Answer:
83
Step-by-step explanation:
Answer:
2/3
Step-by-step explanation:
The gradient of any line in standard form, Ax + By = C is -A/B.
Divide each term by 3 and simplify.
3y = 2x - 6
3y / 3 = y
2x / 3 = 2/3x
6 / 3 = 2
So, y = 2 / 3 x - 2
slope or gradient = 2/3
Explanation:
The first step in finding the slope of a line that is written in standard form is to write the equation in slope-intercept form, y=mx+b. To do this, rearrange the variables. The standard form, Ax + By = C can be rewritten as By = -Ax + C.
Divide by B to simplify
In the equation By = -Ax + C, B needs to be distributed through the equation. To do this, divide both sides by B. The answer is y = (-A/B)x + C/B.
Find the slope
Once the equation of the line is in slope-intercept form and is simplified, then the slope equals the term in front of the x variable. In the standard form from step 2, the slope is -A/B.
Ah, this my friend, is actually easier than it looks. I promise. Sort of. XD
Alright, so let's start with the basics. You have two shapes that look congruent, and obviously ARE congruent, but how they are congruent can be different.
HIJ (Shape 1) is congruently equal to (~=) shape LKJ (The order does indeed matter) by what?
Well, in terms of congruency, you have about 8 different ways, I only remember 4.
SSS (Side, Side, Side)
SAS (Side, Angle, Side)
ASA (Angle, Side, Side)
AAA (Angle, Angle, Angle)
This means that whichever it is, each must be identified as congruent to the other. If it's SAS, you must know, for certain (not you personally, you can guess, but that's not what they want, they want you to know based on the info they give you) that there are 2 sides that are congruent, and 1 angle that are congruent. Same for all the others, just plug and play.
In the text, this question mentions that side HJ is congruently equal to JL. This means you have 1 set of sides identified as congruent.
The text ALSO mentions that angle H is also congruently equal to angle L. This means you now have 1 set of angles that are congruently equal.
So far, you know you have 1 congruent set of sides (S) and One congruent set of angles (A)
Now, you also can see that based on what we already know, HIJ extends to LKJ, meaning the other angle would ALSO be congruent.
This leaves you with "ASA" (Angle, Side, Angle), meaning 2 sets of angles are congruent, and 1 set of sides.
Your answer is A
~Hope this helps!
Answer:
24.72 m
11.53 m
Step-by-step explanation:
Horizontal distance AB can be obtained from △ABC
From trigonometry :
Sin18° = opposite / hypotenus
Sin18° = AB / 80
AB = 0.3090169 * 80
AB = 24.72 m
The height BT, of tower from △ABT
From trigonometry :
Tan25° = opposite / Adjacent
Tan25° = h / 24.72m
h = Tan25 * 24.72
h = 11.527
h = 11.53 m
Hence, height of tower BT = 11.53 m
