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3 years ago

Which equation shows the quadratic formula used correctly to solve 7x2 = 9 + x for x?

Mathematics

1 answer:

IrinaK [193]3 years ago

5 0

39 over the 999999999

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A motorboat travels 220 kilometers in 4 hours going upstream. It travels 260 kilometers going downstream in the same amount of t

aliya0001 [1]

Answer: The rate of boat is 60 kmh.

The rate of current is 5 kmh.

Step-by-step explanation:

Alright, lets get started.

Suppose the rate of boat in still water is : b kmh

Suppose the rate of current is : c kmh

When the boat is going upstream, the relative speed will be : $(b-c)$

When the boat is going downstream, the relative speed will be: $(b+c)$

Boat travels 220 kilometers in 4 hours going upstream.

$speed=\frac{distance}{time}$

$(b-c)=\frac{220}{4}$ .................. equation (1)

It travels 260 kilometers going downstream in the same amount of time.

$(b+c)=\frac{260}{4}$ ................... equation (2)

Adding equation 1 and 2

$b-c+b+c=\frac{220}{4}+\frac{260}{4}$

$2b=\frac{480}{4}$

$2b=120$

$b=60$

Plugging the value of b as 60 in equation 2

$60+c=\frac{260}{4}$

$60+c=65$

$c=5$

Hence the rate of boat is 60 kmh.

Hence the rate of current is 5 kmh.

Hope it will help :)

6 0

3 years ago

(1/3)^3 = ____?<br><br> Im just working in school cheating on khan acad lol

Alexus [3.1K]

Answer:

Step-by-step explanation:

The answer is 1/27

due to

(1/3)^3 = [(1)^3]/[3^3] =1/27

Best regards

3 0

3 years ago

Samantha has 4 boxes of action figures. Each box contains 198 figures. which expression shows a strategy Samantha can use to fin

Lynna [10]

Number of action figures each box contains = 198

Total number of boxes = 4

The product can be found as = $4\times198$

hence, option 2 is the correct answer.

4 x (200 - 2) = $4\times198$

8 0

2 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

Evaluate |2x+y-3z| for x=-2, y=10, and z=3<br> How to solve?

Angelina_Jolie [31]

|2x + y - 3z|
Plug in the values
|-4 + 10 - 9|
= |-3|
= 3

4 0

3 years ago

Read 2 more answers