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3 years ago

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What are the coordinates of the point on the directed line segment from (3, 3) to (7,−5) that partitions the segment into a rati

o of 5 to 3

1 answer:

Annette [7]3 years ago

4 0

Answer:

The coordinates of the point is (5.5, -2)

Step-by-step explanation:

Okay, what we want to do here is to get the point that divides the line that joins the points (3,3) to (7,-5) in the ratio 5 to 3

Generally, given the ratio a:b and we want to divide the line joining the points (x1,y1) and (x2,y2) in that ratio, we use the condensed formula below;

Let’s call the point dividing the line in the given ratio z.

The coordinates of Z is;

{(bx1 + ax2)/(a+b), (by1 + ay2)/(a+b)}

In this question (x1,y1) = (3,3)

While (x2,y2) = (7,-5)

while a:b = 5:3

Substituting these values into the coordinate equation for point z, we have ;

{((3(3) + 5(7))/(5+3), ((3)(3) + 5(-5))/(5+3)}

= {44/8 , -16/8} = {5.5, -2}

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An electrician has a piece of wire that is 4 and 3/8 centimeters long. She divides the wire into pieces that are 1 and 2/3 centi

Vlada [557]

Answer:

She has approximately 3 pieces ( 2.625)

Step-by-step explanation:

To get the number of pieces, we need to divide the length of the wire by the individual length of the pieces.

To get the division done, it would be easier to convert what we have into improper fractions

For the piece of wire, the length which is 4 and 3/8 centimeters long will be 35/8 centimeters

while;

the individual length of each of the piece which is 1 and 2/3 centimeters long will be 5/3 centimeters

The number of pieces is thus 35/8 divided by 5/3 = 35/8 * 3/5 = 21/8 = 2.625 which is approximately 3 pieces

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3 years ago

F (1) = -16. f(n)=-29-f(n-1) f2=

Simora [160]

Step-by-step explanation:

f(n) = - 29 - f( n - 1 )

f(1) = - 16

Now

f(2) = - 29 - f ( 2 - 1 )

= - 29 - f ( 1)

= -29 - ( - 16)

= - 29 + 16

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3 years ago

What is the slope of the line with the equation: <br><br> y=4x+3

Darina [25.2K]

Answer:

4

Step-by-step explanation:

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3 years ago

Read 2 more answers

1. Draw the image of ABC under the dilation with scale factor 2 and center of dilation(-4,-3) . Label the image A'B'C'

ycow [4]

<span>The center of dilation of the question is (-4,-3) .
let say that
x0=-4
y0=-3

Label the image A'B'C'
The new coordinate would be

A(-4,-1)
x=4
y=-1

x'=x0+ 2(x - x0)
x'= -4+ 2(-4 +4)
x'=-4

</span>y'=y0+ 2(y - y0)
y'= -3+ 2(-1 +3)
y'=-3 +4= 1
<span>
______________________________

B(-4,-3)
</span>x=-4
y=-3

x'=x0+ 2(x - x0)
x'= -4+ 2(-4 +4)
x'=-4

y'=y0+ 2(y - y0)
y'= -3+ 2(-3 +3)
y'=-3

______________________________
<span>
C(-1,-3)
</span>x=-1
y=-3

x'=x0+ 2(x - x0)
x'= -4+ 2(-1 +4)
x'=-4 +6= 2

y'=y0+ 2(y - y0)
y'= -3+ 2(-3 +3)
y'=-3

A'(-4,1)
B'(-4,-3)
C'(2,-3)

8 0

3 years ago

Read 2 more answers

Can someone help with these 8 problems and show your work please.

Travka [436]

Answer:

Part 1) option a. $y=(x+1)^{2}$

Part 2) option c. $y(x)=10x+1$

Part 3) option a. Yes , d=-2

Part 4) option b. $y=2x+4$

Part 5) option b. $m=-2$

Part 6) option c. $y=4x+14$

Part 7) option c. $y=4x+5$

Part 8) option a. y=2x-1 and y=x+1

Step-by-step explanation:

Part 1)

we know that

If a ordered pair satisfy a function, then the function pass through the ordered pair

Verify each function with the points (1,4), (2,9) and (3,16)

case a) we have

$y=(x+1)^{2}$

For x=1, y=4

$4=(1+1)^{2}$

$4=4$ ----> is true

For x=2, y=9

$9=(2+1)^{2}$

$9=9$ ----> is true

For x=3, y=16

$16=(3+1)^{2}$

$16=16$ ----> is true

therefore

The function pass through the three points

case b) we have

$y=(x+3)^{2}$

For x=1, y=4

$4=(1+3)^{2}$

$4=16$ ----> is not true

therefore

The function not pass through the three points

case c) we have

$y=7x-5$

For x=1, y=4

$4=7(1)-5$

$4=2$ ----> is not true

therefore

The function not pass through the three points

Part 2)

Let

y------> the number of laps

x-----> the number of hours

we know that

The linear equation that represent this situation is

$y(x)=10x+1$

Part 3) we have

{4,2,0,-2,-4,-6,...}

Let

a1=-4

a2=2

a3=0

a4=-2

a5=-4

a6=-6

we know that

a2-a1=2-4=-2 -----> a2=a1-2

a3-a2=0-2=-2 ----> a3=a2-2

a4-a3=-2-0=-2 -----> a4=a3-2

a5-a4=-4-(-2)=-2----> a5=a4-2

a6-a5=-6-(-4)=-2----> a6=a5-2

therefore

Is an arithmetic sequence, the common difference is -2

Part 4) we know that

The y-intercept of the graph is (0,4)

The x-intercept of the graph is (-2,0)

therefore

the function is $y=2x+4$

because

For x=0 -----> y=2(0)+4 -----> y=4

For y=0 ----> 0=2x+4 --------> x=-2

Part 5) we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$A(3,5)\ B(2,7)$

substitute the values

$m=\frac{7-5}{2-3}$

$m=-2$

Part 6) we know that

The equation of the line into slope point form is equal to

$y-y1=m(x-x1)$

we have

$m=4$

$point(-3,2)$

substitute the values

$y-2=4(x+3)$

Convert to slope intercept form

$y=4x+12+2$

$y=4x+14$

Part 7) we know that

If two lines are parallel, then their slopes are the same

The equation of the given line is $y=4x-2$

so

The slope of the given line is $m=4$

therefore

The line $y=4x+5$ is parallel to the given line

Because the slope is equal to $m=4$

Part 8) we know that

If a ordered pair is a solution of a system of equations, then the ordered pair must satisfy both equations of the system

Verify each case for (2,3)

case a)

y=2x-1 -----> equation 1

y=x+1 -----> equation 2

Substitute the value of x and the value of y in each equation and then compare the results

<em>Verify equation 1</em>

3=2(2)-1

3=3 -----> is true

<em>Verify equation 2</em>

3=2+1

3=3 -----> is true

therefore

The point (2,3) is a solution of the system of equations case a

case b)

y=2x+1 -----> equation 1

y=x-1 -----> equation 2

Substitute the value of x and the value of y in each equation and then compare the results

Verify equation 1

3=2(2)+1

3=5 -----> is not true

therefore

The point (2,3) is not a solution of the system of equations case b

case c)

y=4x-5 -----> equation 1

y=2x -----> equation 2

Substitute the value of x and the value of y in each equation and then compare the results

<em>Verify equation 1</em>

3=4(2)-5

3=3 -----> is true

<em>Verify equation 2</em>

3=2(2)

3=4 -----> is not true

therefore

The point (2,3) is not a solution of the system of equations case c

4 0

2 years ago