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hichkok12 [17]
3 years ago
8

A train traveling 50 mph left a station 30 minutes before a second train running at 55 mph. If 55x represents the distance the f

aster train travels, which of the following algebraic expressions represents the distance of the slower train? 50(x + 0.5) 50(x-0.5) 50(0.5-x)
Mathematics
2 answers:
Lelu [443]3 years ago
6 0
<span>Equation:
distance = distance 
50x = 55(x-(1/2)
50x = 55x - (55/2)
-5x = -55/2
x = 11/2
x = 5 1/2 hrs (time at which the 2nd train overtakes the 1st train)</span>
Lady bird [3.3K]3 years ago
6 0

Answer:

Option 2nd is correct

50(x-0.5) miles

Step-by-step explanation:

Using distance formula:

\text{Distance} = \text{Speed} \times \text{time}

As per the statement:

A train traveling 50 mph left a station 30 minutes before a second train running at 55 mph. If 55x represents the distance the faster train travels.

Second train data:

Let time taken by second train be  x hrs

Speed = 55 mph

then;

Distance = 55x miles

First train data:

Speed = 50 mph

time = x - \frac{30}{60} = x - \frac{1}{2}

then;

\text{Distance} = 50(x-\frac{1}{2}) miles

Since, the second train travels faster than first train

We have to find the distance of the slower train.

Distance of the slower train = 50(x-0.5) miles

Therefore,  the following algebraic expressions represents the distance of the slower train is,  50(x-0.5)

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Reptile [31]

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(9x + 17) +2 \times  ( 5x + 15 ) + (6x - 12) = 360 \\

9x + 17 + 10x + 30 + 6x - 12 = 360 \\

9x + 10x + 6x + 17 + 30 - 12 = 360 \\

Collect like terms

25x + 35 = 360

Subtract sides 35

25x + 35 - 35 = 360 - 35

25x = 325

Divide sides by 25

\frac{25x}{25}  =  \frac{325}{25}  \\

x = 13

Thus ;

RQ  \:  \: arc =2 \times (5x + 15)

RQ  \:  \: arc = 10x + 30

RQ  \:  \: arc = 10(13) + 30

RQ  \:  \: arc = 130 + 30

RQ \:  \:  arc = 160°

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I need help with questions #7 and #8 plz
katen-ka-za [31]

Answer:

7. A = 40.8 deg; B = 60.6 deg; C = 78.6 deg

8. A = 20.7 deg; B = 127.2 deg; C = 32.1 deg

Step-by-step explanation:

Law of Cosines

c^2 = a^2 + b^2 - 2ab \cos C

You know the lengths of the sides, so you know a, b, and c. You can use the law of cosines to find C, the measure of angle C.

Then you can use the law of cosines again for each of the other angles. An easier way to solve for angles A and B is, after solving for C with the law of cosines, solve for either A or B with the law of sines and solve for the last angle by the fact that the sum of the measures of the angles of a triangle is 180 deg.

7.

We use the law of cosines to find C.

18^2 = 12^2 + 16^2 - 2(12)(16) \cos C

324 = 144 + 256 - 384 \cos C

-384 \cos C = -76

\cos C = 0.2

C = \cos^{-1} 0.2

C = 78.6^\circ

Now we use the law of sines to find angle A.

Law of Sines

\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}

We know c and C. We can solve for a.

\dfrac{a}{\sin A} = \dfrac{c}{\sin C}

\dfrac{12}{\sin A} = \dfrac{18}{\sin 78.6^\circ}

Cross multiply.

18 \sin A = 12 \sin 78.6^\circ

\sin A = \dfrac{12 \sin 78.6^\circ}{18}

\sin A = 0.6535

A = \sin^{-1} 0.6535

A = 40.8^\circ

To find B, we use

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8.

I'll use the law of cosines 3 times here to solve for all the angles.

Law of Cosines

a^2 = b^2 + c^2 - 2bc \cos A

b^2 = a^2 + c^2 - 2ac \cos B

c^2 = a^2 + b^2 - 2ab \cos C

Find angle A:

a^2 = b^2 + c^2 - 2bc \cos A

8^2 = 18^2 + 12^2 - 2(18)(12) \cos A

64 = 468 - 432 \cos A

\cos A = 0.9352

A = 20.7^\circ

Find angle B:

b^2 = a^2 + c^2 - 2ac \cos B

18^2 = 8^2 + 12^2 - 2(8)(12) \cos B

324 = 208 - 192 \cos A

\cos B = -0.6042

B = 127.2^\circ

Find angle C:

c^2 = a^2 + b^2 - 2ab \cos C

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