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What are the coordinates of point b on ac such that ab=2/5ac

Answers

Answer 1

Answer:

Answer:

$(-(36)/(7),(40)/(7))$

Step-by-step explanation:

Coordinates of points A and C are (-8, 6) and (2, 5).

If a point B intersects the segment AB in the ratio of 2 : 5

Then coordinates of the point B will be,

x = $(mx_2+nx_1)/(m+n)$

and y = $(my_2+ny_1)/(m+n)$

where $(x_1, y_1)$ and $(x_2,y_2)$ are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.

For the coordinates of point B,

x = $(2* 2+(-8)* 5)/(2+5)$

= $-(36)/(7)$

y = $(2* 5+5* 6)/(2+5)$

= $(40)/(7)$

Therefore, coordinates of pint B will be,

$(-(36)/(7),(40)/(7))$

Answer 2

Answer:

Final answer:

The coordinates of B on segment AC such that AB=2/5AC are given by line segment division theorem as ((2x2 + 5x1) / 7 , (2y2 + 5y1)/ 7), where A is (x1, y1) and C is (x2, y2).

Explanation:

The question is asking for the coordinates of point B on line segment AC such that the length of AB is 2/5 times the length of AC.

Since we don't have any specific coordinates for points A, B and C, we can't determine exact coordinates for point B. However, we can describe how to find B based on given points A and C.

If A and C have coordinates (x1, y1) and (x2, y2), respectively, then the coordinates of B can be found using the theorem of line segment division. This theorem says that the coordinates of the point dividing a line segment in the ratio m:n are given by:

((mx2 + nx1) / (m+n) , (my2 + ny1)/ (m+n))

Given the ratio is 2:5, m is 2 and n is 5, substitute the values into the formula:

((2x2 + 5x1) / (2+5) , (2y2 + 5y1)/ (2+5))

So, point B is at ((2x2 + 5x1) / 7 , (2y2 + 5y1)/ 7).

Learn more about Coordinates finder here:

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Answers

Answer:

the answer is 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hope this helps!!!!!!

Choose the true statement.
0-2<-3
O-2» -3
O -2 = -3

Answers

0-2>-3 is the answer, because negative 2 is greater than negative 3.

Find the measure of 0. (to the nearest tenth).A) 36.9
B) 38.7
C) 51.3
D) 53.1

Answers

Answer:

A) 36.9

Step-by-step explanation:

took the test :)

Answer:

B) 38.7

Step-by-step explanation:

HELP PLEZ TRIGONOMETRY!

Answers

$(2 \sin ^(2) \alpha-1)/(\sin \alpha+\cos \alpha) = sin \alpha - cos \alpha$

Solution:

Given that we have to simplify:

$(2 \sin ^(2) \alpha-1)/(\sin \alpha+\cos \alpha)$ ---- eqn 1

We know that,

$sin^2 x = 1 - cos^2 x$

Substitute the above identity in eqn 1

$(2\left(1-\cos ^(2) \alpha\right)-1)/(\sin \alpha+\cos \alpha)$

Simplify the above expression

$(2-2 \cos ^(2) \alpha-1)/(\sin \alpha+\cos \alpha)$

$(1-2 \cos ^(2) \alpha)/(\sin \alpha+\cos \alpha)$ ------- eqn 2

By the trignometric identity,

$(sin x + cos x)(sin x - cos x) = 1-2cos^2 x$

Substitute the above identity in eqn 2

$((\sin \alpha+\cos \alpha)(\sin \alpha-\cos \alpha))/(\sin \alpha+\cos \alpha)$

Cancel the common factors in numerator and denominator

$((\sin \alpha+\cos \alpha)(\sin \alpha-\cos \alpha))/(\sin \alpha+\cos \alpha)=\sin \alpha-\cos \alpha$

Thus the simplified expression is:

$(2 \sin ^(2) \alpha-1)/(\sin \alpha+\cos \alpha) = sin \alpha - cos \alpha$

Help? Question are above. 15 points

Answers

Answer:

1).

7, rational

2).

2.36 (repeating), irrational

3).

$Simplify:(734)/(1000) / (2)/(2) = (367)/(500)$

4).

$Simplify: (2588)/(1000) /(4)/(4) =(647)/(250) \nIf.you.want.to.convert.it.to.a.mixed.fraction: 2(147)/(250)$

Can you help me to do this please?Determine the inverse of the h(x)

Answers

Answer:

$h^(-1)(x)=x^3+6x^2+12x+7$

Explanation:

Given the below function;

$h(x)=\sqrt[3]{x+1}-2$

We'll follow the below steps to determine the inverse of the above function;

Step 1: Replace h(x) with y;

$y=\sqrt[3]{x+1}-2$

Step 2: Switch x and y;

$x=\sqrt[3]{y+1}-2$

Step 3: Solve for y by first adding 2 to both sides;

$\begin{gathered} x+2=\sqrt[3]{y+1}-2+2 \n x+2=\sqrt[3]{y+1} \end{gathered}$

Step 4: Take the cube of both sides;

$\begin{gathered} (x+2)^3=(\sqrt[3]{y+1})^3 \n (x+2)^3=y+1 \end{gathered}$

Step 5: Expand the cube power;

Recall;

$(a+b)^3=a^3+3a^2b+3ab^2+b^3$

Applying the above, we'll have;

$\begin{gathered} (x+2)^3=y+1 \n x^3+3x^2\cdot2+3x\cdot2^2+2^3=y+1 \n x^3+6x^2+12x+8=y+1 \end{gathered}$

Step 6: Subtract 1 from both sides of the equation;

$\begin{gathered} x^3+6x^2+12x+8-1=y+1-1 \n x^3+6x^2+12x+7=y \n \therefore y=x^3+6x^2+12x+7 \end{gathered}$

Step 7: Replace y with h^-1(x);

$h^(-1)(x)=x^3+6x^2+12x+7$

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