A line passes through points (-4,-9) with a slope of 5/4

Calle had five times as many stickers as sara did and twice as many as juniper. Juniper had 25 stickers. How many stickers did t

n200080 [17]

Calle: has twice as many as Juniper so = 2*25 = 50

she also has 5 times as many as sara so if she has 50, you divide 50/5 = 10

Calle has 50 stickers, Sara has 10 and Juniper has 25.

So all together they have 85 stickers.

3 0

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.

4 0

2 years ago

Help!<br> ANYTHING IS APPRECIATED

Debora [2.8K]

Answer:

A:90

B:105

C:60

D:165

Step-by-step explanation:

Brainliest?

7 0

3 years ago

Which is greater 192 inches or 5yards and 1 foot

makvit [3.9K]

1 yard = 36 inches. We have 5 yards, so 5x36 = 180

1 foot = 12 inches.

So the base 192 is largest.

3 0

3 years ago

1) Order the animals by sleep time from least to greatest.

Zolol [24]

The way to line the animals is to put them in order going down. 0.433 56.3% 19/40 65.8%. Then you try to figure out what you need to convert so that you can get your answer. 56.3% changes to 0.563 because you move the decimal two places to the left. 65.8% changes to 0.658 and 19/40 is 0.475. 0.433 0.563 0.475 0.658. Now you compare each row to figure them out. When you do that your answer will be 0.433, 0.475, 0.563, and 0.658. I sleep about 9/24 of the day which is 0.375 and I will fit right befor 0.433.

4 0

3 years ago