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Ilya [14]
3 years ago
5

Two angles of triangle measure 55° and 20°. Whats is the measure of the third angle of the triangle?

Mathematics
2 answers:
slamgirl [31]3 years ago
8 0

Step-by-step explanation:

105 have a great day cool kiddos

vladimir2022 [97]3 years ago
7 0

We know that the three angles of a triangle always add up to 180.

Therefore, we have the equation:

55+20+x=180.

Solving for x, we get x=105.


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A man travels 20 km by car from Town P to Town Q at an average speed of x km/h. He finds that the time of the journey would be s
yuradex [85]

Answer:

x = 20.

Step-by-step explanation:

First, you should remember the relation:

Distance = Speed*Time.

First, we know that a man travels a distance of 20km at a speed of x km/h, in a time T.

We can write this as:

20km = (x km/h)*T

We know that the time is shortened by 12 minutes if the speed is increased by 5km/h

Rewriting these 12 minutes in hours (remember that 60min = 1 hour)

12 min = (12/60) hours = 0.2 hours

Then from this, he can travel the same distance of 20km in a time T minus 0.2 hours if the speed is increased by 5 km/h

We can write this as:

20km = (x + 5 km/h)*(T - 0.2 h)

Then we have a system of two equations, and we want to find the value of x:

20km = (x km/h)*T

20km = (x + 5 km/h)*(T - 0.2 h)

First, we should isolate the variable T in one of the equations, if we isolate it in the first one, we will get:

20km/(x km/h) = T

Replacing that in the other equation we get:

20km = (x + 5 km/h)*(T - 0.2 h)

20km = (x + 5 km/h)*( 20km/(x km/h) - 0.2 h)

Now we can solve this for x.

Removing the units (that we know that are correct) so the math is easier to read, we get:

20 = (x + 5)*(20/x - 0.2)

We only want to solve this for x.

20 = x*20/x - x*0.2 + 5*20/x - 5*0.2

20 = 20 - 0.2*x + 100/x - 1

subtracting 20 in both sides we get:

20 - 20 = 20 - 0.2*x + 100/x - 1 - 20

0 = -0.2*x + 100/x - 1

If we multiply both sides by x we get:

0 = -0.2*x^2 + 100 - x

-0.2*x^2 - x + 100 = 0

This is just a quadratic equation, we can solve it using the Bhaskara's equation, the solutions are:

x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*(-0.2)*100} }{2*-0.2}  = \frac{1 \pm 9 }{-0.4}

Then the two solutions are:

x = (1 + 9)/-0.4 = -25

x = (1 - 9)/-0.4 = 20

As x is used to represent a speed, the negative solution does not make sense, so we should use the positive one.

x = 20

then the average speed initially is 20 km/h

3 0
2 years ago
Are the given ratios equivalent Explan why or why not 3 : 5 12 : 20​
sasho [114]
Yes you take 3 times 4 and receive 12 and 5 times 4 and receive 20
4 0
2 years ago
W at is 1/8 in decimal form
Oksana_A [137]
Putting it into a calculator, we get 0.125 as our answer
7 0
3 years ago
Read 2 more answers
1.A study was created to test the effects of jazz on people's sleep patterns. The hypothesis of the experiment was
ycow [4]

Answer:

Independent Variable:  Jazz music

Dependent Variable: Sleeping Time

Experimental Group: people sleeping with jazz music

Control Group: people sleeping without jazz music

3 constants:

No of people in group

Jazz music

Sleep

Step-by-step explanation:

The independent variable is the one which is not altered by any outer influence. For example the jazz music will not be interrupted by the sleeping habits of people.

The dependent variable is the one which is affected by external changes such as sleeping time is afffected by external music or noises.

Experimental group on which experiment is being carried out.

Control group is which determines the changes in experimental group.

Constants which do not change for the number of experiment, could be number of people, type of jazz music, volume of jazz music also sleep is a constant .

7 0
3 years ago
Find the following values from the information given<br> cot(theta°); tan(theta°) = −0.0005
Greeley [361]

Answer:

cot(θ°) = 2000 radians

Step-by-step explanation:

Data provided in the question:

The value of tan(θ°) = −0.0005

To solve:

cot(θ°)

Now,

we know the relation between cot and tan function as:

cot(θ°) = \frac{1}{\tan\theta}

therefore on substituting the value of theta in the above relation, we can find the value of cot(θ°)

Thus,

cot(θ°) = \frac{1}{-0.0005}

or

cot(θ°) = 2000

5 0
3 years ago
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