The endpoints of the directed line segment AB are A(−7, 4) and B(8, 9). Find the coordinates of point P along AB¯¯¯¯¯¯¯¯ so that the ratio of AP to PB is 2 to 3.

Answers

Answer 1

Answer:

The coordinates of point P along the segment AB is (-1, 6).

Step-by-step explanation:

It is known that ratio of AP to PB is:

[tex]\frac{AP}{PB} = \frac{2}{3}[/tex]

Or vectorially speaking:

[tex]\overrightarrow{AP} = \frac{2}{3}\overrightarrow{PB}[/tex]

The vector that represents the segment AB is:

[tex]\overrightarrow{AB} = \vec B -\vec A[/tex]

If [tex]\vec A = (-7,4)[/tex] and [tex]\vec B = (8,9)[/tex], then:

[tex]\overrightarrow{AB} = (8,9)-(-7,4)[/tex]

[tex]\overrightarrow {AB} = (8+7,9-4)[/tex]

[tex]\overrightarrow{AB} = (15,5)[/tex]

But [tex]\overrightarrow{AB} = \overrightarrow{AP} + \overrightarrow{PB}[/tex], then:

[tex]\overrightarrow{AB} = \frac{2}{3}\overrightarrow{PB} +\overrightarrow{PB}[/tex]

[tex]\overrightarrow{AB} = \frac{5}{3}\overrightarrow{PB}[/tex]

[tex]\overrightarrow{PB} = \frac{3}{5}\overrightarrow{AB}[/tex]

[tex]\overrightarrow{PB} = \frac{3}{5}(15,5)[/tex]

[tex]\overrightarrow{PB} = \left(9, 3\right)[/tex]

The location of [tex]\vec P[/tex] is derived of this formula:

[tex]\overrightarrow{PB} = \vec B - \vec P[/tex]

[tex]\vec P = \vec B - \overrightarrow{PB}[/tex]

If [tex]\vec B = (8,9)[/tex] and [tex]\overrightarrow{PB} = \left(9, 3\right)[/tex], then:

[tex]\vec P = (8,9) - (9,3)[/tex]

[tex]\vec P = (8-9,9-3)[/tex]

[tex]\vec P = (-1, 6)[/tex]

The coordinates of point P along the segment AB is (-1, 6).


Related Questions

Solve this problem T=u+v/2 solve for u

Answers

Answer:

u = 2T - v

[tex]T = \frac{u + v}{2} [/tex]

Cross multiply

We have

2T = u + v

u + v = 2T

Move v to the right side of the equation to make u stand alone

We have the final answer as

u = 2T - v

Hope this helps you


A line contains the point (8,-5). If the slope of the line is write the equation of the line using point-slope form

Answers

Answer:

             [tex]\bold{y+5=\frac57(x-8)}[/tex]

Step-by-step explanation:

[tex]y-y_1=m(x-x_1)[/tex]      - point-slope form of Equation of the Line

[tex](8,-5)\ \ \implies x_1=8\,,\ y_1=-5\\\\m=\frac57\\\\equation:\\{}\qquad\qquad y-(-5)=\frac57(x-8)\\\\{}\qquad\qquad y+5=\frac57(x-8)[/tex]

Can someone help me with this question please?

Answers

Answer:

a.) (0,4) b.) (-4,0)

Step-by-step explanation:

a.) Let x=0 and solve for y: y=0+4=4. Since we let x=0 the first number will be 0 and we found y to be 4, so our coordinates are (0,4)

b.) Let y=0 and solve for x: 0=x+4, x=-4. Since x=-4 our first number is -4, since y is 0 our second number is 0, so our coordinates are (-4,0)

Hope this helps!

If AC =4.5 what is the measure of AB

Answers

Answer:

f

Step-by-step explanation:

f

Answer:

[tex]\boxed{AB = 9}[/tex]

Step-by-step explanation:

AB = 2(AC) {Because a line segment drawn from a center of a circle bisect the chord opposite to it}

So,

AB = 2(4.5)

AB = 9

Solve the system of equations by substitution.
y=-1/2x-7
2 x - y = -16

Answers

Answer:

Point Form:

( − 46 /3 , − 44 /3 )

Equation Form:

x = − 46 /3 ,  y = − 44 /3

Step-by-step explanation:

Combine  1 /2 and  x .

y = x /2 − 7

2 x − y = − 16

Replace all occurrences of  y  in  2 x − y = − 16  with  x /2 − 7 .

y = x /2 − 7

2 x − ( x /2 − 7 ) = − 16

 Simplify  

2 x − ( x /2 − 7 ) .

y = x /2 − 7

3 x /2 + 7 = − 16

Solve for  

x

in the second equation.

y = x /2 - 7

x = − 46 /3

Replace all occurrences of  x  in  y = x /2 − 7 with  − 46 /3 .

y = − 46 /3 /2 − 7

x = − 46 /3

Simplify  − 46 /3 /2 − 7 .

y = − 44 /3

x = − 46 /3

The solution to the system of equations can be represented as a point.

( − 46 /3 , − 44 /3 )

The result can be shown in multiple forms.

Point Form:

( − 46 /3 , − 44 /3 )

Equation Form:

x = − 46 /3 ,  y = − 44 /3

The question i want to know is linked below. Please help :)

Answers

Answer:

Hey there!

To solve this problem, we want to find the LCM (least common multiple) of the two numbers.

The numbers are 25 and 30.

25=5x5

30=2x3x5

LCM is 5x5x2x3, or 150.

Thus, in 150 minutes is when the next bus will leave.

150 mins is equal to 2 hours and 30 mins, or 2.5 hours.

8 AM + 2.5 hrs = 10:30 AM.

Thus, the next time the busses leave together would be at 10:30 AM.

Let me know if this helps :)

Dave ran 3.52 miles in the same time
that Eric ran 2.44 miles. How much
further did Dave run than Eric?

Answers

Subtract 3.52 - 2.44= 1.08 miles

I need to find the derivative of d). Can someone please fine y’ please.

Answers

Answer:

  = -2x/ ( x^2+5) ^2

Step-by-step explanation:

y = 1/ ( x^2 +5)

y = ( x^2+5) ^ -1

dy/dx = -1 * (x^2 + 5) ^-2  * d/dx  (x^2 + 5)

          -1 * (x^2 + 5) ^-2  * 2x

           = -2x/ ( x^2+5) ^2

The question i want to know is linked below, please help!!

Answers

Answer: 250 metre

Step-by-step explanation:

The radius of the semi circle will be:

Radius r = diameter/ 2

Where diameter = 140

r = 140/2 = 70m

The radius is also equal to the width of the diameter.

Find the quarter of the circumference of a circle.

Circumference of a circle = 2πr

Substitute for r in the formula

Circumference = 2 × 22/7 × 70

Circumference = 44 × 10 = 440 m

Divide the circumference by 4

440/4 = 110 m

The perimeter P of the shaded region will be

P = 110 + 70 + 70

Perimeter = 250 m

Therefore, the perimeter of the shaded region is 250 m

At the beginning of the season, MacDonald had to remove 555 orange trees from his farm. Each of the remaining trees produced 210210210 oranges for a total harvest of 417904179041790 oranges. Write an equation to determine the initial number of orange trees (t)(t)(, t, )on MacDonald's farm. Find the initial number of orange trees on MacDonald's farm. orange trees

Answers

Answer:

Initial number of trees (t)=204

Step-by-step explanation:

t = initial number of trees

Subtract 5 trees from the initial number of trees

we have,

t-5

each remaining tree made 210 oranges for a total of 41,790 oranges

We have,

(t-5) * 210=41790

Solve the equation

(t-5) * 210=41790

Open the bracket

210t-1050=41790

210t=41790+1050

210t=42840

Divide both sides by 210

210t/210=42840/210

t=204

The initial number of trees on MacDonald farm orange trees (t)=204

If 5 is removed from the initial trees

t-5=204-5

=199 trees

199 trees produce 210 oranges

We have,

199*210=41790 oranges

Answer:

Equation: 210t - 1050 = 41790

204 orange trees

Step-by-step explanation:

answer is from khan academy

pls brainliest :|

are the triangles similar? ​

Answers

Answer:

Yes.

Step-by-step explanation:

The angles of the triangles add up to be 180. 180 - 114 - 31 = 35. 180-114-35 = 31. Since the angles of the triangles correspond and are congruent, the triangles are similar, with PQR corresponding to TUS.

Hope this helps !

what is the slope of the line that contains these points (-2 2) and (3 3)

Answers

Answer:

             [tex]\bold{m=\dfrac15}[/tex]

Step-by-step explanation:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\\\(-2,\,2)\ \implies\ x_1=-2\,,\ y_1=2\\(3,\,3)\ \implies\ x_2=3\,,\ y_2=3\\\\m=\dfrac{3-2}{3-(-2)}=\dfrac{1}{3+2}=\dfrac15[/tex]

(-30) x ______ = (-270)

Answers

-9 is your answer




Hope it helps





Pls mark as brainliest ☺️☺️

Find the slope of a line parallel to each given line and graph.

y=9x+5

Answers

Answer:

9

Step-by-step explanation:

This equation is in slope intercept form

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

y = 9x+5

The slope is 9

Parallel lines have the same slope so a line parallel would have a slope of 9

Answer:

i think the slope is 9.

because y= 9x+5 is in the form of slope intercept form.

as y=mx + c (where m is the slope of the equation.)

therefore, the slope (m )= 9....ans

hope it helps....

A linear function has the same y-intercept as x + 4y = 8 and its graph contains the point (4, 3). Fill in the blank to find the y-intercept.

Answers

Answer:

The y - intercept is (0, 4)

Step-by-step explanation:

The equation x + 4y = 8 is in 'standard form.'  Any line parallel to this line has an equation that looks exactly the same EXCEPT for the constant.

So, let's write out x + 4y = 8 and replace the 8 with C.

x + 4y = C

Now take the coordinates of the given point (4, 3) and substitute them into the above equation:  4 + 4(3) = C = 16

Thus, the equation of the line passing through (4, 3) is x + 4y = 16.

To find the y-intercept, set x = 0 and calculate y:

0 + 4y = 16, or y = 4

The y - intercept is (0, 4)

Please answer this question now in two minutes

Answers

88 degrees because the two figures are congruent.

Answer:

67 degrees.

Step-by-step explanation:

The two quadrilaterals are congruent, with angle T corresponding to angle F, angle U corresponding to angle C, angle V corresponding to angle D, and angle W corresponding to angle E.

A quadrilateral's interior angles add to be 360 degrees.

x + 138 + 67 + 88 = 360

x + 293 = 360

x = 67

So, angle D is 67 degrees.

Hope this helps!

Amanda teaches violin lessons for $21.30 per hour. How many hours of lessons must Amanda give to make no less than $894.60?


No less than 42 lessons

No less than 35 lessons

No less than 45 lessons

No less than 33 lessons

Answers

Answer:

No less than 42 lessons

Step-by-step explanation:

To find the total numbers of hours needed to teach, divide the total amount of money needed by the amount of money made an hour.

$894.60/$21.30 = 42

Can someone please help me I really need help please help me thank you

Answers

Answer:

97

Step-by-step explanation:

the shape leans a little so it's more than 90

Which system below has no solution? y = 4x and y = 2x - 3 y = -4x and y = 2x - 3 y = -4x and y = 2x + 3 y = -4-x and y = 2x - 3

Answers

Answer:

y=4x

Step-by-step explanation:

this is because all other systems are defined and can be solved simultaneously...

pls lime and follow me ...i follow back...thanks

Please help me!

30g of cornflakes contain 2.5g of fat
How many grams of fat are there in 566g of cornflakes?
Give your answer to 1 dp

Answers

Answer:

47 .2 Grams 0f Fat

Step-by-step explanation:

[tex]30g ----> 2.5g -fat\\566g ----> xg -fat\\30x = 1415\\\frac{30x}{30} =\frac{1415}{30} \\\\x = 47.1666\\\\x = 47.2g of Fat[/tex]

Find equation of the line.

Answers

Answer:

-1+9

Step-by-step explanation:

-1 divide by -1 =1

so the answer is -1+9

I hope that helped and can you do my answer as a Brainliest PLEASE

If it helped don't forget to thanks

Find the area of this triangle..

Answers

Answer:

Step-by-step explanation:

For this problem, we have to use Heron's Formula.

S= (a + b + c)

     over 2

And then  √S( S-a) (S-b) (S-c)

That's the formula, now to plug in the numbers.

S= 12+12+21.2

      over 2

that equals 45.2/ 2= 22.6'

Now we found s, so we can plug in the second step of the formula...

√22.6 ( 22.6 - 12 ) ( 22.6 - 12 ) ( 22.6 - 21.2 )

This equals √ 22.6 (10.6) (10.6) (1.4)

and that equals...

59.624411 = or rounded it up to 60.

59.624411 or round it up to 60

3
8
9
10
TIMEI
01:
C D
When simplified and written in standard form, which quadratic function is equivalent to the polynomial shown?
2 + 7c-4c2 – 30 + 4
4c2 + 4c + 6
-7c2 + 10C + 6
O4c2 + 4C + 8
0-7c2 + 70 +6

Answers

Answer:

A. -4c^2+4c+6

Step-by-step explanation:

2+7c-4c^2-3c+4

-4c^2+7c-3c+4+2

-4c^2+4c+6

Gwen and Bryn drive to work.
Gwen drives 65 miles in 2.5 hours.
Bryn drives 76 km in 1 hour 15 min.
Work out the difference between their average speeds in km/h

Answers

Answer: 18.96 km/h

Step-by-step explanation:

Gwen:

65 miles = 104.6 km

104.6 km / 2.5 h  =   41.84 km/h

Bryn:

15 min = 0.25 h

76 km / 1.25 h  =  60.8 km/h

Difference:

60.8 - 41.84 = 18.96 km/h

Hope this helps!

find the exact length of the third side

Answers

Answer:

8

Step-by-step explanation:

We will the pythagorian theorem :

let x be the third side x²+6²= 10²x²= 100-36 x=[tex]\sqrt{64}[/tex] x=8

Answer:

b=8

Step-by-step explanation:

We can use the Pythagorean theorem since this is a right triangle:

a^2+ b^2 = c^2 where a and b are the legs and c is the hypotenuse

a=6 and b = 10

6^2 + b ^2 = 10^2

36+ b^2 = 100

b^2 = 100-36

b^2 = 64

Taking the square root of each side

sqrt(b^2) = sqrt(64)

b = 8

i need help from uh all..​

Answers

Answer:

Step-by-step explanation:

Given expression is,

[tex]\text{cot}A=\frac{1}{2}(\text{cot}\frac{A}{2}-\text{tan}\frac{A}{2})[/tex]

To prove this identity we will take the right side of the identity,

[tex]\frac{1}{2}(\text{cot}\frac{A}{2}-\text{tan}\frac{A}{2})=\frac{1}{2}(\frac{1}{\text{tan}\frac{A}{2}}-tan\frac{A}{2})[/tex]

                         [tex]=\frac{1}{2}(\frac{1-\text{tan}^2\frac{A}{2}}{tan\frac{A}{2}})[/tex]

                         [tex]=\frac{1}{2}[\frac{2(1-\text{tan}^2\frac{A}{2})}{2tan\frac{A}{2}}][/tex]

                         [tex]=\frac{1}{2}(\frac{2}{\text{tan}A} )[/tex] [Since [tex]\text{tan}A=\frac{2\text{tan}\frac{A}{2}}{1-\text{tan}^2\frac{A}{2}}[/tex]]

                         = cot A

Hence right side of the equation is equal to the left side of the equation.

what is the measure of x? 68 degrees 70 degrees ​

Answers

Answer:

x = 138°

Step-by-step explanation:

Since the sum of all angles in a triangle is 180°, we find ∠BAC:

m∠BAC = 180 - (68 + 70) = 42°

Since ∠x and ∠BAC are Supplementary Angles, they add up to 180°:

180 - 42 = x

x = 138°

Answer:

138

Step-by-step explanation:

1. 68 + 70 = 138

2. 180 - 38 = 42

3. 180 - 42 = 138

4. X = 138

In the diagram below, AB is parallel to CD. What is the value of x?

Answers

Answer:

A. 120 degrees.

Step-by-step explanation:

The two angles are alternate angles, which means they are congruent. So, x is also 120 degrees.

Hope this helps!

How are the graphs of the functions f(x) = . 16and g(x) = 3/64 related?
The functions f(x) and g(x) are equivalent.
The function g(x) increases at a faster rate.
The function g(x) has a greater initial value.
The function g(x) decreases at a faster rate.

Answers

Answer: A  there are equivalent.

Step-by-step explanation:

f(x) = [tex]\sqrt{16}^x[/tex]  reduces to  f(x)=[tex]4^{x}[/tex]  

g(x)= [tex]\sqrt[3]{64}^{x}[/tex]   also reduces to g(x) = [tex]4^{x}[/tex]  

The function g(x) equal to f(x).

What is the exponent?

A quantity representing the exponent to which a given number or letter is to be raised is usually expressed as a raised symbol beside the number or letter. It is expressed as aˣ is a variable and a is constant.

Given are two functions, f(x) = √16ˣ and g(x) = ∛64ˣ,

We need to find the relation between the function,

So,

√16 = 4

∛64 = 4

Functions can be written as, f(x) = 4ˣ and g(x) = 4ˣ,

It is clear that g(x) equal to f(x) because g(x) is having power equal than f(x).

Thus, It is clear that g(x) is equal to f(x).

More about the exponent link is given below.

brainly.com/question/5497425

#SPJ7

Draw a circle with center A and a radius of your choice. Create three well-spaced points, B, C, and D, on the circle in clockwise alphabetical order. Draw two radii, AB and AC , and draw two chords, DB and DC . Measure and record m∠CAB and m∠CDB. Take a screenshot of your diagram with the measurements, and paste it below.

Answers

Answer:

Please find attached the required circle

It is observed that the angle subtended by the arc CB which are m∠CAB and m∠CDB is such that the angle arc CB subtends at the center,  m∠CAB is two times the angle that the arc CB subtends at the circumference

The measured angle subtended by the arc CB at the center m∠CAB = 64° and the measured angle subtended by the arc CB at the circumference m∠CDB = 32°

Step-by-step explanation:

T

Answer:

from edmentum

Step-by-step explanation:

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