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statuscvo [17]
3 years ago
9

Please write the slope-intercept form for this: A line goes through the points (5,18) and (-3,-14)

Mathematics
1 answer:
balandron [24]3 years ago
6 0

y = 4x - 2

The equation of a line in ' slope- intercept form ' is

y = mx + c → (m is the slope and c the y- intercept )

To calculate m use the ' gradient formula '

m = (y₂ - y₁ )/(x₂ - x₁ )

let ( x₁, y₁ ) = (5, 18) and (x₂, y₂ ) = ( - 3, - 14 )

m = \frac{(- 14 - 18)}{( - 3 - 5)} = \frac{- 32}{- 8} = 4

the partial equation is y = 4x + c

to find c substitute either of the 2 given points into the partial equation

using (5 , 18) then 18 = 20 + c ⇒ c = 18 - 20 = - 2

y = 4x - 2 is the equation in slope- intercept form


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3 years ago
The following are the ages (years) of 5 people in a room:
slava [35]

Answer:

The age of the person who entered the room is 15

Step-by-step explanation:

We are given:

Ages of 5 people in a room are:

17, 16, 15, 17, 22

A person enters room, and then the mean age of 6 people is 17.

We need to find the age of person who entered the room.

The formula to calculate mean is: Mean=\frac{Sum\:of\:all\:data\:values}{Number\:of\:data\:Values}

Now, in question we are given mean of 6 people that is 17

The age of 5 people are given while age of one person who enters the room is unknown.

Let age of person whose age is unknown= x

Now finding x using mean formula

Mean=\frac{Sum\:of\:all\:data\:values}{Number\:of\:data\:Values}\\17=\frac{17+16+ 15+ 17+ 22+x}{6}\\17=\frac{87+x}{6}\\17*6=87+x\\102=87+x\\x=102-87\\x=15

So, The value of x: x=15

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4 0
3 years ago
With reference to the figure, sin X equals?<br> 1.) 0.250<br> 2.)0.447<br> 3.)0.894<br> 4.)1
Flura [38]

Answer:

3.) 0.894

Step-by-step explanation:

✔️First, find BD using Pythagorean Theorem:

BD² = BC² - DC²

BC = 17.89

DC = 16

Plug in the values

BD² = 17.89² - 16²

BD² = 64.0521

BD = √64.0521

BD = 8.0 (nearest tenth)

✔️Next, find AD using the right triangle altitude theorem:

BD = √(AD*DC)

Plug in the values into the equation

8 = √(AD*16)

Square both sides

8² = AD*16

64 = AD*16

Divide both sides by 16

4 = AD

AD = 4

✔️Find AB using Pythagorean Theorem:

AB = √(BD² + AD²)

AB = √(8² + 4²)

AB = √(64 + 16)

AB = √(80)

AB = 8.9 (nearest tenth)

✔️Find sin x using trigonometric ratio formula:

Reference angle = x

Opposite side = BD = 8

Hypotenuse = AB = 8.944

Thus:

sin(x) = \frac{opp}{hyp} = \frac{8}{8.944} = 0.894 (nearest thousandth)

6 0
3 years ago
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