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3 years ago

Find the value of two numbers if their sum is 23 and their difference is 5

Mathematics

1 answer:

yKpoI14uk [10]3 years ago

6 0

Let the two numbers be represented by x and y respectively.

Then x + y = 23, and x - y = 5.

Solve this system of linear equations for x and y. Start by rearranging them vertically:

x + y = 23

x - y = 5

--------------- Combining the two equations eliminates y:

2x = 28.

Then x = 14. If x = 14, then 14 + y = 23, and y = 9..

The solution is (14, 9); that is, x = 14 and y = 9.

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Any REAL help on #16 above??? Can someone check my answer?

babymother [125]

Answer:

The answer to your question is:th first option is correct.

Step-by-step explanation:

Here we have and hyperbola with center (0, 1), and the hyperbola is horizontal because x² is positive.

Equation

y - k = ± $\frac{b}{a} (x - h)$

Process

Find a, b

a² = 9

a = 3

b² = 5

b = √5

h = 0 and k = 1

Substitution

y - 1 = ± $\frac{√5}{3} (x - 0)$

Equation 1

y = $\frac{\sqrt{5} }{3} x + 1$

Equation 2

y = - $\frac{\sqrt{5} }{3} x + 1$

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|x-3|+5 <br> i need to find out the absolute value

Assoli18 [71]

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Step-by-step explanation:

6 0

3 years ago

Calculate pt3 such that a line from pt1 to pt3 is perpendicular to the line from pt1 to pt2, and the distance between pt1 and pt

Leni [432]

Let the point_1 = p₁ = (1,4)
and      point_2 = p₂ = (-2,1)
and      Point_3 = p₃ = (x,y)

The line from point_1 to point_2 is L₁ and has slope = m₁
The line from point_1 to point_3 is L₂ and has slope = m₂
m₁ = Δy/Δx = (1-4)/(-2-1) = 1
m₂ = Δy/Δx = (y-4)/(x-1)
L₁⊥L₂ ⇒⇒⇒⇒ m₁ * m₂ = -1
∴ (y-4)/(x-1) = -1 ⇒⇒⇒ (y-4)= -(x-1)
(y-4) = (1-x) ⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒ equation (1)

The distance from point_1 to point_2 is d₁
The distance from point_1 to point_3 is d₂
d = $\sqrt{Δx^2+Δy^2}$
d₁ = $\sqrt{(-2-1)^2+(1-4)^2}$
d₂ = $\sqrt{(x-1)^2+(y-4)^2}$
d₁ = d₂
∴ $\sqrt{(-2-1)^2+(1-4)^2} = \sqrt{(x-1)^2+(y-4)^2}$ ⇒⇒ eliminating the root
∴(-2-1)²+(1-4)² = (x-1)²+(y-4)²
(x-1)²+(y-4)² = 18
from equatoin (1) y-4 = 1-x
∴(x-1)²+(1-x)² = 18            ⇒⇒⇒⇒⇒ note: (1-x)² = (x-1)²
2 (x-1)² = 18
(x-1)² = 9
x-1 = $\pm \sqrt{9} = \pm 3$
∴ x = 4 or x = -2
∴ y = 1 or y = 7

Point_3 = (4,1) or (-2,7)

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4 years ago

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Scorpion4ik [409]

Answer:

Yes

Step-by-step explanation:

Draw a vertical line on the x value of 1/4

It's just a straight line upwards

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3 years ago

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