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2 years ago

What are ALL the true statements.

Mathematics

2 answers:

ale4655 [162]2 years ago

8 0

Answer:

C, E, F

Step-by-step explanation:

A is false because dilations can not only increase the length of line segments, but also decrease the length of line segments.

B is a true statement.

C is true because when angles undergo dilations, their "size" does not change.

D is false because dilations do not increase the measures of angles.

E is false because a triangle that underwent a dilation becomes similar, not congruent.

F is true because of E's reasoning.

sweet [91]2 years ago

3 0

I think it’s C,E,F
Step by step

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jeyben [28]

Answer:

Event is not unusual(p>0.05).

Step-by-step explanation:

Given that :

$p=0.10\\\\n=1100\\\\x=121$

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$\hat p=\frac{x}{n}\\\\=\frac{121}{1100}\\\\=0.1100$

#Mathematically, the z-value is the value decreased by the mean then divided the standard deviation :

$z=\frac{\hat p- p}{\sqrt{\frac{p(1-p)}{n}}}\\\\\\\\=\frac{0.11-0.10}{\sqrt{\frac{0.10(1-0.10)}{1100}}}\\\\\\=1.1055$

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$P(X\geq 121)=P(Z>1.1055)\\\\=0.1314$

Hence, the probaility is more than 0.05, thus the event not unusual and thus this is not necessarily evidence that the proportion of Americans who are afraid to fly has increased.

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2 years ago

Prove ΔPAB is isosceles.

Licemer1 [7]

Answer:

See explanation

Step-by-step explanation:

If $PX\cong PY,$ then triangle PXY is isosceles triangle. Angles adjacent to the base XY of an isosceles triangle PXY are congruent, so

$\angle 1\cong \angle 2$

and

$m\angle 1=m\angle 2$

Angles 1 and 3 are supplementary, so

$m\angle 3=180^{\circ}-m\angle 1$

Angles 2 and 4 are supplementary, so

$m\angle 4=180^{\circ}-m\angle 2$

By substitution property,

$m\angle 4=180^{\circ}-m\angle 2=180^{\circ}-m\angle 1=m\angle 3$

Hence,

$\angle 3\cong \angle 4$

Consider triangles APX and BPY. In these triangles:

$PX\cong PY$ - given;
$\angle 5\cong \angle 6$ - given;
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so $\triangle APX\cong \triangle BPY$ by ASA postulate.

Congruent triangles have congruent corresponding sides, then

$AP\cong BP$

Therefore, triangle APB is isosceles triangle (by definition).

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