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3 years ago

What is the point-slope form of a line that has a slope of –4 and passes through point (–3, 1)?

Mathematics

2 answers:

dimaraw [331]3 years ago

8 0

Answer:

y - 1 = - 4(x + 3)

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

Here m = - 4 and (a, b) = (- 3, 1), hence

y - 1 = - 4(x - (- 3)), thus

y - 1 = - 4(x + 3) ← in point- slope form

dybincka [34]3 years ago

7 0

Answer:

$y-1=-4(x+3)$

Step-by-step explanation:

Given: A line has a slope of -4 and the line passes through a point $(-3, 1)$ .

To find: The point-slope form of this line.

Solution:

We know, the point-slope form of a line can be given as

$y-y_{1}=m(x-x_{1} )$

Here, $m$ is the slope of the line, and $(x_{1}, y_{1})$ is the point through which it passes.

The slope of the line is -4, and the point is $(-3, 1)$ .

So, $m=-4$ , $x_{1} =-3$ , and $y_{1} =1$ .

Now, putting the values in the equation, we get

$y-1=-4(x-(-3))$

$y-1=-4(x+3)$

Therefore, the point-slope form of the line is $y-1=-4(x+3)$ .

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100 POINTS!!!! CAN ANYONE PLEASE HELP ME OUT WITH THIS??!!

JulsSmile [24]

The two boats picked for the trip are the steamboat and the tall ship. Let us assume that we will take the steamboat going to the island, and then we will take the tall ship for the return trip. We will then relate the distances travelled by both ships to each other.

2. We know that the steamboat takes five hours to complete the trip. The tall ship takes more time, at ten hours to complete the trip. We do not have the exact speeds of the steamboat or of the tall ship, but we do know that the tall ship is 10 knots slower than the steamboat. We likewise do not know the exact distance travelled by either ship, but we do know that both travel the same distance. We want to find out how fast each boat travels. We expect the answers to be in knots, with a difference of 10.

3. We know that distance is equivalent to the product of speed of a boat multiplied by the time of travel. For the trip going to the island, we will use the steamboat. Let its speed be x knots (equivalent to x nautical miles per hour), and let the distance going to the island be d nautical miles. Given that the time takes is 5 hours, this means that d = 5x.

4. If we let x be the speed of the boat you are taking to the island (the steamboat), then we know that the speed of the other boat (the tall ship) is 10 knots less than the steamboat's. So the speed of the tall ship (for the return trip) is (x - 10) knots.

5. Similar to part 3: we will multiply speed by time to determine the distance from the island. From part 4, we have determined that the speed of the tall ship to be used in returning is (x - 10) knots. Meanwhile, the given in the problem says that the tall ship will take 10 hours to make the trip. Therefore the distance will be equal to d = 10(x - 10) = 10x - 100 nautical miles.

6. We can assume that the distance travelled going to the island is the same distance travelled coming back. Therefore, we can equate the formula for distance from part 3 for the steamboat, to the distance from part 5 for the tall ship.
5x = 10x - 100

7. Solving for x: 5x = 10x - 100
-5x = -100
x = 20
Since x is the speed of the steamboat, x = 20 means that the steamboat's speed is 20 knots.

8. We determined in part 4 that the speed of the second boat (in our case, the tall ship) is (x - 10) knots. Since we have calculated in part 7 that the steamboat travels at x = 20 knots, then the speed of the tall ship is (x - 10) = 20 - 10 = 10 knots.
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3 years ago

In kite ABCD, AB = BC and CD = DA. AB = (3x + 4), BC = x + 8, CD = y + 7, and DA = 2y + 5, find the perimeter of the kite

lana [24]

3x + 4 = x+ 8 > 3x - x = 2x > 2x + 4 = 8 > 8 - 4 = 4 > 2x / 2 crosses out > 4 / 2 = 2 > x=2
2y + 5 = y + 7 > 2y - y = y > y+ 5 = 7 > 7-5= 2 > y=2

the perimeter of the kite is 4

8 0

3 years ago

Point B has coordinates (4,1). The x-coordinate of point A is -4. The distance between point A and point B is 10 units. What a

klasskru [66]

Given:

Point B has coordinates (4,1).

The x-coordinate of point A is -4.

The distance between point A and point B is 10 units.

To find:

The possible coordinates of point A.

Solution:

Let the y-coordinate of point A be y. Then the two points are A(-4,y) and B(4,1).

Distance formula:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The distance between point A and point B is 10 units.

$\sqrt{(4-(-4))^2+(1-y)^2}=10$

Taking square on both sides, we get

$(8)^2+(1-y)^2=100$

$(1-y)^2=100-64$

$(1-y)^2=36$

Taking square root on both sides, we get

$(1-y)=\pm \sqrt{36}$

$-y=\pm 6-1$

$y=1\mp 6$

$y=1-6$ and $y=1+6$

$y=-5$ and $y=7$

Therefore, the possible coordinates of point A are either (-4,-5) or (-4,7).

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3 years ago

Which fraction is equivalent to 38%?<br> 3/8<br> 9/25<br> 19/50<br> 3 4\5

KonstantinChe [14]

In order to find a fraction, We know that a percentage is out of a 100. This means we can now place our fraction as:

38/100

In order to find the actual fraction, we will want to simplify. Lets find our least common factor and work down from there. Since we know that 2 can go into both of them, lets reduce by 2.

This means our fraction will now look like:

19/50

Since 19 is a prime number and cannot be divided by anything but 1 and itself, we know that this is our simplified form.

This means:

19/50 is the fraction equivalent to 38%.

5 0

3 years ago

Read 2 more answers

Write an equation of the perpendicular bisector of the segment with endpoints G 9,8       and H 3,2      .

Norma-Jean [14]

Answer:

y = -x + 11

Step-by-step explanation:

The equation of a straight line is is given by:

y = mx + b; where m is the slope and b is the y intercept

The equation of the line joining G(9, 8) and H(3, 2) is given as:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-8=\frac{2-8}{3-9}(x-9)\\\\y-8=x-9\\\\y=x-1$

The perpendicular bisector of the line joining G(9, 8) and H(3, 2) is perpendicular to the line joining G(9, 8) and H(3, 2) and passes through the midpoint of line joining G(9, 8) and H(3, 2).

Let (x, y) be the midpoint of the line joining G(9, 8) and H(3, 2). Hence:

x = (9 + 3)/2 = 6

y = (8 + 2)/2 = 5

The midpoint = (6, 5)

Two lines are perpendicular if the product of their slopes is -1.

The line joining G(9, 8) and H(3, 2) has a slope of 1, hence, the slope of the perpendicular bisector would be -1.

This means that the perpendicular bisector has a slope of -1 and passes through (6, 5). Using:

$y-y_1=m(x-x_1)\\\\y-5=-1(x-6)\\\\y-5=-x+6\\\\y=-x+11$

The equation of the perpendicular bisector is y = -x + 11

8 0

3 years ago