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3 years ago

Find the equation of the line through the pair of points (1/2,1/8) and (-1/7,1/9)in standard form using only integers.

1 answer:

3 0

The first thing that we need to do is find the slope (m). In order to find the slope we need two points. The first point is (x1,y1) and the second point is (x2,y2). The slope is m = (y2-y1)/(x2-x1) = (1/9 - 1/8)/(-1/7 - 1/2) = (8/72 - 9/72)/
(-2/14 - 7/14) = -(1/72)/(-9/14) = 1(14)/72(9) = 7/(36)(9) = 7/324 (Wow!)

Now we can use the point slope formula to make the equation:
y - 1/8 = (7/324)(x - 1/2) Point slope equation
y - 1/8 = (7/324)x - 7/648
y =(7/324)x - 7/648 + 81/648
y = (7/324)x +74/648
y = (7/324)x + 37/324 This is the slope intercept form
-(7/324)x + y = 37/324 This is the standard form

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3x + 2y = 2

iragen [17]

A) (-2,4) hope this helps

6 0

3 years ago

The bases of the trapezoid are 6 and 10. The height is 4. Find the area.

kari74 [83]

<h2>Answer:</h2>

$b. \ \boxed{32 \sq. \ units}$

<h2>Step-by-step explanation:</h2>

A trapezoid is a quadrilateral where at least one pair of opposite sides are parallel. In a trapezoid, the both parallel sides are known as the bases of the trapezoid. So we have two bases, namely, $b_{1}\,and\,b_{2}$ . Also, the height $H$ of the trapezoid is the length between these two bases that's perpendicular to both sides. So the area of a trapezoid in terms of of $b_{1},b_{2}\:and\:H$ is:

$A=\frac{(b_{1}\text{+}b_{2})h}{2}$

Since:

$b_{1}=6, \ b_{2}=10, \ and \ H=4$

The area is:

$A=\frac{(6\text{+}10)4}{2}=\boxed{32 \sq. \ units}$

6 0

3 years ago

A silo is a composite of a cylindrical tower with a cone for a roof. Find the volume of the silo if the

xxMikexx [17]

Answer:

5127079.21 cubic feet

Step-by-step explanation:

The silo is in the shape of a cylinder and a cone.

The volume of the silo will be the sum of the volumes of the cylinder and the cone.

Therefore, its volume is:

$V = \pi r^2h + \frac{1}{3} \pi rH$

where r = radius of cylinder and cone

h = height of cylinder

H = height of cone

The radius of the base is 120 feet, the height of the roof (cone) is 25 feet. The height of the entire silo is 130 feet. This means that the height of the cylinder is:

130 - 25 = 105 feet

Therefore, the volume of the silo is:

$V = (\pi * 120^2 * 105) + (\frac{1}{3} * 120^2 * 25)\\\\V = 4750088.09 + 376991.12\\\\V = 5127079.21 ft^3$

The volume of the silo is 5127079.21 cubic feet.

3 0

2 years ago

Solving systems equations by elimination

pishuonlain [190]

I won't answer them all for you (don't want to cheat - need to learn something).
But for the first one given:

<span>-2x-9y=-25
-4x-9y=-23

you set up either x or y (which ever one you want to eliminate) so that one of them cancels.
So this one is easy - you just have to multiply an entire row by negative (doesn't matter which one) - so that the y's will be + and -

Since they're both 9 and they're subracting NOW - you can eliminate the y value. Now add/subtract the x's. So it'd be -2 or 2 depending on how you eliminated y. Then add the number outside of the = sign. Now just solve for x. After that plug in whatever you got for x into both of the rows. Then find the y value.

Hopefully this wasn't confusing -- reply if it is and I will try to simplify. I can give you contact if you need help with the rest

Good luck!</span>

3 0

2 years ago

Find the area of the triangle formed by the origin and the points of intersection of parabolas y=− 1/3 (x−1)^2+8 and y=x^2−2x−3.

Kobotan [32]

Answer:

The area of the triangle formed by origin, and the points (4,5) and (-2,5) will be 15 sq. units.

Step-by-step explanation:

The two parabolas are $y = - \frac{1}{3}(x - 1)^{2} + 8$ and y = x² - 2x - 3.

Now, solving those two equations we will get the points of intersection.

So, $- \frac{1}{3}(x - 1)^{2} + 8 = x^{2} - 2x - 3$

⇒ - (x - 1)² + 24 = 3x² - 6x - 9

⇒ -x² + 2x - 1 + 24 = 3x² - 6x - 9

⇒ 4x² - 8x - 32 = 0

⇒ x² - 2x - 8 = 0

⇒ x² - 4x + 2x - 8 = 0

⇒ (x - 4)(x + 2) = 0

So, x = 4 or - 2.

Now, for x = 4 , y = 4² - 2(4) - 3 = 5 and the point of intersection is (4,5).

Or, for x = - 2, y = (- 2)² - 2(- 2) - 3 = 5 and the point of intersection is (-2,5).

Now, points (4,5) and (-2,5) make a straight line parallel to the x-axis at a perpendicular distance of 5 units from origin and its length is (4 - (- 2)) = 6 units.

So, the area of the triangle formed by origin, and the points (4,5) and (-2,5) will be = 0.5 × 5 × 6 = 15 sq. units. (Answer)

8 0

2 years ago