Which transformation will create a similar and a congruent triangle?

I need help with a prople on my math for 8 grade it is y = -8x - 2

Nadusha1986 [10]

Answer:

M=8 Y=-2

Step-by-step explanation:

this is the slope and b

8 0

3 years ago

3. What is the perimeter of a 6-inch square?

nirvana33 [79]

Answer:

24

Step-by-step explanation:

6+6 =12

12+6 = 18

18+6 = 24

7 0

3 years ago

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9 and 5/12 - 3 and 2/3

lana [24]

Recall to always convert the mixed fractions to "improper" fractions first,

$\bf \stackrel{mixed}{9\frac{5}{12}}\implies \cfrac{9\cdot 12+5}{12}\implies \stackrel{improper}{\cfrac{113}{12}}
\\\\\\
\stackrel{mixed}{3\frac{2}{3}}\implies \cfrac{3\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{11}{3}}\\\\
-------------------------------\\\\
\cfrac{113}{12}-\cfrac{11}{3}\impliedby \textit{clearly our LCD is 12}\implies \cfrac{113-(4)11}{12}
\\\\\\
\cfrac{113-44}{12}\implies \cfrac{69}{12}\implies 5\frac{9}{12}$

5 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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What is the equation of the parabola with focus (3, 0) and directrix x = –3?

nikitadnepr [17]

Answer:

x = $\frac{1}{12}$ y²

Step-by-step explanation:

Any point (x, y ) on the parabola is equidistant from the focus and the directrix

Using the distance formula, then

$\sqrt{(x-3)^2+(y-0)^2}$ = | x + 3 |

Squaring both sides

(x - 3)² + y² = (x + 3)² ← expanding both sides

x² - 6x + 9 + y² = x² + 6x + 9 ← subtract x² + 6x + 9 from both sides

- 12x + y² = 0 ( subtract y² from both sides )

- 12x = - y² ( divide both sides by - 12 )

x = $\frac{1}{12}$ y²

4 0

3 years ago

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