6 per cent compounded daily yields
(1 + .(06/365) )^365
=
<span>
<span>
<span>
1.0618313107
</span>
</span>
</span>
-1=
<span>
<span>
<span>
6.18313107 % annually
Total = </span></span></span><span>4,000 * (1.0618313107)^(92/365) =
</span><span>$ 4,060.95
Here's a compound interest calculator:
http://www.1728.org/compint.htm
</span>
The theorem that justifies why triangles ABC and DEF are congruent is: HL.
<h3>What is the Hypotenuse-Leg Congruence Theorem (HL)?</h3>
The hypotenuse-leg congruence theorem (HL) states that if two triangles that are right triangles have a pair of congruent hypotenuse and a pair of corresponding congruent legs, then both right triangles are proven to be congruent to each other. This means both right triangles are have the same shape and size.
Given that:
angle ABC = angle DEF = 90° (congruent right angles, this means both triangles are right triangles)
AC = FD (a pair of congruent hypotenuse)
AB = DE (a pair of congruent legs)
Thus, we can conclude that since triangle ABC and triangle DEF have a pair of congruent hypotenuses and a pair of congruent legs, therefore, the two right triangles, triangle ABC and triangle DEF are congruent to each other by the HL congruent theorem.
Thus, the theorem that justifies why both triangles are congruent is: HL.
Learn more about the HL congruence theorem on:
brainly.com/question/2102943
#SPJ1
If the radiation level is 100%, it would take 2.4 days to take the radiation level to 50%. However, the situation implies that the radiation level is 25% only, so we need to take 25% from 2.4 days to know the timeframe for a room to be emptied from the radioactive gas. 2.4 days multiplied by 0.25 will give a result of 0.6 day - the timeframe needed to empty the room out of the radioactive gas.
Answer:
Step-by-step explanation:
<u><em>The complete question is:</em></u>
Find the equation of the line that passes through: (-5, 5), and is perpendicular to the line y = 5/9x - 4
step 1
Find the slope of the line
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
The equation of the given line is
The slope of the given line is
The opposite reciprocal is equal to
----> slope of the perpendicular line
step 2
Find the equation of the line in point slope form
we have
substitute
step 3
Convert to slope intercept form
Isolate the variable y
The ratio of bows to headbands is 8:4. This means that for every 8 bows, there are 4 headbands, Then, a true statement is the second option.
Since there are 8 bows + 4headbands = 12 accessories, this also implies that for every 12 hair accesories, there are 4 headbands. This solution corresponds to the last option.
Hence, the true statements are the second and last options.
