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Mathematics

1 answer:

Virty [35]3 years ago

7 0

A) an acute
a) scalene
c) 0 sides of equal length
d) all acute angles

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Given: Quadrilateral PAST, TX = AX; TP || AS<br> Prove: Quadrilateral PAST is a parallelogram.

poizon [28]

1) Quadrilateral PAST, TX=AX, $\overline{TP} \parallel\overline{AS}$ (given)

2) $\angle XPT \cong \angle XSA$ and $\angle XTP \cong \angle XAS$ (alternate interior angles theorem)

3) $\triangle TXP \cong \triangle AXS$ (AAS)

4) $\overline{TP} \cong \overline{AS}$ (CPCTC)

5) PAST is a parallelogram (a quadrilateral with two pairs of opposite congruent sides is a parallelogram)

8 0

2 years ago

Write the ratio as a ratio of a whole numbers using fractional notation 6 1/2 to 15 1/6

motikmotik

$\bf 6\frac{1}{2}:15\frac{1}{6}\qquad 
\begin{cases}
6\frac{1}{2}\implies \cfrac{6\cdot 2+1}{2}\\\\
15\frac{1}{6}\implies \cfrac{15\cdot 6+1}{6}
\end{cases}\implies \cfrac{ \frac{6\cdot 2+1}{2}}{\frac{15\cdot 6+1}{6}}\\\\
-----------------------------\\\\
\cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\qquad thus
\\\\\\
\cfrac{6\cdot 2+1}{2}\cdot \cfrac{6}{15\cdot 6+1}$

simplify away

5 0

4 years ago

Jon is in a raft 100m from the base of a 54m cliff. What is the angle of depression from the he top of the cliff to the raft? Le

kvv77 [185]

Answer:

28.4 degrees

Step-by-step explanation:

In the diagram attached

Height of the cliff, AB=54 m

Distance of the raft to the base of the cliff, AC=100m

We want to determine the angle of depression from the top of the cliff to the raft. This is angle OBA.

$\angle OBA = \angle BAC $ (Alternate Angles)\\Therefore, in the right triangle ABC\\\tan A =\dfrac{BC}{AC}\\ \tan A =\dfrac{54}{100}\\\tan A =0.54\\A=\arctan 0.54\\A=28.4^\circ$ (to the nearest tenth)$