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3 years ago

Write this equation in standard form of each line passing through the two given points (2,3);(1,-2)

1 answer:

7 0

The given points
(x₁,y₁) = (2,3)
(x₂,y₂) = (1,-2)

There are 2 formulas we will use.
The first is formula to find the slope, and the second is formula to find the line equation.
To find the slope
m = (y₂ - y₁)/(x₂ - x₁)
To find the line equation
y - y₁ = m(x - x₁)

Find the slope, input the numbers to the formula
m = (y₂ - y₁)/(x₂ - x₁)
m = (-2-3) / (1-2)
m = -5/-1
m = 5

Find the line equation, input the numbers to the formula
y - y₁ = m(x - x₁)
y - 3 = 5(x - 2)
5(x - 2) = y - 3
5x + 10 = y - 3
5x - y = -3 - 10
5x - y = -13

The equation of the line is
5x - y = -13

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Quadrilateral ABCD is located at A (−2, 2), B (−2, 4), C (2, 4), and D (2, 2). The quadrilateral is then transformed using the r

Mademuasel [1]

New cordinates are formed by adding 7 in x and subtracting 2 from y
A(−2, 2) =A ' (-2 +7 , 2 - 1 ) = A' (5,1)
B(−2, 4) = B' (-2 + 7 , 4 -1 )= B' (5,3)
C(2, 4) = C' (2 + 7 , 4 -1 )= C' (9,3)
D(2, 2) D' (2 + 7 , 2 -1 ) = D' ( 9 , 1)

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3 years ago

What is the prime factorazation of 50

Aleonysh [2.5K]

Answer:

Prime factorization of 50 is 2 x 5 x 5 or 2 x 5^2

Step-by-step explanation:

6 0

3 years ago

Solve for z. -30 = 5(x+1)

melisa1 [442]

-30= 5 (x+1 )

-5 from 5= 0
-5 from -30= -35

-35= (x+1)

1/-35= -35

6 0

3 years ago

A ramp leading into a building makes a 15 degree angle with the ground. The end of the ramp is 10 feet from the base of the buil

stiks02 [169]

Answer:

The length of the ramp is x = AC = 10.35 feet

Step-by-step explanation:

From the ΔABC

AC = x = length of ramp

BC = 10 feet

$\theta = 15$ °

$\cos 15 = \frac{BC}{AC}$

$\cos 15 = \frac{10}{x}$

x = 10.35 feet

Therefore the length of the ramp is x = AC = 10.35 feet

5 0

4 years ago

How many L of A 90% saline solution must be mixed with 4 L of a 50% saline solution to make a 74% solution ?

insens350 [35]

Answer:

6 L

Step-by-step explanation:

Given two solutions:

1st solution is 90% saline solution. Let the volume of this solution be $x$ litres.

2nd solution is 50% saline solution. Volume of this solution = 4 L

Resultant solution is 74% saline.

To find:

The volume of 1st solution = ?

Solution:

Total volume of the 74% saline mixture = (4+ $x$ ) Litres

We can write equation here, as per the percentage of saline in the mixtures.

90% of $x$ L + 50% of 4 L = 74% of ( $x$ +4)

$\Rightarrow \dfrac{90x}{100} + \dfrac{50}{100}\times 4 = \dfrac{74}{100}\times (x+4)\\\Rightarrow 90x + 200 = 74x+296\\\Rightarrow 90x-74x = 296-200\\\Rightarrow 16x = 96\\\Rightarrow x = \bold{6\ L}$

Therefore, the volume must be 6 L.

8 0

3 years ago