All categories

2 years ago

What is the y-intercept of the line that passes through the points (2,-1) and (-3,9)

Mathematics

1 answer:

krek1111 [17]2 years ago

4 0

Answer:

The equation of the straight line y = -2x +3

y-intercept = 3 and m =-2

Step-by-step explanation:

Step(i):-

Given that the points are ( 2,-1) and (-3,9)

The slope of the line

$m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } = \frac{9-(-1)}{-3-(2)} = \frac{10}{-5} = -2$

Step(ii):-

The equation of the straight line passing through the point ( 2,-1) and slope m=-2

y-y₁ = m( x- x₁)

y -(-1) = -2 ( x-2)

y +1 = -2x +4

2x +y +1-4 =0

2x +y -3 =0

Final answer:-

The equation of the straight line y = -2x +3

You might be interested in

Five point six times four point eight

LenaWriter [7]

Answer:

26.88

Step-by-step explanation:start eight times four is 32

and than eight times six is 48 than add a zero and do four times six is 24

and four times five is twenty add it up and line up the decimal points

hope i helped !!

3 0

3 years ago

Marco drove 75 miles in hours. How many miles can he drive in 1 hour?

Nutka1998 [239]

Answer:

Step-by-step explanation:

75m/hr

3 0

3 years ago

The mean annual income for people in a certain city is 37 thousand dollars, with a standard deviation of 28 thousand dollars. A

Aloiza [94]

Answer:

$P( 31 < \bar X< 41)$

And we can ue the z score formula given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And using this formula we got for the limits:

$z = \frac{31-37}{\frac{28}{\sqrt{50}}}= -1.515$

$z = \frac{41-37}{\frac{28}{\sqrt{50}}}= 1.01$

So we want to find this probability:

$P(-1.515$

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the annual income of a population, and for this case we know the following info:

$\mu=37$ and $\sigma=28$ and we are omitting the zeros from the thousand to simplify calculations

We select a sample size of n=50>30.

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we want to find this probability:

$P( 31 < \bar X< 41)$

And we can ue the z score formula given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And using this formula we got for the limits:

$z = \frac{31-37}{\frac{28}{\sqrt{50}}}= -1.515$

$z = \frac{41-37}{\frac{28}{\sqrt{50}}}= 1.01$

So we want to find this probability:

$P(-1.515$

4 0

3 years ago

Hello! How do I find the surface area of this prism? Thanks!

Studentka2010 [4]

Answer: Choice C) 124 square cm

------------------------------------------------------------------

Explanation:

Let's calculate the area of the trapezoid shown
b1 and b2 are the parallel bases; h is the height of the 2D trapezoid
b1 = 2
b2 = 5
h = 1.5

A = h*(b1+b2)/2
A = 1.5*(2+5)/2
A = 1.5*7/2
A = 10.5/2
A = 5.25
The area of one 2D trapezoid is 5.25 sq cm
There are two of these trapezoids that form the base faces of the trapezoidal prism. So the total base area is 2*5.25 = 10.5 sq cm
Keep this value (10.5) in mind. We'll use it later.

------------

Now onto the lateral surface area (LSA)
It turns out that the formula for the LSA is
LSA = p*d
where
p = perimeter of the trapezoid shown
d = depth or height of the 3D trapezoid (I'm not using h as it was used earlier)
This formula works for any polygonal base. It doesn't have to be a trapezoid.

In this case the perimeter is,
p = 1.7+2+2.65+5
p = 11.35

So
LSA = p*d
LSA = 11.35*10
LSA = 113.5

Add this LSA to the base area found earlier
10.5+113.5 = 124

The total surface area is 124 square cm

8 0

3 years ago

Please help! i really need help with this! question is below!

ira [324]

Step-by-step explanation:

Area of the square:

a^2: 4^2=16in^2

Area of the circle:

πr^2: π(4.5)^2= 63.6

Area of white part:

63.6 - 16 = 47.6

Probability of landing on square:

16/63.6 = 0.25

Probability of landing on white part:

63.6/16 = 3.975

7 0

2 years ago