Ask question

Ask question

All categories

3 years ago

12

J has coordinates (-2,8) R has coordinates (-7,-3) find the coordinates of point A that partition (JR) in the ratio 5:2 and sket

ch points J,A,R, and (JA) on the coordinate plane below.

1 answer:

kolbaska11 [484]3 years ago

4 0

J Coordinates: (-2,8)

R Coordinates: (-7,-3)

A cuts JR in the ratio of 5:2

We have to find out the coordinates for A. Let coordinates of A be (x,y)

The section formula helps us determine a point (x,y) that divides the line joining two points (x1,y1) and (x2,y2) in the ratio of m:n

x1, y1 represents the point which is more on the left side of the x axis, while x2,y2 represents the point which is more on the right side of the x axis

So here x1 = -7, y1 = -3, x2 = -2, y2 = 8, m = 5, n = 2

As per section formula, x = (mx₂ + nx₁) / (m + n), and y = (my ₂ + ny₁) / (m + n))

⇒ x = ((5*-2) + (2*-7)) / (7)

⇒ x = (-10+ (-14)) / (7)

⇒ x = -24 / 7

⇒ x = -3.43

and y = ((5*8) + (2*-3)) / (7)

⇒ y = (40 - 6) / 7

⇒ y = 4.86

So coordinates of A are (-3.43,4.86)

Please see the attached image for seeing the points and line on chart.

You might be interested in

Enter the coordinates of the point on the unit circle at the given angle. 150 degrees. please help!

Katarina [22]

Answer:

$\boxed{(-\frac{\sqrt{3}}{2}, \frac{1}{2})}$

Step-by-step explanation:

Method 1: Using a calculator <em>instead</em> of the unit circle

The unit circle gives coordinates pairs for the <em>cos</em> and <em>sin</em> values at a certain angle. Therefore, if an angle is given, use a calculator to evaluate the functions at cos(angle) and sin(angle).

Method 2: Using the unit circle

Use the unit circle to locate the angle measure of 150° (or 5π/6 radians) and use the coordinate pair listed by the value (see attachment).

This coordinate pair is (-√3/2, 1/2).

8 0

3 years ago

Read 2 more answers

Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation:

Vikentia [17]

Answer:

a

$\= x = 18.5$ , $\sigma = 5.15$

b

$15.505 < \mu < 21.495$

c

$14.93 < \mu < 22.069$

Step-by-step explanation:

From the question we are are told that

The sample data is 21, 14, 13, 24, 17, 22, 25, 12

The sample size is n = 8

Generally the ample mean is evaluated as

$\= x = \frac{\sum x }{n}$

$\= x = \frac{ 21 + 14 + 13 + 24 + 17 + 22+ 25 + 12 }{8}$

$\= x = 18.5$

Generally the standard deviation is mathematically evaluated as

$\sigma = \sqrt{\frac{\sum (x- \=x )^2}{n}}$

$\sigma = \sqrt{\frac{\sum ((21 - 18.5)^2 + (14-18.5)^2+ (13-18.5)^2+ (24-18.5)^2+ (17-18.5)^2+ (22-18.5)^2+ (25-18.5)^2+ (12 -18.5)^2 )}{8}}$

$\sigma = 5.15$

considering part b

Given that the confidence level is 90% then the significance level is evaluated as

$\alpha = 100-90$

$\alpha = 10\%$

$\alpha = 0.10$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table the value is

$Z_{\frac{ \alpha }{2} } = 1.645$

The margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E =1.645 * \frac{5.15 }{\sqrt{8} }$

=> $E = 2.995$

The 90% confidence interval is evaluated as

$\= x - E < \mu < \= x + E$

substituting values

$18.5 - 2.995 < \mu < 18.5 + 2.995$

$15.505 < \mu < 21.495$

considering part c

Given that the confidence level is 95% then the significance level is evaluated as

$\alpha = 100-95$

$\alpha = 5\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table the value is

$Z_{\frac{ \alpha }{2} } = 1.96$

The margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E =1.96 * \frac{5.15 }{\sqrt{8} }$

=> $E = 3.569$

The 95% confidence interval is evaluated as

$\= x - E < \mu < \= x + E$

substituting values

$18.5 - 3.569 < \mu < 18.5 + 3.569$

$14.93 < \mu < 22.069$

8 0

3 years ago

PLEASE HELP AND QUICK

3241004551 [841]

I think it is 70 but not sure

8 0

2 years ago

Two ropes, AD and BD, are tied to a peg on the ground at point D. The other ends of the ropes are tied to points A and B on a fl

Lisa [10]

Answer: 5(√3-1) unit.

Step-by-step explanation:

Since, By the below diagram,

For triangle BDC,

We can write,

$tan 30^{\circ}=\frac{BC}{DC}$

⇒ $\frac{1}{\sqrt{3}}=\frac{BC}{5\sqrt{3}}}$

⇒ $\sqrt{3}=\frac{5\sqrt{3}}{BC}$

⇒ $BC=\frac{5\sqrt{3} }{\sqrt{3} }$

⇒ $BC=5\text{ unit}$

Now, In triangle ADC,

$tan45^{\circ}=\frac{AC}{DC}$

⇒ $1=\frac{AB+BC}{DC}$

⇒ $1=\frac{DC}{AB+BC}$

⇒ $1=\frac{5\sqrt{3}}{AB+5}$

⇒ $AB+5=5\sqrt{3}$

⇒ $AB=5\sqrt{3}-5=5(\sqrt{3}-1)\text{ unit}$

8 0

3 years ago

Read 2 more answers

What is 5.9% of 7000? Round to the nearest hundredth (if necessary).

Vedmedyk [2.9K]

Answer:

413

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers