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Mamont248 [21]
3 years ago
14

If triangle DEF has a 90° angle at vertex E, which statements are true? Check all that apply.

Mathematics
2 answers:
Margaret [11]3 years ago
8 0
Draw a diagram (shown below as attachment)

check each option

1st one: obtuse triangle
osbuse means that the triangle has an angle more than 90 degrees
remember that all angles add to 180
90 is one
90+D+F=180
D+F=90
so those 2 mystery angles both have to be less than 90 so therefor none of them can be obtuse
not 1st option


2nd: angle at D is acute
acute means less than 90
so we remember that
D+F=90
no angle can be 0 so let's say F is a very small number like 0.0001
then D would be 89.9999
still less than 90, it is acute
this 2nd optin is right

3rd: angle at F is obtuse
wrong, from 1st one,  no obtuse angles
3rd option is wrong

4th: right triangle
duh, a right triangle has a right angle in it
90 degrees is a right angle
yes
4th optin is right

5th: D is obtuse
naw, fam. no obtuse angles here



the right answers are 2nd and 4th or
The angle at vertex D is acute and
Triangle DEF is a right triangle

choli [55]3 years ago
8 0

Answer:

In other words, A, D.

Step-by-step explanation:

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a line whose perpendicular distance from the origin is 4 units and the slope of perpendicular is 2÷3. Find the equation of the l
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Answer:

\huge\boxed{y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{2}{3}x+\dfrac{4\sqrt{13}}{3}}

Step-by-step explanation:

The equation of a line:

y=mx+b

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substitute:

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The formula of a distance between a point and a line:

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Point:

(x_0,\ y_0)

Distance:

d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+b^2}}

Convert the equation:

y=\dfrac{2}{3}x+b     |<em>subtract y from both sides</em>

\dfrac{2}{3}x-y+b=0    |<em>multiply both sides by 3</em>

2x-3y+3b=0\to A=2,\ B=-3,\ C=3b

Coordinates of the point:

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substitute:

d=4

4=\dfrac{|2\cdot0+(-3)\cdot0+3b|}{\sqrt{2^2+(-3)^2}}\\\\4=\dfrac{|3b|}{\sqrt{4+9}}

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4\sqrt{13}=|3b|\iff3b=-4\sqrt{13}\ \vee\ 3b=4\sqrt{13}   |<em>divide both  sides by 3</em>

b=-\dfrac{4\sqrt{13}}{3}\ \vee\ b=\dfrac{4\sqrt{13}}{3}

Finally:

y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{4\sqrt{13}}{3}

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