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2 years ago

The bases on a baseball diamond are 90 feet apart. how far is it from home plate to second base?

Mathematics

2 answers:

Karolina [17]2 years ago

3 0

See diagram

so we got a right triangle

so for a right triangle, when we've got legs a and b and hytponuse c then
a²+b²=c²

so the legs are 90 and 90
hytponuse is distance from home to 2nd

so
90²+90²=c²
8100+8100²=c²
16200=c²
sqrt both sides
90√2=c
aprox
127.279ft
about 127ft

Brilliant_brown [7]2 years ago

3 0

Assuming that the bases are all within right angles of each other:
Form a triangle with vertices at home base, first, and second. Home to first is 90ft and first to second is also 90ft.
Use the formula a^2+b^2=c^2 to find the the missing length.
90^2+90^2=c^2
8100+8100=c^2
16200=c^2
Sqrt(16200)=c
c=127.279

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2 years ago

F(x) = x2 – 3x – 2 is shifted 4 units left. The result is g(x). What is g(x)?

Ray Of Light [21]

$\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... your expression is not in vertex form, that's ok... to do a horizontal shift to the left by 4 units, we can simply, add the C and B component to the "x" variable, C=4, B =1, that way the horizontal shift of C/B or 4/1 is just +4, giving us a horizontal shift to the left

$\bf f(x)=x^2-3x-2\impliedby \textit{let's change that for }f(1x+4)
\\\\\\
f(1x+4)=(1x+4)^2-3(1x+4)-2
\\\\\\
f(x+4)=x^2+8x+16-3x-12-2
\\\\\\
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8 0

2 years ago

Read 2 more answers

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Nikolay [14]

Answer:

Step-by-step explanation:

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5 0

3 years ago

PLEAS HELP ASAP :)))))

Jet001 [13]

Answer:

18 inches

Step-by-step explanation:

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2 years ago