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2 years ago

Write equations for the horizontal and vertical lines passing through the point (6,4).

Mathematics

1 answer:

liberstina [14]2 years ago

4 0

Check the picture below.

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Solve the system: 2/x - 3/y =-5; 4/x + 6\y =14

sertanlavr [38]

The solution is $x = 2 \text{ and } y = \frac{1}{2}$

Solution:

Let us assume,

$a = \frac{1}{x}\\\\b = \frac{1}{y}$

Given system of equations are:

$\frac{2}{x} - \frac{3}{y} = -5$

$\frac{4}{x} + \frac{6}{y} = 14$

Rewrite the equation using "a" and "b"

2a - 3b = -5 ------------ eqn 1

4a + 6b = 14 -------------- eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 2

2(2a - 3b = -5)

4a - 6b = -10 ------------- eqn 3

Add eqn 2 and eqn 3

4a + 6b = 14

4a - 6b = -10

( - ) --------------------

8a = 4

$a = \frac{4}{8}\\\\a = \frac{1}{2}$

Substitute a = 1/2 in eqn 1

$2(\frac{1}{2}) -3b = -5\\\\1 - 3b = -5\\\\3b = 6\\\\b = 2$

Now let us go back to our assumed values

Substitute a = 1/2 in assumed values

$a = \frac{1}{x}\\\\\frac{1}{2} = \frac{1}{x}\\\\x = 2$

Substitute b = 2 in assumed value

$b = \frac{1}{y}\\\\2 = \frac{1}{y}\\\\y = \frac{1}{2}$

Thus the solution is $x = 2 \text{ and } y = \frac{1}{2}$

3 0

3 years ago

corinne earns an hourly wage on top of her weekly gas allowance for her delivery job. her weekly earnings can be shown using the

Aliun [14]

Corrine earns an hourly wage on top of her weekly gas allowance for her delivery job.

Her weekly earnings can be expressed as:

Earnings = 40 + 7.50h

When h=0, her earnings will be 40

This constant represents, the fixed gas allowance she is receiving for her delivery job. 7.50h represents that she get paid $7.50 for an hour of work.

So, the constant term in the expression represent her weekly gas allowance.

6 0

3 years ago

Which expression is equivalent to (x-3)(2x+5)?

NeX [460]

Answer:

$2x {}^{2} - x - 15$

Step-by-step explanation:

$(x - 3)(2x + 5) = \\ x(2x + 5) - 3(2x + 5) = \\ 2 {x}^{2} + 5x - 6x - 15 = \\ 2 {x}^{2} - x - 15$

4 0

3 years ago

How turtles run in 1 hour

IgorC [24]

Since they walk a little slower

7 0

3 years ago

What is the equation of this circle in standard form?

Musya8 [376]

Answer:

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k ) = (2, 3 ) and r = 6, thus

(x - 2)² + (y - 3)² = 6², that is

(x - 2)² + (y - 3)² = 36 → D

3 0

3 years ago