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2 years ago

Solve for x in the equation p(m+qx)=rx+n

1 answer:

6 0

$p(m+qx)=rx+n\\\\\implies pm+pqx = rx+n\\\\\implies pqx-rx = n-pm\\\\\implies x(pq -r) = n-pm\\\\\implies x = \dfrac{n-pm}{pq-r}$

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George has $49 which he decides to spend on x and y. commodity x costs $5 per unit and commodity y costs $11 per unit. he has th

FromTheMoon [43]

We are given the equations:

5 x + 11 y = 49 --> eqtn 1

u = 3 x^2 + 6 y^2 --> eqtn 2

Rewrite eqtn 1 explicit to y:

11 y = 49 – 5 x

y = (49 – 5x) / 11 --> eqtn 3

Substitute eqtn 3 to eqtn 2:

u = 3 x^2 + 6 [(49 – 5x) / 11]^2

u = 3 x^2 + 6 [(2401 – 490 x + 25 x^2) / 121]

u = 3 x^2 + 14406/121 – 2940x/121 + 150x^2/121

u = 4.24 x^2 – 24.3 x + 119.06

Derive then set du/dx = 0 to get the maxima:

du/dx = 8.48 x – 24.3 = 0

solving for x:

8.48 x = 24.3

x = 2.87

so y is:

y = (49 – 5x) / 11 = (49 – 5*2.87) / 11

y = 3.15

Answer:

George will choose some of each commodity but more y than x.

7 0

3 years ago

Cole biked at 5 mph for 1 1/2 hours. Which of the following choices show how far he biked?

Citrus2011 [14]

Answer:

Should be 5 1/2 if thats on there

Step-by-step explanation:

u take 11/2 and take out the 1 u get 10/2 so u cut 10 in half get 5 then add the one and make it 5 1/2

3 0

3 years ago

Read 2 more answers

F(x)=5x-1 Domain {-1,0,1,2} Find the range:

Katena32 [7]

Answer:

Step-by-step explanation:

Putting the values in F(x)=5x-1

= -6,-1,5,9

Range =highest -lowest =9--6

=15

3 0

3 years ago

A 5-gallon jug of cleaning solution contains 6% bleach. How much pure water should be added to it to dilute to 4% bleach?

mihalych1998 [28]

Let's bear in mind that 5 gallons with a solution of 6% bleach, contains some water plus some bleach, how much bleach? well, is just 6% of 5 gallons or namely (6/100) * 5 gallons, or 0.30 gallons.

if we use "x" gallons of water, well pure water has no bleach, so is 0% bleach, and it has a (0/100) * x or 0x gallons of bleach.

the mixture will be say "y" gallons, and is 4% bleach, so (4/100) * y is 0.04y gallons in the mixture of bleach.

$\bf \begin{array}{lcccl}
&\stackrel{gallons}{quantity}&\stackrel{\textit{\% of bleach}}{amount}&\stackrel{\textit{gallons of bleach}}{amount}\\
&------&------&------\\
\textit{pure water}&x&0.00&0x\\
\textit{6\% solution}&5&0.06&0.3\\
-----&------&------&------\\
mixture&y&0.04&0.04y
\end{array}
\\\\\\
\begin{cases}
x+5=\boxed{y}\\
0x+0.3=0.04y\\
---------\\
0.3=0.04\left( \boxed{x+5} \right)
\end{cases}
\\\\\\
0.3=0.04x+0.2\implies 0.1=0.04x\implies \cfrac{0.1}{0.04}=x\implies 2.5=x$

3 0

3 years ago

What is the probability of drawing a king, then an ace (with replacement)?

alexandr1967 [171]

Answer:

So there is a 2 in 13 chance to pull out either an ace or king from the deck

Step-by-step explanation:

3 0

2 years ago