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3 years ago

What is the slope of a line whose equation is 5y + 6 x - 2 =0

Mathematics

2 answers:

RoseWind [281]3 years ago

8 0

5y= -6x+2
5y/5 =-6x/5 +2/5
y = -1.2x +0.4

the slope is -1.2 and y intercept is 0.4

Svetlanka [38]3 years ago

5 0

5y+6x-2=0 ---------------Original Equation

2+5y+6x-2=0+2 --------Add 2 on both sides of the equal sign

5y+6x=2

6x-5y+6x=2-6x----------Subtract 6x on both sides of the equal sign

5/5y= -6x+2/5-------------Divide by 5 on both sides of the equal sign

y= -6/5x+2/5

<h3>So the slope would be -6/5.</h3>

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3 years ago

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Find the area of the region bounded by the line y=3x-6 and line y=-2x+8.

Vikentia [17]

Answer:

A = 12/5 units

Step-by-step explanation:

USING ALGEBRA:

We can find the intersection point between these two lines;

y = 3x - 6

y = -2x + 8

Set these two equations equal to each other.

3x - 6 = -2x + 8

Add 2x to both sides of the equation.

5x - 6 = 8

Add 6 to both sides of the equation.

5x = 14

Divide both sides of the equation by 5.

x = 14/5

Find the y-value where these points intersect by plugging this x-value back into either equation.

y = 3(14/5) - 6

Multiply and simplify.

y = 42/5 - 6

Multiply 6 by (5/5) to get common denominators.

y = 42/5 - 30/5

Subtract and simplify.

y = 12/5

These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.

Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.

Set both equations equal to 0.

(I) 0 = 3x - 6

Add 6 both sides of the equation.

6 = 3x

Divide both sides of the equation by 3.

x = 2

Set the second equation equal to 0.

(II) 0 = -2x + 8

Add 2x to both sides of the equation.

2x = 8

Divide both sides of the equation by 2.

x = 4

The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.

The height of the triangle is 12/5 units.

Formula for the Area of a Triangle:

A = 1/2bh

Substitute 2 for b and 14/5 for h.

A = (1/2) · (2) · (12/5)

Multiply and simplify.

A = 12/5

The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

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3 years ago

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miv72 [106K]

Step-by-step explanation:

55.44=2464

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3 years ago

Student Practice: Follow the steps in the example.

Sergio039 [100]

Answer:

1) Option B - 25.12 ft

2) Option C - 24.1 ft

Step-by-step explanation:

1) Given : The circular rug has a diameter of 8.2 feet.

To find : Which measurement is closest to the circumference of the rug in feet?

Solution :

The circumference of rug is given by $C=\pi d$

Where, d is the diameter = 8.2 feet.

$C=3.14\times 8.2$

$C=25.748\ ft$

The most closest measurement is 25.12 ft.

Therefore, option B is correct.

2) Given : A circle has a diameter of 5.2 feet.

To find : Which measurement is closest to the circumference of the circle in feet?

Solution :

The circumference of circle is given by $C=\pi d$

Where, d is the diameter = 5.2 feet.

$C=3.14\times 5.2$

$C=16.328\ ft$

The most closest measurement is 24.1 ft.

Therefore, option C is correct.

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3 years ago

When the positive integer n is divided by 7, the remainder is 2. What is the remainder when 5n is divided by 7?

ser-zykov [4K]

Therefore the reminder is 3 when 5n is divided by 7.

Step-by-step explanation:

we know that

Dividend = quotient × Divisor +Reminder

⇔ n = Q(n) × 7 + 2 [ let Q(n) is quotient]

multiplying by 5 both sides

5n = 5 Q(n) ×7 + 2×5

⇔5n = 5 Q(n) ×7 +10

⇔5n= 5 Q(n) ×7 +7 +3

⇔ 5n = (5Q(n) +1) × 7 +3

Therefore the reminder is 3 when 5n is divided by 7.

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