On the first on it is the first answer and the last one.
second: the second and the third one.
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:
y=5,902,060*(.957)^t
Step-by-step explanation:
Since the original amount would be decreasing and it's an exponential one, hence the "every year", we can determine that it's an exponential decay equation.
The exponential delay equation is y=A*(1-r)^t. The y is the remaining amount, A is the original amount, r is the rate in decimal form, and t is for years. "1-r" is for decreasing rates and "1+r" is for increasing rates.
First thing we need to do is turn the rate, 4.3%, from a percentage to a decimal. You can do this by moving the decimal two places to the right, which gives you 0.043.
Now plug the numbers into the equation.
y=5,902,060*(1-0.043)^t
Simplify what's inside the parenthesis and get your final equation.
y=5,902,060*(.957)^t
The amount more annually a $115,000 10-year term insurance at age 35 cost Bernard than someone of the same age without health issues is $24.
<h3>What are insurance premiums?</h3>
The insurance premium is paid as a cost to cover a possible loss that is unseen.
The annual premium rate as a percentage of the value insured a person at age 35 has to pay is 0.14%.
From the given information, we have that the amount a 35-year-old without health issues will pay per $1,000 is $1.40
The amount to be paid for $115,000 is 115 × $1.4 = $161
The amount Bernard pays = 15% more
= 1.15 × $161
= $185.15
Therefore,
The amount more Bernard has to pay = $185.15 - $161
= $24.15 ≈ $24
Learn more about insurance premiums here:
brainly.com/question/3053945