 and 12.

By the Pythagorean Theorem, the hypotenuse is √(5²+12²) = 13

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Find the zero of f (x-5) (-x to the second power +3x-3)

FromTheMoon [43]

Answer:

1 =x-5 = as pytanerosa tery says

Step-by-step explanation:

6 0

2 years ago

What is the equation for the line? enter your answer in the box

Igoryamba

To get the equation of the line, you need two points that belong to this line.
From the given graph, we can choose any two points: (0,-4) and (-2,0)

The general for of the linear straight line is:
y = mx + c where m is the slope and c is the y-intercept

First, we will calculate the slope using the following rule:
slope = (y2-y1) / (x2-x1)
slope (m) = (0--4) / (-2-0) = 4/-2 = -2
The equation of the line now is: y = -2x + c

Then, we will get the value of the c. To do so, we will choose any point and substitute in the equation. I will choose the point (0,-4)
y = -2x + c
-4 = -2(0) + c
c = -4

Based on the above calculations, the equation of the line is:
y = -2x - 4

7 0

2 years ago

For what values of $x$ is $$\frac{x^2 + x + 3}{2x^2 + x - 6} \ge 0?$$ note: be thorough and explain why all points in your answe

Rus_ich [418]

To solve the inequality $\frac{x^2+x+3}{2x^2+x-6}\ge \:0$

$\mathrm{Factor\:the\:left\:hand\:side\:}\frac{x^2+x+3}{2x^2+x-6}:$

The numerator $x^2+x+3$ is not factorizable.

so factor the denominator $2x^2+x-6$ :

$2x^2+x-6=\left(2x^2-3x\right)+\left(4x-6\right)=x\left(2x-3\right)+2\left(2x-3\right)\\ \mathrm{Factor\:out\:}x\mathrm{\:from\:}2x^2-3x\mathrm{:\quad }x\left(2x-3\right)\\ \mathrm{Factor\:out\:}2\mathrm{\:from\:}4x-6\mathrm{:\quad }2\left(2x-3\right)\\$