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3 years ago

A garden has a length of 90 feet and a width of 60 feet. what is the area of the garden in square yards? use 1 yard = 3 feet.

Mathematics

1 answer:

Sunny_sXe [5.5K]3 years ago

7 0

You just need to multiply
$90 \times 60 \div 3$
then divide by 3

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Write y=-3(x-7)^2-8 in vertex form

Veronika [31]

It's in the verex form:

$f(x)+a(x-h)^2+k\\\\(h,\ k)-vertex$

$y=-3(x-7)^2-8\\\\(7,\ -8)-vertex$

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3 years ago

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I need help with #11

Troyanec [42]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\

\begin{array}{rllll} 
% left side templates
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}$

$\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\end{array}$

$\bf \begin{array}{llll}


\bullet \textit{ vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\\\
\qquad if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}
\end{array}$

now, with that template in mind, let's take a peek at this function

$\bf \begin{array}{lllcclll}
y=&2(&1x&-2)^2&-4\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}\\\\
-----------------------------\\\\
A\cdot B=2\impliedby \textit{shrunk by a factor of 2, of half-size}\\\\
\cfrac{C}{B}= \cfrac{-2}{1}\implies -2\impliedby \textit{horizontal right shift of 2 units}\\\\
D=-4\impliedby \textit{vertical down shift of 4 units}$

so, the graph of y=2(x-2)²-4, is really the same graph of y=x², BUT, narrower, and moved about horizontally and vertically

8 0

3 years ago

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Find p(-4) and p(2) for the function p(x)=11x^5-11x^4-5x^2+15x-8

egoroff_w [7]

hi,

you must replace x by the number between parenthese.

I show you with the first one and let you do the second one

p(x) = 11x^5 -11x^4 - 5x^2 +15x-8

p(-4) = 11 (-4)^5 - 11 (-4)^4 -5(-4)² +15(-4) -8

p(-4) = 11 ( -1024- 256) - 5*16 -60-8

p(-4) = 11 ( -1280) -80-60-8

p(-4) = - 14080 - 148

p(-4) = - 14 228

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3 years ago

For AB, point A has coordinates (3, -5) and point B has coordinates (-1, 9). What are the coordinates of the midpoint of AB?

kow [346]

The coordinates midpoint of AB are (1,2)

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3 years ago

Can someone solve 5 + 2x = + 6<br><br> and n - 3n = 14 - 4n<br><br> and 7 ( 5a - 4 ) - 1 = 14 - 8a

professor190 [17]

Answer:

5 + 2x = 6

2x = 6-5

2x = 1

x = 0.5

n -3n = 14 -4n

-2n = 14-4n (since 4n is negative, change the sign to make it positive and then add 4n to both sides of the equation)

2n = 14

n = 7

7 (5a - 4) - 1 = 14 - 8a

35a - 28 - 1 = 14 -8a

35a -29 = 14 - 8a

43a = 43

a = 1

6 0

3 years ago

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