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EleoNora [17]
2 years ago
12

Find an equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0)

Mathematics
1 answer:
Anna007 [38]2 years ago
5 0

The equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0) is 8x -3y = -16

<h3>Equation of a straight line</h3>

From the question, we are to determine the equation of the line parallel to the given equation and that passes through the given point

Lines that are parallel to each other will have the same slope.

First, we will determine the slope of the line in the given equation.

The given equation of the line is

8x − 3y = 1

Express the equation in the slope-intercept form of a line, y = mx + b

Where m is the slope and

b is the y-intercept

That is,

8x − 3y = 1

8x -1 = 3y

3y = 8x - 1

y = 8/3(x) - 1/3

By comparing,

∴ The slope of the line is 8/3

Since we are to find the equation of a line parallel to this, the slope of the line will also be 8/3

Now, find the equation of a line containing the point (-2, 0) and that has  a slope of 8/3

Using the point-slope form of a line

y - y₁ = m(x - x₁)

x₁ = -2

and y₁ = 0

∴ y - 0 = 8/3(x - -2)

y = 8/3(x +2)

3y = 8(x +2)

3y = 8x + 16

8x -3y = -16

Hence, the equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0) is 8x -3y = -16

Learn more on Equation of a line here: brainly.com/question/13763238

#SPJ1

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Circle F has a diameter of 36m and = 240o. Find the length of . Leave your answer in terms of pi.
andrezito [222]

Answer:

So, the arc length is 24\pi

Step-by-step explanation:

We are given

diameter =36m

so, we can find radius

r=\frac{36}{2}=18m

and angle as

\theta=240

Since, it is in degree

so, we can change it in radian

\theta=240\times \frac{\pi}{180}

\theta=\frac{4\pi}{3}

now, we can find arc length

L=r\times \theta

now, we can plug values

L=18\times \frac{4\pi}{3}

L=24\pi


5 0
3 years ago
What is the surface area? 10 cm 7 cm 3 cm square centimeters
alexandr1967 [171]

Answer:

242cm^2

Step-by-step explanation:

The formula for surface area of a rectangular(assuming that's what you have) is Perimeter of the Base(height) + 2(Area of the Base)

Or you could add up all the sides, or use this formula

SA=2(length*width)+2(length*height)+2(height*width)

2×(10×7 + 10×3 + 7×3)

helpful links:

https://www.khanacademy.org/math/ basic-geo/basic-geo-volume-sa/basic-geometry-surface-area/v/surface-area-of-a-box

http://www.math.com/tables/geometry/surfareas.htm

https://www.basic-mathematics.com/surface-area-formula.html

6 0
3 years ago
36A^4+16Y^2<br> Can someone help me
Alenkasestr [34]

Answer:

4(9a^4+4y^2)

Step-by-step explanation:

factor out common term

6 0
3 years ago
Write the equation for a parabola with a focus at (6,-4) and a directrix at y= -7
shtirl [24]

Given:

The focus of the parabola is at (6,-4).

Directrix at y=-7.

To find:

The equation of the parabola.

Solution:

The general equation of a parabola is:

y=\dfrac{1}{4p}(x-h)^2+k                  ...(i)

Where, (h,k) is vertex, (h,k+p) is the focus and y=k-p is the directrix.

The focus of the parabola is at (6,-4).

(h,k+p)=(6,-4)

On comparing both sides, we get

h=6

k+p=-4                            ...(ii)

Directrix at y=-7. So,

k-p=-7                            ...(iii)

Adding (ii) and (iii), we get

2k=-11

k=\dfrac{-11}{2}

k=-5.5

Putting k=-5.5 in (ii), we get

-5.5+p=-4

p=-4+5.5

p=1.5

Putting h=6, k=-5.5,p=1.5 in (i), we get

y=\dfrac{1}{4(1.5)}(x-6)^2+(-5.5)

y=\dfrac{1}{6}(x-6)^2-5.5

Therefore, the equation of the parabola is y=\dfrac{1}{6}(x-6)^2-5.5.

4 0
3 years ago
Duc has a trapezoid shaped section of his yard fenced off for his pets. The lengths of the parallel sides of the trapezoid are 8
noname [10]
Area of the trapezoid = 1/2(B+b)h
where
B= length of the longer side of the trapezoid which is equal to 14 ft
b= shorter shorter side of the trapezoid  which equal 8 ft
h = height of the trapezoid which is equal to 4 ft
Area of the trapezoid = 1/2 (14+8)4
Area of the trapezoid yard fence of Duc is 44ft^2
5 0
3 years ago
Read 2 more answers
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