I have 30 ones, 2 thousands, 4 hundred thousands,60 tens and 100 hundreds. What number am I?

Mike has coffee worth $4 per pound that he wishes to mix with 20 pounds of coffee worth $7 per pound to get a mixture that can b

Alinara [238K]

$\bf \begin{array}{lccclll}
&\stackrel{lbs}{amount}&\stackrel{per~lb}{price}&\stackrel{amount}{price}\\
&------&------&------\\
\textit{\$4/lb coffee}&x&4&4x\\
\textit{\$7/lb coffee}&20&7&140\\
------&------&------&------\\
mixture&y&5&5y
\end{array}$

so, we know the mixture is the sum of both types of coffee, thus x + 20 = y, and 4x + 140 = 5y.

$\bf \begin{cases}
x+20=\boxed{y}\\
4x+140=5y\\
----------\\
4x+140=5\left( \boxed{x+20} \right)
\end{cases}
\\\\\\
4x+140=5x+100\implies 140-100=5x-4x\implies 40=x$

5 0

2 years ago

Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form? Y = 3 (x minus seven-halves) squared minus StartFraction 27

densk [106]

Answer: y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction

or

$y=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}$

Step-by-step explanation:

Vertex form of equation : $f (x) = a(x - h)^2 + k,$ where (h, k) is the vertex of the parabola.

$y=3(x-2)^2-(x-5)^2\\\\=3(x^2+4-4x)-(x^2+25-10x)\\\\=3x^2+12-12x-x^2-25+10x\\\\=2x^2-2x-13\\\\=2(x^2-x-\dfrac{13}{2})\\\\=2(x^2-x+\dfrac{1}{4}-\dfrac{1}{4}-\dfrac{13}{2})\\\\=2((x-\dfrac{1}{2})^2-\dfrac{1+26}{4})\\\\=2((x-\dfrac{1}{2})^2-\dfrac{27}{4})=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}$

Hence, the vertex form of the equation is $y=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}$

8 0

2 years ago

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Charles uses a graphing calculator to find a quadratic regression model f for a given set of data. When he compares model f to a

makvit [3.9K]

B I hope this helped I’m not sure

7 0

2 years ago

Tony wants to plant no more than 400 acres of corn and soybeans. He earns $300 per acre of soybeans and $200 for corn. He needs

inna [77]

In this item, we let x be the number of corns and Y represent soybeans. The sum of these variables is 400. This is represented by the equation,
x + y = 400
The amount that needs to be earn by Tony is then represented by,
200x + 300y ≥ $60,000

9 0

2 years ago

Two positive integers have their Hcf as 12 and their product as 6336. The number of possible pairs for the numbers is

oksano4ka [1.4K]

the answer is 4? I am not sure

7 0

2 years ago

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