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3 years ago

Andrew and Michael are 15 miles apart. If they walk towards each other, they meet in 3

Mathematics

2 answers:

aleksandr82 [10.1K]3 years ago

6 0

Yes they are for andrew-1.875 and micheal- 3.125

andrew11 [14]3 years ago

4 0

Answer: Andrew - 1.875 Michael- 3.125

Step-by-step explanation:

If Andrew overtakes in 8 hours, we can divide 15 miles by 8 to see how many miles per hour he goes.

15/8 = 1.875

Then we can multiply 1.875 by 3 to see how much he traveled while walking towards Michael.

1.875*3=5.265- the distance he traveled

Now subtract that by 15 to see how many miles Michael walked.

15-5.625=9.375

That means Michael walked 9.375 miles.

Divide 9.375 by 3 to see how many miles he walked per hour

9.375/ 3 = 3.125

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Doreen traveled 35 miles.

Step-by-step explanation:

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What is the simplified expression for 3 a squared + 9 a b + 5 minus 4 a squared minus 4 a b + 3? Negative a squared + 5 a b + 8

MArishka [77]

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The answer is option 1.

Step-by-step explanation:

In order to simplify the expressions, you have to collect like terms :

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3 years ago

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What is 1 and 1/4 minus 3/8?

matrenka [14]

Answer: 7/8

Step-by-step explanation:

You can change all the fractions to have equivalent denominators.

The Least Common Denominator of 1 1/4 and 3/8 is 8. Now we can change the fractions.

1 1/4 = 1 2/8 = 10/8.

3/8 = 3/8.

Now we can subtract. Subtract the numerators of the first fraction from the numerators of the second fraction, and the denominators oft he first fraction to the denominators of the second fraction.

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3 years ago

Two lighthouses are located 75 miles from one another on a north-south line. If a boat is spotted S 40o E from the northern ligh

yuradex [85]

Answer:

The northern lighthouse is approximately $24.4\; \rm mi$ closer to the boat than the southern lighthouse.

Step-by-step explanation:

Refer to the diagram attached. Denote the northern lighthouse as $\rm N$ , the southern lighthouse as $\rm S$ , and the boat as $\rm B$ . These three points would form a triangle.

It is given that two of the angles of this triangle measure $40^{\circ}$ (northern lighthouse, $\angle {\rm N}$ ) and $21^{\circ}$ (southern lighthouse $\angle {\rm S}$ ), respectively. The three angles of any triangle add up to $180^{\circ}$ . Therefore, the third angle of this triangle would measure $180^{\circ} - (40^{\circ} + 21^{\circ}) = 119^{\circ}$ (boat $\angle {\rm B}$ .)

It is also given that the length between the two lighthouses (length of $\rm NS$ ) is $75\; \rm mi$ .

By the law of sine, the length of a side in a given triangle would be proportional to the angle opposite to that side. For example, in the triangle in this question, $\angle {\rm B}$ is opposite to side $\rm NS$ , whereas $\angle {\rm S}$ is opposite to side ${\rm NB}$ . Therefore:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of NB}}{\sin(\angle {\rm S})} \end{aligned}$ .

Substitute in the known measurements:

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of NB}}{\sin(21^{\circ})} \end{aligned}$ .

Rearrange and solve for the length of $\rm NB$ :

$\begin{aligned} & \text{length of NB} \\ =\; & (75\; \rm mi) \times \frac{\sin(21^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 30.73\; \rm mi\end{aligned}$ .

(Round to at least one more decimal places than the values in the choices.)

Likewise, with $\angle {\rm N}$ is opposite to side ${\rm SB}$ , the following would also hold:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of SB}}{\sin(\angle {\rm N})} \end{aligned}$ .

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of SB}}{\sin(40^{\circ})} \end{aligned}$ .

$\begin{aligned} & \text{length of SB} \\ =\; & (75\; \rm mi) \times \frac{\sin(40^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 55.12\; \rm mi\end{aligned}$ .

In other words, the distance between the northern lighthouse and the boat is approximately $30.73\; \rm mi$ , whereas the distance between the southern lighthouse and the boat is approximately $55.12\; \rm mi$ . Hence the conclusion.

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