What is the size of the triangle angles?

locate the point on the line segment A (3,-5) and B (13,-15) given that the point is 4/5 of the way from A to B. Show your work

rjkz [21]

Answer:

The coordinates of the point on the line segment between A (3 , -5) and B (13 , -15) given that the point is 4/5 of the way from A to B would be: (11 , -13)

Step-by-step explanation:

As the line segment has the points:

A(3, -5)

B(13, -15)

Let (x, y) be the point located on the line segment which is 4/5 of the way from A to B.

Using the formula

$x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$

$y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

Here, the point (x , y) divides the line segment having end points (x₁, y₁) and (x₂, y₂) in the ratio m₁ : m₂ from the point (x₁, y₁).

As (x, y) be the point located on the line segment which is 4/5 of the way from A to B, meaning the distance from $A$ to $(x , y)$ is $4$ units, and the

distance from $(x , y)$ to B is 1 unit, as $5 - 4 = 1$ .

Thus

m : n = 4 : 1

so

Finding x-coordinate:

$x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$

$x=\frac{\left(3\right)\left(1\right)+\left(13\right)\left(4\right)}{4+1}$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$x=\frac{3\cdot \:1+13\cdot \:4}{4+1}$

$x=\frac{55}{4+1}$ ∵ $3\cdot \:1+13\cdot \:4=55$

$x=\frac{55}{5}$

$\mathrm{Divide\:the\:numbers:}\:\frac{55}{5}=11$

$x=11$

Finding y-coordinate:

$y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

$y=\frac{\left(-5\right)\left(1\right)+\left(-15\right)\left(4\right)}{4+1}$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$y=\frac{-5\cdot \:\:1-15\cdot \:\:4}{4+1}$

$=\frac{-65}{4+1}$ ∵ $-5\cdot \:1-15\cdot \:4=-65$

$=\frac{-65}{5}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}$

$y=-\frac{65}{5}$

$y=-13$

so

The x-coordinate = 11

The y-coordinate = -13

Therefore, the coordinates of the point on the line segment between A (3 , -5) and B (13 , -15) given that the point is 4/5 of the way from A to B would be: (11 , -13)

7 0

3 years ago

Weight gain during pregnancy. In 2004, the state of North Carolina released to the public a large data set containing informatio

pychu [463]

Answer:

1. B. H0: μ1−μ2=0, HA: μ1−μ2≠0

2. z=1.2114

3. P-value=0.2257

4. Do not reject H0

Step-by-step explanation:

We have to perfomr an hypothesis test to see if there is strong evidence that there is a significant difference between the two population means.

The null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a: \mu_1-\mu_2\neq0$

Being μ1 the mean average gain for younger mothers and μ2 the mean average gain for mature mothers.

(NOTE: we are comparing means, not proportions, as it is the random variable is the weight gain).

As we are claiming "strong evidence", the level of significance will be 0.01.

For younger mothers, the sample size is n1=840, the sample mean is 30.7 and the sample standard deviation is s1=14.91.

For mature mothers, the sample size is n2=132, the sample mean is 29.15 and the sample standard deviation is s2=13.46.

The difference between means is

$M_d=\mu_1-\mu_2=30.7-29.15=1.55$

The standard error of the difference between means is

$s_M=\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2}}=\sqrt{\dfrac{14.91^2}{840}+\dfrac{13.46^2}{132}}=\sqrt{ 0.2647+1.3725}=\sqrt{1.6372}\\\\\\s_M=1.2795$

Then, the statistic can be calculated as:

$z=\dfrac{M_d-(\mu_1-\mu_2)}{s_M}=\dfrac{1.55-0}{1.2795}=1.2114$

The P-value for this z-statistic in a two tailed test is:

$P-value=2P(z>1.2114)=0.2257$

As the P-value is greater than the significance level, the null hypothesis failed to be rejected.

There is no enough evidence to claim that the real average weight gain differs from mature and youger mothers.

5 0

3 years ago

Number 17 thanks pls ASAP ASAP

RideAnS [48]

Answer:

$\frac{1}{2}$ which agrees with answer B

Step-by-step explanation:

First write the equation that represents this type of variation:

$y=\frac{5}{x}$

then we need to solve for "x" when y = 10 as shown below:

$y=\frac{5}{x} \\10=\frac{5}{x} \\10*x=5\\x=\frac{5}{10} \\x=\frac{1}{2}$

5 0

3 years ago

Find the volume of a right circular cone that has a height of 3.9 ft and a base with a circumference of 16.3 ft. Round your answ

MissTica

Answer:

The answer to your question is Volume = 27.5 ft³

Step-by-step explanation:

Data

Volume = ?

height = 3.9 ft

Circumference = 16.3 ft

Process

1.- Calculate the radius of the Cone

Circumference = 2πr = 16.3 ft

-Solve for r

r = 16.3/2π

r = 16.3/6.28

r = 2.5955 ft

2.- Calculate the volume

Volume = 1/3πr²h

-Substitution

Volume = 1/3(3.14)(2.5955)²(3.9)

-Simplification

Volume = 1/3(82.4966)

-Result

Volume = 27.5 ft³

8 0

3 years ago

Read 2 more answers

Assume the 72-gon is a regular polygon. The measure of one interior angle is how many

Greeley [361]

9514 1404 393

Answer:

interior: 175°
exterior: 5°

Step-by-step explanation:

The sum of exterior angles is 360°, so the exterior angle can be easiest to find first.

exterior angle = 360°/72 = 5°

The interior angle is the supplement of this.

interior angle = 180° -5° = 175°

The measure of one interior angle is 175°; one exterior angle is 5°.

8 0

3 years ago