Length of outer boundary =30m
So area of outer boundary =30×30
= 900m²
Length of inner boundary of path=30-1= 29m
Inner area =29×29 =841m²
So area of path is= outer area - inner area
=900- 841
= 59m²
It is a very high probability. If you role two dice no matter what you will get 12 or less.
Answer:
PG ≅ SG (Given)
PT ≅ ST (Given)
GT = GT (Common)
∴ ∠GPT ≅ ∠GST (SSS Congruency Axiom)
Step-by-step explanation:
<u>Given</u>: PG ≅ SG and PT ≅ ST
<u>To Prove</u>: ∠GPT ≅ ∠GST
<u>Proof</u>: PG ≅ SG (Given)
PT ≅ ST (Given)
GT = GT (Common)
∴ ∠GPT ≅ ∠GST (SSS Congruency Axiom).
<u>SSS Congruency Axiom</u>: If three pairs of sides of two triangles are equal in length, then the triangles are congruent.
<u>Congruence</u>: Two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.
Answer:
![-2\sqrt{a}](https://tex.z-dn.net/?f=-2%5Csqrt%7Ba%7D)
Step-by-step explanation:
![\lim_{x \to a} \frac{a-x}{\sqrt{x} -\sqrt{a} } \\ =-\lim_{x \to a} \frac{x-a}{\sqrt{x} -\sqrt{a} } \\=-\lim_{x \to a} \frac{(\sqrt{x} -\sqrt{a})(\sqrt{x} +\sqrt{a})}{\sqrt{x} -\sqrt{a} } \\=- \lim_{x \to a} \sqrt{x} +\sqrt{a}\\=-2\sqrt{a}](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20a%7D%20%5Cfrac%7Ba-x%7D%7B%5Csqrt%7Bx%7D%20-%5Csqrt%7Ba%7D%20%7D%20%5C%5C%20%3D-%5Clim_%7Bx%20%5Cto%20a%7D%20%5Cfrac%7Bx-a%7D%7B%5Csqrt%7Bx%7D%20-%5Csqrt%7Ba%7D%20%7D%20%20%5C%5C%3D-%5Clim_%7Bx%20%5Cto%20a%7D%20%5Cfrac%7B%28%5Csqrt%7Bx%7D%20-%5Csqrt%7Ba%7D%29%28%5Csqrt%7Bx%7D%20%2B%5Csqrt%7Ba%7D%29%7D%7B%5Csqrt%7Bx%7D%20-%5Csqrt%7Ba%7D%20%7D%20%20%5C%5C%3D-%20%5Clim_%7Bx%20%5Cto%20a%7D%20%5Csqrt%7Bx%7D%20%2B%5Csqrt%7Ba%7D%5C%5C%3D-2%5Csqrt%7Ba%7D)
15x-20<130
15x<130+20
15x<150
X=150/15
x<10