Please help me with these !!! ❤️❤️ I need it thank youuu!

Mathematics

1 answer:

lisov135 [29]3 years ago

7 0

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 supplementary 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:

$x+x+24=180$ , or $2x+24=180$

Solving for x:

$(2x+24)-24=180-24\\2x=156\\(2x)/2=(156)/2\\x=78$

So, x = 78°.

For question 5, the definition of a pair of parallel lines is a pair of lines which never intersect, so "always" would be the appropriate answer.

You might be interested in

A number line shows the whole numbers from 0 to 10 describe where you would plot square root 30

ASHA 777 [7]

Square root of 30 is 5.477. So I would plot my point right in the middle of 5 and 6 on the number line

4 0

2 years ago

Brienne and 3 friends bought tickets to the movies. They spent a total of $27.00 on the tickets. Which equation represents this

Sindrei [870]

Hello!

The equation that represents this situation is A. 3t = 27.

Explanation:

This is because an equation is a "mathematical sentence" and this equation says that if you multiply the costs of the three friends' tickets, the total cost would be $27.

5 0

3 years ago

A cup of coffee contains about 100 mg of caffeine. Caffeine is metabolized and leaves the body at a continuous rate of about 12%

Mamont248 [21]

Answer:

a. $A = C_{0}(1-x)^t\\x: percentage\ of \ caffeine\ metabolized\\$

b. $\frac{dA}{dt}= -11.25 \frac{mg}{h}$

Step-by-step explanation:

First, we need tot find a general expression for the amount of caffeine remaining in the body after certain time. As the problem states that every hour x percent of caffeine leaves the body, we must substract that percentage from the initial quantity of caffeine, by each hour passing. That expression would be:

$A= C_{0}(1-x)^t\\t: time \ in \ hours\\x: percentage \ of \ caffeine\ metabolized\\$

Then, to find the amount of caffeine metabolized per hour, we need to differentiate the previous equation. Following the differentiation rules we get:

$\frac{dA}{dt} =C_{0}(1-x)^t \ln (1-x)\\\frac{dA}{dt} =100*0.88\ln(0.88)\\\frac{dA}{dt} =-11.25 \frac{mg}{h}$