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2 years ago

What is the equation of the line that passes through the point (8,3) and has a slope of 1/4

Mathematics

1 answer:

saul85 [17]2 years ago

4 0

Answer:

equation of the line having slope 1/4

that passes through (8,3) is given by

y - 3 = 1/4 ( x - 8)

or, 4y - 12 = x -8

or, 4y -12 - x + 8 = 0

or, 4y - x - 4 = 0 , which is the required equation.

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You are a traffic accident investigator. You have arrived at the scene of an accident. Two trucks of equal mass (3,000 kg each)

Kazeer [188]

Answer:

1) Kinetic energy of the truck 1 is 600,000 joules.

Kinetic energy of the truck 2 is 1,837,500 joules.

2 a)Potential energy of truck 1 is 646,800 Joules.

b) Energy lose by the truck 1 just got converted into heat and sound energy during the collision.

Step-by-step explanation:

Mass of the truck 1 and truck 2,m = 3000 kg

Velocity of the truck 1, $v_1$ = = 20 m./s

Velocity of the truck 2, $v_2$ = 35 m./s

1. Kinetic energy of the truck 1: $\frac{1}{2}mv_{1}^2=\frac{1}{2}\times 3000 kg\times (20 m/s)^=600,000 joules$

Kinetic energy of the truck 2: $\frac{1}{2}mv_{2}^2=\frac{1}{2}\times 3000 kg\times (35 m/s)^=1,837,500 joules$

2.a) Energy loose by the truck 1:

Initial height of the truck on the hill = 22 m

At that height potential energy will be maximum:

Potential energy of truck 1 at that height = $mgh=3000\times 9.8 m/s^2\times 22 m=646,800 Joules$

b) Energy lose by the truck 1 just got converted into heat and sound energy during the collision.

3 0

4 years ago

The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers r

jolli1 [7]

Answer:

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=28$ represent the sample mean

$\mu$ population mean (variable of interest)

s=10 represent the sample standard deviation

n=25 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=25-1=24$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that $t_{\alpha/2}=2.064$

Now we have everything in order to replace into formula (1):

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

7 0

3 years ago

What is the radius of the circle in the example? 3 cm 5 cm 7 cm

Strike441 [17]

Answer:

Step-by-step explanation:

3 0

3 years ago

The bearing of Y from X is 63

zimovet [89]

Answer:

117°

Step-by-step explanation:

As per diagram:

∠NXY ≅ ∠XYZ as alternate interior angles since XN and YN are parallel and XY is transversal
m∠XYZ = m∠XZY = 63° since ΔXYZ is isosceles

Find the measure of ∠YXZ:

m∠YXZ = 180° - 2*63° = 54°

Find the bearing of Z from X:

m∠NXZ = m∠NXY + m∠YXZ = 63° + 54° = 117°

8 0

3 years ago

Solve for D, E, F, and G

Sergio039 [100]

Answer:

D=135

E=72

F=20

G=101

D: (360-90)/2

E: 45+27

F: (135-15)/6

G: 86+15

6 0

3 years ago

What is the equation of the line that passes through the point (8,3) and has a slope of 1/4 ​

What is the equation of the line that passes through the point (8,3) and has a slope of 1/4