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allsm [11]
3 years ago
5

Write in slope-intercept form an equation of the line that passes through the points (−5,−9) and (5,1).

Mathematics
1 answer:
o-na [289]3 years ago
3 0

Answer:

y=x-4

Step-by-step explanation:

The slope is given by

m = (y2-y1)/(x2-x1)

m = (1--9)/(5--5)

m = (1+9)/(5+5)

    = 10/10

   = 1

The slope is 1

We have the slope and a point,so we can use point slope form

y-y1 = m(x-x1)

y-1 = 1(x-5)

y-1 = x-5

Add 1 to each side

y-1+1 = x-5+1

y=x-4

This is slope intercept form (y= mx+b)

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Given: △ABC, AB=5sqrt2 <br> m∠A=45°, m∠C=30°<br> Find: BC and AC
Marysya12 [62]

BC is 10 units and AC is 5+5\sqrt{3} units

Step-by-step explanation:

Let us revise the sine rule

In ΔABC:

  • \frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}
  • AB is opposite to ∠C
  • BC is opposite to ∠A
  • AC is opposite to ∠B

Let us use this rule to solve the problem

In ΔABC:

∵ m∠A = 45°

∵ m∠C = 30°

- The sum of measures of the interior angles of a triangle is 180°

∵ m∠A + m∠B + m∠C = 180

∴ 45 + m∠B + 30 = 180

- Add the like terms

∴ m∠B + 75 = 180

- Subtract 75 from both sides

∴ m∠B = 105°

∵ \frac{AB}{sin(C)}=\frac{BC}{sin(A)}

∵ AB = 5\sqrt{2}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}

- By using cross multiplication

∴ (BC) × sin(30) = 5\sqrt{2} × sin(45)

∵ sin(30) = 0.5 and sin(45) = \frac{1}{\sqrt{2}}

∴ 0.5 (BC) = 5

- Divide both sides by 0.5

∴ BC = 10 units

∵ \frac{AB}{sin(C)}=\frac{AC}{sin(B)}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}

- By using cross multiplication

∴ (AC) × sin(30) = 5\sqrt{2} × sin(105)

∵ sin(105) = \frac{\sqrt{6}+\sqrt{2}}{4}

∴ 0.5 (AC) = \frac{5+5\sqrt{3}}{2}

- Divide both sides by 0.5

∴ AC = 5+5\sqrt{3} units

BC is 10 units and AC is 5+5\sqrt{3} units

Learn more:

You can learn more about the sine rule in brainly.com/question/12985572

#LearnwithBrainly

6 0
3 years ago
-7,-12,-17,-22,-27 find the nth term
Bess [88]

Answer:

-2 - 5n

Step-by-step explanation:

-7, -12, -17, -22, -27.....

Arithmetic Sequence

first term a = -7

difference = d = -12 - (-7) = -12 + 7 =  (-5)

nth term = a + (n-1)d

              =  -7 + (n-1)*(-5)

              = -7 + (-5)*n -1 * (-5)

             = -7 - 5n + 5

            = -2 - 5n

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Step-by-step explanation:

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Answer:

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