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3 years ago

Through (-6, 8); perpendicular to 9x + 5y = 66. Write the equation in y = mx + b form.

Mathematics

1 answer:

zzz [600]3 years ago

3 0

simplified original equation: y=-9/5x+13.2

perpendicular slope: 5/9

equation passing through (-6,8): y-(8)=5/9(x-(-6))

y=mx+b form: y = 5/9x + 14

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VERY URGENT HAVE A TEST TO TAKE

Daniel [21]

The easiest way is to try the point (-4,1), that is, x=-4, y=1,
to see which equation works.
b works.

The usual way to do it is to find the equation of the circle
standard form of a circle is (x-h)²+(y-k)²=r², (h,k) are the coordinates of the center, r is the radius.
in this case, the center is (-2,1), so (x+2)²+(y-1)²=r²
the given point (-4,1) is for you to find r: (-4+2)²+(1-1)²=r², r=2
so the equation is (x+2)²+(y-1)²=2²
expand it: x²+4x+4+y²-2y+1=4
x²+y²+4x-2y+1=0, which is answer b.

5 0

3 years ago

Two-thirds a number plus 4 is 7

ICE Princess25 [194]

The equation (form) is: $\frac{2}{3}x + 4 = 7$

The solution of the equation is: $x = \frac{9}{2}$

Explanation:

First, let's call the number we are going to solve for "x".

Then two thirds of this number can be written as:

$\frac{2}{3}x$

Then "plus 4" means add 4 we get:

$\frac{2}{3}x + 4$

"is 7" means that the above expression is equal to 7 (as follows):

$\frac{2}{3}x + 4 = 7$

The solution of the above equation is:

$\frac{2}{3}x + 4 = 7 \\ \frac{2}{3}x = 3 \\ x = \frac{9}{2}$

6 0

3 years ago

A box measures 3 1/2 ft by 1 1/3 ft by 2/14 ft what is the volume

asambeis [7]

Answer: 2/3^3

Step-by-step explanation:

To find the volume of a box, you use the formula, Lenth*Width*Height=Volume

The Lenth is 3 1/2. The width is 1 1/3 and the height is 2/14

Plug the values in formula

3 1/2*1 1/3*2/14

Covert the mixed numbers into imporper fractions so it is easier to solve

3 1/2=7/2

1 1/3=4/3

7/2*4/3*2/14

Reduce 2/14

2/14=1/7

7/2*4/3*1/7=7*4*1/(2*3*7)=28/42

Reduce 28/42=14/21=2/3

2/3 ft^3

5 0

3 years ago

Jack mails 10 packages that each weigh the same amount. If the combined weigh of all 10 package is 67 1/2 pounds, how much does

kykrilka [37]

The answer is 6.75, I hope this helped

7 0

3 years ago

Hello people ~

Luden [163]

Cone details:

height: h cm

radius: r cm

Sphere details:

radius: 10 cm

================

From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.

Using Pythagoras Theorem

(a)

TO² + TU² = OU²

(h-10)² + r² = 10² [insert values]

r² = 10² - (h-10)² [change sides]

r² = 100 - (h² -20h + 100) [expand]

r² = 100 - h² + 20h -100 [simplify]

r² = 20h - h² [shown]

r = √20h - h² ["r" in terms of "h"]

(b)

volume of cone = 1/3 * π * r² * h

===========================

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (\sqrt{20h - h^2})^2 \ ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20h - h^2) (h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20 - h) (h) ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} \pi h^2(20-h)$

To find maximum/minimum, we have to find first derivative.

(c)

First derivative

$\Longrightarrow \sf V' =\dfrac{d}{dx} ( \dfrac{1}{3} \pi h^2(20-h) )$

apply chain rule

$\sf \Longrightarrow V'=\dfrac{\pi \left(40h-3h^2\right)}{3}$

Equate the first derivative to zero, that is V'(x) = 0

$\Longrightarrow \sf \dfrac{\pi \left(40h-3h^2\right)}{3}=0$

$\Longrightarrow \sf 40h-3h^2=0$

$\Longrightarrow \sf h(40-3h)=0$

$\Longrightarrow \sf h=0, \ 40-3h=0$

$\Longrightarrow \sf h=0,\:h=\dfrac{40}{3}$

maximum volume: when h = 40/3

$\sf \Longrightarrow max= \dfrac{1}{3} \pi (\dfrac{40}{3} )^2(20-\dfrac{40}{3} )$

$\sf \Longrightarrow maximum= 1241.123 \ cm^3$

minimum volume: when h = 0

$\sf \Longrightarrow min= \dfrac{1}{3} \pi (0)^2(20-0)$

$\sf \Longrightarrow minimum=0 \ cm^3$

6 0

2 years ago

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