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stellarik [79]
3 years ago
8

Write y = 4/3 * x - 2/3 in standard form Helpplppppp

Mathematics
1 answer:
raketka [301]3 years ago
3 0

Answer:

4x - 3y = 2

Step-by-step explanation:

First, let's review what "standard form" signifies:  Ax + By = C.

Starting with y = 4/3 * x - 2/3, multiply all three terms by 3 to eliminate the fractions:

3y = 4x - 2

Next, subtract 3y from both sides:

0 = 4x - 3y - 2.

It would be nice (tho' not essential) to have the coefficient of x positive.  That is why I've left 4x on the right side and subtracted 3y from both sides.

finally, add 2 to both sides, obtaining 4x - 3y = 2.  This is the equation in standard form.

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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
3 years ago
Write an equation in standard form using integers <br><br> Y= - x<br> —<br> 5
kykrilka [37]

Answer:

x + y = - 5

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

y = - x - 5 ( add x to both sides )

x + y = - 5 ← in standard form

8 0
3 years ago
Plz help ASAP!!!!!!!!!!!
e-lub [12.9K]

Answer:

83 degrees.

Step-by-step explanation:

The angle of this line is 180.  So take 180 - 97 and you should get 83 degrees.  Hope this helped!

-Kirito

5 0
3 years ago
Read 2 more answers
How much should you put in an investment paying a simple interest rate of​ 5% if you needed​ $4000 in eighteen​ mont
Eddi Din [679]

now, there are 12 months in a year, so 18 months is really 18/12 of a year, thus

~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$4000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\to \frac{18}{12}\dotfill &\frac{3}{2} \end{cases} \\\\\\ 4000=P[1+(0.05)(\frac{3}{2})]\implies 4000=P(1.075) \\\\\\ \cfrac{4000}{1.075}=P\implies 3720.93\approx P

6 0
2 years ago
43 points, 86 for brainliest! Answer correct!! Be wise! According to the image attached, whats the answer?
Snezhnost [94]

Answer:

p = 32\:  \: in

a = 49 {in}^{2}

Step-by-step explanation:

perimeter \\  = 8 + 8+8+8 \\  = 32 \:  \: in

area \\   1)3 \times 8 = 24 \\ 2)5 \times 5 = 25 \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: = 49 {in}^{2}

hope this helps

brainliest appreciated

good luck! have a nice day!

6 0
3 years ago
Read 2 more answers
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