Answer:
cos(z) = .3846153846 and angle z = 67.38°
Step-by-step explanation:
Side UV is corresponding to side YX. Side VW is corresponding to side YZ. Side UW is corresponding to side XZ.
Starting with the first corresponding pair, we are told that side UV is 36, and that side YX is 3/5 of that. So side YX is

We are next told that side VW is 39, so side YZ is

In order to find the cos of angle z, we need the adjacent side, which is side XZ. Side XZ is 3/5 of side UW. Right now we don't know the length of side UW, so we find it using Pythagorean's Theorem:
and
so
UW = 15
Now we can say that side XZ is

The cos of an angle is the side adjacent to the angle (9) over the hypotenuse of the triangle (23.4) so our ratio is:

which divides to
cos(z) = .3846153846
If you need the value of the angle, use the inverse cosine function on your calculator in degree mode to find that
angle z = 67.38°
Answer:
The amount invested in funds that earned 12% profit is 31000
The amount invested in stock that suffered 5% loss is 6,000.
Step-by-step explanation:
Let x be the amount invested in funds that earned 12%.
Then the amount invested in stock that suffered 5% loss is 37000 - x.
The profit from investment in funds is = 12% of x
= 0.12·x
The loss from investment in stock is = 5% of (37000 - x)
= 0.05 × (37000 - x)
The net profit is 0.12·x - 0.05 × (37000 - x)
As the net profit given in the problem is $3420, we have :
0.12·x - 0.05 × (37000 - x) = 3420
Solving for x, we have :
12·x - 5 × (37000 - x) = 342000 (multiply both sides by 100)
12·x - 185000 + 5·x = 342000
17·x = 527000
⇒ x = 31000
Hence, The amount invested in funds that earned 12% profit is 31000 and the amount invested in stock that suffered 5% loss is 37000 - x = 37000 - 31000 = 6,000.
Answer:$3600 hope this helps
Step-by-step explanation:
Product of 3 negatives equals a negative answer
Product of 3 positives equals a positive answer
We have been given that Jonathan is using the microscope in lab. He saw a chain of bacteria that was 10 millimeters long. We are asked to find the length of chain of bacteria in centimeters.
We know that 1 millimeter is equal to 0.1 centimeter.
To convert 10 milllimeters into centimeters, we will multiply 10 by 0.1.



Therefore, the chain of the bacteria is 1 cm long.