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vlada-n [284]
3 years ago
8

what is the equation in slope form of the line that is parallel to the given line and passes through the point (-3,1)​

Mathematics
1 answer:
viktelen [127]3 years ago
6 0

Answer:

D

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate the slope of the given line using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, - 4) and (x₂, y₂ ) = (2, 2) ← 2 points on the line

m = \frac{2+4}{2+2} = \frac{6}{4} = \frac{3}{2}

Parallel lines have equal slopes and using (a, b) = (- 3, 1), then

y - 1 = \frac{3}{2}(x - (- 3)), that is

y - 1 = \frac{3}{2}(x + 3) ← in point- slope form

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By how many degrees did the direction of the boat change
gulaghasi [49]

Answer:

The boat turned <u>39°</u> degrees when it made its first turn.

Step-by-step explanation:

The question is as following:

A boat traveled north for 28 miles, then tuned x° south west and traveled for 25 miles before stopping. When it stopped, the boat was 18 miles from its starting point.

By how many degrees did the direction of the boat change when it made its first turn? Round to the nearest degree.

===================================================

See the attached figure which represent explanation of the problem.

The boat start from point A to point B then stopped at point C

AB = 28 miles, BC = 25 miles and AC = 18 miles.

It is required to find the angle x

By applying the cosine Rule:

AC² = AB² + BC² - 2 * AB * BC * cos x

18² = 28² + 25² - 2 * 28 * 25 * cos x

2 * 28 * 25 * cos x = 28² + 25² - 18²

1400 cos x = 1085

Cos x = 1085/1400 = 0.775

x = Cos⁻¹ 0.775 = 39.2° = 39° to the nearest degree.

So, the boat turned <u>39°</u> degrees when it made its first turn.

8 0
3 years ago
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Oksana_A [137]

Answer:

The scale of the map is inch = 20 feet.

This statement must be incorrect or the fraction of the inch is missing.

Because 6" long, at a scale of one inch = 20 feet, would only be 120 feet x 120 feet.

120 x 120 = 14,000 ft^2 and each of the four quadrants wouls only be 3600 ft^2.

5 0
2 years ago
write the equation of the line in slope-intercept form that has a y-intercept that is -5 and a slope of 8
Alex777 [14]

Answer:

Step-by-step explanation:

y + 5 = 8(x - 0)

y + 5 = 8x - 0

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7 0
2 years ago
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NeTakaya

Answer:

x = 30

Step-by-step explanation:

1/2(x+6) = 18

Distribute

1/2 x + 3 = 18

Subtract 3 from each side

1/2x +3-3 = 18-3

1/2x = 15

Multiply each side by 2

1/2x*2 = 15*2

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6 0
3 years ago
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Three oblique pyramids have the same regular square base. Which one has a volume of 15 cubic units if the area of the bases are
deff fn [24]

Answer:

The one which has a height of 3 units. H=3

Step-by-step explanation:

Well, the volume of pyramid is equal to the area of base multiply by the height of pyramid and divide by 3. Writing as a formula it can be expressed as V=(A*H)/3 where V is volume of pyramid, A is area of base and H is the height of pyramid. If V=15 cubic units and A=15 square units, H should be equal to 3 (to be cancelled out by 3. Please look at formula above) in order to make V=15.

8 0
2 years ago
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