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3 years ago

Find the equation,in standard form, of the line passing through the point (2,-3) and (4,2)

Mathematics

2 answers:

VLD [36.1K]3 years ago

8 0

The standard form:

$Ax+By=C$

The point-slope form:

$y-y_1=m(x-x_1)$

m - slope

(x₁, y₁) - point

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (2, -3) and (4, 2). Substitute:

$m=\dfrac{2-(-3)}{4-2}=\dfrac{5}{2}$

$y-(-3)=\dfrac{5}{2}(x-2)$

$y+3=\dfrac{5}{2}(x-2)$ use distributive property

$y+3=\dfrac{5}{2}x-5$ multiply both sides by 2

$2y+6=5x-10$ subtract 6 from both sides

$2y=5x-16$ subtract 5x from both sides

$-5x+2y=-16$ change the signs

$\boxed{5x-2y=16}$

sukhopar [10]3 years ago

5 0

Answer:

5x - 2y = 16

Step-by-step explanation:

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The probability distribution for the number of defects in a shipment of alarm clocks, based on past data, is given below. Find t

Kay [80]

Answer:

0.29

Step-by-step explanation:

Given :

n : ___ 0 _____ 1 ____ 2 ____ 3 ____ 4

P(n) : 0.82___ 0.11 ___0.04 _0.02 ___0.01

The expected number of defect in a shipment can be obtained using the expected value formula :

Expected value, E(X) = Σx*p(x)

Σx*p(x) = (0*0.82) + (1*0.11) + (2*0.04) + (3*0.02) + (4*0.01)

E(X) = 0.29

Hence, the expected number of defect in shipment is 0.29

3 0

3 years ago

A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the mi

g100num [7]

legs of the triangles

Each triangle 30-60-90 is:

   one leg: 15 ft => short diagonal = 2 * 15ft = 30ft

   other leg, x:

   tan(30) = 15 / x => x = 15 ft / tan(30) = 25.98 ft

=> long diagonal = 2 * 25.98ft = 51.96 ft

side of the rhoumbus = hypotenuse of one triangle

side of the rhombus = √ [ (15)^2 + (25.98)^2 ] = √(900) = 30 ft

Area of the rhombus:

4 * area of one triangle = 4 [base*height/2] = 4*15*25.98/2 = 779.43 ft^2

The shortest distance accross the garden is equal to the side of the rhombus = 30 ft

5 0

3 years ago

Read 2 more answers

If f (x) = 4x - 7 and G(x) = 2x + 4 , evaluate f(x) + g(x) for x = -3

avanturin [10]

Hi there!

• x = - 3

Let's first calculate f(x) and g(x) individually :-

• f(x) = 4x - 7

⇒ 4(- 3) - 7

⇒ - 12 - 7 = - 19

$\boxed{\text{f(x)} = - 19}$

• g(x) = 2x + 4

⇒ 2(- 3) + 4

⇒ - 6 + 4 = - 2

$\boxed{\text{g(x)} = - 2}$

According to th' question :-

f(x) + g(x)

⇒ - 19 + (- 2)

⇒ - 19 - 2

⇒ - 21

$\boxed{\text{f(x) + g(x)} = - 21}$

~ Hope it helps!

6 0

3 years ago

An unknown number b is 10 more than an unknown number k. the number b is also k less than 8. the equations to find k and b are s

Dmitriy789 [7]

Just add the two equations together.
2b = 18
b = 18/2
b = 9

9 = k + 10
9 - 10 = k
k = - 1

6 0

3 years ago

Read 2 more answers

b) If a shopkeeper allows 20% discount and sells an article for Rs 200, find the marked price of the article.

zzz [600]

Answer:

250

Step-by-step explanation:

mp=sp+d%of mp

x = 200+20÷100×x

100x-20x = 20000

x= 250

3 0

2 years ago