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SAT MATH
25 Terms
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![<p>The equation is:</p><p>\[ \sqrt{k-x}=54-x \]</p><p>Step 1: Square both sides and rearrange.</p><p>\[ k-x=(54-x)^2 \]</p><p>\[ k=x+(54-x)^2 \]</p><p>Step 2: Use the vertex formula.</p><p>For a quadratic \(ax^2+bx+c\), the vertex occurs at</p><p>\[ x=-\frac{b}{2a} \]</p><p>Expand the expression:</p><p>\[ k=x+x^2-108x+2916 \]</p><p>\[ k=x^2-107x+2916 \]</p><p>So,</p><p>\[ x=\frac{107}{2}=53.5 \]</p><p>Step 3: Substitute to find the minimum \(k\).</p><p>\[ k=53.5+(54-53.5)^2 \]</p><p>\[ k=53.5+0.25=53.75 \]</p><p>Step 4: Calculate the answer.</p><p>\[ 4k=4(53.75)=\boxed{215} \]</p><p>SAT shortcut to remember</p><p>Whenever you need the minimum of a quadratic, use</p><p>\[ \boxed{x=-\frac{b}{2a}} \]</p><p></p>](https://assets.knowt.com/user-attachments/c20fab42-d8f5-4be6-b0ea-35cec0eaadb4.png)
The equation is:
\[ \sqrt{k-x}=54-x \]
Step 1: Square both sides and rearrange.
\[ k-x=(54-x)^2 \]
\[ k=x+(54-x)^2 \]
Step 2: Use the vertex formula.
For a quadratic \(ax^2+bx+c\), the vertex occurs at
\[ x=-\frac{b}{2a} \]
Expand the expression:
\[ k=x+x^2-108x+2916 \]
\[ k=x^2-107x+2916 \]
So,
\[ x=\frac{107}{2}=53.5 \]
Step 3: Substitute to find the minimum \(k\).
\[ k=53.5+(54-53.5)^2 \]
\[ k=53.5+0.25=53.75 \]
Step 4: Calculate the answer.
\[ 4k=4(53.75)=\boxed{215} \]
SAT shortcut to remember
Whenever you need the minimum of a quadratic, use
\[ \boxed{x=-\frac{b}{2a}} \]
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![<p>Step 1: Write the first relationship</p><p>\[ a=6800\%\cdot c \]</p><p>Convert the percentage to a decimal:</p><p>\[ a=68c \]</p><p>Step 2: Write the second relationship</p><p>C is \(0.008\%\) of B:</p><p>\[ c=0.00008b \]</p><p>Solve for \(b\):</p><p>\[ b=\frac{c}{0.00008}=12{,}500c \]</p><p>Step 3: Add \(a+b\)</p><p>Substitute both expressions:</p><p>\[ a+b=68c+12{,}500c \]</p><p>\[ \boxed{12{,}568c} \]</p><p>Answer: D</p><p>SAT tip: Remember that \(6{,}800\%=68\), while \(0.008\%=0.00008\). Always divide percentages by 100 before using them in equations.</p>](https://assets.knowt.com/user-attachments/952479bd-e6e7-4a26-b720-688bf5b1fd9b.png)
Step 1: Write the first relationship
\[ a=6800\%\cdot c \]
Convert the percentage to a decimal:
\[ a=68c \]
Step 2: Write the second relationship
C is \(0.008\%\) of B:
\[ c=0.00008b \]
Solve for \(b\):
\[ b=\frac{c}{0.00008}=12{,}500c \]
Step 3: Add \(a+b\)
Substitute both expressions:
\[ a+b=68c+12{,}500c \]
\[ \boxed{12{,}568c} \]
Answer: D
SAT tip: Remember that \(6{,}800\%=68\), while \(0.008\%=0.00008\). Always divide percentages by 100 before using them in equations.
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dencity formula is what?
dencity equals mass over volmume mass/vol
because its meters (normal) per second squared (we want in minutes so since the time element is squared we do times 60 squared) then we want in miles so we times the nomral (or power 1 meters) by a regular 1609 (its meters normal per minuts squared )
or tern the equation into something times n = k then substitute 2x+1 equals that (this case it would be dividing 4/3 by 2/5 which is the same ok it may be easeir)
mistake was I didn’t do the squared formula just remmbember to do it
sinse the slope times x ….. and they don’t give it to you like that we can use the slope to find the missing variable (coeficeint of x / coeficeint of y to get slope remember)
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memorize the formula
becaues only the years after year on is counted (-1) and very year has 6 months (2(x) ) and that’s all there is to it
