pedro goes to the gym every eight days but tennis is every twelve days if today is september 27 when will he do both again

Naddika [18.5K]

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

$\frac{3}{5}*36=21.6$

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

$\frac{3}{5}*39=23.4$

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:

$39^2-36^2=UW^2$ and

$UW^2=225$ so

UW = 15

Now we can say that side XZ is

$\frac{3}{5}*15=9$

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:

$cos(z)=\frac{9}{23.4}$

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°

3 0

2 years ago

Susan Marciano invested part of her $37,000 bonus in a fund that paid a 12% profit and invested the rest in stock that suffered

Bad White [126]

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.

6 0

3 years ago

If a 50-inch flat-screen now costs $1200, what will it cost in three years?

Wewaii [24]

Answer:$3600 hope this helps

Step-by-step explanation:

8 0

1 year ago

The sign of the product of 2 integers with the same sign is positive. what is the sign of the product of 3 integers with the sam

klemol [59]

Product of 3 negatives equals a negative answer
Product of 3 positives equals a positive answer

6 0

3 years ago

Jonathan is using the microscope in lab. He saw a chain of bacteria that was 10 millimeters long,

AysviL [449]

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.

$\text{Length of bacteria in cm}=10\text{ mm}\times \frac{0.1\text{ cm}}{\text{1 mm}}$

$\text{Length of bacteria in cm}=10\times 0.1\text{ cm}$

$\text{Length of bacteria in cm}=1\text{ cm}$

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

6 0

3 years ago