All categories

2 years ago

Write the equation of a linear function with slope m, initial value b, independent

Mathematics

1 answer:

Mrac [35]2 years ago

4 0

Answer:

y=mx+b

Step-by-step explanation:

You might be interested in

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 $2x^2+x-6$ :

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

Now take $\mathrm{Factor\:out\:common\:term\:}\left(2x-3\right)$

Then we get factor of the denominator as $\left(2x-3\right)\left(x+2\right)$

Thus $\frac{x^2+x+3}{2x^2+x-6}=\frac{x^2+x+3}{\left(x+2\right)\left(2x-3\right)}$

Now $\mathrm{Compute\:the\:signs\:of\:the\:factors\:of\:}\frac{x^2+x+3}{\left(x+2\right)\left(2x-3\right)}\\$

Signs of $x^2+x+3>0$

$\mathrm{Choosing\:ranges\:that\:satisfy\:the\:required\:condition:}\:\ge \:\:0$

$x\frac{3}{2}$ is the required solution of the given inequality.

5 0

3 years ago

Read 2 more answers

Find the slope of the line. A.) 3/2 B.) - 2/3 C.) - 3/4 D.) 4/3

Julli [10]

Option C is your answer.

It's a negative sloping line which eliminates A and D. Then you just do the whole rise-over-run deal to get the 3/4 part.

8 0

3 years ago

Explain how to find the estimated sum of 5/8+2/9 . Make sure to include at least one type of model.

OverLord2011 [107]

In this expression you would have to use the PEMDAS method. First divide, so (5 divided by 8) + (2 divided by 9).
The answer you would get is: (0.625) + (0.222)
The final answer is: 0.847

8 0

3 years ago

What is the value of x 1) 18 2) 22.5 3) 30 4) 54

11111nata11111 [884]

30 if the answer.....................
.I am 100%shore

4 0

3 years ago

Read 2 more answers

5x + 4y = 11 2x + 6y = -7

olga55 [171]

$\left\{\begin{array}{ccc}5x+4y=11&|\cdot2\\2x+6y=-7&|\cdot(-5)\end{array}\right\\\underline{+\left\{\begin{array}{ccc}10x+8y=22\\-10x-30y=35\end{array}\right}\ \ \ \ |add\ both\ sides\ of\ the\ equations\\.\ \ \ \ \ \ \ \ \ \ \ -22y=57\ \ \ \ |:(-22)\\.\ \ \ \ \ \ \ \ \ \ \ y=-\dfrac{57}{22}\\\\substitute\ the\ value\ of\ y\ to\ the\ first\ equation\\\\5x+4\left(-\dfrac{57}{22}\right)=11\\\\5x-2\cdot\dfrac{57}{11}=11\ \ \ \ |\cdot11\\\\55x-114=121\ \ \ \ |+114\\\\55x=135\ \ \ \ |:55$

$x=\dfrac{135}{55}\\\\x=\dfrac{27}{11}\\\\Answer:\ x=\dfrac{27}{11}\ and\ y=-\dfrac{57}{22}\to\left(\dfrac{27}{11},\ -\dfrac{57}{22}\right)$

8 0

3 years ago