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3 years ago

P.

Mathematics

1 answer:

zavuch27 [327]3 years ago

8 0

Answer:

x = z

x + y = 180

Step-by-step explanation:

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A jogger runs 140 m due west, then changes direction for the second leg of her run. At the end of the run, she is 374 m away fro

USPshnik [31]

Answer:

The length of her second displacement = 247.12 m.

The direction of her second displacement = 31.24° from west.

Step-by-step explanation:

As per the question,

From the figure as drawn below,

Let the starting point be O. After running 140 m due west, she reached at point A.

∴ OA = 140 m

And At the end of the run, she is 374 m away from the starting point at an angle of 20° north of west.

∴ OP = 374 m

We have to find the distance AP = x.

By using the cosine rule in triangle OAP

$cos \theta = \frac{OA^{2}+OP^{2}-AP^{2}}{2\times OA\times OP}$

After putting the given value, we get

$cos 20= \frac{140^{2}+374^{2}-x^{2}}{2\times 140\times 374}$

$x^{2}=140^{2}+374^{2} - 2\times 140\times 374\times cos 20$

∴ x = 247.12 m

Hence,the length of her second displacement = 247.12 m.

Again,

By using the cosine rule in triangle OAP, we get

$cos \alpha = \frac{OA^{2}+AP^{2}-OP^{2}}{2\times OA\times AP}$

After putting the given value, we get

$cos \alpha = \frac{140^{2}+247.12^{2}-374^{2}}{2\times 140\times 247.12}$

∴ α = 148.759°

Hence, the direction of her second displacement = 180° - α = 180° - 148.759 = 31.24° from west.

8 0

3 years ago

Hamdi lives 452 miles from her

scZoUnD [109]

Answer:

It's 317 miles.

Step-by-step explanation:

You just take the amount of miles it is from her grandparents house and the amount of miles to her cousins house and then you subtract them.

452-135=317 miles apart.

7 0

3 years ago

Kevin and Randy Muise have a jar containing 70 coins, all of which are either quarters or nickels. The total value of the coins

Nikitich [7]

Answer:

50 nickels, 20 quarters.

Step-by-step explanation:

System of equations (q = # of quarters, n = # of nickels):

q + n = 70, 0.25q + 0.05n = 7.50

the first equation can be changed to q = 70 - n, so we are able to substitute q with 70 - n.

So, it will look like 0.25*70 - 0.25n + 0.05n = 7.50. This can be simplified to 0.2n = 10, which means that n = 50.

Knowing that we can solve q + 50 = 70, which means that q = 20.

6 0

3 years ago

N-(-7)= 12 how do you rewrite

DiKsa [7]

Answer:

N + 7 = 12

Step-by-step explanation:

When you have a number minus a negative number, it's the same as addition.

4 0

3 years ago

Read 2 more answers

Make x the subject of the formula y= 2x +5

Kryger [21]

Answer:

x= (y-5)/2

Step-by-step explanation:

Isolate the x variable.

y= 2x +5

Subtract 5 from both sides.

y-5=2x

Divide both sides by 2.

(y-5)/2= x

5 0

3 years ago