Answer:
Second option, scale factor is 2.5
Step-by-step explanation:
We see that ∠B ≅ ∠E and ∠C ≅ ∠F, therefore, ΔABC ~ ΔDEF by the AA Similarity for Triangles Theorem which states that if two pairs of corresponding angles are congruent in two triangles, then those two triangles are similar. To find the scale factor, all we have to do is DF / AC = 5/2 or 2.5.
For number 4, we'll need a few facts to answer our question:
- Two supplementary angles add up to 180°, forming a straight angle (the angle formed by a straight line)
- The interior angles of a triangle add up to 180°
Given those, we notice that the one unlabeled angle in the figure shares a line with 156°. In fact, this angle is <em>supplementary</em> to 156°, which means that the two add up to 180°. To find the measure of this mystery angle, we can subtract 156 from 180 to obtain 180 - 156 = 24°.
Now, let's look at the triangle. We already know the measure of one of the angles is 24°, and the other two are x°. What else do we know about the angles of a triangle? From the two facts listed at the beginning, we know their interior angles add up to 180°, so let's use that fact to solve for x.
We have:
, or
Solving for x:
So, x = 78°.
For question 5, the <em>definition</em> of a pair of parallel lines is a pair of lines which <em>never intersect</em>, so "always" would be the appropriate answer.
Answer:
pp
Step-by-step explanation:
8.5x + 55 = 123
You would use the formula: mx + b = y
The slope is the amount of money each day(mx),and the y-intercept would be the fee(b) and the total cost would be y.
Answer:
19.80
Step-by-step explanation:
tan 22= 8/x
tan 22 = 8/x
x = 8/tan 22
x = 19.80