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3 years ago

Please help with my math

Mathematics

1 answer:

shusha [124]3 years ago

5 0

Answer:

Step-by-step explanation:

These triangles are similar triangles, so there is a number that you can multiply the sides of TUV to find the side lengths of QRS. looking at the triangle, the similar sides are RS being similar to UV and RQ being similar to UT.

If RS~UV, then there is a ratio between them. 54/36=1.5. The ratio is 1.5.

RQ~UT, and by a factor of 1.5, so divide RQ by the scale factor. 24/1.5=16. UT=16=x+5.

x+5=16, subtract 5 from both sides.

x=11

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3 years ago

Read 2 more answers

The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that

tekilochka [14]

Answer:

a) P(X∩Y) = 0.2

b) $P_1$ = 0.16

c) P = 0.47

Step-by-step explanation:

Let's call X the event that the motorist must stop at the first signal and Y the event that the motorist must stop at the second signal.

So, P(X) = 0.36, P(Y) = 0.51 and P(X∪Y) = 0.67

Then, the probability P(X∩Y) that the motorist must stop at both signal can be calculated as:

P(X∩Y) = P(X) + P(Y) - P(X∪Y)

P(X∩Y) = 0.36 + 0.51 - 0.67

P(X∩Y) = 0.2

On the other hand, the probability $P_1$ that he must stop at the first signal but not at the second one can be calculated as:

$P_1$ = P(X) - P(X∩Y)

$P_1$ = 0.36 - 0.2 = 0.16

At the same way, the probability $P_2$ that he must stop at the second signal but not at the first one can be calculated as:

$P_2$ = P(Y) - P(X∩Y)

$P_2$ = 0.51 - 0.2 = 0.31

So, the probability that he must stop at exactly one signal is:

$P = P_1+P_2\\P=0.16+0.31\\P=0.47$

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3 years ago

Lines a and b are parallel.

VashaNatasha [74]

I have added a screenshot with the complete question along with a diagram representing the scenario.

Answer:
s = 22°

Explanation:
1- getting the top right angle of line B:
We are given that:
the top right angle of line A = 158°
Since lines A and B are parallel, therefore, the top right angle of line A and the top right angle of line B are corresponding angles which means that they are equal
This means that:
Top right angle of line B = 158°

2- getting the value of s:
Now, taking a look at line B, we can note that:
angle s and the top right angle form a straight angle. This means that the sum of these two angles is 180°
Therefore:
180 = s + 158
s = 180 - 158
s = 22°

Hope this helps :)