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3 years ago

Write an equation in slope-intercept form for the line with slope 4 and y-intercept - 2

Mathematics

1 answer:

ladessa [460]3 years ago

6 0

Answer:

The slope intercept form is typically in the form of

y=mx+c

c=-2

m=4

The slope intercept form of the equation is

y=4x-2

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Express the pair of fractions using the least common denominator of the two.<br> 2/3, 1/4

Fed [463]

Answer:

8/12, 3/12

Step-by-step explanation:

Least common multiple for 3 and 4 is 12. So the denominator should be 12.

For the fraction 2/3, multiply the numerator and denominator by 4 so you will get :

2/3 * 4/4 = 8/12

For the fraction 1/4, multiply the number and denominator by 3 so you will get:

1/4 * 3/3 = 3/12

7 0

3 years ago

Pls help, easy geometry question

Lemur [1.5K]

x^2 + y^2 + 2x - 6y + 1 = 0

x^2 +2x + 1 + y^2 - 6y = 0

x^2 + 2( x × 1) + 1^2 + y^2 - 2(y×3) + 3^2 -3^2 =0

(x+1)^2 + (y-3)^2 = 3^2

comparing with circle equation

(x-a)^2 + (y - b)^2 = r^2

where (a , b) is centre of circle.

so we get center of circle is

(-1, 3)

3 0

3 years ago

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The points (12,23) and (14,45) lie on a line.<br> What is the slope of the line?

Irina18 [472]

Answer:11

Step-by-step explanation:

so that is easy it is rise over run!!!

y2-y1 over x2-x1!!! look at picture!!!

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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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2 years ago

HELP ME PLS<br> Which of these figures has rotational symmetry?

Vlada [557]

Answer:

Step-by-step explanation:

When you rotate the shape it will be the same as it was before .

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3 years ago

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