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densk [106]
3 years ago
10

In triangle STU, u2 = s2 + t2.

Mathematics
1 answer:
sineoko [7]3 years ago
3 0

Answer:

(B) The measure of angle SUT is equal to 90 degrees

Step-by-step explanation:

It is given that in In triangle STU, u^2=s^2+t^2.

We can see from the triangle and also the given condition that the triangle will be right triangle as it is satisfying the Pythagoras theorem.

(Hyp)^2=(Base)^2+(Perpendicular)^2

that is:

u^{2}=s^{2}+t^{2}

where u is the hypotenuse, s is the base and t is the perpendicular.

Thus, the angle SUT should be of 90°.

Thus, The measure of angle SUT is equal to 90 degrees.

Hence, option B is correct.

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Find the value of r so the line that passes through (-5,2) and (3,r) has a slope of -1/2
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The value of r so the line that passes through (-5,2) and (3,r) has a slope of -1/2 is -2

<u>Solution:</u>

Given that line is passing through point (-5, 2) and (3, r)

Slope of the line is \frac{-1}{2}

Need to determine value of r.

Slope of a line passing through point \left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right)  is given by following formula:

\text { Slope } m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}  --- eqn 1

\text { In our case } x_{1}=-5, y_{1}=2, x_{2}=3, y_{2}=\mathrm{r} \text { and } m=-\frac{1}{2}

On substituting the given value in (1) we get

\begin{array}{l}{-\frac{1}{2}=\frac{r-2}{3-(-5)}} \\\\ {\text { Solving the above expression to get value of } r} \\\\ {=>-\frac{1}{2}=\frac{r-2}{3+5}} \\\\ {=>-8=\frac{r-2}{3+5}} \\\\ {=>-8=2(r-2)} \\\\ {=>-8=2 r-4} \\\\ {=>2 r=-8+4} \\\\ {=>2 r=-4} \\\\ {=>r=\frac{-4}{2}=-2}\end{array}

Hence the value of "r" is -2

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