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2 years ago

Select the locations on the number line to plot the points −17/8 and 13/8.

Mathematics

2 answers:

elena55 [62]2 years ago

8 0

-17/8 < 13/8

<h3><em><u> </u></em><em><u>♡</u></em><em><u>Discussion:</u></em></h3>

≤ Means maximum
≥ minimum
> means greater than
< means less

Jlenok [28]2 years ago

6 0

Answer: With this information the answer would be GO down twice into the negatives and make you plot point, next go down eleven times and make your plot point, and last go down seventeen times and make your plot point.

Step-by-step explanation: What you have to do is make the number line with a zero at in the middle on the left of the zero you go down into the the negative numbers and on the right you go up into the positive numbers

Step-by-step explanation:

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A self own company charges $40 per month +0.05 cents for each text message sent.Select expression is there a percent of cost in

kondaur [170]

<h3>The monthly cost of cell phone is A = 40 + 0.005 m</h3>

Step-by-step explanation:

The monthly fixed charges by mobile company = $40

The cost of sending each text message = 0.05 cents

Now, 100 cents = 1 dollar

⇒ 1 cent =$ $(\frac{1}{100} )$

⇒ 0.05 cent s =$ $(\frac{1}{100} \times 0.05) =0.0005$

Also, the number of text messages send = m

So, the cost of sending m text message = m x ( cost of 1 text )

= m x ( $ 0.0005) = 0.0005 m

Now, Total bill = Fixed rate + cost of m texts

⇒ A =$40 + $ 0.0005 m

Hence, the monthly cost of cell phone is A = 40 + 0.005 m

7 0

4 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.