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3 years ago

What is the equation for the line with a slope of - 2/3 that passes through (0, -2)

Mathematics

1 answer:

viktelen [127]3 years ago

5 0

Answer:

y= -2/3x-2

Step-by-step explanation:

Since we have a point and a slope, we can use the point slope formula

$y-y_{1} =m(x-x_{1})$

m is the slope. In this case, m is -2/3

y1 is the y coordinate of the point. In this case, it is -2

x1 is the x coordinate. In this case it is 0.

We can substitute these values into the formula

y- -2= -2/3(x-0)

Distribute -2/3

y+2 = -2/3*x + -2/3*0

y+2= -2/3x+0

Subtract 2 from both sides. We want to get y by itself. This is because we want our line to be in y=mx+b form.

y+2-2= -2/3x+0-2

y= -2/3x -2

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A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5. What

krok68 [10]

The area of the required triangle is 9/π²(3 + √3) sq. units.

In the question, we are given that a triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5.

We are asked for the area of the triangle.

Now, the circumference of the circle = 3 + 4 + 5 = 12 units.

The formula for the circumference is 2πr, which gives is:

2πr = 12,

or, r = 6/π.

The length of the arcs are proportional to its central angle, making the angles: 3θ, 4θ, and 5θ, which needs to sum up to 360°, giving us θ = 360°/12 = 30°.

Thus, the three arcs subtends angles of θ₁ = 3θ = 90°,θ₂ = 4θ = 120°, and θ₃ = 5θ = 150°.

The area of the circle can be calculated as:

Area = (1/2)r² sin θ₁ + (1/2)r² sin θ₂ + (1/2)r² sin θ₃ = r²/2(sin θ₁ + sin θ₂ + sin θ₃).

Substituting the values, we get:

Area = 36/2π²(sin 90° + sin 120° + sin 150°),

or, Area = 36/2π²( 1 + √3/2 + 1/2),

or, Area = 9/π²(3 + √3).

Thus, the area of the required triangle is 9/π²(3 + √3) sq. units.

Learn more about a triangle at

brainly.com/question/13734546

#SPJ4

5 0

1 year ago

HI can someone do these 5 problems? it will really help me out I'll give out brainliest to the person who answers them. (No link

Softa [21]

Answer:

$73.60

$345

simple interest = amount deposited x time x interest rate

600 + (600 x 0.055 x 5) = $765

600 + (600 x 0.055 x 5) > $2000

$765 $2000

He would not have $2000 in 5 years

Step-by-step explanation:

Total cost of items purchased = $75 + (2 x $8.50) = 92

If there is a 20% discount, he would pay (100 - 20%) 80% of the total cost =

0.8 x $92 = $73.60

commission earned = percentage commission x amount of sales

10% x $3450

= 0.1 x 3450 = 345

Amount he would have in his account = amount deposited + simple interest

simple interest = amount deposited x time x interest rate

600 x 0.055 x 5 = $165

Amount in his account in 5 years = $165 + 600 = $765

He would have less than $2000 in his account. he would have $765

4 0

2 years ago

Total surface area of a cube is 1014cm^2. It's volume will be :

Karolina [17]

Answer:

Option A (2197 cm³)

Step-by-step explanation:

For a cube with length of each side "a" , it's

Total Surface Area = 6a²
Volume = a³

_____________________________________________

According to the question ,

Total Surface Area = 1014 cm²

Let the length of each side of cube be 'a'.

Using the formula ,

$6a^{2} =1014$

$=> a^{2} =\frac{1014}{6} = 169$

$=> a = \sqrt{169} = +13 \: or -13$

But length can't be negative . So , length of each side = 13 cm

∴ Volume of cube = 13³ = 2197 cm³

8 0

3 years ago

2log(x+11) = (1/2)^x

Lina20 [59]

X = -1

Hope this helps!

7 0

3 years ago

Read 2 more answers

Find the perimeter of a right triangle whose legs are 6cm and 8cm

MAVERICK [17]

P = Perimeter

A = 1 leg

B = 2 leg

- BRAINLIEST answerer

4 0

3 years ago