In ΔOPQ, m∠O = (3x+12)^{\circ}(3x+12)

Mathematics

1 answer:

zaharov [31]3 years ago

6 0

Answer:

The measure of angle P is 80 degrees

Step-by-step explanation:

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

In this problem we have that

$m\angle O+m\angle P+m\angle Q=180^o$

substitute the given values

$(3x+12)^o+(4x+4)^o+(x+12)^o=180^o$

solve for x

$(8x+28)=180$

$8x=180-28$

$8x=152$

$x=19$

Find the measure of angle P

$m\angle P=(4x+4)^o$

substitute the value of x

$m\angle P=(4(19)+4)=80^o$

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I’ll mark brainest! Find all the real cube roots of -0.000125

Ymorist [56]

Answer:

-0.05

Step-by-step explanation:

This will become much easier if we can get the ugly decimal into a nice fraction form.

Start by recognising $\frac{1}{8}=0.125$ . This is almost correct except the fraction is out by some number of factors of 10 (because the 125 part is correct but the number of 0s isn't).

$\frac{1}{80} = 0.0125\\\frac{1}{800}=0.00125\\\frac{1}{8000}=0.000125$

And hence we see that $-0.000125=-\frac{1}{8000}$ and now the cube root becomes easy to compute:

$\sqrt[3]{-0.000125} = \sqrt[3]{\frac{-1}{8000}} = \frac{\sqrt[3]{-1}}{\sqrt[3]{8000}} = \frac{-1}{20} = -0.05$ .

Advanced: You ask for all real cube roots. however the function $y=\sqrt[3]{x}$ is described as bijective. This means for all x, there is only one y corresponding to it. (And also for all y there is only one x corresponding to that). This means there can only ever be one cube root of any real number.