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3 years ago

What is the x-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:5?

Mathematics

2 answers:

Marianna [84]3 years ago

6 0

Answer:

Second option is correct. The x-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:5 is -2.

Step-by-step explanation:

From the given graph it is noticed that the endpoints of the line segment JK are J(-6,-2) and K(8,-9).

The formula to find x intercept.

$x=\frac{m}{m+n}(x_2-x_1)+x_1$

The ratio is 2:5, therefore the value of m is 2 and the value of n is 5.

$x=\frac{2}{2+5}(8-(-6))+(-6)$

$x=\frac{2}{7}(14)-6$

$x=4-6$

$x=-2$

Therefore the x-coordinate is -2 and second option is correct.

VLD [36.1K]3 years ago

5 0

Answer:

-2

Step-by-step explanation:

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3 years ago

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3 years ago

Find the value of k so that 48x-ky=11 and (k+2)x+16y=-19 are perpendicular lines.

Rufina [12.5K]

Answer: k = -1 +/- √769

Step-by-step explanation:

48x - ky = 11

-48x -48x

-ky = -48x + 11

$\frac{-ky}{-k} = \frac{-48x}{-k} + \frac{11}{-k}$

$y =\frac{48x}{k} - \frac{11}{k}$

Slope: $\frac{48}{k}$

*************************************************************************

(k + 2)x + 16y = -19

- (k + 2)x -(k + 2)x

16y = -(k + 2)x - 19

$\frac{16y}{16} = -\frac{(k + 2)x}{16} - \frac{19}{16}$

$y = -\frac{(k + 2)x}{16} - \frac{19}{16}$

Slope: $-\frac{(k + 2)}{16}$

**********************************************************************************

$\frac{48}{k}$ and $-\frac{(k + 2)}{16}$ are perpendicular so they have opposite signs and are reciprocals of each other. When multiplied by its reciprocal, their product equals -1.

$-\frac{(k + 2)}{16}$ * $\frac{k}{48}$ = -1

$\frac{(k + 2)k}{16(48)}$ = 1

Cross multiply, then solve for the variable.

(k + 2)(k) = 16(48)

k² + 2k - 768 = 0

Use quadratic formula to solve:

k = -1 +/- √769

5 0

3 years ago

Which system of inequalities represents reglon Z? 6

yKpoI14uk [10]

Answer:

The system of inequalities is

y\geq 3x-2

y<-(1/5)x+2

Step-by-step explanation:

step 1

Find the equation of the solid blue line

Let

A(0,-2), B(1,1)

Find the slope of AB

m=(1+2)/(1-0)=3

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

y=mx+b

we have

m=3

b=-2 - ----> the point A is the y-intercept

substitute

y=3x-2 - -----> equation of the solid blue line

The solution of the inequality is the shaded area above the solid line

therefore

The first inequality is

y\geq 3x-2

C(0,2), D(5,1)

step 2

Find the equation of the dashed red line

Let

Find the slope of CD

m=(1-2)/(5-0)=-1/5

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

y=mx+b

we have

m=-1/5

b=2 ----> the point C is the y-intercept

substitute

y=-(1/5)x+2 -----> equation of the dashed red line

The solution of the inequality is the shaded area below the dashed line

therefore

The second inequality is

y<-(1/5)x+2

The system of inequalities is

y\geq 3x-2

y<-(1/5)x+2

3 0

3 years ago

Divide 1.20m in the ratio 2:3:4 in a clear way

tatuchka [14]

2:3:4 gives 9 equal parts.
1.20 divided by 9 is 0.133.

2 * 0.133 would be 0.266m
3 * 0.133 would be 0.399m
4 * 0.133 would be 0.533m

To check this calculate 0.533 + 0.399 + 0.266 would be 1.198m (close enough)

4 0

3 years ago