The definition of similar triangles says that 2 triangles are similar if they have the same shape but different size. There are two criteria to check for this:
1) If all angles in one triangle are equal to the angles in another one, then the 2 are equal.
2) If the sides have the same proportions, then the 2 triangles are similar.
1) We have that all the angles of the 2 triangles have an equal angle in the other triangle. In specific, Q is matched to B, P to A and R to C. Hence, since corresponding angles are congruent, the two triangles are similar.
2) Here we are given information about the sides of the triangles, so we will check the second criterion. We form the ratio of the largest sides of each trangle and the shortest sides. 30/5=6. For the shortest sides, 18/3=6. Finally for the middle sides, 24/4=6. Hence, we have that the triangles are similar since the ratios are equal. (it doesn't matter whether we take the bigger or the smaller side as a numerator, as long as we are consistent).
Answer:
Step-by-step explanation:
Let the equation of the line be 
where, 'm' is its slope and 
is a point on it.
Given:
The equation of a known line is:
A point on the unknown line is:
Both the lines are perpendicular to each other.
Now, the slope of the known line is given by the coefficient of 'x'. Therefore, the slope of the known line is 
When two lines are perpendicular, the product of their slopes is equal to -1.
Therefore,
Therefore, the equation of the unknown line is determined by plugging in all the given values. This gives,
The equation of a line perpendicular to the given line and passing through (4, -6) is .
Answer:
$26,096
Step-by-step explanation:
property taxes = 31 January + 28 February + 31 March + 30 April + 31 May + 4 June = 155 days
property taxes = (155 days/365 days) x $5,309 = $2,254
agent's commission = 7% x $547,000 = $38,290
seller's net = $547,000 - $480,000 (mortgage) - $38,290 (agent's commission) - $360 (home warranty) - $2,254 (property taxes) = $26,096
<em>A 64 ounce bottle of organic orange juice costs $14.72. What is the price
</em>
<em>per ounce?; </em>0.23
<em>Anna typed 600 words in 15 minutes. How many words can she type per
</em>
<em>minute?; </em> 40 words per minute
Answer:
Step-by-step explanation:
Find the parabola through (
−
8
,
6
) with vertex (
−
6
,
-5
)
.
Standard Form: y
=
−
11
/4x
²−
44
x
−
170
Vertex Form: y
=
−
11
/4
(
x
+
8
)
2
+
6
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