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2 years ago

8

If one leg of a right triangle measures 3 centimeters and the other leg measures 6 centimeters, what is the length of the hypote

nuse in centimeters?

1 answer:

siniylev [52]2 years ago

5 0

Pythagorean theorem- a²+b²=c²
so a= 3 b=6 c=hypotenuse
3²+6²=c²
9+36=45
square root of 45 is 6.708203932 so 7.1 (1dp) is the answer

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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

A walkway forms one diagonal of a square playground. the walkway is 16 m long. how long is a side of the playground?

prohojiy [21]

Side of the playground would be : a²+a² = 16²

2a² = 256

a² = 128

a = √128

a = 11.31 m

3 0

3 years ago

Read 2 more answers

2) 4 tot he power of 3 = _______

Ghella [55]

Answer:

64

Step-by-step explanation:

4^3=64

4*4=16

16*4=64

8 0

2 years ago

May I please get help.

Karo-lina-s [1.5K]

Answer:

$y = -\frac{2}{3} +6$

Step-by-step explanation:

To be parallel to the original line, the slope has to be the same $(-\frac{2}{3})$ . For the line to go through the point (6,2) the y-intercept has to be 6.

The graph shows the original line (black) and new line that goes through the point (yellow).

Hope it helps!

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2 years ago

At 2:00 AM in Alaska, the temperature was -1°F. The temperature dropped 3 degrees each hour after that. What

Harman [31]

Answer:

-10* F

Step-by-step explanation:

What confuses me is that the answers you have provided aren't correct, when I made a number line starting at 0 and ending at -23* F and I had counted three degrees for each hour I got -10* F.

2am 3am 4am 5am

0 <u>-1</u> -2 -3 <u>-4 </u>-5 -6 <u>-7</u> -8 -9 <u>-10</u> -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23

2am is at -1* F, 3am is at -4* F, 4am is at -7* F, and 5am is at -10* F.

This is over the course of three hours after 2am so unless I got this wrong you might want to ask your teacher.

7 0

2 years ago