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Zielflug [23.3K]

3 years ago

8

A chemist working on a flu vaccine needs to mix a 20% sodium iodine solution with a 30% sodium iodine solution to make a 40 mil

mixture. write the amt of sodium iodine in the mixture (S) in the mixture in mil, as a function of mil of the 20% solution used (x).

1 answer:

Varvara68 [4.7K]3 years ago

8 0

Answer:

4

Step-by-step explanation:

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frosja888 [35]

Just do this :
-1 + 30 - 5y
29 - 5y
or -5y + 29
the answer is C

6 0

3 years ago

How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y

son4ous [18]

Solution:

Given:

$x^2=6y$

Part A:

The vertex of an up-down facing parabola of the form;

$\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}$

Rewriting the equation given;

$\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\ \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\ \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\ \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\ \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}$

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

$\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}$

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

$\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}$

Therefore, the focus is;

$(0,\frac{3}{2})$

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

$\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}$

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

$\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}$

Therefore, the directrix is;

$y=-\frac{3}{2}$

3 0

1 year ago

Divide using long division. <br><br> <img src="https://tex.z-dn.net/?f=%284x%5E%7B2%7D%20-5x%2B3%29" id="TexFormula1" title="(4x

frez [133]

Answer:

The quotient = 4x - 17 and the remainder = 54

Step-by-step explanation:

$\frac{4x^{2}-5x+3 }{x+3}=4x+\frac{-17x+3}{x+3}$

$\frac{-17x+3}{x+3}=-17+\frac{54}{x+3}$

The quotient = 4x - 17 and the remainder = 54

6 0

3 years ago

Read 2 more answers

The price of a gallon of unleaded gas was $2.80 yesterday. Today, the price rose to $2.87 . Find the percentage increase. Round

marin [14]

Earlier price is 2.80
Current price is 2.87

Increment is
2.87 - 2.80
0.07

Increment percentage is
(0.07 / 2.80) * 100
2.5 %

4 0

3 years ago

Solve the rational function of (check image) and check for extraneous solutions

Oxana [17]

Answer:

Option A is correct.

i.e. x = 1, x = 0 is an extraneous solution.

Step-by-step explanation:

Given the expression

$\frac{5}{x}=\frac{4x+1}{x^2}$

Solving the rational function

$\frac{5}{x}=\frac{4x+1}{x^2}$

Apply fraction across multiply: if $\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c$

$5x^2=x\left(4x+1\right)$

Subtract x(4x+1) from both sides

$5x^2-x\left(4x+1\right)=x\left(4x+1\right)-x\left(4x+1\right)$

Simplify

$5x^2-x\left(4x+1\right)=0$

5x² - 4x² - x = 0

x² - x = 0

Factor x² - x = x(x-1)

so

x(x-1) = 0

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

$x=0\quad \mathrm{or}\quad \:x-1=0$

Thus, the solution to the equation is:

$x=0,\:x=1$

But, it is clear that if we substitute x = 0, the equation becomes undefined because we can not have the denominator to be 0.

In other words, the equation is undefined for x = 0

Thus, x = 0 is an extraneous solutions.

Therefore, option A is correct.

i.e. x = 1, x = 0 is an extraneous solution.

5 0

3 years ago